urc 10-m viv test marintek report

MARINTEK REPORT TITLE

VIV Suppression Tests on High L/D Flexible Cylinders Main Report DRAFT

AUTHOR(S)

Erik Lehn

CLIENT(S)

Norwegian Marine Technology Research Institute Postal address: P.O.Box 4125 Valentinlyst NO-7450 Trondheim, NORWAY Location: Marine Technology Centre Otto Nielsens veg 10 Phone: +47 7359 5500 Fax: +47 7359 5776 http://www.marintek.sintef.no Enterprise No.: NO 937 357 370 MVA

ExxonMobil Upstream Research Company

FILE CODE CLASSIFICATION CLIENTS REF.

MT51 F03-167 Declassified, Mar. 2008 Michael A. Tognarelli CLASS. THIS PAGE ISBN PROJECT NO. NO. OF PAGES/APPENDICES

512382 REFERENCE NO. PROJECT MANAGER (NAME, SIGN.) VERIFIED BY (NAME, SIGN.)

512382 P Halvor Lie REPORT NO. DATE APPROVED BY (NAME, POSITION, SIGN.)

512382.00.01 draft 2003-07-15 Terje Nedrelid, Division Manager ABSTRACT

This report presents the work and results related to the vortex induced vibration (VIV) model tests with a high length-to-diameter ratio (L/D) riser for ExxonMobil Upstream Research Company (URC. The towed instrumented riser model was tested with and without suppression devices in a uniform and a linearly varying sheared current profile with different towing speds. This was obtained by towing the riser vertically and in inclined positions in a rotation rig that was located in the model test tank.

KEYWORDS ENGLISH NORWEGIAN

GROUP 1 Hydrodynamics Hydrodynamikk GROUP 2 Model tests Modellforsøk SELECTED BY AUTHOR Flexible cylinders Fleksible rør Vortex induced vibrations (VIV) Virvelinduserte vibrasjoner (VIV)

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TABLE OF CONTENTS

1. INTRODUCTION...............................................................................................................................4

2. OBJECTIVES .....................................................................................................................................4

3. RISER MODEL ..................................................................................................................................5 3.1 Dimensions and Mass Ratio .........................................................................................................5 3.2 VIV Suppression: Fairings............................................................................................................6 3.3 VIV Suppression: Strakes .............................................................................................................7 3.4 Free Surface Penetration ...............................................................................................................7 3.5 Bending Stiffness..........................................................................................................................8 3.6 Wake Calculation..........................................................................................................................9

4. TEST ARRANGEMENT .................................................................................................................10 4.1 Test Facility ................................................................................................................................10 4.2 Description of Test Rig...............................................................................................................10 4.3 Model-Rig Interaction.................................................................................................................11

5. INSTRUMENTATION AND MEASUREMENTS........................................................................12 5.1 Co-ordinate Systems ...................................................................................................................12 5.2 Instrumentation Plan ...................................................................................................................12 5.3 Calibration of Transducers..........................................................................................................13 5.4 Accuracy ....................................................................................................................................13 5.5 Instrumentation/DAS Verification and Experimental Modal Test .............................................13 5.6 Data Acquisition .........................................................................................................................14 5.7 Visual Recordings.......................................................................................................................14

6. TEST PROGRAM AND TEST PROCEDURES ...........................................................................15 6.1 Instrumentation Verification and Experimental Modal Testing .................................................15

6.1.1 Component Level Instrumentation Verification Tess.........................................................15 6.1.2 In-air DAS Verification and Experimental Modal Tests ....................................................16 6.1.3 In-water DAS Verification and Experimental Modal Tests ...............................................16

6.2 VIV-Tests in Rotating Rig..........................................................................................................16

7. ANALYSIS AND PRESENTATION OF RESULTS.....................................................................18 7.1 Data Reduction ...........................................................................................................................18 7.2 Post-processing of Data ..............................................................................................................19 7.3 Component Level Instrumentation Verification .........................................................................19 7.4 In-air DAS Verification and Experimental Modal Tests ............................................................20

7.4.1 Static DAS Verification Tests ............................................................................................20 7.4.2 Dynamic/Experimental Modal Tests ..................................................................................20

7.5 In-water DAS Verification and Experimental Modal Tests........................................................21 7.6 Uncertainty Budgets ...................................................................................................................21 7.7 Validation of Software................................................................................................................22 7.8 Video and Photo..........................................................................................................................23 7.9 Scaling ....................................................................................................................................23

8. COMMENTS ....................................................................................................................................24 8.1 Riser End Transducers ................................................................................................................24 8.2 Set-Down ....................................................................................................................................24 8.3 Moment Transducers ..................................................................................................................25 8.4 Spikes ....................................................................................................................................25

Figures ....................................................................................................................................26

Tables ....................................................................................................................................42

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APPENDIX 1 URC Specification for Instrumentation Verification and Experimental Modal Testing

....................................................................................................................................65 I. Component Level Instrumentation Verification .........................................................................66

1.1 A/D Converter ....................................................................................................................66 1.2 DC Amplifiers ....................................................................................................................67 1.3 Analog Filters .....................................................................................................................67 1.4 Accelerometers, Load Cell, and Bridge Completions ........................................................67

II. In-Air : Data Acquisition System Verification and Experimental Modal Test...........................68 III. In-Water : Data Acquisition System Verification and Experimental Modal Test ......................69

APPENDIX 2 Component Level Instrumentation Verification............................................................70 Component Level Instrumentation Verification .................................................................................71

A/D converter .............................................................................................................................72 DC amplifiers..............................................................................................................................75 Analog filters ..............................................................................................................................80 Accelerometers, load cell and bridge completion.......................................................................84

APPENDIX 3 Dynamic/Experimental Modal Tests...............................................................................87

APPENDIX 4 Uncertainty Budgets .........................................................................................................89

1. Curvature sensors error budget ......................................................................................90 2. Accelerometers error budget .................................................................................................107

APPENDIX 5 Validation of Software....................................................................................................121

Spectral- and Statistical Routines in Express and Timsas...................................................................121

1. INTRODUCTION ..................................................................................................................123

2. ACTUAL PROGRAMS .........................................................................................................123

3. ACCEPTANCE CRITERIA..................................................................................................123

4. DESCRIPTION OF METHOD.............................................................................................124 4.1 Generation of Time Series...................................................................................................124 4.2 Calculation...........................................................................................................................125 4.3 Theoretical Values...............................................................................................................125

5. PRESENTATION OF RESULTS .........................................................................................127 5.1 Spectral Plots .......................................................................................................................127 5.2 Spectral Moments ................................................................................................................127 5.3 Main Statistical Parameters .................................................................................................128

APPENDIX 6 Spectral Analysis.............................................................................................................129

APPENDIX 7 Statistical Analysis...........................................................................................................134

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1. INTRODUCTION ExxonMobil Upstream Research Company (URC) wanted to undertake a high length-to-diameter ratio (L/D) riser hydrodynamic testing program to meet the specifications outlined in the "Request for Proposal for VIV Suppression Tests on High L/D Flexible Cylinders" from URC, dated 28 January 2003. The instrumented riser model, with or without suppression devices, was tested both vertically and in inclined positions in a rotating rig in order to obtain uniform and linearly varying sheared current. The rig was located in the model test tank. While the vertical riser was excited by one vortex shedding frequency, the inclined riser experienced more than one vortex shedding frequency to the linearly varying sheared flow. The model tests were carried out in Marintek’s Ocean Basin laboratory in June 2003. The documentation from the tests comprises: Report

512382.00.01

VIV Suppression Tests on High L/D Flexible Cylinders Main Report

Report 512382.00.02 VIV Suppression Tests on High L/D Flexible Cylinders Data Report

Including: - Video and photos from selected test sequences - VHS copies of video recordings - DVD-ROM with all time series in Matlab-format

2. OBJECTIVES The main purpose of the model test program was to acquire high quality data on the behaviour of high L/D risers subjected to vortex induced vibrations (VIV) in uniform and sheared flow. The primary focus of the tests was to compare the multi-mode VIV response of risers without suppression devices to that of risers with varying lengths of suppression coverage. The objective of the present report is to give a detailed documentation of the riser model, instrumentation, test arrangement, test program and data analysis. According to the scope of work, the majoryty of the data reduction should be carried out by URC, and is thus not included in this report.

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3. RISER MODEL

3.1 Dimensions and Mass Ratio The riser model was made of a brass pipe with an outer diameter of 20 mm and a wall thickness of 0.45 mm. Since the strain gauges and accelerometers were glued to the outside of the brass pipe surface, the riser diameter was locally increased at the instrumented sections (bumps). See Figure 3.1 for details. The dimensions of the riser model were determined by the total number of transducers, the diameter of the instrument cables, fatigue data on the riser material and the highest eigenfrequency of the riser model. The riser model was designed to be excited up to 8th vibration mode, bounded by fatigue. Detailed physical properties of the riser model are given in Table 3.1. The mass and the length of the riser model refer to the length between the centres of the universal joints at the ends (pin to pin). The effective length of the riser model was:

LRiser = 9.63 m After completion of the tests, a detailed weighing of the riser model in air was performed. A summary of the mass data of the riser model is given in the table below.

Mass Parameter

kg kg/m

Mass of riser model in air, without internal water 5.644 0.586

Mass of internal water 1.087 0.113

Total mass in air, incl. internal water 6.731 0.699

Mass of displaced volume (D=20 mm) 3.024 0.314 The table below shows a comparison between the mass determined from weighing before, during and after the tests.

Total mass of bare riser in air, incl. internal water kg kg/m

Before tests, weighing in air 6.799 0.706

During test period, weighing in water (corrected for buoyancy) 6.664 0.692

After tests, weighing in air 6.731 0.699 From the table above, it is seen that the difference between the maximum - and minimum mass determined from the different measurements is 2 %, only.

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Based on the mass from weighing after the tests, the mass ratio of the bare riser, defined as the total mass in air divided by the displaced mass, was 0.699/0.314 = 2.23. During the test period, the weight of the riser model was measured prior to each of the configuration changes, and the results are presented in Table 3.2

3.2 VIV Suppression: Fairings The fairing design was provided by the client and was a pivoted streamlined fairing with a length to thickness ratio of 2.33 and with a dive-break flap. The fairings were made from a plastic material and fitted to the riser model in lengths of 88.2 mm. The gap between each element was 2 mm. The fairings were neutrally buoyant and were free to rotate on the riser. The fairings were constrained in axial direction. This was obtained by use of a pair of plastic sleeves clamped to the riser pipe inside some of the fairings (see also Figure 3.1). The distance between each axial constraint was approximately 1 m. There was enough space inside the fairings for the instrumentation. Details of the fairing are given in Figure 3.1, in Table 3.3, in the Photo Section and in the table below.

Parameter Dimension

Length 84 mm

Maximum thickness 36 mm

Length to thickness ratio 2.33

Height of dive-break flap 10 mm

Centre of pivot from LE 16 mm

Weight in air (one element) 1.050 N

Weight in water (one element) 0.000 N

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3.3 VIV Suppression: Strakes The triple start helical strakes were cast with correct geometry from silicone material and glued to the riser model with the specified pitch-to-diameter ratio of 16. The strakes had a triangular shape with a hight of 5 mm and a width of 5 mm. The strakes were neutrally buoyant. Details of the strakes are given in Figure 3.1, in the Photo Section and in the table below.

Parameter Dimension

Height 0.005 m

Width 0.005 m

Unit weight in air 0.245 N/m

Unit weight in water 0.000 N/m

Pitch/D1) 16

1) D is nominal diameter of riser model.

3.4 Free Surface Penetration The upper end of the riser was connected to the rig via a vertical beam that penetrated the free surface. The beam was streamlined to limit disturbance of the flow. For all tests, the riser model was completely submerged. The top end transducer was submerged for all tests in sheared current, while in uniform current the top end transducer became submerged only for the highest speeds, approximately at a current speed of 1.7 m/s.

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3.5 Bending Stiffness Ideally, the bending of the riser model should be tension-dominated. The natural frequency of combined tension and bending stiffness can be expressed as: 222

nEInTn ωωω +=

where nω : Angular frequency of riser model

nTω : Angular frequency due to tension

nEIω : Angular frequency due to bending stiffness

It can be shown that the natural frequency of the riser is dominated by tension (80%) if the following criterion is satisfied:

2224

LEInT π≥

where T : tension n : mode EI : bending stiffness L : riser length. Table 3.4 presents theoretical eigenfrequencies of the bare brass riser in air, at a tension of 817 N. As can be seen from this table, the eigenfrequencies due to tension are larger than the eigenfrequencies due to bending stiffness for about the 8 lowest modes. Table 3.5 shows a comparison between the theoretical eigenfreqencies and the natural frequencies obtained from the simplified decay tests in air (see Section 6.1.2).

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3.6 Wake Calculation After one rotation of the rotating rig, the cylinder catches up with its own wake. Schlichting1 has solved the equations of motions in a wake by use of different mixing theories from L. Prandtl. The problem is also dealt with by Huse2. Both for laminar and turbulent two-dimensional wake, the centre-line velocity 'depression' decreases with (x/D)-1/2. According to Huse, the following expressions describing the wake are given:

21

0

−

=

Dx

CUu

S

D

where

D

S CDxx 4+=

Here x is the longitudinal distance between the centre of the riser and the point to be calculated. The term 4D/CD represents the distance to a so-called virtual source. Using the radius of the rotating rig of 4.65 m, a diameter of the riser model of 0.02 m and a drag coefficient of CD = 2.0, we get: x/D = 1460 u/U0 = 0.037 According to these calculations, about 3.7 % of the velocity "remains" in the wake when the riser model catches up with its own wake after one rotation of the test rig. For CD = 3.0 the corresponding value is about 4.5 %.

1 Schlichting, H.; "Boundary layer Theory"; McGraw-Hill, Inc.; 1968. 2 Huse, E.; "Interaction in Deep-Sea Riser Arrays."; OTC 1993, Paper No. OTC 7237.

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4. TEST ARRANGEMENT

4.1 Test Facility The tests were performed in Towing Tank No. III at Marintek, which has a length of 80 m a breadth of 10.5 m and a depth of 10 m. The tank is equipped with a double-flap, hydraulic operated wave maker, denoted BM1, capable of generating long-crested, irregular as well as regular waves. The maximum height that can be generated is 0.9 m. The tank has a wave absorption beach at the downwave end. Figure 4.1 shows the principal dimensions of the Towing Tank No. III. The towing carriage of the tank was positioned close to the test site. The URC engineers could observe the tests at the test site. The project team had immediate access to raw and processed data from computers on the towing carriage. The URC personnel had access to "raw" data that had been checked by the project team on their own PC's at the test site via an ethernet cable interface, in order to control that the actual test and measured data had sufficuient quality. Data was also available from marintek's web-hotel (eRoom). (eRoom is a secure Web-based workspace, that can be quickly tailored for the actual project. More information can be found at http://www.documentum.com/products/collateral/collaboration/ds_eroom_dw.pdf.)

4.2 Description of Test Rig The tests were performed with a rotating test rig mounted in Tank III. Figures 4.2-4.3 shows a sketch of the test rig. It consists of a 13 m long vertical cylinder A with a diameter of 0.485 m. At the top of the cylinder there are two horizontal arms B in opposite directions, and at the bottom there is one horizontal arm C. About 0.15 m above the water surface, a sloping beam D is attached to the cylinder. A hinged arm E, which can be placed in different positions, is attached to this beam. The top end of the riser is fastened to the outer point of this arm and a spring system holds the arm. The spring system resembles a heave compensator system with low heave damping, resulting in nearly constant tension within each test. It comprised of 6 springs, with a total vertical stiffness of:

kheavecomp = 1593 N/m. The maximum current speed that was modelled at the top of the riser was about 2.3 m/s. Pictures of the upper part of the riser model, force transducer and the heave compensator are shown in the Photo Section.

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The riser ends were fixed to the test rig via pinned, universal joints, and exposed to constant tension. The upper end point F was located at two different positions, in order to model the effect of sheared current.

4.3 Model-Rig Interaction During the tests period, accelerations of the test rig and the riser model were measured. Reference is made to Section 7.5.

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5. INSTRUMENTATION AND MEASUREMENTS

5.1 Co-ordinate Systems Two co-ordinate systems are referred to in this report: - A global co-ordinate system - A local coordinate suystem The global co-ordinate system is a right-handed Cartesian co-ordinate system fixed to the rotating rig, with the origin at the centre of the rig at the water surface. The z-axis is pointing upward and negative y-axis is pointing toward the riser model. The local co-ordinate system is a right-handed Cartesian co-ordinate system fixed to the riser model, with the origin at the centre of the riser at the riser top end. The z-axis is pointing upward and positive x-axis is pointing toward the incoming current. The two co-ordinate systems are shown in Figure 5.1.

5.2 Instrumentation Plan Altogether 68 transducers were fitted to the riser model, according to the following table.

Signal In-line (IL) Cross-flow (CR)

Bending moments 35 17

Accelerations 8 8

The instrumented sections were distributed equidistant on the riser model, at a distance of about 0.270 m. The CF moment transducers were located at every second IL moment transducer, and the accelerometer pairs (x- and y-accelerometers) were distributed at every fourth IL moment transducer. The exact positions of the different transducers on the riser model are given in Figure 5.2. In addition to the transducers on the riser model, the following instrumentation was included:

Signal Direction Transducer

Accelerations of test rig upper end x, y and z Linear accelerometers

Accelerations of test rig lower end x, y and z Linear accelerometers

Riser force upper end x, y and z Strain gauge transducer

Riser force lower end x, y and z Strain gauge transducer

Riser top set-down z Linear spring-transducer system

Rotational speed test rig Angular Potentiometer

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All instrument cables were shielded. The complete channel list is presented in Table 5.1 and a sketch of the instrumentation plan is shown in Figure 5.3.

5.3 Calibration of Transducers The instruments were calibrated before the tests. The transducers were calibrated and the instrumentation was checked according to Marintek's procedures for instrumentation. Before completing instrumentation installation on the riser model and prior to waterproofing, the following calibration tasks were performed: • The instrumented riser model was rotated in order to check the calibration and to document

the directional alignment of the accelerometers. • Each strain gage was shunt-calibrated for curvature at the strain gage, with the full length of

cabling used in the tests. (See comments in Section 8.3.)

5.4 Accuracy The approximate measuring accuracy was:

- Force transducers1) +/- 2% - Accelerometers2) +/- 2.9 % - Moment transducers2) +/- 2.4 %

1) Percentage of measured value for significant response level. 2) Ref. Section 7.6

5.5 Instrumentation/DAS Verification and Experimental Modal Test Component level and system wide verification tests were performed on the instrumentation and data acquisition prior to the start of the testing. For details of the verification exercises, reference is made to Appendix 1. In addition to instrumentation verification, an in-air experimental modal test was conducted on the riser model and rotating rig. Repeated runs of earlier tests with the same riser configuration were built into the test matrix to verify instrument performance throughout the test program.

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5.6 Data Acquisition Filter type, cut-off frequency and data sampling frequency were chosen with respect to the maximum response frequency in order to prevent aliasing, i.e. folding of high frequency response (noise) onto the low frequency response. Based on estimation of the maximum response frequency for the riser model and data and observations from previous VIV-tests, a sampling frequency of 1000 Hz was chosen. Before data sampling, the data was filtered by analog anti-aliasing Butterworth filters of order 8, with a cut-off frequency of 250 Hz.

5.7 Visual Recordings Video recordings for a selected number of tests were done by three cameras. One camera was positioned at the tank side, viewing the total set-up. The two other cameras were mounted on the rotating rig under water, viewing the riser from downstream and the side. The cameras were positioned in such a way that they did not interfere with the inflow conditions to the riser. Still photos of the test set up were also taken and presented. The recording system was in BETACAM while the delivered videotapes were in VHS format in NTSC.

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6. TEST PROGRAM AND TEST PROCEDURES The tests performed can be divided in the following two groups:

1. Instrumentation verification and experimental modal testing. 2. VIV-tests in rotating rig

A brief description of the test program is given in the following subsections.

6.1 Instrumentation Verification and Experimental Modal Testing The instrumentation verification and experimental modal testing consist of the following tests:

• Component Level Instrumentation Verification Tests • In-Air Tests • In-Water Tests

The test procedures for the tests are described in detail in Appendix 1. A brief description is given in the following sub-sections.

6.1.1 Component Level Instrumentation Verification Tess Verification tests were performed on subsets of all components that were used in the data acquisition system for the tests. The components that were used in the instrument/data acquisition system are listed in the following table.

Component Manufacturer Model Number

DC amplifier Hottinger Baldwin

Messtechnik KWS and MGC+

Analog Filters GEPA MOM-MKT (8-pole

Butterworth) A/D Converter Data Translation DT3003 - 12 bit

Strain Gages Vishay -

MicroMeasurements EA-13-250PD-120

Accelerometers Measurement Specialties ICSensors - 3031 (+/- 100g) Load Cells Marintek N/A

The verification tests required for each component type are described in Appendix 1 as well as the number of components to be tested. The data were recorded via the data acquisition system for all verification tests.

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6.1.2 In-air DAS Verification and Experimental Modal Tests Prior to the start of VIV testing, the functionality of the data acquisition system (DAS) was verified with both static and dynamic tests in-air. The objectives of these tests were to confirm the polarity and calibrations for all sensors and quantify noise and drift in the DAS. An experimental modal test was also performed on the riser model to measure natural frequencies and damping of the riser model experimentally. For these tests, the rotating rig structure was fully assembled and laid out horizontally with the support arms that hold the riser model oriented parallel to the floor. The central column was supported so that it did not translate or rotate when a force was applied to the riser model during these tests. The fully instrumented riser model was installed in the rotating rig structure and tensioned to the mean pre-tension expected during the VIV tests. The following type of tests were performed in air:

• Static DAS verification tests • Dynamic/experimental modal tests

Full descrition of the tests are given in Appendix 1. The dynamic/experimental modal tests were subcontracted to Campus Marine, while the static DAS verification tests were performed by Marintek. In addition to the modal tests, simplified decay tests in air were performed in order to document natural frequencies up to 3rd order. The tests were performed by exciting the riser model manually.

6.1.3 In-water DAS Verification and Experimental Modal Tests After installation of the rotating rig and riser model in the towing basin, verification tests were performed to evaluate the DAS functionality. In addition, a simplified experimental modal test (pluck test) was conducted on the rig. The purpose of these tests was to determine the natural frequencies of riser model (if possible) and of the rotating rig. Details of the tests are described in Appendix 1

6.2 VIV-Tests in Rotating Rig For the uniform current profile, the riser model was suspended vertically in the rotating rig, with both end points of the riser model mounted approximately 4.63 m from the centre of rotation of the rig. For the sheared current profile, the upper end point of the riser model was attached closer

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to the centre of the rotating rig. The positions of the riser end points are given in Table 6.2. For details of the test rig, reference is made to Section 5.1. The test program consisted of about 250 runs, varying the current speed and the current shear for the bare riser and for the riser with various fairing- and strake configurations. Approximately 20 current speeds were run for each configuration. Uniform current and one sheared current condition were modelled. The following riser configurations were tested:

% coverage Current condition Riser config. Suppression type

25 50 75 100 Uniform Sheared Bare riser - - - - - x x

Straked riser Trippel start helical strakes x x x x x x Faired riser Streamlined pivoted fairings x x - x

Before testing in each configuration, the weight of the riser in water was measured before attaching it to the lower load cell. The following index code was used for identifying the tests. Each test was given a unique four-digit identification number. The first digit refers to the actual riser configuration, i.e.

• 1 = Naked riser • 2 = Faired riser, Faired length 100 %: Faired 100 • 3 = Faired riser, Faired length 50 %: Faired 50 • 4 = Straked riser, Strake length 100 % : Straked 100 • 5 = Straked riser, Strake length 75 %: Straked 75 • 6 = Straked riser, Strake length 50 %: Straked 50 • 7 = Straked riser, Strake length 25 %: Straked 25

The second digit refers to the actual current profile, i.e.

• 1 = Uniform flow, (U) • 2 = Shear, (S)

The two last digits refer to the actual test, where mainly the speed was varied. The complete test program is presented in Table 6.1.

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7. ANALYSIS AND PRESENTATION OF RESULTS

7.1 Data Reduction According to the scope of work, the majority of the data reduction should be carried out by URC. Marintek performed the following data analysis for each individual test:

• Immediately after each test, main statistical data as maximum, minimum, mean and standard deviation of all channels were calculated.

• During the post-processing of the data, standard spectral- and statistical analyses were

performed for all channels. The spectral tables present:

• m0-, m1-, m2-, m3- and m4 spectral moments • T1- and T2 periods • spectral peak period • significant value

The statistical tables present:

• mean-, maximum- and minimum value, standard deviation • number of local maxima and local minima • significant local peak-to-peak maximum- and minimum value • skewness • excess of kurtosis

The transient part of the time series at the start and the end of the tests has been excluded in the analyses. A short description of methods and definition of parameters is given in the Appendix 6 "Spectral Analysis" and in Appendix 7 "Statistical Analysis". The results from the spectral and statistical analyses, and all time series from the VIV-tests are presented in the Data Report.

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7.2 Post-processing of Data During the data recording analogue low-pass (LP) filters of 250 Hz were used for all measuring channels. Generally, no extra filtering has been performed on the data. However, due to spikes and irregularities in some signals, the time series have been corrected during the post-processing of the data. The corrections that have been performed on the signals are described in Table 7.1. The spikes have been removed by a routine based on the derivative of the signal. An example of the time series of a typical spike that have been removed is shown in Figure 7.1. See also comments in Section 8.4. Due to possible unstability of the z-component of the riser top transducer, the static values applied for the force channels are defined in Table 7.2. See also comments in Section 8.1.

7.3 Component Level Instrumentation Verification The complete results from the component level instrumentation verification are presented in Appendix 1. In this report, only a summary of the analysis with respect to time delays between measuring channels are presented. Time Delay Between Measuring Channels Due to serial sampling of data, there is a certain time delay between signals at different spatial locations. The time delay is generally dependent on the sampling frequency and the number of channels on the actual A/D converter. Prior to the tests, the time delay was determined for the two A/D converters applied in the tests. For the actual tests, A/D converter no. 1 had 40 channels, with a time delay of 25.0 microseconds between two neighbouring channels. A/D converter no. 2 had 45 channels, with a time delay of 22.2 microseconds between two neighbouring channels. A sketch of the instrumentation plan is shown in Figure 4.2. There was also a time delay between the two A/D converters. Based on 20 tests, the time delay between channel no. 1 on A/D converter no. 1 and channel no. 1 on A/D converter no. 2 was found to vary between 5.8 and 14.9 microseconds. For the purpose of beeing able to correct for this random time delay between the two A/D converters, a sinusiodal signal with a frequency of 10 Hz was input on channel no. 1 on both A/D converters in all tests. During the tests it was discovered that the sampling frequency of the two A/D converters were slightly different. By use of the sinusoidal wave function, the sampling frequency of A/D

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converter no. 1 was found to be 1000 Hz, and the sampling frequency of A/D converter no. 2 was found to be 1001 Hz. This difference was most probably due to a combination of a slightly difference of the frequency of the crystal clock and the aggregation rate of the two A/D converters. The time delays and the difference in sampling frequency for the two A/D converters, as described above, are not corrected for in the Data Report. A complete presentaton of the results is given in Appendix 2 " Component Level Instrumentation Verification". Summary results are presented in the table below.

Time delay (microseconds)

A/D converter no. Between channels

Between ch 1 on A/D converters

"Effective" sampling frequency

(Hz)

1 25.0 1000

2 22.2 5.8-14.9

1001

7.4 In-air DAS Verification and Experimental Modal Tests

7.4.1 Static DAS Verification Tests The noise level and signal drift have been documented in all sensor channels by collecting 60 seconds of data with all sensors powered and amplifiers set to operating gain levels. The riser model was laid out horizontally on a table, supported by V-framed structures every half metre. The bit resolution on the A/D converter was 5 mV and the maximum signal was +/- 10 V. With the gain factor set at 0.1, it was found that the noise level was within 2-3 bit resolutions. A maximum signal drift of approximately 8 bits could be observed.

7.4.2 Dynamic/Experimental Modal Tests The dynamic/experimental modal tests were subcontracted to Campus Marine. The results are presented in Appendix 3 "Dynamic/Experimental Modal Tests". The results from the simplified decay tests in air are summarized in Table 3.5. The resonance frequencies from the simplified decay tests are about 6-8 % than theoretical. This may be due to the suspension of the riser model and the heave-compensator and the riser sag, which is not taken care of in the theoretical model.

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7.5 In-water DAS Verification and Experimental Modal Tests Some typical results from the simplified impact tests on the rotating rig for evaluation of possible interactions betwen the riser model and the rig, are presented in Figures 7.2-7.8. The channels "Acc_x_top", "Acc_y_top" and "Acc_z_top" are accelerometers on top of the test rig, close to the riser top point. Figures 7.2-7.3 presents the acceleration spectra for the test rig alone, without the riser model attached. As seen from figures, dominant resonant vibrations of the test rig seem to be in the frequency ranges 20-40 Hz and 40 -60 Hz. Figures 7.4-7.8 present details of the acceleration spectra of "Acc_x_top" and various accelerometers along the riser from test 1104, with the riser model connected. From Figure 7.4 no influence from the test rig can be observed. The spectrum tops at about 5 and 6.2 Hz for "Acc_x_top" is due to excitation from the riser. The frequency top at 5 Hz has been isolated by filtering, and the time series of the acceleration signals are shown in Figure 7.5. While the riser oscillates with typical amplitude of 2 mm, the amplitude of the test rig is typically 0.18 mm. From the other figures, no influence from the test rig can be observed.

7.6 Uncertainty Budgets As a part of the documentation of the instrumentation and data reduction system, an uncertainty budget was performed for two types of measurements: curvature sensors and acceleration sensors. In calculating the uncertainty budget estimate, input from data sheets from the manufacturer, data from calibrations performed by Marintek and estimated values have been used. A summary is given in the table below.

Sensor Value Rel. expanded

uncertainty %

Coverage factor

Coverage %

Curvature 149.7 E-06 m/m +/- 2.4 2.0 95

Acceleration 9.89 ms-2 +/- 2.9 2.0 95 The results from the uncertainty analysis are presented in Appendix 4, "Uncertainty Budgets".

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7.7 Validation of Software Six different time series were used in the validation of the software used in the main analyses: 3 regular wave signals and 3 irregular wave signals. The time series were generated numerical by an in-house program (Express). Except for one irregular time series, all generated time series had analytical solutions. The table below defines the time series applied in the verification. Channel

No. Name Description

1 F_vary The frequency increases lineraly from f=1/40 to f=1/19.927 Hz.

2 Reg_1600 A regular wave with an amplitude 1.0 and period 16 s with first sample equal to zero.

3 Reg_2048 A regular wave with an amplitude 1.0 and period 20.48 s with first sample equal to zero.

4 Reg_sum Sum of channel 2 and 3.

5 Bpass_1 Time series based on flat raw spectrum equal to 5000 m2 Hz from frequency f=(20-1)/(4096 * 0.5) Hz to f=(150-1)/(4096 * 0.5). The spectrum is dropping linearly to zero to next sample outside this range.

6 Bpass_2

Time series based on a raw spectrum linearly increasing from 4000 m2 Hz at frequency f=(20-1)/(4096 * 0.5) Hz to 9000 m2 Hz at frequency f=(150-1)/(4096 * 0.5) Hz. The spectrum is dropping linearly to zero to next sample outside this range.

The time series were subject to spectral- and statistical analyses with the programs that should be validated, and the output from the analysis programs were compared to the analytical solutions and output from programs as e.g. Matlab. The following parameters were selected for the validation:

Spectral routines : spectral plots and spectral moments up to 4th order. Statistical routines : standard deviation, skewness and kurtosis.

The results from the validation are presented in Appendix 5 "Validation of Software". The results of the analyses and calculations based on the actual programs and the selected parameters showed that the results based on the programs were in accordance with the analytical results.

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7.8 Video and Photo The video recordings from the testst are presented in VHS format in NTSC. Still photos of the test set up are presented in the Photo Section and on CD-ROM.

7.9 Scaling All results are given in model-scale dimensions.

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8. COMMENTS

8.1 Riser End Transducers The z-component (Fz) of the riser bottom transducer showed irregularities in form of spikes and jumps in tests 1212-1225. The transducer was replaced after test 1225. Before and after these tests, the transducer was stable. In the post-processing of the data, "drift" was discovered in the signals of Fz of the riser top transducer in tests 5110-5118. The transducer has been replaced two times, but without eliminating the "drift". (See also comments in Section 8.2.) Due to the irregularities with the riser top transducer, the value Fz of the top transducer at the start of the test was set to the mean value of the Fz of the riser bottom transducer pluss the submerged weight of the riser model for all tests, and Fy of the top transducer was set to minus Fy of the bottom transducer.

8.2 Set-Down During the test program, it was observed that the measured set-down at the end of the test did not correspond to the set-down at the start of the test. In test 1120, for instance, the difference was about 0.05 m, corresponding to a tension of about 80 N. In this test a difference in Fz of about 75 N was found for the top transducer. However, no difference was found in Fz for the bottom transducer, which should be espected if the "drift" could be explained by hysteresis in the heave-compensator system. The set-down transducer has been replaced by another transducer, but the same phenomenon was observed. The set-down transducer has also been checked by pulling the transducer manually a predefined distance and registrating the set-down, but the measured set-down was in accordance with the predefined value. By starting a new registration about seven minutes after completion of a test, but without taking a new zero, the measurements showed that the set-down value was back to zero again. The position of the riser top has also been inspected visually before and after the test in several tests, without revealing any explanation of the behaviour. We have until now not found any explanation of this behaviour of the system

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8.3 Moment Transducers Since the moment transducers were calibrated by shunt-calibration, the calibration factor is depending on the position of the gauge on the pipe. At each measuring section, a total of four gauges were used. Two and two gauges was glued diametrically to the outside of the brass pipe on each side. With a distance between the centrelines of the two gauges on the same side of the pipe of 3.2 mm, a diameter of the brass pipe of 20 mm, the distance between the gauge pairs became 1.3 % less than the diameter of the pipe. Thus, the calibration factor will be increased by 1.3 %. This is, however, not corrected for in the presented data.

8.4 Spikes For actual channels, generally one spike occured during the whole test. The spikes are of very short duration and do not affect the spectral values. However, since the spikes affects the extreme values, they have been removed by a routine based on the derivative of the signals (see Figure 7.1).

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Figures

Figure 3.1 Details of the fairing and strakes Figure 4.1 Towing Tanks Figure 4.2 Sketch of test rig Figure 4.3 Details of test rig Figure 5.1 Co-ordinate systems Figure 5.2 Positions of transducers on riser model Figure 5.3 Instrumentation plan Figures 7.1 Example of typical spike Figure 7.2 Model-rig interactions. Results from pluck tests. Figure 7.3 Model-rig interactions. Results from pluck tests. Figure 7.4 Model-rig interactions. Results from test 1104. Figure 7.5 Model-rig interactions. Results from test 1104. Figure 7.6 Model-rig interaction. Results from test 1104. Figure 7.7 Model-rig interaction. Results from test 1104. Figure 7.8 Model-rig interaction. Results from test 1104.

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Figure 3.1 D

etails of the fairing and strakes

M

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Figure 4.1 The Towing Tank

11

4

10 9 8 7

136

5

3 2 1

15.

610

.0

28

39 85260

13.5

10.5

Model storeDrawing officeReceptionTank IIShip model manufacturing shopTrimming tankNC milling machine for model productionInstrumentation workshop

Carpenter workshopPropeller model manufacturing shopCavitation laboratoryDock gateWave absorber, Tank I + IIIWavemaker, Tank III and Tank I+IIIWave absorber, Tank III

12 15

12345

67

8

910

11121314

15

TANK I TANK III 14

Tank 1 TankII TankIII Tank I + III* Length 175.0 m 25.0 m 85.0 m 260.0 m Width 10.5 m 2.8 m 10.5 m 10.5 m

Depth 5.6 m 1.0 m 10.0 m 5.6/10.0 m * Tank I and III can be used simultaneously and also as one long tank (Tank I +III) by removing the gate (12) and wave absorber (15).

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Figure 4.2 Sketch of test rig

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Figure 4.3 Details of test rig

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Figure 5.1 Co-ordinate systems

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Figure 5.2 Positions of transducers on riser m

odel

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Figure 5.3 Instrum

entation plan

M

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/

Figures 7.1 Example of typical spike

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/

Figure 7.2 Model-rig interactions. Results from pluck tests.

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/

Figure 7.3 Model-rig interactions. Results from pluck tests.

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Figure 7.4 Model-rig interactions. Results from test 1104.

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Figure 7.5 Model-rig interactions. Results from test 1104.

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Figure 7.6 Model-rig interaction. Results from test 1104.

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/


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/


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Tables

Table 3.1 Physical properties of riser model Table 3.2 Weight in water of different riser model configurations Table 3.3 Riser fairing geometry Table 3.4 Riser eigen frequencies and Strouhal frequencies Table 3.5 Eigen frequencies of horizontal riser, heave compensator and test rig in air Table 5.1 Channel list Table 6.1 Test program for VIV-tests in rotating rig Table 6.2 Co-ordinates of riser end points Table 7.1 Corrections performed during post-processing of data Table 7.2 Static values of force channels

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Table 3.1 Physical properties of riser model

Parameter Dimension

Total length between pinned ends 9.63 m

Outer diameter 20 mm

Wall thickness of pipe 0.45 mm

Bending stiffness, EI1) 135.4 Nm2

Young modulus for brass, E1) 1.025 1011 N/m2

Axial stiffness, EA1) 2.83 106 N

Weigt in air (filled with water) 6.857 N/m 1) EI determined from bending test with brass pipe. E and EA determined from EI and measured pipe dimensions.

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Table 3.2 Weight in water of different riser model configurations

Riser

configuration

Weight in water

(N)

Naked 40.52

Faired50 40.261)

Faired100 39.99

Straked100 41.68

Straked75 41.16

Straked50 41.40

Straked25 41.08 1) Calculated by use of the weights for "Faired100" and "Naked"

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Table 3.3 Riser fairing geometry

Position X

(mm) Y

(mm) 1 0 0

2 18.00 18.00

3 24.26 17.61

4 30.52 16.72

5 36.78 15.46

6 43.04 13.96

7 49.30 12.33

8 55.57 10.67

9 61.83 8.92

10 68.09 7.07

11 74.35 5.26

12 80.61 3.35

13 82.80 2.70

14 83.97 4.73

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Tab

le 3

.4

Ris

er e

igen

freq

uenc

ies a

nd S

trou

hal f

requ

enci

es

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Table 3.5 Eigen frequencies of horizontal riser, heave compensator and test rig in air

Mode Test Measured (Hz)

Calculated1) (Hz)

Deviation (%)

1. Mode CF 9766 1.90 1.79 6.1

2. Mode CF 9768 3.90 3.67 6.3

3. Mode CF 9770 6.10 5.73 6.5

1. Mode IL 9762 2.06 1.79 15.1

2. Mode IL 9763 3.95 3.67 7.6

3. Mode IL 9765 6.16 5.73 7.5

1) Referring Table 3.4 Riser eigen frequencies and Strouhal frequencies Comments: - IL is in vertical riser plane. - Pretension: 817 N - Mass of riser: 0.699 kg/m

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Tab

le 5

.1

Cha

nnel

Lis

t: M

easu

red

chan

nels

Cha

nnel

no.

: C

hann

el n

ame:

Ph

ysic

al d

escr

iptio

n:

Uni

t:

Coo

rdin

ate

Syst

em

Posi

tive

dire

ctio

n:

Sens

or ty

pe e

tc.:

1 Si

nus_

1_1

Con

trol s

igna

l AD

con

verte

r no

1 V

2 Se

t-dow

n

Set d

own

at to

p ris

er e

nd

m

Glo

bal

Pos.

z-di

r. St

rain

gau

ge w

ith sp

ring

3 A

cc_x

_top

A

ccel

erat

ions

of t

est r

ig u

pper

end

in x

dir.

m

/s2

Glo

bal

Pos.

x-di

r.A

ccel

erom

eter

4

Acc

_y_t

op

Acc

eler

atio

ns o

f tes

t rig

upp

er e

nd in

y d

ir.

m/s

2

Glo

bal

Pos.

y-di

r.A

ccel

erom

eter

5 A

cc_z

_top

A

ccel

erat

ions

of t

est r

ig u

pper

end

in z

dir.

m

/s2

G

loba

lPo

s. z-

dir.

Acc

eler

omet

er6

Fx_t

op

Ris

er fo

rce

uppe

r end

in x

-dir.

N

G

loba

l Po

s. x-

dir.

Stra

in g

auge

tran

sduc

er

7 Fy

_top

R

iser

forc

e up

per e

nd in

y-d

ir.

N

Glo

bal

Pos.

y-di

r. St

rain

gau

ge tr

ansd

ucer

8

Fz_t

op

Ris

er fo

rce

uppe

r end

in z

-dir.

N

G

loba

l Po

s. z-

dir.

Stra

in g

auge

tran

sduc

er

9 St

rain

_IL0

1 St

rain

in in

-line

dir.

sect

ion

1 E-

06

Loca

l N

eg. x

-dir.

St

rain

gau

ge tr

ansd

ucer

10

St

rain

_IL0

2 St

rain

in in

-line

dir.

sect

ion

2 E-

06

Loca

l N

eg. x

-dir.

St

rain

gau

ge tr

ansd

ucer

11

St

rain

_IL0

3 St

rain

in in

-line

dir.

sect

ion

3 E-

06

Loca

l N

eg. x

-dir.

St

rain

gau

ge tr

ansd

ucer

12

St

rain

_IL0

4 St

rain

in in

-line

dir.

sect

ion

4 E-

06

Loca

l N

eg. x

-dir.

St

rain

gau

ge tr

ansd

ucer

13

St

rain

_IL0

5 St

rain

in in

-line

dir.

sect

ion

5 E-

06

Loca

l N

eg. x

-dir.

St

rain

gau

ge tr

ansd

ucer

14

St

rain

_IL0

6 St

rain

in in

-line

dir.

sect

ion

6 E-

06

Loca

l N

eg. x

-dir.

St

rain

gau

ge tr

ansd

ucer

15

St

rain

_IL0

7 St

rain

in in

-line

dir.

sect

ion

7 E-

06

Loca

l N

eg. x

-dir.

St

rain

gau

ge tr

ansd

ucer

16

St

rain

_IL0

8 St

rain

in in

-line

dir.

sect

ion

8 E-

06

Loca

l N

eg. x

-dir.

St

rain

gau

ge tr

ansd

ucer

17

St

rain

_IL0

9 St

rain

in in

-line

dir.

sect

ion

9 E-

06

Loca

l N

eg. x

-dir.

St

rain

gau

ge tr

ansd

ucer

18

St

rain

_IL1

0 St

rain

in in

-line

dir.

sect

ion

10

E-06

Lo

cal

Neg

. x-d

ir.

Stra

in g

auge

tran

sduc

er

19

Stra

in_I

L11

Stra

in in

in-li

ne d

ir. se

ctio

n 11

E-

06

Loca

l N

eg. x

-dir.

St

rain

gau

ge tr

ansd

ucer

20

St

rain

_IL1

2 St

rain

in in

-line

dir.

sect

ion

12

E-06

Lo

cal

Neg

. x-d

ir.

Stra

in g

auge

tran

sduc

er

21

Stra

in_I

L13

Stra

in in

in-li

ne d

ir. se

ctio

n 13

E-

06

Loca

l N

eg. x

-dir.

St

rain

gau

ge tr

ansd

ucer

22

St

rain

_IL1

4 St

rain

in in

-line

dir.

sect

ion

14

E-06

Lo

cal

Neg

. x-d

ir.

Stra

in g

auge

tran

sduc

er

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Table 5.1 Channel List: Measured channels

Channel no.:

Channel name: Physical description: Unit: Coordinate

System Positive

direction: Sensor type etc.:

23 Strain_IL15 Strain in in-line dir. section 15 E-06 Local Neg. x-dir. Strain gauge transducer 24 Strain_IL16 Strain in in-line dir. section 16 E-06 Local Neg. x-dir. Strain gauge transducer 25 Strain_IL17 Strain in in-line dir. section 17 E-06 Local Neg. x-dir. Strain gauge transducer 26 Strain_IL18 Strain in in-line dir. section 18 E-06 Local Neg. x-dir. Strain gauge transducer 27 Strain_IL19 Strain in in-line dir. section 19 E-06 Local Neg. x-dir. Strain gauge transducer 28 Strain_IL20 Strain in in-line dir. section 20 E-06 Local Neg. x-dir. Strain gauge transducer 29 Strain_IL21 Strain in in-line dir. section 21 E-06 Local Neg. x-dir. Strain gauge transducer 30 Strain_IL22 Strain in in-line dir. section 22 E-06 Local Neg. x-dir. Strain gauge transducer 31 Strain_IL23 Strain in in-line dir. section 23 E-06 Local Neg. x-dir. Strain gauge transducer 32 Strain_IL24 Strain in in-line dir. section 24 E-06 Local Neg. x-dir. Strain gauge transducer 33 Strain_IL25 Strain in in-line dir. section 25 E-06 Local Neg. x-dir. Strain gauge transducer 34 Strain_IL26 Strain in in-line dir. section 26 E-06 Local Neg. x-dir. Strain gauge transducer 35 Strain_IL27 Strain in in-line dir. section 27 E-06 Local Neg. x-dir. Strain gauge transducer 36 Strain_IL28 Strain in in-line dir. section 28 E-06 Local Neg. x-dir. Strain gauge transducer 37 Strain_IL29 Strain in in-line dir. section 29 E-06 Local Neg. x-dir. Strain gauge transducer 38 Strain_IL30 Strain in in-line dir. section 30 E-06 Local Neg. x-dir. Strain gauge transducer 39 Strain_IL31 Strain in in-line dir. section 31 E-06 Local Neg. x-dir. Strain gauge transducer 40 Strain_IL32 Strain in in-line dir. section 32 E-06 Local Neg. x-dir. Strain gauge transducer 41 Sinus_2_2 Control signal AD converter no 2 V 42 Strain_IL33 Strain in in-line dir. section 33 E-06 Local Neg. x-dir. Strain gauge transducer 43 Strain_IL34 Strain in in-line dir. section 34 E-06 Local Neg. x-dir. Strain gauge transducer 44 Strain_IL35 Strain in in-line dir. section 35 E-06 Local Neg. x-dir. Strain gauge transducer

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Table 5.1 List:

Channel no.:


System Positive


512382.00.01 draf 2003-07-15

Channel Measured channels

45 Strain_CF02 Strain in cross-flow dir. section 2 E-06 Local Neg. y-dir. Strain gauge transducer 46 Strain_CF04 Strain in cross-flow dir. section 4 E-06 Local Neg. y-dir. Strain gauge transducer 47 Strain_CF06 Strain in cross-flow dir. section 6 E-06 Local Neg. y-dir. Strain gauge transducer 48 Strain_CF08 Strain in cross-flow dir. section 8 E-06 Local Neg. y-dir. Strain gauge transducer 49 Strain_CF10 Strain in cross-flow dir. section 10 E-06 Local Neg. y-dir. Strain gauge transducer 50 Strain_CF12 Strain in cross-flow dir. section 12 E-06 Local Neg. y-dir. Strain gauge transducer 51 Strain_CF14 Strain in cross-flow dir. section 14 E-06 Local Neg. y-dir. Strain gauge transducer 52 Strain_CF16 Strain in cross-flow dir. section 16 E-06 Local Neg. y-dir. Strain gauge transducer 53 Strain_CF18 Strain in cross-flow dir. section 18 E-06 Local Neg. y-dir. Strain gauge transducer 54 Strain_CF20 Strain in cross-flow dir. section 20 E-06 Local Neg. y-dir. Strain gauge transducer 55 Strain_CF22 Strain in cross-flow dir. section 22 E-06 Local Neg. y-dir. Strain gauge transducer 56 Strain_CF24 Strain in cross-flow dir. section 24 E-06 Local Neg. y-dir. Strain gauge transducer 57 Strain_CF26 Strain in cross-flow dir. section 26 E-06 Local Neg. y-dir. Strain gauge transducer 58 Strain_CF28 Strain in cross-flow dir. section 28 E-06 Local Neg. y-dir. Strain gauge transducer 59 Strain_CF30 Strain in cross-flow dir. section 30 E-06 Local Neg. y-dir. Strain gauge transducer 60 Strain_CF32 Strain in cross-flow dir. section 32 E-06 Local Neg. y-dir. Strain gauge transducer 61 Strain_CF34 Strain in cross-flow dir. section 34 E-06 Local Neg. y-dir. Strain gauge transducer 62 Acc_IL04 Accelerations in in-line dir. section 4 m/ss Local Pos. x-dir. Accelerometer 63 Acc_IL08 Accelerations in in-line dir. section 8 m/ss Local Pos. x-dir. Accelerometer 64 Acc_IL12 Accelerations in in-line dir. section 12 m/ss Local Pos. x-dir. Accelerometer 65 Acc_IL16 Accelerations in in-line dir. section 16 m/ss Local Pos. x-dir. Accelerometer 66 Acc_IL20 Accelerations in in-line dir. section 20 m/ss Local Pos. x-dir. Accelerometer

51

Table 5.1 Channel List: Measured channels

Channno.: el

Channel name: Physical description: Unit:

Coordinate

System

Positive direction:

Sensor type etc.:

67 Acc_IL24 Ac 4 celerations in in-line dir. section 2 E-06 Local Pos. x-dir. Strain gauge transducer 68 Acc_IL28 Ac 8 celerations in in-line dir. section 2 E-06 Local Pos. x-dir. Strain gauge transducer 69 Acc_IL32 Ac celerations in in-line dir. section 32 E-06 Local Pos. x-dir. Strain gauge transducer 70 Acc_CF04 Ac n 4 celerations in cross-flow dir. sectio E-06 Local Pos. y-dir. Strain gauge transducer 71 Acc_CF08 Ac n 8 celerations in cross-flow dir. sectio E-06 Local Pos. y-dir. Strain gauge transducer 72 Acc_CF12 Ac n 12 celerations in cross-flow dir. sectio E-06 Local Pos. y-dir. Strain gauge transducer 73 Acc_CF16 Ac n 16 celerations in cross-flow dir. sectio E-06 Local Pos. y-dir. Strain gauge transducer 74 Acc_CF20 Ac n 20 celerations in cross-flow dir. sectio E-06 Local Pos. y-dir. Strain gauge transducer 75 Acc_CF24 Ac n 24 celerations in cross-flow dir. sectio E-06 Local Pos. y-dir. Strain gauge transducer 76 Acc_CF28 Ac n 28 celerations in cross-flow dir. sectio E-06 Local Pos. y-dir. Strain gauge transducer 77 Acc_CF32 Ac n 32 celerations in cross-flow dir. sectio E-06 Local Pos. y-dir. Strain gauge transducer 78 Speed_bot Velocity at lower riser end m/s Global Pos. x-dir. Tachometer 79 Fx_bot Riser force lower end in x-dir. N Global Pos. x-dir. Strain gauge transducer 80 Fy_bot Riser force lower end in y-dir. N Global Pos. y-dir. Strain gauge transducer 81 Fz_bot Riser force lower end in z-dir. N Global Pos. z-dir. Strain gauge transducer 82 Acc_X_bot Ac ir. celerations of test rig lower end in x d m/ss Global Pos. x-dir. Accelerometer 83 Acc_Y_bot Ac ir. celerations of test rig lower end in y d m/ss Global Pos. y-dir. Accelerometer84 Acc_Z_bot Ac . celerations of test rig lower end in z dir m/ss Global Pos. z-dir. Accelerometer85 Weight_riser Weight of riser in water N Strain gauge

MT51 F03-167 / t / 512382.00.01 draf 2003-07-15

52

MT51 F03-167 / t /

Table 5.1 el List: De

Channel no.:


System Positive


512382.00.01 draf 2003-07-15

Chann rived channels

86 Ftot_top Total force at upper riser end E-06 Derived from ch 6-8 Global 87 Pos_IL04 Displacem . ent in in-line dir. section 04 m Local Pos. x-dir Derived from accelerations

89 Pos_IL12 Displacement in in-line dir. section 12 . ions m Local Pos. x-dir Derived from accelerat90 Pos_IL16 Displacement in in-line dir. section 16 . ions m Local Pos. x-dir Derived from accelerat91 Pos_IL20 Displacement in in-line dir. section 20 . ions m Local Pos. x-dir Derived from accelerat92 Pos_IL24 Displacement in in-line dir. section 24 m Local . ions Pos. x-dir Derived from accelerat93 Pos_IL28 Displacement in in-line dir. section 28 m Local . ions Pos. x-dir Derived from accelerat94 Pos_IL32 Displacement in in-line dir. section 32 m Local . ions Pos. x-dir Derived from accelerat95 Pos_CF04 Displacement in cross-flow dir. section 04 . ions m Local Pos. y-dir Derived from accelerat96 Pos_CF08 Displacement in cross-flow dir. section 08 . ions m Local Pos. y-dir Derived from accelerat97 Pos_CF12 Displacement in cross-flow dir. section 12 . ions m Local Pos. y-dir Derived from accelerat98 Pos_CF16 Displacement in cross-flow dir. section 16 . ions m Local Pos. y-dir Derived from accelerat99 Pos_CF20 Displacement in cross-flow dir. section 20 . ions m Local Pos. y-dir Derived from accelerat100 w dir. section 24 . m accelerations Pos_CF24 Displacement in cross-flo m Local Pos. y-dir Derived fro101 28 ir. section 28 . ions Pos_CF Displacement in cross-flow d m Local Pos. y-dir Derived from accelerat102 32 ir. section 32 . ions Pos_CF Displacement in cross-flow d m Local Pos. y-dir Derived from accelerat103 t Ftot_bo Total force at lower riser end N Global Derived from ch 79-81

88 Pos_IL08 Displacement in in-line dir. section 08 m Local Pos. x-dir. Derived from accelerations

54

MT51 F03-167 / 512382.00.01 draft / 2003-07-15

Table 6.1 Test program for VIV-tests in rotating rig Test no.

File head text

Comments

1103 Naked_riser Uniform V0.20 1104 Naked_riser Uniform V0.28 1105 Naked_riser Uniform V0.42 1106 Naked_riser Uniform V0.56 1107 Naked_riser Uniform V0.70 1108 Naked_riser Uniform V0.84 1109 Naked_riser Uniform V0.98 1110 Naked_riser Uniform V1.12 Overflow Fx_bot 1111 Naked_riser Uniform V1.12 1112 Naked_riser Uniform V1.26 1113 Naked_riser Uniform V1.40 1115 Naked_riser Uniform V1.54 1117 Naked_riser Uniform V1.68 1118 Naked_riser Uniform V1.82 1119 Naked_riser Uniform V1.96 1120 Naked_riser Uniform V2.10 1121 Naked_riser Uniform V2.24 1122 Naked_riser Uniform V2.38 1123 Naked_riser Uniform V1.96 rep 1124 Naked_riser Uniform V0.24 1125 Naked_riser Uniform V0.35 1127 Naked_riser Uniform V0.28 rep 1128 Naked_riser Uniform V0.49

1201 Naked_riser Shear V0.20 1202 Naked_riser Shear V0.24 1203 Naked_riser Shear V0.28 1204 Naked_riser Shear V0.35 1205 Naked_riser Shear V0.42 1206 Naked_riser Shear V0.49 1207 Naked_riser Shear V0.56 1208 Naked_riser Shear V0.35 rep 1209 Naked_riser Shear V0.70 1210 Naked_riser Shear V0.84 1211 Naked_riser Shear V0.98 1212 Naked_riser Shear V1.12 Fz_bot not good 1213 Naked_riser Shear V1.26 1214 Naked_riser Shear V1.40 1215 Naked_riser Shear V1.12 Fz_bot not good 1216 Naked_riser Shear V1.54 Overflow Fx_bot and Fy_bot 1217 Naked_riser Shear V1.54 Fz_bot not good 1218 Naked_riser Shear V1.68 Fz_bot not good 1219 Naked_riser Shear V1.82 Fz_bot not good 1220 Naked_riser Shear V1.96 Fz_bot not good

55

MT51 F03-167 / 512382.00.01 draft / 2003-07-15

Table 6.1 (cont.) Test program Test no.

File head text

Comments

1221 Naked_riser Shear V1.68 rep Fz_bot not good 1222 Naked_riser Shear V2.10 Fz_bot not good 1223 Naked_riser Shear V2.10 Fz_bot not good 1224 Naked_riser Shear V2.24 Fz_bot not good 1225 Naked_riser Shear V2.38 Fz_bot not good

2202 Faired100_riser Shear V0.56 2203 Faired100_riser Shear V0.60 2204 Faired100_riser Shear V0.64 2205 Faired100_riser Shear V0.70 2206 Faired100_riser Shear V0.75 2207 Faired100_riser Shear V0.80 2208 Faired100_riser Shear V0.84 2209 Faired100_riser Shear V0.90 2210 Faired100_riser Shear V0.94 Fishtailing 2211 Faired100_riser Shear V1.0-0.7 Fishtailing 2212 Faired100_riser Shear V0.94 No fishtailing 2213 Faired100_riser Shear V1.12 Fishtailing. Stopped quit soon.

3203 Faired50_riser Shear V0.28 3205 Faired50_riser Shear V0.35 3206 Faired50_riser Shear V0.42 3207 Faired50_riser Shear V0.49 3208 Faired50_riser Shear V0.56 3211 Faired50_riser Shear V0.70 3212 Faired50_riser Shear V0.60 3212 Faired50_riser Shear V0.64 3213 Faired50_riser Shear V0.70 3214 Faired50_riser Shear V0.75 3215 Faired50_riser Shear V0.80 No fishtailing 3216 Faired50_riser Shear V0.84 Fishtailing 3218 Faired50_riser Shear V0.80 Fishtailing 3219 Faired50_riser Shear V0.5-0.8-0.5 3220 Faired50_riser Shear V0.8-0.5

4101 Straked100_riser Uniform V0.20 4102 Straked100_riser Uniform V0.24 4103 Straked100_riser Uniform V0.28 4104 Straked100_riser Uniform V0.35 4105 Straked100_riser Uniform V0.42 4106 Straked100_riser Uniform V0.49 4107 Straked100_riser Uniform V0.56 4108 Straked100_riser Uniform V0.70 4109 Straked100_riser Uniform V0.84 4110 Straked100_riser Uniform V0.98

g9yang1

Cross-Out

g9yang1

Cross-Out

56

Table 6.1 (cont.) Test program

Test no.

File head text

Comments

4111 Straked100_riser Uniform V0.84 rep 4112 Straked100_riser Uniform V1.12 4113 Straked100_riser Uniform V1.26 4114 Straked100_riser Uniform V1.40 4115 Straked100_riser Uniform V1.54 4116 Straked100_riser Uniform V1.68 4117 Straked100_riser Uniform V2.10 4118 Straked100_riser Uniform V1.82 4119 Straked100_riser Uniform V1.96 4120 Straked100_riser Uniform V2.24 4121 Straked100_riser Uniform V2.38 verflow Fx_top O4122 Straked100_riser Uniform V2.38

4201 Straked100_riser Shear V0.20 4202 Straked100_riser Shear V0.24 4203 Straked100_riser Shear V0.28 4204 Straked100_riser Shear V0.35 4205 Straked100_riser Shear V0.42 4206 Straked100_riser Shear V0.49 4207 Straked100_riser Shear V0.56 4208 Straked100_riser Shear V0.70 4209 Straked100_riser Shear V0.84 4212 Straked100_riser Shear V0.84 rep

4214 Straked100_riser Shear V1.12 4215 Straked100_riser Shear V1.26 4216 Straked100_riser Shear V1.40 4217 Straked100_riser Shear V1.54 4218 Straked100_riser Shear V1.68 4219 Straked100_riser Shear V1.82 4220 Straked100_riser Shear V1.96 4221 Straked100_riser Shear V1.96 rep 4222 Straked100_riser Shear V2.10 4223 Straked100_riser Shear V2.24 4224 Straked100_riser Shear V2.38

5101 Straked75_riser Uniform V0.20 rift on ch 27 D5102 Straked75_riser Uniform V0.24 rift on ch 27 D5103 Straked75_riser Uniform V0.28 Drift on ch 27 5104 Straked75_riser Uniform V0.35 Drift on ch 27 5105 Straked75_riser Uniform V0.42 Drift on ch 27 5106 Straked75_riser Uniform V0.49 5107 Straked75_riser Uniform V0.56 5108 Straked75_riser Uniform V0.70

4213 Straked100_riser Shear V0.98

MT51 F03-167 / 512382.00.01 draft / 2003-07-15

57

MT51 F03-167 /

able 6.1 (cont.) Test program

512382.00.01 draft / 2003-07-15

Test no.

File head text

Comments

5109 Straked75_riser Uniform V0.84 5110 Straked75_riser Uniform V0.98 Drift on c8 5111 Straked75_riser Uniform V0.98 rep Drift on c8 5112 Straked75_riser Uniform V1.12 Drift on c8 5113 Straked75_riser Uniform V1.26 Drift on c8

S D5115 Straked75_riser Uniform V1.54 rift on c8 D5116 Straked75_riser Uniform V1.68 rift on c8 D5117 Straked75_riser Uniform V1.82 rift on c8 D5118 Straked75_riser Uniform V1.96 rift on c8 D5119 Straked75_riser Uniform V2.10 5120 Straked75_riser Uniform V2.24 5121 Straked75_riser Uniform V2.38 5122 Straked75_riser Uniform V2.38 rep

5201 Straked75_riser Shear V0.20 5202 Straked75_riser Shear V0.24 5203 Straked75_riser Shear V0.28

S 5205 Straked75_riser Shear V1.82 5206 Straked75_riser Shear V1.96 5207 Straked75_riser Shear V1.82 rep 5208 Straked75_riser Shear V1.96 rep 5209 Straked75_riser Shear V2.10 5210 Straked75_riser Shear V2.24 5211 Straked75_riser Shear V2.38 5212 Straked75_riser Shear V0.35 5213 Straked75_riser Shear V0.42 5214 Straked75_riser Shear V0.49 5215 Straked75_riser Shear V0.56 5216 Straked75_riser Shear V0.70 5217 Straked75_riser Shear V0.84 5218 Straked75_riser Shear V0.98 5219 Straked75_riser Shear V1.12

S 5221 Straked75_riser Shear V1.40 5223 Straked75_riser Shear V1.54

6101 Straked50_riser Uniform V0.20 6102 Straked50_riser Uniform V0.24 6103 Straked50_riser Uniform V0.28 6104 Straked50_riser Uniform V0.35 6105 Straked50_riser Uniform V0.42 6106 Straked50_riser Uniform V0.49

T

5114 traked75_riser Uniform V1.40 rift on c8

5204 traked75_riser Shear V1.68


58

MT51 F03-167 /

able 6.1 (cont.) Test program

File head text

Comments

512382.00.01 draft / 2003-07-15

TTest no.

6108 Straked50_riser Uniform V0.56 rep 6109 Straked50_riser Uniform V0.70 6110 Straked50_riser Uniform V0.84 6111 Straked50_riser Uniform V0.98 Overflow AccCF04 6112 Straked50_riser Uniform V0.98 6114 Straked50_riser Uniform V1.12 6115 Straked50_riser Uniform V1.26 6116 Straked50_riser Uniform V1.40 6117 Straked50_riser Uniform V1.54 6118 Straked50_riser Uniform V1.68 6119 Straked50_riser Uniform V1.82 6120 Straked50_riser Uniform V1.96

S 6122 Straked50_riser Uniform V2.24 6123 Straked50_riser Uniform V2.38 6124 Straked50_riser Uniform V2.38 rep

6201 Straked50_riser Shear V0.20 6203 Straked50_riser Shear V0.24 6204 Straked50_riser Shear V0.28 6205 Straked50_riser Shear V0.35 6206 Straked50_riser Shear V0.42 6207 Straked50_riser Shear V0.49 6208 Straked50_riser Shear V0.56 6209 Straked50_riser Shear V0.70 6210 Straked50_riser Shear V0.84 6211 Straked50_riser Shear V0.98 6212 Straked50_riser Shear V1.12 6213 Straked50_riser Shear V1.26 Overflow Strain_IL35 6215 Straked50_riser Shear V1.26 6216 Straked50_riser Shear V1.40 6217 Straked50_riser Shear V1.54 6218 Straked50_riser Shear V1.68 6219 Straked50_riser Shear V1.82 6220 Straked50_riser Shear V1.96

S 6222 Straked50_riser Shear V2.10 rep 6223 Straked50_riser Shear V2.24 6224 Straked50_riser Shear V2.38 6225 Straked50_riser Shear V2.38 rep

7101 Straked25_riser Uniform V0.20 7102 Straked25_riser Uniform V0.24

6107 Straked50_riser Uniform V0.56

6121 traked50_riser Uniform V2.10


g9yang1

Cross-Out

59

MT51 F03-167 /

Tabl conTest

xt

Comments

512382.00.01 draft / 2003-07-15

e 6.1 ( t.) Test program

no. File head te7103 Straked25_riser Uniform V0.28 7104

7106 Straked25_riser Uniform V0.49 7107 Straked25_riser Uniform V0.56 7108 Straked25_riser Uniform V0.56 rep 7109 Straked25_riser Uniform V0.70 7110 Straked25_riser Uniform V0.70 rep 7111 Straked25_riser Uniform V0.84 7112 Straked25_riser Uniform V0.98 7113 Straked25_riser Uniform V1.12 7114 Straked25_riser Uniform V1.26 7115 Straked25_riser Uniform V1.40 7116 Straked25_riser Uniform V1.54 7117 Straked25_riser Uniform V1.68 7118 Straked25_riser Uniform V1.82 Overflow AccXtop 7119 Straked25_riser Uniform V1.82

S 7121 Straked25_riser Uniform V2.10 7122 Straked25_riser Uniform V2.24 7123 Straked25_riser Uniform V2.38 verflow Fy_bot O7124 Straked25_riser Uniform V2.38

7201 Straked25_riser Shear V0.20 7202 Straked25_riser Shear V0.24 7203 Straked25_riser Shear V0.28 7204 Straked25_riser Shear V0.35 7205 Straked25_riser Shear V0.42 7206 Straked25_riser Shear V0.49 7207 Straked25_riser Shear V0.56 7208 Straked25_riser Shear V0.70 7210 Straked25_riser Shear V0.84 7211 Straked25_riser Shear V0.98 7213 Straked25_riser Shear V1.12 7214 Straked25_riser Shear V1.26 7215 Straked25_riser Shear V1.40 7216 Straked25_riser Shear V1.40 rep 7217 Straked25_riser Shear V1.54 7218 Straked25_riser Shear V1.68 7219 Straked25_riser Shear V1.82

S 7221 Straked25_riser Shear V1.96 7222 Straked25_riser Shear V2.10 7223 Straked25_riser Shear V2.24 7224 Straked25_riser Shear V2.38

Straked25_riser Uniform V0.35 7105 Straked25_riser Uniform V0.42

7120 traked25_riser Uniform V1.96

7220 traked25_riser Shear V1.82 rep

60

MT51 F03-167 /

able 6.2 Coordinates of riser ends

Riser end point Flow x [m] y [m] r [m] z [m]

512382.00.01 draft / 2003-07-15

T

Sheared 0.370 -0.529 0.646 -0.95 Top

Uniform 0.370 -4.67 4.685 -0.03 0

Bottom -4.630 4.645 -9.66 0.374

oordin s given in global coordinate syste

(x2 + y

All c ate m. r = √ 2)

61

MT51 F03-167 /

Tabl processing of data.

ts - channels,

512382.00.01 draft / 2003-07-15

e 7.1 Corrections made during post-

Spikes removed from the following tes T1103 12, 24, 62 T110 0 T110 2, T111 , 5 T111 , 2T111 , 9T111 6, T111 7, T111 7, T112 9, T112 2, T112 8 T112 1, T112 9, T120 3 T120 9, T121 9, T121 8 T121 7, T121 5, 53, 54 57, 64, 65, 73, 81 T121 8, 53, 56 58, 81, 83 T121 , 8T121 1, T121 , 4T122 2, 55, 57 59, 62, 67, 68, 71, 74, 75, 77, 81 T1222 - ch 25, 29, 38, 40, 42, 43, 46, 48, 54, 81 T122 6, T220 3, T220 3, T220 6 T220 1 T221 8, 72 T221 7 T221 , 1 4, 44, 48, 8, 68, 79 T321 5, T321 0, T321 3 T322 , 1 7, 50, 51, 2, 60, 70, 80, 84 T410 0 T411 9, T411 1, T411 9 T411 7, T411 8, T411 9, T411 , 6T4120 - ch 73, 75

- ch 4 - ch 47 - ch 2 24, 53 0 - ch 32 - ch 7 7, 28, 30 3 - ch 4 , 55, 71, 76, 77 5 - ch 4 52, 53 7 - ch 3 38, 45 9 - ch 5 59 0 - ch 3 55, 58, 66, 73 1 - ch 12 - ch 4

17, 33, 50, 56, 62, 64, 70, 72, 74

4 - ch 3 40, 52 5 - ch 1 20, 26, 29, 30, 32, 34, 35, 45, 54

7 - ch 59 - ch 6 70, 73, 77 0 - ch 1 39, 40, 42, 54, 56, 57, 58, 62, 63, 67 1 - ch 62 - ch 33 - ch 2

59, 66, 79, 81 27, 28, 29, 35, 36, 39, 40, 42, 44, 47, ,

4 - ch 1 20, 21, 22, 23, 26, 30, 31, 34, 50, 52, , 6 - ch 5 1, 84 8 - ch 1 24, 38, 40, 42, 43, 81 9 - ch 3 , 13, 33, 37, 72, 81 0 - ch 1 14, 17, 19, 32, 35, 36, 39, 45, 49, 51, ,

4 - ch 7 81

5 - ch 7 75 6 - ch 2 25 7 - ch 79 - ch 60 - ch 1 35, 36, 37, 43, 47, 57, 59, 69, 71, 1 - ch 73 - ch 9 3, 15, 16, 17, 23, 25, 30, 31, 33, 3 5

6 - ch 4 65, 73 8 - ch 2 22, 27, 31, 34, 36, 37, 39, 42, 73 9 - ch 40 - ch 7 8, 19, 21, 23, 24, 25, 35, 44, 46, 4 5

6 - ch 20 - ch 5 73 1 - ch 7 75 3 - ch 65 - ch 6 76 6 - ch 6 77 7 - ch 5 70, 71 9 - ch 5 5, 83

62

MT51 F03-167 /

T412 3

4223 - ch 74 4224 - ch 75

5105 - ch 9, 21 0, 3

5108 - ch 54, 79 5109 - ch 61

T5111 - ch 44 T5113 , 71 T5114 - ch 4, 20 T5115 - ch 7 T511

5117 - ch 34, 63, 75

5120 - ch 45, 66 4

5122 - ch 20, 55, 67, 72

5204 - ch 4, 74, 75 5205 - ch 71, 83 5207 - ch 72

T5210 - ch 58, 76, 79 T5217 - ch 84 T5223 - ch 5, 71, 74 T6108 - ch 9 T6110 - ch 10, 39, 68, 77 T6112 - ch 82, 84 T6119 - ch 70, 71, 74 T6120 - ch 28, 38 T6121 - ch 20 T6122 - ch 19, 22, 31, 45, 54 T6123 - ch 34 T6124 - ch 13, 18, 57 T6204 - ch 42 T6208 - ch 25 T6215 - ch 47, 57 T6216 - ch 51, 52, 53, 60 T6218 - ch 53 T6219 - ch 12, 72, 73, 74, 75 T6220 - ch 49, 59, 60, 66, 70, 71, 77 T6221 - ch 11, 33 T7106 - ch 28 T7109 - ch 9, 10, 34, 37, 43, 63, 67, 68, 69 T7110 - ch 45, 54 T7111 - ch 62 T7115 - ch 39, 82 T7116 - ch 28, 46 T7117 - ch 51, 52

512382.00.01 draft / 2003-07-15

1 - ch 8

TT TT5106 - ch 1 4, 40, 44 TTT5110 - ch 9, 18

- ch 70

6 - ch 74 TT5118 - ch 65 T5119 - ch 59 TT5121 - ch 38, 8T TTT

63

MT51 F03-167 /

3 7119 - ch 9, 19, 44, 54, 57, 60

7121 - ch 16, 18, 31, 32, 48, 55, 61, 71, 75, 76, 79

12, 21, 24, 29

5 51, 59, 70, 76

57, 63, 68, 74

40, 43, 72, 76

5, 54, 65 52, 53, 60, 67

ges

512382.00.01 draft / 2003-07-15

T7118 - ch 8TT7120 - ch 17, 56 TT7122 - ch 62 T7123 - ch 11, T7124 - ch 23 T7207 - ch 37 T7210 - ch 47, 52, 53, 60, 73, 7T7211 - ch 46, 48, 50, T7213 - ch 62, 67, 69 T7216 - ch 55, 56, T7217 - ch 58, 61 T7218 - ch 45, 75

66, 71, 84 T7219 - ch 28,T7220 - ch 27, 29, 34, T7221 - ch 5, 64, 70, 73

7222 - ch 59, 77 TT7223 - ch 4, 2T7224 - ch 38, 41, 46, 51, Additional chan

Timeseries cut at 90 sec. t at 190 sec.

ading text, V2.10. se.

0.24. Timeseries cut at 200 sec.

5121 Timeseries cut at 45 sec. Timeseries cut at 40 sec. Changed sign for ch 6. Changed gain for ch 36 from 0.5 to 1.0.

Timeseries cut at 135 sec. .

6119 Changed gain for ch 62 from 0.5 to 0.2 Changed filename from T5301

Changed heading text, Removed ”Pretension”

T1116 Changed heading text, V1.82. T1213,T1214,T1216 Ch 81 has been HP filtered to remove drift. T2211 T3205 Timeseries cuT4117 Changed heT4201-T4212 Changed gain for ch 59. from 0.1 to 1.0 and LP filtered to remove noiT4202 Changed heading text, VT5104 TT5122 T5201-T5204

T5210 T5217 T5218 Changed heading text, V0.98

Timeseries cut at 230 sec. T6103 T6112 Changed gain for ch 70-77 from 0.1 to 0.2 TT6201 T6224 Timeseries cut at 50 sec.T7101-T7103

64

MT51 F03-167 /

tic values of force channels

Tests

512382.00.01 draft / 2003-07-15

Table 7.2 Sta Channel

1100 1200 2200 3200 4100 4200 5100 5200 6100 6200 7100 7200

Fy_top -287 -261 -273 -268 -263 -263 -263

Fz_top -694 -622 -586 -609 -701 -601 -700 -590 -634 -592 -630 -591

Fy_bot 287 261 273 268 263 263 263

Fz_bot 654 582 546 569 661 561 660 550 594 552 589 550

Tests Channel

824,9826 9832-9835 9854-9856 9912-9914 9823,9

Fy_top -287 -261

Fz_top -694 -622 -586 -630

Fy_bot 287 261

Fz_bot 654 582 546 589

65

MT51 F03-167 /

APPENDIX 1

Specification for Instrumentation xperimental Modal Testing

512382.00.01 draft / 2003-07-15

URCVerification and E

66

MT51 F03-167 /

rification

erification tests will be performed on subsets of all components to be used in the data acquisition ystem for the ExxonMobil VIV tests. The results of the verification tests will be compared to the alibration and specification data provided by the m cturers of the different components. If

n v t t fi l ne required for all components of that type. Based on communications between URC and

Marintek, the com ts use in t rum nt/data acquisition system are listed in Table 1.

Com

512382.00.01 draft / 2003-07-15

I. Component Level Instrumentation Ve Vsc anufaany tested compo ents fail its specific erifica ion tes s, veri cation testing or reca ibratio will b

ponen that will be d he inst e

DC amplifie ger Bal M dwin KWS and GC+ponent Manufacturer Model Number

r HottinAnalog Filters GEPA MOM-MKT (8-pole A/D Converter Data Translation DT3003 - 12 bit Strain Gages Vishay - EA-13-250PD-120

Accelerometers Measurement Specialties ICSensors - 3031 (+/- 100g)Load Cells Marintek N/A

Table 1. Data Acquisition System Co ts for ExxonMobil VIV Tests

The verification tests required for each component type are described below as well as the number o nents to be tested. Testing of the components should be carried out in the order in which t iscussed. Data will be recorded via the data acquisition system for all ve 1.1 A/D Converter

he following verification tests will be performed on the DT3003 A/D converters. 1. Input a constant amplitude sinusoid into the A/D converter and use the recorded time series to

calculate the spectra of the input. Using the measured spectra, calculate the signal to noise ratio (ratio of signal peak (dB) and noise peak (dB) in spectra) and the effective number of bits (defined below).

Theoretical Signal to Noise Ratio : SNR = 6.02N + 1.76dB, where N = number of bits

Effective number of bits :

mponen

f compohey are d rification tests.

T

02.676.1 dBSNR

ENOB ACTUAL −=

2. Input a constant amplitude sinusoid into six A/D converter channels and determine the time

delays between channels (confirm 3 µs value). 3. Compare results of the verification tests to the manufacturers specifications for the A/D

converter.

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MT51 F03-167 /

1.2 DC Amplifiers Verification tests will be performed on two KWS odel amplifiers. The built-in filter in the MGC+ amplifiers will not be used du ng tests, and therefore not used during verification tests. The following verification tests ill be performed on the DC amplifier units. 1. Apply a constant bridge unbalance using a Hottinger Baldwin calibration units as input to the

amplifier to verify the static performance of the unit (unbalance = 2mV/V for G = 1, 2, 5, 10). 2. A 10V amplitude sinusoid sign attenuated to 10mV using a

voltage divider and used as inp signals of different frequencies to the amplifier to verify the dynamic perform nce of the unit (signal input = sin(2πfit) ; where fi = 2, 20, fc, and 1.5fc). Record the raw input signal on channel 1 and the amplified signal on channel 2. Since fc=200Hz, and the time delay between neighbouring signals will never exeed 0.3 degrees, which makes phase corrections due to AD converting unnecessary.

3. Com unit.

Verification of DC gain and corner frequency will be performed on four GEPA, MOM_MKT filter channels to be used in the tests. The following verification tests will be performed on the analog filter channels. 1. Apply +10VDC and -10VDC signals to the filters and record the raw and filtered signals to

determine the filter gain. Apply sinusoid signals (at frequencies that must include the following three frequencies: 0.5fc, fc, 1.5fc) to the filters and record the raw and filtered signals. Vary the frequency until the phase difference is 360 degrees to determine the corner frequency (Butteworth filter) Since fc=200Hz, and the time delay between neighbouring AD channels is only 3µs, the phase difference between the raw and the amplified signals will never exeed 0.3 degrees, which make phase corrections due to AD converting unnecessary.

2. Verify corner frequencies are correct and compare the performance of the unit tested to the

manufacturer's calibration sheet for the unit. 1.4 Accelerometers, Load Cell, and Bridge Completions The following verification tests will be performed on two of the Measurement Specialties, ICSensors 3031 accelerometers and one of the load cells used to measure riser end force. 1. Apply known static loads (500 N, 1000 N) to the load cell to verify the calibration factors.

Load cell orientation should be adjusted so that all three axes of the load cell are verified.

512382.00.01 draft / 2003-07-15

and two MGC+ mri w

a

pare performance of the units tested to the manufacturer's calibration sheets for each 1.3 Analog Filters

al from frequency generator is ut to the DC amplifiers. Apply

68

MT51 F03-167 /

Mo known mass. Oscillate the weight at different frequencies using a spring-mass oscillator (frequencies ≈ 2, 20, 50 Hz; amplitudes =

s .

II. In-Air : Data Acquisition S tion and Exp Test Prior to the sting, the fun ty of the data acq ) will be verified w d dynam e objectives e to confirm the polarit s fo noiexperimenta ill also be p iser model and r rig structure to measure na

pplied to the riser model during these tests. The fully instrumented riser model will be installed and tensioned to the mean pre-tension expected during the VIV tests.

he tasks to verify the data acquisition system and perform the experimental modal test are

Theinst

1. Null al2. With the model support arms horizontal (parallel to the floor), zero all "cross-flow"

acceler arity of all "in-line" accelerometer channels using gravity load, and "zero" all "in-line" channels to read 1 g output.

3. Docum sensor channels by collecting 30 seconds of data

ured signal, and inspect the time series for

4. irect curvature calibration of the strain gage sensors by varying the riser sag (different pre-tensions with a free hanging riser). Compare these direct calibration results with the indirect shunt calibration results.

512382.00.01 draft / 2003-07-15

2. unt the accelerometer to be tested on a weight with a

1 large, 1 small). Measure the force using the load cell and calculate the calibration factor (magnitude and phase) for the accelerometer.

3. Compare results of the verification test to the manufacturer's calibration for the accelerometerand load cell tested. Use of a DC amplifier to boost the signal level is acceptable for this testThe DC amplifier verification tests must be completed prior to their use in the accelerometer/load cell verification.

ystem Verifica

erimental Modal

start of VIV te ctionali uisition system (DASit nh both static a of these tests will b

r all sensors and quantify se and drift in the DAS. An erformed on the r otating

To perform these system checks and modal test, the rotating rig structure will be fully assembled and laid out horizontally with the support arms that hold the riser model oriented parallel to the floor. The central column should be supported so that it will not translate or rotate when a force is a

Tdescribed in the following paragraphs.

l strain gage channels.

ent noise levels and signal drift in all with all sensors powered and amplifiers set to operating gain levels. Calculate statistics (mean, max, min, rms) and spectra for the measvisible signal drift. Perform a d

ic tests in-air. Thy and calibration

l modal test wtural frequencies and damping of the model experimentally.

in the rotating rig structure

Static DAS Verification Tests

following static verification tests will be performed on the data acquisition system and rumentation.

ometer channels, check pol

69

MT51 F03-167 /

esults to document noise levels and signal drift over time.

es f the model riser, and evaluate possible interactions between the model and the rotating rig.

1. oss-

2.

ween the model and rotating rig.

accelerations to find the natural frequencies and damping for each mode of the riser model. these calculations is ± 1% on natural frequency and ± 10% on

damping coefficient.

. Aft ll aga . The .

1. . Document noise levels and signal drift in all sensor channels by collecting 30 seconds of data

ured signal, and inspect the time series for visible signal drift.

o determine the natural frequencies of the riser model when it is fully submerged, a simplified

easured sing the embedded accelerometers and the natural frequencies for the first ten in-line and cross-

512382.00.01 draft / 2003-07-15

5. Repeat 3 and compare r

o

Attach an electromagnetic shaker to the riser model using the appropriate push rod or "stinger". The point of attachment should be chosen to excite the first ten "in-line" and "crflow" modes of the model riser (shaker not located at a node of any of these modes). Using the shaker, excite the model across the frequency band of interest (first ten natural frequencies) and measure the force input by the shaker and the response from the accelerometers and strain gages. During this task, data should also be collected from all other measurement channels for DAS verification and evaluation of the interaction bet

3. Calculate the frequency response functions for the structure using the measured forces and

4. Verify that all channels of the DAS are functioning properly under dynamic loading. 5. Evaluate the interaction that occurs between the riser model and the rotating rig structure.

2with all sensors powered and amplifiers set to operating gain levels. Calculate statistics (mean, max, min, rms) and spectra for the meas

Timpact tests will be performed. The riser model will be impacted with an appropriate tool (metallic rod or hammer) to provide an impulse load. The response of the model will be mu

Dynamic / Experimental Modal Tests The following procedure will be used to dynamically test the DAS, calculate the modal properti

The target accuracy for

III In-Water : Data Acquisition System Verification and Experimental Modal Test

er installation of the rotating rig and riser model in the towing basin, verification tests wiin be perform to evaluate the DAS functionality and a simplified modal test will be conducted following performance checks will be conducted on the DAS prior to the start of VIV testing

Null all strain gage channels and zero all accelerometer channels.

flow natural modes will be extracted from the spectra of the acceleration response.

70

MT51 F03-167 /

APPENDIX 2

Verification

512382.00.01 draft / 2003-07-15

Component Level Instrumentation

71

MT51 F03-167 /

ctivity: Title: Reference:

512382.00.01 draft / 2003-07-15

A

ELe Description:

APPENDIX D in the Project Offer T03-51.030 (PO App. D): C Specification for Instrumentation Verification and Experimental Modal Testing. UR

8.18.18.1

8.1

The activity is divided into the following three sub-activities:

: Component level instrumentation verification .1: A/D converter .2: DC amplifiers

8.1.3: Analog filters .4: Accelerometers, load cell and bridge completions

Comments:

PO App. D Responsible: 8.1 Component Level Instrumentation Verification

Each sub-activity is described in detail on separate sheets.

72

MT51 F03-167 /

Activity: Title: Reference:

512382.00.01 draft / 2003-07-15

PO App. D Ch. I.1.1

Responsible: 8.1.1 A/D converter

JJe Description: The following verification tests will be performe 1. Input a constant amplitude sin e

series to calculate the spectra of the input. Using the measured spectra, calculate the signal to noise ratio (ratio of signal peak (dB) and noise peak (dB) in spectra) and the effective number of bits (defined below).

T er o

Effective number of bits

d on the DT3003 A/D converters.

usoid into the A/D converter and use the recorded tim

heoretical Signal to Noise Ratio : SNR = 6.02N + 1.76dB, where N = numbf bits

: 76.1 dBSNRENOB ACTUAL −

=02.6

2. Input a constant amplitude sinusoid into six A/D converter channels and determine the

time delays between channels (confirm 3 µs value). 3. Compare results of the verification tests to the manufacturers specifications for the A/D

converter. Comments: 1. Effective number of bits (ENOB) i) Tests performed 2003-05-21 Measurements on AD converter number 2 were performed as specified for signal frequencies 12.5Hz, 25.0Hz, 50.0Hz and 100.0Hz. The amplitude was 9.5V. A Hanning window was applied to the time series prior to calculation the spectra. The ENOB was found to vary from 10.9 to 11.1 bits. ii) Tests performed 2003-06-09 Measurements were performed on both AD converter number 1 and AD converter number 2. The signal frequency was 50Hz, and the signal amplitude was 9.5V. A Hanning window was applied to the time series prior to calculation the spectra. The ENOB was found to be 12.6 bits for AD converter number 1, and 12.7 bits for AD converter number 2. (The S/N ratio for the two AD converters was 77.1dB and 78.3dB.)

73

MT51 F03-167 /

iscussion pe aller ENOB than the tests perfo -06-09.

The reason for this is that the AD converter picked up some noise in the first te e was absent in the last te

ormed 2003-06-09 resulted in ENOBs larger than the number of bits of the AD onverters. This is obviously erroneous. The reason for this may be due to the procedure used to

. Time delay between channels (2003-05-20):

512382.00.01 draft / 2003-07-15

DThe tests rformed 2003-05-21 showed a sm rmed 2003

sts. This noissts.

The tests perfccalculate the ENOB. 2

T

TST NN 21

⋅=−

where

1N

N : Number of channels sampled by the A/D converter

the sampling frequency is 1000Hz, and we’re sampling 40 channels, the time delay between neighbouring channels is 25µs, while the delay between channel 1 and channel 40 is 975µs. ii) AD converter no. 2 The time delays between channels on AD converter no. 2 are identical to the delays for AD converter no. 1. iii) Time delay between AD converter no. 1 and AD converter no. 2 The logging program starts each of the two AD converter boards with a separate command. The time delay between the two boards therefore varies between tests. Logging 20 tests with the same sinusoid signal on channel 1 on board 1 and channel 1 on board 2 resulted in time delays between 5.8ms and 14.9ms. The figure below shows the test results.

he time delay between two channels were found to be: i) AD converter no. 1

( )N

NN 12 −

2NT → 1N 2N: The time delay between channels and

: Sampling period ST

If

74

Time delay between AD board 1 channel 1 and AD board 2 channel 1

8

12

14

Tde

2

4

6ime

10

lay

[ms]

16

09315 9320 9325 9330 9335

Test number

/

3. Comparison with manufacturer’s specifications

3. Comparison with manufacturer’s specifications The manufacturer specifies ENOB to be 11.5 bits, corresponding to a S/N ratio of 71dB. We found S/N ratios better than this. The time delays between channels are as specified by the manufacturer.

MT51 F03-167 512382.00.01 draft / 2003-07-15

75

MT51 F03-167 /

Title: Reference:

512382.00.01 draft / 2003-07-15

Activity:

PO App. D Ch. I.1.2 8.1.2 DC amplifiers

JJe Description: Verification tests will be performed on two KWS and two MGC+ model amplifiers. The

uilt-in filter in the MGC+ amplifiers will not be used during tests, and therefore not used n tests will be performed on the DC

. Apply a constant bridge unbalance using a Hottinger Baldwin calibration units as input to the amplifier to verify the static performance of the unit (unbalance = 2mV/V for G = 1, 2, 5, 10).

. A 10V amplitude sinusoid signal from frequency generator is attenuated to 10mV using ltage divider and used as input to the DC amplifiers. Apply signals of different

frequencies to the amplifier to verify the dynamic performance of the unit (signal input = sin(2πfit wher e pu signal on channel 1 and the amplified signal on channel 2. Since fc=200Hz, and the time delay between neighbouring signals will never exeed 0.3 degrees, which makes phase corrections due to AD on rting

bduring verification tests. The following verificatioamplifier units. 1

2a vo

) ; e fi = 2, 20, fc, and 1.5fc). Record th raw in t

c ve unnecessary. 3. Compare performance of the units tested to the manufacturer's calibration sheets for

each unit.

1A constant DC voltage was applied to two KWS and two MGC+ amwas measured for different gain settings. The results are shown in the tables below. The tables also show the difference between the measured values and a fitted straight line.

KWS 57351

Responsible:

Comments:

. Static performance plifiers. The output voltage

Amplification [V/V]

Measured: Uut [V]

Regression: Uut [V]

Difference [V] Error [%]

19800 9.024 9.027 0.002 0.039900 4.078 4.073 -0.005 -0.123960 1.101 1.100 -0.001 -0.091980 0.108 0.110 0.002 1.6

990 -0.388 -0.386 0.002 -0.49

76

KWS 74489

Amplification [V/V]

Measured: Uut [V]

Regression: Uut [V]

Difference [V] Error [%]

19800 9.001 9.004 0.004 0.049900 4.071 4.063 -0.008 -0.213960 1.097 1.097 0.000 0.011980 0.107 0.109 0.002 2.01

990 -0.387 -0.385 0.002 -0.59

MGC+ nr. 01 Amplification

[V/V] Measured:

Uut [V] Regression:

Uut [V] Difference [V] Error [%]

10000 -9.884 -9.886 -0.002 0.025000 -4.952 -4.948 0.004 -0.082000 -1.986 -1.985 0.000 -0.011000 -0.996 -0.998 -0.002 0.17

500 -0.503 -0.504 -0.001 0.13

MGC+ nr. 02 Amplification

[V/V] Measured:

Uut [V] Regression:

Uut [V] Difference [V] Error [%]

10000 -9.922 -9.924 -0.002 0.025000 -4.971 -4.967 0.004 -0.082000 -1.994 -1.993 0.001 -0.041000 -1.000 -1.001 -0.001 0.14

500 -0.504 -0.506 -0.001 0.25 2. Dynamic performance We have tested the dynamic performance of two KWS and two MGC amplifiers. The figures elow show the results. The phase delay results are corrected for the delays in the AD converter.

ote: For the KWS 74489 amplifier the results for 400Hz input signal are missing. The difference in the amplitude results for the KWS and MGC amplifiers are due to different gain settings.

b N

MT51 F03-167 / 512382.00.01 draft / 2003-07-15

77

/

DC amplifiers - amplitude characteristics

0.2

0.8

1

100 200 300 400 5000

0

0.4

0.6

U_i

n / U

_out

1.2

Frequency [Hz]

KWS 57351

KWS 74489

MGC 1073

MGC 1075

-20

-10

Phas

e [°

] KWS 57351

KWS 74489

MGC 1073

MGC 1075

DC amplifiers - phase

-25

-15

-5

00 100 200 300 400 500

Frequency [Hz]

MT51 F03-167 512382.00.01 draft / 2003-07-15

78

MT51 F03-167 /

3. Comparison with manufacturer’s specifications

512382.00.01 draft / 2003-07-15

i) Static performance KWS The KWS da et specifies: “Switching tolera .25%”. In a we have ev d the effect of non ity and tem re drift (ref. the error budgets f ature sensorsaccelerometers) from the data o give an of ±0.002V. T c verificatio howed results in accordance with these specifications (±0.25% error or ±0.002V).

M

ta she nce < 0 dditionperatu or curv and

sheet t he stati n testss

GC+ amplifi lass 0.03, m that th be ±0.0 nge (

tests sh V as m ference e mea and th e for bo em just

The ession g ard err tercept of 0.002V, which, when

Dyn perfoamic nce

plitude in ou/UWS 74 ier amplitud onse deviates betw

the lue. The sinusoid signal from thcalibrator unit of class 0.5, resulting in an 0.5% uncertainty in the true input to the amplifier. T“amplification” of the calibrator is therefore GCal = 0.001V/V ± 0.5%.

The amplification, GBA, of the DC amplifier was set to 1000 by using the same Hottc GBA

aluate-linear

fset of

The MGC+ ers are of c eaning e error can 3% of full ra 10V), i.e. ±0.003V. erification owed 0.004 aximum dif between th sured output signal e fitted lin th amplifiers, which places th outside the specifications. linear regr ave a stand or of the in

ken into account, can place the amplifiers just inside the specifications. ii) rmaKWS

The v

ta

The KWS 57351 amplifier am response (U t) deviates between -0.2% and 3.1% from the nominal v while the K 489 amplif e resp een –0.3% and 0.6% from nominal va

e function generator was first divided by 1000 with a Hottinger he

inger alibrator unit:

=UBAset/(UEmset*Sset)

where

UBAset is the voltage output from the bridge amplifier when setting the amplifier gain = 10V ±0.05V. This is an evaluation of how accurate the operator can adjust the output voltage by monitoring an analogue needle indicator.

UEmset is the bridge voltage during bridge amplifier gain setting = 5.0V ±0.1%. This voltage is supplied by the DC amplifier, which is of class 0.1 (0.1% error).

Sset is the calibrator unit unbalance during bridge amplifier gain setting = 2mV/V ±0.5%. The calibrator unit is of class 0.5 (0.5% error).

The above values results in GBA = 1000V/V ± 1.1%.

alue,

79

MT51 F03-167 /

The total amplification, GTot = GCal * GBA, was therefore GTot = 1V/V ± 1.6%. The results for the KWS 74489 amplifier are within these limits, and are therefore within specifications. The results for KWS 57351, however, shows an amplitude response 3.1% above the nominal value, and the amplifier performance does therefore not comply with the specifications. The phase lags for KWS 57351 was –67.7µs at 20Hz to –35.5µs at 400Hz. For KWS the lags were –29.5µs at 20Hz to –21.0µs at 250Hz. The KWS data sheet says: Phase lag time: < 12µs. Since these phase lags were measured between the signal input to the voltage divider (the Hottinger calibrator) and the DC amplifier output, it is difficult to say how much of the lag can be ascribed to the DC amplifier alone. But assuming that the voltage divider impedance is pure resistive, we can conclude that the DC amplifiers does not comply with the specifications. MGC+

512382.00.01 draft / 2003-07-15

The MGC+ amplifier amplitude response (Uin/Uout) deviates between 0.4% and 0.7% from the nominal value. The MGC+ amplifiers are of class 0.03, meaning that the error can be ±0.03% of full range (10V), i.e. ±0.003V. The voltage divider (a Hottinger calibration unit) was of class 0.5, resulting in an 0.5% uncertainty in the true input to the amplifier. For MGC+ amplifier output .0V this means an uncertainty of ±0.04%. The total error between voltage divider input and DC mplifier output will therefore be ±0.5%. The results from the verification tests puts MGC+ 1075 ithin these limits (0.4% to 0.5%), while the results for MGC+ 1073 falls without these limits .6% to 0.7%). The latter amplifier therefore seems to not comply with specifications.

oth the input and output signals to MGC+ amplifiers can be filtered. The output filter has been disabled, while we can’t disable the input filter. For input filter we chose Butterworth low-pass, with 10kHz cut-off frequency. The results for the phase response for the MGC+ amplifiers shows a linear phase response, and can be attributed to the filter.

7aw

B

(0

80

MT51 F03-167 /

tle: Reference:

512382.00.01 draft / 2003-07-15

Activity: Ti

Ch. I.1.3 Responsible:

8.1.3 Analog filters

JJe Description: Verification of DC gain and corner frequency will be performed on four GEPA,

must include the following three frequencies: 0.5fc, fc, 1.5fc) to the filters and record the raw and filtered

ency until the phase difference is 360 degrees to determine the ner frequency (Butteworth filter) Since fc=200Hz, and the time delay between

MOM_MKT filter channels to be used in the tests. The following verification tests will be performed on the analog filter channels. 1. Apply +10VDC and -10VDC signals to the filters and record the raw and filtered signals

to determine the filter gain. Apply sinusoid signals (at frequencies that

corneighbouring AD channels is only 3µs, the phase difference between the raw and the amplified signals will never exeed 0.3 degrees, which make phase corrections due to AD converting unnecessary.

2. Verify corner frequencies are correct and compare the performance of the unit tested to

the manufacturer's calibration sheet for the unit. Comments: 1i) Static r pones se +MOM afi

PO App. D

signals. Vary the frequ

. Filter response

9.5VDC and –9.5VDC signals were applied to filter channels 1, 21, 42, and 64 on the GEPA nalog filter. The input and output signals were sampled at 1000Hz for 10 seconds. The

gure below shows the results.

81

/

he phase gs are corrected for the delay in the AD converter. The figures below show the responses.

he phase gs are corrected for the delay in the AD converter. The figures below show the responses.

ii) Dynamic response We have measured the dynamic amplitude and phase response for four filter channels. Thase response for four filter channels. Tlala

GEPA MOM filter - Amplitude

0

GEPA MOM filter - static test

1.003

0.996

0.997

0.998

0.999

1.000

1.001

Am

plifi

catio

n

GEPA MOM ch

ann

GEPA MOM ch

ann

GEPA MOM ch

ann

GEPA MOM ch

ann

-9.50V

+9.50V

0.995

1.002

el 1

el 21

el 42

el 64

-60

-50

-40

-30

-20

-10

10 100 1000

Frequency [Hs]

Am

plifi

catio

n [d

B]

Channel 1Channel 21Channel 42Channel 64Theoretical

MT51 F03-167 512382.00.01 draft / 2003-07-15

GEPA MOM filter - phase

-400

-200

-100

10 100

Channel 21

82

/

2. C cturer’s specificationsomparison with manufai)The manufacturer’s specifies the error voltage to be ≤ 2mVDC at output (typical). The meas

lts are within these limits. iiT

s

Channel no. 1 248.2

21 249.6 42 248.1 64 249.2

-600

-500

Frequency [H ]

-300

Phas

e [°

]

01000

z

Channel 1

Channel 42Channel 64Theoretical

Static performance

ured resu

) Distribution of cut-off frequencies at fc = 250Hz he actual cut-off frequencies for the four filter channels were found by fitting the measured

at the nominal cut-off frequency to an ideal Butterworth response. The results are ummed up in the table below.

attenuation

Actual cut-off [Hz]

All four cut-off frequencies fall within ±2% of the nominal value, as specified by the manufacturer. iii) Distribution of cut-off frequencies at fc = 1000Hz The filter manufacturer has measured the filter attenuation for all the 96 filter channels at a nominal cut-off frequency of 1000Hz. These results are provided as curves. In addition, the attenuation at input frequency 1000Hz is given as numbers. By fitting an ideal 8 pole Butterworth low-pass filter to this data set we get the distribution of the actual cut-off frequencies for the filters. The figure below shows this distribution. The red line shows the average value, while the

MT51 F03-167 512382.00.01 draft / 2003-07-15

83

dashed yellow lines marks one and two standard deviations. All cut-off frequencies fall within ±2% of the nominal value, as specified by the manufacturer. dashed yellow lines marks one and two standard deviations. All cut-off frequencies fall within ±2% of the nominal value, as specified by the manufacturer.

GEPA MOM filter - distribution of cut-off frequencies

5

10

15

20

25

30

Num

ber

0980 985 990 995 1000 1005 1010

Frequency [Hz]

MT51 F03-167 /

The curves shown above show that the amplitudes are more attenuated than the ideal Butterworth filter response from frequencies of approximately 100Hz up the cut-off frequency (250Hz), while it is less attenuated above the cut-off. The phase delay follows the ideal curve up to approximately 200Hz. The phase delay becomes less than the ideal response above this frequency.

The curves shown above show that the amplitudes are more attenuated than the ideal Butterworth filter response from frequencies of approximately 100Hz up the cut-off frequency (250Hz), while it is less attenuated above the cut-off. The phase delay follows the ideal curve up to approximately 200Hz. The phase delay becomes less than the ideal response above this frequency.

512382.00.01 draft / 2003-07-15 2003-07-15

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Activity: Title: Reference:

512382.00.01 draft / 2003-07-15

PO App. D Ch. I.1.4

Responsible: 8.1.4 Accelerometers, load cell and bridge completion.

JJe Description: The following verification tests will be performed on two of the Measurement Specialties, ICSensors 3031 accelerometers and one of the load cells used to measure riser end force. 1. Apply known static loads (500 N, 1000 N) to the load cell to verify the calibration

factors. Load cell orientation should be adjusted so that all three axes of the load cell are verified.

2. Mount the accelerometer to be tested on a weight with a known mass. Oscillate the weight at different frequencies using a spring-mass oscillator (frequencies ≈ 2, 20, 50 Hz; amplitudes = 1 large, 1 small). Measure the force using the load cell and calculate the calibration factor (magnitude and phase) for the accelerometer.

. Compare results of the verification test to the manufacturer's calibration for the mplifier to boost the signal level is

test. The DC amplifier verification tests must be completed prior to

3

acceptable for this their use in the accelerometer/load cell verification.

Comments: 1. Load cell Static loads of 0kg, 40kg, and 100kg were applied to each axis of the load cell. The measured oltages were scaled with the previously obtained calibration matrix. The table below shows the

res

v

red force [N]

981.0 980.52 -0.480.0 -0.11 -0.110.0 0.98 0.98

392.4 393.90 1.50981.0 982.20 1.20

0.0 0.40 0.40

accelerometers and load cell tested. Use of a DC a

ults.

Nominal force [N] Measu Difference [N] 0.0 -0.14 -0.14

392.4 392.23 -0.17981.0 980.96 -0.04

0.0 0.63 0.630.0 -0.02 -0.02

392.4 392.28 -0.12

2. Accelerometer

85

MT51 F03-167 /

ge

512382.00.01 draft / 2003-07-15

Note: This section will be updated in the final version, with excitation tests in the frequency ran0-100 Hz. The accelerometer tests were performed by the Campus Marine AS representative who also performed the modal test on the riser. He mounted the accelerometers on a Brüel & Kjær 4094 calibrator, which was most recently calibrated 2002-09-23. The calibrator excited the accelerometers with 10m/s2 at 1000 rads/s (159.2Hz). The signals were amplified and filtered with Marintek’s amplifiers and filters and digitized in Campus Marine’s Pulse system for analysis. From the autospectrum he calculated the accelerometer’s calibration factors. Note that the calibration factors were only tested at one frequency (159.2Hz), and at one amplitude.

Calibration factor: 10[m/s2] / 406[mV] = 24.63 [(m/s2)/V]

86

Cal 3. C

ibration factor: 10[m/s2] / 300[mV] = 33.33 [(m/s2)/V]

omparison with manufacturer’s specifications i) Load cell

he measured deviations from the true values varies from –0.05% to +0.15% of the full range of e measurements (981N).

ecified by the manufacturer, see the table below. The values specified by the anufacturer are for 100Hz excitation.

Tth ii) Accelerometers The calibration factors measured by Campus Marine were both slightly larger (4.0%) than the values spm

23.69

Calibration factor [(m/s )/V] 2

Accelerometer S/N Campus Marine Manufacturer

Deviation [%]

9428-009 24.63 3.97 9428-010 33.33 32.05 3.99

MT51 F03-167 / 512382.00.01 draft / 2003-07-15

87

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Dynamic/Experimental Modal Tests

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APPENDIX 3

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There are 2 Excel files:

1. Modalpar_a.xls

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contains the resonance frequencies and damping percentages from the modal analysis suite ME'scope

2. ShapeTable_a.xls contains the mode shapes also derived using ME'scope for measurement

X3 onwards. The damping values varied by +/- 20% dependent on the frequency interval used for the curve fitting - this is particularly so when the damping is below 1%. The "final" fit on both the magnitude and phase of the responses has been checked. The H2 transfer function has been used throughout as the basis for the calculations. The mode shapes appear to be sensible apart from the first mode for tests X3, X4, X6 and Y1. Marintek's calibration factors have been used to calculate the final magnitudes. The Mode shapes above about no: 6 do not fully represent the shape due to the number of accelerometers under sampling the pipe shape.

https://project.sintef.no/eRoom/marintek/512381ExxonMobil/0_5a8d/Modalpar_a.xls

https://project.sintef.no/eRoom/marintek/512381ExxonMobil/0_5a8d/ShapeTable_a.xls

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APPENDIX 4

Uncertainty Budgets

Curvature sensors error budget Accelerometers error budget

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s error budget

1.1 DTheButterworth low pass filter, and finally it is digitized by an AD-converter. The measured strain, ε, an then be described by the formula:

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1. Curvature sensor

I EAL MEASUREMENT sig r is first amplified by a bridge amplifier, then it is filtered by a nal from the senso

c

ε = K * S * UEm * GBA * Gf * GAD

here

Em l bridge energizing voltage during measurement GBA is the bridge amplifier gain Gf is the filter gain GAD is the analog to digital converter gain

1.2 ERRORS IN AMPLIFIERS When taking offset errors of the amplifiers into account we can rewrite the above formula as:

ε = K * ((( S * UEm * GBA + δUBA ) * Gf + δUf ) * GAD + δUAD ) where

δUBA is the bridge amplifier output offset δUf is the filter output offset δUAD is the analog to digital converter output offset

In addition to the offset errors, the gain factors now also have accosiated errors.

K is the calibration coefficient from shunt calibration. S is the curvature sensor bridge unbalance during measurement U is the actua

w

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1.3 ERROR IN CALIBRATION COEFFICIENT The calibration coefficient, K, was calculated from shunt calibration using the formula:

K = ( 1 - Rs / ( R + Rs ) ) / ( 4 * kc * Us ) K = ( 1 - Rs / ( R + Rs ) ) / ( 4 * kc * Us * ( GBACal / GBAnom ) ) where

Rs is the shunt resistanR is the strain gage resistance kc is the gage factor during calibratio

Us is the average of four separate measurements from the calibration GBAcal is the bridge amplifier gain during calibration GBAnom is the (if there were no errors)

The factor ( GBAcal / GBAnom ) accounts for uncertainty in setting the bridge amplifier's amplification during calibration, see the discussion of bridge amplifier gain errors below. The gage factor, kc, is the average of the factors f m the gages from two batches:

kc = ( k01 + k02 ) / 2 where

k01 is the gage factor for gages from batch 1 k02 is the gage factor for gages from batch 2

The average measured voltage from the calibration is calculated by:

Us = ( Us1 + Us2 + Us3 + Us4 ) / 4 where

Us1 is the voltage measured during calibration 1 Us2 is the voltage measured during calibration 2 Us3 is the voltage measured during calibration 3 Us4 is the voltage measured during calibration 4

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ce

n

nominal amplification of the bridge amplifier

ro

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RESISTOR f a null balance resistor is used to balance the bridge, the unbalance of the bridge due to

curvature, Sc, will be:

) - 1 ) /

here

km is the gage factor during measurement (see formula below) is the radius of the riser bend

∆r is the diameter of the riser r ( Gz = 1 / Rz )

When a the bridge will start to be sensitive to axial strain. The unbalance of the bridge due to axial strain, Sa, will be:

Sa = ( -km * εa + ( 1 + 1 / ( R * Gz ) ) / ( 1 + 1 / ( R * Gz * ( 1 + km * εL ) ) ) - 1 ) / 4

εa is the axial strain

he measured strain should now be written:

ε = K * ( ( ( ( Sc + Sa ) * UEm * GBA + δUBA ) * Gf + δUf ) * GAD + δUAD )

1.5 ERRORS DUE TO THERMAL EFFECTS IN THE STRAIN GAGES uring measurements the gage factor can vary due to temperature variations:

km = ( k01 + k02 ) * ( 1 + cT * ∆T ) / 2

here

k01 is the gage factor for strain gages from batch 1 k02 is the gage factor for strain gages from batch 2 cT is the gage factor temperature coefficient ∆T is the temperature range

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1.4 ERRORS DUE TO NULL BALANCEI

Sc = ( 3 * km * ∆r / r + ( 1 + 1 / ( R * Gz ) ) / ( 1 + 1 / ( R * Gz * ( 1 + km * ∆r / r ) )4 w

r

Gz is the nominal conductance of the null balance resistoR is the strain gage resistance

n l balance resistor is introduced, ul

where

T

D

w

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OF THE CABLE RESISTANCE

mplifier. The bridge amplifier input resistance is high, so the resistance variations in the bridge amplifi

oltage from the bridge amplifier to the bridge can't be neglected, however. The bridge nergizing voltage during measurement, UEm, can be found from the formula:

UEm = RB * UE0 / ( RC1 + RC2 + RB ) where

plifier resis

RC2 is the resistance of cable 2

where

4pz is the resistance of strain gage 4 in parallel with the null balance resistor (see formula elow)

The res ll balance resistor is:

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1.6 ERRORS DUE TO THERMAL VARIATIONSIf temperature varies, so will the resistance of the cables between the sensor to the bridgea

er input cables can be neglected. esistance variations in the cables providing bridge en ing v

Rergiz

e

R is the bridge diagonal resistance (see formula below) B

U the bridge energizing voltage output from the amE0 isR he tance of cable 1

The bridge diagonal resistance is:

RB = 2 * R * ( R + R4pz ) / ( 3 * R + R4pz )

R

b

is nce of strain gage 4 in parallel with the nuta

R4pz = R * Rz / ( R + Rz )

C1 is t

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ing calibration, GBAcal, is:

here

UBAsetCal is the full range of the amplifier needle indicator as set by the operator for calibra

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1.7 ERRORS IN THE BRIDGE AMPLIFIER GAIN

GBAcal = UBAsetCal / ( UEmsetCal * SsetCal )

w

tio n

setC e from the amplifier during calibration al is the bridge unbalance as set on the calibration unit during calibration

Similar he asurement, GBA, is:

here

BAsetMeas

ment UEmsetMeas is the bridge energizer voltage from the amplifier during measurement

nbalance as set on the calibration unit during measurement

AUGES If the s riser bending will become ystematically lower than the correct signal (a cosine factor). The sensor will also start to be

sensitive to axial strain. We estimate the skewness of the strain gauges to be maximum 1°. Using t the measured

ese numbers are o small that we have not included this effect in the budget.

MMENT his error budget only takes random errors into account. Systematic errors are not included in this

discuss hat the strain gauge pairs are not separat train gauges on each side of the riser are sep nce is slightly less than a diameter, one will make a iameter of 20mm, and a separation between the centers of

e strain gauges on one side of the riser of 3.2mm, one will get a systematic error of +1.3% for e calculated radius of the curvature.

UEm al is the bridge energizer voltagSsetC

ly, t resulting gain used during me

GBA = UBAsetMeas / ( UEmsetMeas * SsetMeas )

U is the full range of the amplifier needle indicator as set by the operator for measure

S is the bridge usetMeas

1.8 ERRORS DUE TO SKEW STRAIN Gtrain gauges are not parallel with the riser axis, the signal due to

s

a typical pre-tension of 800N, and with other values as in this budget, we find thasystematic strain offset is 0.01µS, with an expanded uncertainty of 0.004µS. Ths

1.9 COT

io . If, for example, one does not take into account ted y exactly one riser diameter, but, since the two s bar ted by a few millimeters, the effective distaa systematic error. For a riser d

thth

The bridge amplifier gain is set using a calibration unit and adjusting offset and gain. Theresulting gain used dur

w

n

95

1.10 Model Equation:

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1)

Em=RB*UE0/(RC1+RC2+RB); RB=2*R

4pz=R*Rz z);=UBAsetCal/(UEmsetCal*SsetCal);

setMeas/(UEmsetMeas*SsetMeas);

1.11 L

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ε=K*((((Sc+Sa)*UEm*GBA+δUBA)*Gf+δUf)*GAD+δUAD); K=(1-Rs/(R+Rs))/(4*kc*Us*(GBACal/GBAnom)); kc=(k01+k02)/2; Us=(Us1+Us2+Us3+Us4)/4; Sc=(3*km*∆r/r+(1+1/(R*Gz))/(1+1/(R*Gz*(1+km*∆r/r)))-1)/4; Sa=(-km*εa+(1+1/(R*Gz))/(1+1/(R*Gz*(1+km*εL)))- /4; km=(k01+k02)*(1+cT*∆T)/2; U

*(R+R4pz)/(3

*R+R4pz); /(R+RR

GBACalGBA=UBA

ist of Quantities:

Qua tnti y Unit Definition

ε m/m Indicated strain from the curvature sensor

K m/m/V Calibration coefficient from shunt calibration

Sc V/V The curvature sensor bridge unbalance due to curvature during em asurement

Sa V/V The curvature sensor bridge unbalance due to axial strain during measurement

UEm V Actual bridge energizing voltage during measurement

GBA V/V Bridge amplifier gain

δU V Bridge amplifier offset BA

Gf V/V Filter gain

δ utput offset Uf V Filter o

G V/V Analog to digital converter gain AD

δU D V Analog to digital converter output offset A

R Ω Shunt resistance s

R Ω Strain gage resistance

k Gage factor during calibration c

U V Average measured voltage during shunt calibration s

GBACal V/V Bridge amplifier gain during calibration

GBAnom V/V Nominal bridge amplifier gain (no errors)

k Nominal gage factor batch 1 01

k Nominal gage factor batch 2 02

U V Measured voltage during shunt calibration 1 s1

96

Quantity Unit Definition

Us2 V Measured voltage during shunt calibration 2

Us3 V Measured voltage during shunt calibration 3

U V asure tag ring shunt calibration 4 s4 Me d vol e du

km Gage factor during measurement

∆r m Riser radius

r m Radius of the riser bend

Gz 1/Ω Null resistance conductance

εa m/m Strain due axial strain during measurement

cT 1/°C Gage factor temperature coeffisient

∆T °C Temperature range

R ance during measurement B Ω Bridge diagonal resist

U V Bridge voltage from the amplifier during measurement E0

RC1 Ω Cable resistance 1 during measurement


R4pz Ω The resistance of strain gage 4 parallel with the null balance resistor during measurement

Rz Ω Null balance resistance

UBAsetCal V The voltage output from the bridge amplifier when setting the amplifier gain for calibration

UEmsetCal V Bridge voltage during bridge amplifier gain setting for calibration

SsetCal V/V The calibrator unit unbalance during bridge amplifier gain setting for calibration

UBAsetMeas V The voltage output from the bridge amplifier when setting the amplifier gain for measurement

UEmsetMeas V Bridge voltage during bridge amplifier gain setting for measurement

SsetMeas V/V The calibrator unit unbalance during bridge amplifier gain setting for measurement

ε: Result K: Interim Result

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t specifies the output offset voltage t

/

Interim Result

δU : on

Value: 0.000 V Halfwidth of Limits: 0.002 V This is evaluati e manufacturer's data sheet. Gf: Type B rectangular distributiValue: 1.000 V/V Halfwidth of Limits: 0.01 V/ The manufacturer's data shee δUf: Type B rectangular distributiValue: 0.000 V Halfwidth of Limits: 0.002 V The manufacturer's data shee o be 2mV GAD: Type B rectangular distributiValue: 1.000 V/V Halfwidth of Limits: 0.01 V/V The manufacturer's data shee ter has 12 digits and a +/-10V range δUAType B rectangular distributiValue: 0.000 V Halfwidth of Limits: 0.0025 The manufacturer's data sheet does not specify this, so this a guessed number.

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an on of the ffect of non-linearity and temperature drift from the

on

V

t specifies <1%

on

on

t specifies the nonlinearity as +/-1.0LSB. The AD conver

D: on

V

Sc:

Sa: Interim Result UEm: Interim Result GBA: Interim lt Resu

BAType B rectangular distributi

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Rs: Type B rectangular distribution Value: 40000 Ω Halfwidth of Limits: The shunt resistance was mea which for the 40kΩ range has a specified accuracy of (0.2 R: Type B rectangular distributiValue: 120 Ω Halfwidth of Limits: 0.480 Ω The manufacturer's data shee 120Ω +/-0.2%. kc: Interi ult There train gage m t e here we've used the average of the two nominal gage tors certainty of the two nominal values into account. Us: Interim sult Av unting our incorporates the variances of ell as the uncertainty in these me due to erta ge, the u ertainty in th tim GBACal: In GBAnom: CoValue: 1000.0 V/V k01: Type B rectangular distributi

alue: 2.045 lfwidth of Limits: 0.010

he data sheet specifies 2.045 +/- 0.5% at 24°C

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90 Ω

sured with a Fluke digital voltmeter, +/- %+10Ω).

on

t specifies the value as

m Res

are s s fro wo batches mounted on the riser. For the valu fac . The uncertainty is found from taking the un

Re

erage of sh all f strain gages in the full bridge. The uncertainty of this average value the individual measurements, as w

asurements unc inties in the bridge amplifier gain setting, the bridge amplifier offset voltanc e mul eter indicated value, and the multimeter offset.

terim Result

nstant

on VHa T

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ular distribution alue: 2.055

width of Limits: 0.010

he data sheet specifies 2.045 +/- 0.5% at 24°C

ype B rectangular distribution 2.48 V

mits: 0.021 V

inty is due to uncertainty in the bridge amplifier gain setting, the bridge amplifier offset voltage, indicated value, and the multimeter offset. (Ref. "Estimation of

e bridge amplifier gain setting.smu")

:

alue: 2.513 V width of Limits: 0.021 V

to uncertainty in the bridge amplifier gain setting, the bridge amplifier offset voltage, r indicated value, and the multimeter offset. (Ref. "Estimation of

ncertainty in the bridge amplifier gain setting.smu")

: B rectangular distribution

its: 0.021 V

ncertainty is due to uncertainty in the bridge amplifier gain setting, the bridge amplifier offset voltage, Ref. "Estimation of

ncertainty in the bridge amplifier gain setting.smu")

distribution

alfwidth of Limits: 0.021 V

e to uncertainty in the bridge amplifier gain setting, the bridge amplifier offset voltage, e uncertainty in the multimeter indicated value, and the multimeter offset. (Ref. "Estimation of

inty in the bridge amplifier gain setting.smu")

e we've used the average of

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k02: Type B rectangVHalf T Us1: TValue:Halfwidth of Li Uncertathe uncertainty in the multimeteruncertainty in th Us2Type B rectangular distribution VHalf Uncertainty is due the uncertainty in the multimeteu Us3Type Value: 2.536 V Halfwidth of Lim Uthe uncertainty in the multimeter indicated value, and the multimeter offset. (u Us4: Type B rectangularValue: 2.453 V H Uncertainty is duthuncerta km: Interim Result There are strain gages from two batches mounted on the riser. For the value her

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e two nominal gage factors. The uncertainty is found from taking the uncertainty of the two nominal es into account, and also taking a +/-5°C temperature variation into account.

tion alue: 0.020

ased on 71 measurements on the riser.

e: 0.00001 1/Ω mits: 0.00001 1/Ω

can null balance resistor -> infinite resistance) and 0.00002 (50kΩ).

ular distribution alue: 0.0 m/m

ular distribution alue: 0.00013 1/°C

of Limits: 0.00002 1/°C

ture coefficient of gage factor = +1.3 +/- 0.2% / 100°C

B: terim Result

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thvalu ∆r: Type B rectangular distribuVHalfwidth of Limits: 0.00004 B r: Constant Value: 100 m Gz: Type B rectangular distribution ValuHalfwidth of Li A typical null balance resistor can vary from 50kΩ to 1MΩ, i.e. a conductance from 0.000001S to 0.00002S. Here we model this as a conductance with a nominal value of 0.00001S (100kΩ), and which vary between 0.0S (no εa: Type B rectangVHalfwidth of Limits: 0.001 m/m To see the effect of pure axial strain when a null resistor is introduced, we let εL have a nominal value of 0,and let it vary between -1000µS and +1000µS. cT: Type B rectangVHalfwidth Data sheet: Tempera ∆T: Type B rectangular distribution Value: 0.001 °C Halfwidth of Limits: 5.0 °C A +/- 5°C temperature range. RIn

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gular distribution


he manufacturer's data sheet specifies error as +/-0.1%.

ular distribution

alfwidth of Limits: 1.20 Ω

4pz: m Result

alue: 35000 Ω

BAsetCal: B rectangular distribution

its: 0.05 V

his is an evaluation of how accurate the operator can adjust the output voltage by monitoring an analogue

ype B rectangular distribution e: 5.000 V

mits: 0.005 V

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UE0: Type B rectanValue: 5.000 V H T RC1: Type B rectangValue: 60.0 Ω H The temperature coefficient of resistance of copper is approximately 0.4% per °C. A +/-5°C temperature range is assumed. RC2: Type B rectangular distribution Value: 60.0 Ω Halfwidth of Limits: 1.20 Ω The temperature coefficient of resistance of copper is approximately 0.4% per °C. A +/-5°C temperature range is assumed. RInteri Rz: Constant V Typical value for a null balance resistor. UType Value: 10.000 V Halfwidth of Lim Tneedle indicator. UEmsetCal: TValuHalfwidth of Li The manufacturer's data sheet specifies error as +/-0.1%.

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ype B rectangular distribution e: 0.002 V/V

V

specifies max error as 0.5%.

ype B rectangular distribution lue: 10.000 V

of Limits: 0.05 V

his is an evaluation of how accurate the operator can adjust the output voltage by monitoring an analogue le indicator.

alue: 5.000 V

eas:

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SsetCal: TValuHalfwidth of Limits: 0.00001 V/ The manufacturer's data sheet UBAsetMeas: TVaHalfwidth Tneed UEmsetMeas: Type B rectangular distribution VHalfwidth of Limits: 0.005 V The manufacturer's data sheet specifies error as +/-0.1%. SsetMType B rectangular distribution Value: 0.002 V/VHalfwidth of Limits: 0.00001 V/V The manufacturer's data sheet specifies max error as 0.5%.

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Uncertainty Budget:

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1.12

Quantity Value Standard Uncertainty

Sensitivity Coefficient

Uncertainty Contribution

Index

K 146.167·10-6 m/m/V

850·10-9 m/m/V

Sc 409.877·10 V/V

959·10 V/V -6 -9

S 0.0 V/V a 355·10-9 V/V

UEm 2.4989 V 0.0107 V

GBA 1000.00 V/V 4.12 V/V

δUBA 0.0 V 1.15·10-3 V 150·10-6 170·10-9 m/m 0.9 %

Gf 1.00000 V/V 5.77·10-3 V/V 150·10-6 860·10-9 m/m 23.2 %

δUf 0.0 V 1.15·10-3 V 150·10-6 170·10-9 m/m 0.9 %

GAD 1.00000 V/V 5.77·10-3 V/V 150·10-6 860·10-9 m/m 23.2 %

δUAD 0.0 V 1.44·10-3 V 150·10-6 210·10-9 m/m 1.4 %

Rs 40000.0 Ω 52.0 Ω -3.7·10 -190·10 m/m 1.2 % -9 -9

R 120.000 Ω 0.277 Ω 1.9·10-6 520·10-9 m/m 8.3 %

kc 2.05000 4.08·10-3

Us 2.49550 V 6.06·10-3 V

GBAnom 1000.0 V/V

k01 2.04500 5.77·10-3 -4.5·10-12 -26·10-15 m/m 0.0 %

k02 2.05500 5.77·10-3 -4.5·10-12 -26·10-15 m/m 0.0 %

Us1 2.4800 V 0.0121 V -15·10-6 -180·10-9 m/m 1.0 %

U 2.5130 V 0.0121 V -15·10-6 -180·10-9 m/m 1.0 % s2

Us3 2.5360 V 0.0121 V -15·10-6 -180·10-9 m/m 1.0 %

U s4 2.4530 V 0.0121 V -15·10-6 -180·10-9 m/m 1.0 %

km 2.05000 4.15·10-3

∆r 0.0200000 m 23.1·10-6 m 7.5·10-3 170·10-9 m/m 0.9 %

r 100.0 m

Gz 10.00·10-6 1/Ω 5.77·10-6 1/Ω -4.5·10-3 -26·10-9 m/m 0.0 %

εa 0.0 m/m 577·10-6 m/m -220·10-6 -130·10-9 m/m 0.5 %

cT 130.0·10-6 1/°C 11.5·10-6 1/°C 150·10-9 1.7·10-12 m/m 0.0 %

104

Quantity Value Standard Se

Uncertainty nsitivity

Coefficient Uncertainty

Contribution Index

∆T 0.0 °C 2.89 °C 19·10-9 56·10-9 m/m 0.0 %

RB 119.897 Ω 0.277 Ω

UE0 5.00000 V 2.89·10-3 V 30·10-6 86·10-9 m/m 0.2 %

RC1 60.000 Ω 0.693 Ω -620·10-9 -430·10-9 m/m 5.8 %

RC2 60.000 Ω 0.693 Ω -620·10-9 -430·10-9 m/m 5.8 %

R4pz 119.590 Ω 0.275 Ω

Rz 35000.0 Ω

UBAsetCal 10.0000 V 0.0289 V -15·10-6 -430·10-9 m/m 5.8 %

UEmsetCal 5.00000 V 2.89·10-3 V 30·10-6 86·10-9 m/m 0.2 %

S setCal 2.00000·10-3 V/V

5.77·10-6 V/V 0.075 430·10-9 m/m 5.8 %

UBAsetMeas 10.0000 V 0.0289 V 15·10-6 430·10-9 m/m 5.8 %

UEmsetMeas 5.00000 V 2.89·10-3 V -30·10-6 -86·10-9 m/m 0.2 %

SsetMeas 2.00000·10-3 5.77·10-6 V/V -0.075 -430·10-9 m/m 5.8 %

V/V

ε 149.71·10-6 1.80·10-6 m/m m/m

Result: Quantity: ε

Expanded Uncertainty: ±3.6·10-6 m/m

Relative Expanded Uncertainty: ±2.4 %

Coverage Factor: 2.00

Coverage: 95% (t-table 95.45%)

Value: 149.7·10-6 m/m

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.13 Curvature sensor expanded uncertainty

To see how the different parameters contribute to the uncertainty at different accelerations, we provide the graph elow, which shows the major contributors.

.13 Curvature sensor expanded uncertainty

To see how the different parameters contribute to the uncertainty at different accelerations, we provide the graph elow, which shows the major contributors.

512382.00.01 draft / 2003-07-15 2003-07-15

11 To see how the expanded unc To see how the expanded uncertainty varies with the strain signal from the sensor, we provide the graph below. In this ll the va budget above have been held constant, except the bending radius.

ertainty varies with the strain signal from the sensor, we provide the graph below. In this ll the va budget above have been held constant, except the bending radius.

Curvature sensor error

0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

40.0

Expa

nded

unc

erta

inty

[um

/m]

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

Expa

nded

unc

erta

inty

[%]

Expanded uncertainty [um/m]Ex d unce

graph agraph a lues from thelues from the

pande rtainty [%]

0.0 500.0 1000.0 1500.0Strain [um/m]

106

Curvature sensor err tors

0.0

5.0

20.0

35.0

Erro

r con

tribu

tion

[%] G_f

dU_fAD

dU_ADRepsilon_LR_C1

Basetet

or contribu

10.0

15.0

25.0

30.0

0.00 500.00 10/m]

00.00 1500.00Strain [um

dU_BA

G_

R_C2U_S_s

/

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107

2. Accelerometers error budget

MT51 F03-167 /

2.1 IDEAL MEASUREMENT The signal from the accelerometer is first amplified by a bridge amplifier, then it is filtered by a Butterworth low pass filter, and finally it is digitized by an AD-converter. The measured acceleration, a, can then be described by the formula:

a = K * Us * GBA * Gf * GAD where

K is the calibration coefficient from the calibration. Us signal from the accelerometer GBA is the bridge amplifier gain Gf is the filter gain GAD is the analog to digital converter gain

2.2 ERRORS IN AMPLIFIERS When taking offset errors of the amplifiers into account we can rewrite the above formula as:

a = K * ( ( ( Us * GBA + δUBA ) * Gf + δUf ) * GAD + δUAD )

δUBA is the bridge amplifier output offset δUf is the filter output offset δUAD is the analog to digital converter output offset

In addition to the offset errors, the gain factors now also have accosiated errors.

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where

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2.3 ERROR IN CALIBRATION COEFFICIENT The accelerometers were calibrated by rotating the riser and registering the amplified, filtered, and digitized signal. The voltage difference between the max and min voltages represent a difference in acceleration of 2g (acceleration of gravity). The calibration coefficient, K, was then calculated using the formula:

K = g / ( ( Umax - Umin ) * ( GBAcal / GBAnom ) / 2 ) where

g is the acceleration of gravity Umax is the maximum registered voltage Umin is the minimum registered voltage GBAcal is the bridge amplifier gain during calibration GBAnom is the nominal amplification of the bridge amplifier (if there were no errors)

The factor ( GBAcal / GBAnom ) accounts for uncertainty in setting the bridge amplifier's mplification during calibration, see the discussion of bridge amplifier gain errors below.

2.4 ERRORS IN THE ACCELEROMETER SIGNAL The signal from the accelerometer, Us, can be written as:

Us = Up + Ut + UN where

Up is the signal from acceleration parallel to the accelerometer axis Ut is the signal from acceleration transverse to the accelerometer axis UN is random noise from the accelerometer

The signal due to acceleration parallel to the accelerometer axis is:

Up = Sp * UEm * ap where

Sp is the accelerometer sensitivity to accelerations parallel to the axis, normalized to bridge energizing voltage 1.0V

UEm is the actual bridge voltage during measurement ap is the acceleration parallel to the accelerometer axis

512382.00.01 draft / 2003-07-15

a

109

The parallel sensitivity, Sp, is:

MT51 F03-167 /

Sp = ( F * ( 1 + CT + CNL ) / g ) / UE0n

T

n er r coefficient UE0n is the nominal bridge energizing voltage

The signal due to acceleration transverse to the accelerometer axis is:

St

512382.00.01 draft / 2003-07-15

where

F is the sensitivity in V/g, as given on the data sheet C is the temperature error coefficient CNL is the no -linearity ro

Ut = * UEm * at where

erations transverse to the axis at is the acceleration transverse to the accelerometer axis

St = Sn * Ct

here

Ct is the transverse error coefficient

2.5 ER R HE CABLE RESISTANCE f temperature varies, so will the resistance of the cables between the sensor to the bridge

amplifier. The bridge amplifier input resistance is high, so the resistance variations in the bridge mplifier input cables can be neglected. Resistance variations in the cables providing bridge nergizing voltage from the bridge amplifier to the bridge can't be neglected, however. The bridge nergizing voltage during measurement, UEm, can be found from the formula:

UEm = RB * UE0 / ( RC1 + RC2 + RB )

here

RB is the bridge diagonal resistance (see formula below) UE0 is the bridge energizing voltage output from the amplifier RC1 is the resistance of cable 1 RC2 is the resistance of cable 2

St is the accelerometer sensitivity to accel

S can be written: t

w

RO S DUE TO THERMAL VARIATIONS OF TI

aee

w

110

MT51 F03-167 /

.6 ERRORS IN THE BRIDGE AMPLIFIER GAIN The bridge amplifier gain is set using a calibration unit and adjusting offset and gain. The resulting gain used during calibration, G is:

dle indicator as set by the operator for

alibration EmsetCal is the bridge energizer voltage from the amplifier during calibration

S Cal is the bridge unbalance as set on the calibration unit during calibration Similar ent, GBA, is:

where

or for measurement

U is the bridge energizer voltage from the amplifier during measurement setMeas on the calibration unit during

.7 COMMENTS we should get a = ap. In this budget we don't get this answer: ap = 10.0m/s2 and a =

9.89m/s2. The reason for this is that we evaluate the signal from the accelerometer using the sensitiv s s ion using the measured calibration coefficient:

F = 0.405 mV/g Calibration Enominal Eactual BA

( ( 9.807 / 24.6220 ) * ( 5.0 / 4.86333 ) ) / 1000.0 = 0.409 mV/g

For this budget we must therefore not interpret this discrepancy as an error. Only the stated uncerta mu

512382.00.01 draft / 2003-07-15

2

BAcal,

GBAcal = UBAsetCal / ( UEmsetCal * SsetCal )

where

UBAsetCal is the full range of the amplifier neec

Uset

ly, the resulting gain used during measurem

GBA = UBAsetMeas / ( UEmsetMeas * SsetMeas )

UBAsetMeas is the full range of the amplifier needle indicator as set by the operat

EmsetMeas

S is the bridge unbalance as set measurement

2Ideally,

ity a tated on the data sheet, while we evaluate the measured accelerat

DataSheet

F = ( ( g / K ) * ( U / U ) ) / G=

inty st be used as an evaluation of the error for a measurand of 10.0m/s2.

111

2.8 Model Equation:

MT51 F03-167 /

a=K*(((Us*GBA+δUBA)*Gf+δUf)*GAD+δUAD); K=g/((U

s=Up+Ut+UN; Em*ap;

*at; p=(F*(1+CT+CNL)/g)/UE0n;

St=Sp*CtUEm=RB RC1GBAcal=U l/(GBA=UBAsetMeas/(UEmsetMeas*SsetMeas);

.9 List of Quantities:

512382.00.01 draft / 2003-07-15

max-Umin)*(GBAcal/GBAnom)/2); UUp=Sp*UUt=St*UEmS

; *UE0/( +RC2+RB);

BAsetCa UEmsetCal*SsetCal);

2


a m/s2 Measured acceleration

K (m/s2)/V Calibration coefficient from shunt calibration

Us V Signal voltage from accelerometer

GBA V/V Bridge amplifier gain

δUBA V Bridge amplifier offset

Gf V/V Filter gain

δUf V Filter output offset

GAD V/V Analog to digital converter gain

δUAD V Analog to digital converter output offset

g 2 y m/s Acceleration of gravit

Umax V Max voltage when rotating the riser

Umin V Min voltage when rotating the riser

GBAcal V/V Bridge amplifier gain during calibration

GBAnom V/V Nominal bridge amplifier gain (no errors)

Up V Signal from parallel acceleration

Ut V Signal from transverse acceleration

UN V Noise from accelerometer

S eter sensivity, normalized to UE = 1.0V p 1/(m/s2) Parallel accelerom

UEm V Actual bridge energizing voltage during measurement

ap m/s2 Parallel acceleration experienced by the accelerometer

S alized to UE = 1.0V t 2

1/(m/s2) Transverse accelerometer sensivity, norm

at m/s Transversal acceleration experienced by the accelerometer

F ecified on manufacturer's data sheet V/g Sensitivity as sp

112


CT Temperature coefficient sensitivity

CNL Non-linearity coefficient sensitivity

U V minal bridge energizing voltage specified for accelerometer E0n No

Ct Transverse sensitivity coefficient

RB Ω Bridge diagonal resistance during measurement

U VE0 Bridge voltage from the amplifier during measurement



UBAsetCal V The voltage output from the bridge amplifier when setting the amplifier gain for calibration

UEm a V idge vo dur bridge amplifier gain setting for calibration setC l Br ltage ing

SsetCal V/V The calibrator unit unbalance during bridge amplifier gain setting for calibration

UBAsetMeas V The voltage output from the bridge amplifier when setting the gain for measurement amplifier

UEms Vm

etMeas Bridge voltage during bridge amplifier gain setting for easurement

SsetMeas V/V The calibrator unit unbalance during bridge amplifier gain setting for measurement

a:

Us: Interim GBA: Interim Result

alue: 0.000 V


his is an evaluation of the effect of non-linearity and temperature drift from the manufacturer's ata sheet.

Result K: Interim Result

Result

δUBA: Type B rectangular distribution

VH Td

MT51 F03-167 / 512382.00.01 draft / 2003-07-15

113

MT51 F03-167 /

Gf: Type B rectangular distribution

Limits: 0.01 V/V

sheet specifies <1%

f

n

alue: 0.000 V

2 V

Th es the output offset voltage to be 2mV GAD: Type ectangu uValue: 1.000 V/V

Halfwidth of Limi 1 V The cturer's a sh arity as +/-1.0LSB. The AD converter has 12 digits and a +/-10V range δUAD: Type r tangula ibuValue: 0.000 V

Halfwidth of Limits: 0.0025 V The nufacturer's data sh ssed number. g: Constant Value: 9.807 m/s2 Acceleration of gravity Umax: Type B rectangular distribution

Value: 0.7935 VHalfwidth of Limits: 0.001 V The h width is e ed from the accelerometer w in Umin: Type B ectangula tribuValue .003104

512382.00.01 draft / 2003-07-15

Value: 1.000 V/V

Halfwidth of The manufacturer's data

δUyp rect ular d ribu

: T e B ang ist tioVHalfwidth of Limits: 0.00

e manufacturer's data sheet specifi

B r lar distrib tion

ts: 0.0 /V

manufa dat eet specifies the nonline

B ec r distr tion

ma eet does not specify this, so this a gue

alf stimat from the curve used to determine max and min voltageshen rotat g the riser.

r: -0

r disV

tion

114

MT51 F03-167 /

Halfwidth of Limi 01 V The halfwidth is estimated from the curve used to determine max and min voltages from the accel eter when rotating the riser. GBAcal: Interim esult GBAno : ConsValue: 1000.0 V/V Up: Int m Result Ut: Int lt UN: Type B rectangular distribuValue: 0.000 V

Halfwidth of Limits: 0.000

Data sheet: Typical 1.0µV

512382.00.01 draft / 2003-07-15

ts: 0.0

erom

R

m

tant

eri

erim Resu

tion

001 V

pp Sp: Interim Result

: Result

Value: 10.0 m/s2

an acceleration parallel to the accelerometer axis.

Value: 10.0 m/s2

n example of an acceleration transversal to the accelerometer axis.

UEm

Interim ap: Constant

An example of

St: Interim Result

at: Constant

A F: Constant

115

MT51 F03-167 /

Value: 0.000405 V/g

distribution

alfwidth of Limits: 0.01

Info from manufacturer: Less than 2% for 25°C +/- 5°C for uncomensated circuits. We're using 1% here, since we don't expect more than half of this temperature range.

Type B rectangular distribution

alue: 0.0

sheet: Typical +/- 0.5%

alue: 5.00 V

oltage used by the manufacturer when specifying the accelerometer sensitivity F.

lar distribution

alfwidth of Limits: 0.01

ata sheet: Typical 1%


alue: 4270 Ω

Ω

23.9Ω for +/- 5°C

E0


alue: 5.000 V

The manufacturer's data sheet specifies the error as +/- 0.1%.

512382.00.01 draft / 2003-07-15

CT: Type B rectangularValue: 0.0

H

CNL:

UE0n:

V Nominal bridge exitation v

Ct: Type B rectanguValue: 0.0

H D RB:

Halfwidth of Limits: 23.9

Data sheet: 22.4%/100°C => +/-

VHalfwidth of Limits: 0.005

Data

Constant

V

U :

VHalfwidth of Limits: 0.005 V

116

MT51 F03-167 /

n

alue: 60.0 Ω

The temperature coefficient of resistance of copper is approximately 0.4% per °C. A +/- 2.5°C ature range is assumed.

RC2: rectangular distribution

Value: 60.0 Ω

: 0.60 Ω

e coefficient of resistance of copper is approximately 0.4% per °C. A +/- 2.5°C temperature range is assumed.


e: 10.000 V

ate the operator can adjust the output voltage by monitoring an analogue needle indicator. UEmsetCal:

e B rectangular distribution

Halfwidth of Limits: 0.005 V

er's data sheet specifies the error as +/- 0.1%.

ctang ar distribution

manufacturer's data sheet specifies max error as 0.5%.

UBAsetMeas: e B rectangular distribution

.000 V

its: 0.05 V

t voltage by monitoring an nalogue needle indicator.

512382.00.01 draft / 2003-07-15

RC1: Type B rectangular distributioV

mp

ype

Halfwidth of Limits

The temperatur

UBAsetCal:

V luaHalfwidth of Limits: 0.05 V This is an evaluation of how accur

Halfwidth of Limits: 0.60 Ω

te er

T B

TypValue: 5.000 V

The manufactur SsetCal: Type B re ulValue: 0.002 V/VHalfwidth of Limits: 0.00001 V/V

The

TypValue: 10Halfwidth of Lim This is an evaluation of how accurate the operator can adjust the outpua

117

MT51 F03-167 /

stribution

Value: 5.000 V

width of Limits: 0.005 V

cturer's data sheet specifies the error as +/- 0.1%.

setMeas:

Halfwidth of Limits: 0.00001 V/V

ecifies max error as 0.5%.

.10 Uncertainty Budget:

512382.00.01 draft / 2003-07-15

UEmsetMeas: Type B rectangular di

H lfa The manufa SType B rectangular distribution

Value: 0.002 V/V

The manufacturer's data sheet sp

2

U

GAD

Umin -3.104·10 V -3 577·10-6 V 12 7.2·10-3 m/s2 0.3 %

GBAcal 1000.00 V/V 4.12 V/V

GBAnom 1000.0 V/V

p

-6

N

Sp 8.2594·10 53.3·10-9 1/(m/s2)

-6

1/(m/s2)

Quantity Value Standard Uncertainty

Sensitivity Coefficient


Index

K 24.622 (m/s2)/V 0.105 (m/s2)/V

s 401.68·10-6 V 3.53·10-6 V

GBA 1000.00 V/V 4.12 V/V

δUBA 0.0 V 1.15·10-3 V 25 0.028 m/s2 4.0 %

Gf 1.00000 V/V 5.77·10-3 V/V 9.9 0.057 m/s2 16.0 %

δU 0.0 V 1.15·10-3 V 25 0.028 m/s2 4.0 % f

1.00000 V/V 5.77·10-3 V/V 9.9 0.057 m/s2 16.0 %

δUAD 0.0 V 1.44·10-3 V 25 0.036 m/s2 6.2 %

g 9.807 m/s2

Umax 0.793500 V 577·10-6 V -12 -7.2·10-3 m/s2 0.3 %

U 401.68·10-6 V 2.60·10-6 V

Ut 0.0 V 2.32·10 V

U 0.0 V 577·10-9 V 25000 0.014 m/s2 1.0 %

UEm 4.86333 V 2.89·10-3 V

ap 10.0 m/s2

118

Quantity Value Standard

Uncertainty Sensitivity Coefficient


Index

S 0.0 1/(m/s2) t 47.7·10-9 1/(m/s2)

a 10.0 m/s2t

F 405.0·10-6 V/g

CT 0.0

UE0n 5.0 V

Ct

UE0 5.00000 V 2.89·10-3 V 2.0 5.7·10-3 m/s2 0.2 %

RC1 60.000 Ω 0.346 Ω -2.3·10-3 -780·10-6 m/s2 0.0 %

RC2 60.000 Ω 0.346 Ω -2.3·10-3 -780·10-6 m/s2 0.0 %

UBAsetCal 10.0000 V 0.0289 V -0.99 -0.029 m/s2 4.0 %

UEmsetCal 5.00000 V

UEmsetMeas 5.00000 V 2.89·10-3 V -2.0 -5.7·10-3 m/s2 0.2 %

SsetMeas

2 R.11 esult:

xpanded Uncertainty: ±0.29m/s

Coverage Factor: 2.00

: 95% (t-table 95.45%)

Quantity: a 2Value: 9.89 m/s

2ERelative Expanded Uncertainty: ±2.9 %

overag

5.77·10-3 9.9 0.057 m/s2 16.0 %

CNL 0.0 2.89·10-3 9.9 0.029 m/s2 4.0 %

0.0 5.77·10-3 9.9 0.057 m/s2 16.0 %

RB 4270.0 Ω 13.8 Ω 63·10-6 870·10-6 m/s2 0.0 %

2.89·10-3 V 2.0 5.7·10-3 m/s2 0.2 %

S 2.00000·10-3 5.77·10-6 V/V 4900 0.029 m/s2 4.0 % setCal

V/V

UBAsetMeas 10.0000 V 0.0289 V 0.99 0.029 m/s2 4.0 %

2.00000·10-3 5.77·10-6 V/V -4900 -0.029 m/s2 4.0 %

V/V

a 9.890 m/s2 0.143 m/s2

C e

MT51 F03-167 / 512382.00.01 draft / 2003-07-15

119

MT51 F03-167 /

2.12 Accelerometer expanded uncertainty is

To see how the different parameters contribute to the uncertainty at different accelerations, we provide the graph below, which shows the major contributors.

2.12 Accelerometer expanded uncertainty is

To see how the different parameters contribute to the uncertainty at different accelerations, we provide the graph below, which shows the major contributors.

512382.00.01 draft / 2003-07-15 2003-07-15

To see how the expanded uncertTo see how the expanded uncertgraph all the valgraph all the valparallel to the accelerometer separallel to the accelerometer se

Accelerometer error

0.5

1

1.5

Expa

nded

unc

erta

inty

[m/s

^2] 2.5

0 20 40 60 80 100Acceleration [m/s^2]

3

Expanded un[um/m]

ainty varies with acceleration, we provide the graph below. In thues from the budget above have been held constant, except the acceleration

nsitive axis.

ainty varies with acceleration, we provide the graph below. In thues from the budget above have been held constant, except the acceleration

nsitive axis.

0

3

0

6

9

12

15

18

Expa

nded

unc

erta

inty

[%]

certainty

Expanded uncertainty [%]

2

120

Acc rro rs

0

50

60

0 60 80

Erro

r con

tribu

tion

[%]

dU_BAG_fdU_f

AD_ADT

C_NLC_t

Asetset

elerometer e r contributo

30

40

G_dUC_

20

10 U_BS_

20 40 100

-10cceleratio 2]A n [m/s^

/

MT51 F03-167 512382.00.01 draft / 2003-07-15

121

MT51 F03-167 /

APPENDIX 5

Validation of Software

Spectral- and Statistical Routines in Express and Timsas

512382.00.01 draft / 2003-07-15

122

MT51 F03-167 /

TABLE OF CONTENTS

1. INTRODUCTION .............................................................................................................123

2. ACTUAL PROGRAMS ....................................................................................................123

3. ACCEPTANCE CRITERIA.............................................................................................123

4. DESCRIPTION OF METHOD........................................................................................124 4.1 Generation of Time Series............................................................................................124 4.2 Calculation ...................................................................................................................125 4.3 Theoretical Values........................................................................................................125

5. PRESENTATION OF RESULTS ....................................................................................127 5.1 Spectral Plots................................................................................................................127 5.2 Spectral Moments.........................................................................................................127 5.3 Main Statistical Parameters ..........................................................................................128

512382.00.01 draft / 2003-07-15

123

MT51 F03-167 /

1. INTRODUCTION When validating software code, the practical way paring calculated and theoretical values of a selected number of significant parameters. In doing so, one must bring in mind if the code is written in single or double precision, the number of significant digits on the datafiles that are input to the programs and the number of significant digits on the printed tables. In this context, we will use a practical approach to the validation. We will simply use the results from the standard output of the ac ocess. This means that the parameters are represented with th tandard tables from the programs.

2. ACTUAL PROG Program name: Express (single precision program) Timsas, version 7.23 (single precision program) Routines: Spectral- and statistical.

3. ACCEPTANCE CRITERIA The acceptance criterion is based on the target value itself, and not what it is going to be used to. Criterion: The program routine is said to be correct if a calculated value deviates from the target

value by less than 0.1 %.

For a target value equal to zero, a representative value, for instance the standard deviation, will be applied.

The criterion above implies that an error (∆) will affect the 4th digit of a number. Notice that a computer code that is written in single precision, gives an error in the 6th digit and a force measurement in an experiment normally is given with an accuracy of 2%.

512382.00.01 draft / 2003-07-15

to do the validation is by com

tual programs involved in the pre number of digits given in the s

RAMS

124

MT51 F03-167 /

DESCRIPTION OF METHOD

1 Generation of Time Series

x different time series were used in the validation: 3 regular wave signals and 3 irregular wave generated by Express and consisted of 4096 samples, with a time step

f 0.5 s.

Channel

512382.00.01 draft / 2003-07-15

4.

4. Sisignals. All time series were

The time series are defined in the following table.

No. Name Description

o

1 F_vary The frequency increases lineraly from f=1/40 to f=1/19.927 Hz.

2A regular wave with an amplitude 1.0 and period 16 s with first sample

Reg_1600 equal to zero.

3 Reg_2048 pleA regular wave with an amplitude 1.0 and period 20.48 s with first sam

equal to zero. 4 Reg_sum Sum of channel 2 and 3.

5spectrum is dropping linearly to zero to next sample outside this range.

Time series based on flat raw spectrum equal to 5000 m2 Hz from Bpass_1 frequency f=(20-1)/(4096 * 0.5) Hz to f=(150-1)/(4096 * 0.5). The

6 Bpass_2

Time series based on a raw spectrum linearly increasing from 4000 m2 Hz at frequency f=(20-1)/(4096 * 0.5) Hz to 9000 m2 Hz at frequency f=(150-1)/(4096 * 0.5) Hz. The spectrum is dropping linearly to zero to next sample outside this range.

The rectangular and trapeziodal spectra are defined in the table below.

Rectangular Trapezoidal f

S S

0.0087890625 0.0 0.0

0.0092773438 5000.0 4000.0

0.0727539063 5000.0 9000.0

0.0732421875 0.0 0.0

125

4.2 Calculation

MT51 F03-167 /

.3 Theoretical Values

512382.00.01 draft / 2003-07-15

The six time series defined in Section 4.1 were subject to spectral- and statistical analyses with theprograms that should be validated. The following parameters were selected for the validation: Spectral routines: Spectral plots and spectral moments up to 4th order. Statistical routines: Standard deviation, skewness and kurtosis.

4

Spectral Moments For a sine wave with amplitude a and a frequency f, the spectral moments are defined by:

nn fam 2

21

=

For a contineous spectrum, the spectral moments are defined by:

or a spectrum varying linearly between f1 and f2, the spectral moments are then given by:

dfffSf

f

nn ∫=

2

1

)( m

F

1 )(2

1)(1

21

221

11

120

++++ −+

+−+

= nnnnn ffa

nffa

nm

where:

upper frequenzy

1 spectrum ordinate at f1

2 spectrum ordinate at f2

f1 lower frequency f2

a0 constant defining the spectrum = S1 - a1 f1 a1 constant defining the spectrum = (S2 - S1)/(f2 - f1) SS

https://project.sintef.no/eRoom/Marintek/512381ExxonMobil/Reports/Modalpar_a.xls

126

MT51 F03-167 /

ts of the time series used in the validation are resented in Table 4.1.

tatistical Parameters

512382.00.01 draft / 2003-07-15

The theoretical values of the spectral momenp

S The standard deviation for sine wave signals is given by:

0. mdevSt =

here m0 is the area of the spectrum.

Since skewness and kurtosis are parameters related to the normal distribution, these parameters have no m r a For egu e a sum of sine waves, the theoretical values of skewness and kurtosis are:

w

eaning fo pure sine wave.

irr lar time seri s consisting of

0=Skewness

0.3=Kurtosis Notice that the theoretilen . Sin lida l differ from the theoreti

he theoretical values of the statistical parameters of the time series used in the validation are resented in Table 4.2.

cal values for skewness and kurtosis yields for time series of infinite tion is performed with time series of final length, these parameters wilcal values.

gth ce the va

Tp

127

MT51 F03-167 /

N OF RESULTS

as are shown in Figures 5.1-5.12.

5.7-5.12 show the

he smoothing bandwidth is 0.

5.2 Spectral Moments

able 5.1 shows the main spectral results from the analyses with Express and Table 5.2 shows the

The tables below summarize the comparison of spectral moments for the rectangular- and trapeziodal spectrum time series.

512382.00.01 draft / 2003-07-15

5. PRESENTATIO

5.1 Spectral Plots

The spectral plots from the analyses with Express and Tims

Figures 5.1-5.6 show the results from the analyses with Express and Figures results from the analyses with Timsas. T

Tmain spectral results from the analyses with Timsas.

Rectangular spectrum

Express Timsas Spectral moment

Theoretical Value % dev. Value % dev.

0 319.82 319.82 0.000 319.82 0.000 1 13.118 13.118 0.000 13.118 0.000 2 0.64709 0.64707 -0.003 0.64710 0.002 3 0.035486 0.035485 -0.003 0.035490 0.011 4 0.0020728 0.0020727 -0.005 0.0020730 0.010

Trapezoidal spectrum

Express Timsas

Spectral T

moment V lueheoretical

% dev. Value % dev. a 0 415.77 415.77 0 0. 00 415.77 0.000 1 18.7 1 7 18.771 0.000 18.771 0.000 2 0.98213 0.98211 -0.002 0.98210 -0.003 3 0.055856 0.055854 -0.004 0.055850 -0.011 4 0.0033417 0.0033415 -0.006 0.0033420 0.009

128

5.3 Main Statistical Parameters

MT51 F03-167 /

able 5.3 shows the main statistical results calculated with Express and Table 5.4 shows the main statistical results calculated with Timsas.

For some parameters, theoretical values do not exist due to time series of finite length. In such to be compared with each other.

The tables below summarize the comparison of spectral moments for the rectangular- and trapeziodal spectrum time series.

ectangular spectrum

512382.00.01 draft / 2003-07-15

T

cases, the values calculated with Express and Timsas have

R

Express Timsas Matlab

Parameter Theoretical

Std. dev. 17.8841) 17.886 17.886 17.8858 Skewness 02) 0.2844 0.28450

Kurtosis 3.03) 3.490 3.49020

1) From spectral analysis (=m00.5)

2) Depending on length of time series. Equal to zero for infinite time series. 3) Depending on length of time series. Equal to 3.0 for infinite time series.

rapezoidal spectrumT

tical Express Timsas Matlab

Parameter Theore

Std. dev. 20.3901) 20.393 20.393 20.393 Skewness 02) 0.2657 0.26580

Kurtosis 3.03) 3.409 3.40880

1) From spectral analysis (=m00.5)

2) Depending on length of time series. Equal to zero for infinite time series. 3) Depending on length of time series. Equal to 3.0 for infinite time series.

129

MT51 F03-167 /

PENDIX 6

Spectral Analysis

512382.00.01 draft / 2003-07-15

AP

130

SPECTRAL ANALYSIS

MT51 F03-167 /

Power Spectra a

by a aussian-shaped frequency window with a standard deviation

1The power spectra are estimated from Fast Fourier Transform (FFT) of the data. To obtainconsistent estimate, the raw spectrum, based on the full length of the time series, is smoothed

σ . The smoothing bandwidth 2 σG is normally 0.02 Hz (model scale), but it depends on the length of the time series. 2 Estimates Based on the Power Spectra

pectrum is defined by

The physical si of so nts ar = are resp r area under spectrum or variance

The n'th moment of the s

∫∞

=o

nn fSfm ( df)

gnificance me mome e:

mean squ onse oom ( )2σ onse

rom the moments the following parameters are estimated:

lue =

2m = mean square velocity of resp

4m = mean square acceleration of response

F

om4 Estimated significant va

512382.00.01 draft / 2003-07-15

Energy average period: =o mf

m 11,T1

Average zero cr riod:ossing pe 2 m

=

omm1

2

mT o=

For wave analys is also calculated is, the spectral peakedness Qp

∫∞

⋅=oo

p Sfm

Q 22 dff )(2

In addition the period corresponding to peak value of the spectrum is presented (the spectral peak period).

131

MT51 F03-167 /

3 Transfer Functions Linear transfer functions or R.A.O curves and relative phases when required are estimated from cross-spectral analysis, (see the next section) accor ing to the formula:

d

)()(

)(fSfS

fHxx

xy=

where H(f) is the complex transfer function, such that: RAO = modulus of H Phase = Phase angle Here Sxy is the cross spectrum between the response y and the reference x, and is the reference spectrum (alternatively, the RAO may be defined as the square root of the ratio between the power spectrum of the response divided by the power spectrum of the reference wave). The R.A.O. curves will be with

of H

xxS

the following unit:

meterresponseofunitbasic

The function is normally plotted in the range where the coherence (see the next section) is larger than 40 %, and where reference spectrum is larger than 1% of its peak value. In seakeeping tests the reference wave is normally corrected to the actual frequency of encounter. The reference wave used in the calculation of the transfer functions is normally the wave at the location of the model (middle of the Ocean Basin) without the model present. The results from the spectral analysis are normally presented as shown in Fig. 1. The most important spectral parameters are also presented in tables.

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Coherence Functions and Cross-spectra e coherence function between 2 signals x(t) (reference) and y(t) (response) is described as follows:

4 Th

)( fS [ ])()()

)( fjxy

xyxy

xyexkpff φγ ⋅== γ()( yx fSfS

where

><= )()(1)( * fYfXfS TTxy cross-spectrum between x and y T

where

)(* )()()()( xyjefYfXfYfX φφ −⋅⋅=⋅ TTTT

><= 2)(1)( fXT

fS Tx = autospectrum of x

= 21)( XT

fy >< )( fS T = autospectrum of y

∞−

= ()( TTT f ∫ −=⋅ )2()( exp)() ftjfj tdtxefXX x πφ = Four∞

ier transform of a sample record of length T of x(t)

)(* )()( fj

TTxefXf φ−⋅= X

∫∞

∞−

−=⋅= )2()( exp)()()( ftjT

fjTT tdtyefYf y πφY = Fourier transform of a sample record of length T of y(t)

or

1)(),()()( ≡⋅= ffXfHfY xyTT γ F

) = complex conjugate

j = imaginar unit

(linear relation between x and y

*

)( fxφ = phase of reference

512382.00.01 draft /

)( fxyφ = relative phase

| | means 'absolute value' < > means 'statistical expectation value'

)( fyφ = phase of response

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Fig. 1 Example of results from spectral analysis.

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/

APPENDIX 7

cal Analysis

Statisti

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STATISTICAL ANALYSIS 1 Main Statistics of Time Series For each test run the responses are collected and listed immediately after each run giving the following parameters:

- Mean value of record: ∑=

=N

iiX

Nx

1

1

- Maximum value: (crest to zero)

- Minimum value: (trough to zero)

- Standard deviation:

+maxX

−minX

( )∑=

−−

=N

ii xX

N 1

2

11σ

where N is the total number of samples. Xi is a discrete sample of the parent time series. 2 Peak Value Statistics MARINTEK's standard statistical program is a computer program which is finding the local, or global peaks (maxima and minima). From one maximum to the following minimum the double amplitudes are also calculated. The values are used to calculate the peak value statistics as specified below. The program can also calculate the cumulative distribution and the statistical density function. To avoid that very small peaks as for instance signal noise are taken as maxima or minima, some limitations to define the maxima or minima are specified. The standard values are: - The time step from one extreme value to the next shall be longer than the sample interval. - wing (previous) minimum shall be more

than 2% of the standard deviation σ.

ocal peaks: May also include e.g. maxima lower than the mean value.

lobal peaks: Defined by mean-crossing. In our standard post-processing analysis the following parameters are derived:

The difference between one maximum and the follo

L G

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MT51 F03-167 /

Skewness: 33

1 σγ

m= (expected 0 for a Gaussian process)

Kurtosis:

-

344

2 −=σ

γm - (also called excess of kurtosis, expected 0 for a Gaussian process)

Mean value: X - - Standard deviation: σ

Number of maximum values: N+ Number of minimum values: N -

mber of mean value upcrossings: N(u)

- Maximum value:

- Minimum value:

- Significant double amplitude (2X)1/3 i.e. the mean of the one-third highest peak to peak (crest to trough) values (local or global)

- Largest double amplitude (2X)max - Significant maxima; X1/3

+ i. t to zero values (local or global)

- Significant minima; X1/3- i.e. the mean of the one-third highest trough to zero values (local or

global) For Gaussian single-peaked records, (2X)1/3 is normally around 95 - 98 % of 4 σ. The test results are normally presented in tables. 3 Probability Analysis of Peak Values - Weibull Scale Axis The cumulative distribution of a randomly selected peak value AK is written as P[AK < A], or simply as P[A]. Thus 1-P[A] is the exceedance probability at the given level A. Diagram examples are shown in Fig. D.1. The analysis indicates whether large extreme values are simply results of statistical uncertainties, or results from more systematic trends. Weibull scaled axes are used in the diagrams in order to have the tail of the distributions emphasized. This is achieved by logarithmic axis for A, and the P[A] - axis plotted as 1n [ - ln (1-P(A))]. The Weibull distribution.

- - - Nu

+maxX

−maxX

e. the mean of the one-third highest cres

[ ]

−−−= GXA

GAP

σ1exp1

will then appear as a straight line in the plot.

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In the above distribution

1 X = mean value of record [ Xi ] σ = standard deviation of Xi

or G = 2, one has the commonly used Rayleigh model for statistical distribution of peak values, normally assumed valid for linear responses in irregular waves. G = 1 gives the exponential

gh curve is i icated with a fully drawn line in the diagrams (based on the ctual mean value

G = shape parameter describing the slope of the Weibull curve F

distribution. The Raylei nd1X and standard deviation σ of the measured record). Examples of sample

pectively, are shown in Fig. 1. adistributions with G close to 1 and 2, res

Fig. 2 Example of cumulative probability distributions.

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urc 10-m viv test marintek report

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