Third Chinese-German Joint Symposium on Coastal and Ocean Engineering National Cheng Kung University, Tainan

November 8-16, 2006

Modal Strain Energy Decomposition Method for Damage Detection of an Offshore Structure

Using Modal Testing Information

Huajun Li*, Shuqing Wang and Hezhen Yang Institute of Coastal and Offshore Engineering, Ocean University of China, Qingdao

*huajun@ouc.edu.cn

Abstract A newly derived damage location algorithm is proposed to predict location of damage in offshore structures using changes in mode shapes from modal testing. This method decomposes elemental modal strain energy into two parts, and defines two damage indicators: axial damage indicator and transverse damage indicator. Analyzing the joint information of the two damage indicators can localize damage elements. In order to validate the damage detection method, a physical platform model was manufactured and several damage cases were simulated. Results demonstrates that the proposed method is effective for the structural damage detection and achieves satisfactory precision.

1 Introduction Offshore structures, during their service life, continually accumulate damage that results from the action of various environmental forces. The only way to ensure the safety of human life and to reduce the loss of wealth is to detect the existence and location of significant damage on the structure (Rytter, 1993). Structural damage detection based on vibration measurements holds promise for the global nondestructive damage detection of structures. Doebling et al. (1998) present a thorough review of the vibration-based damage identification methods. Many researchers provide various damage detection techniques based on modal parameters. But most of them have some limitations in practice. For example, some methods need mass normalized mode shapes; some methods need complete mode parameters (including structural rotational degree of freedoms, high modal parameters), or some methods need the environmental loading.

A damage index method base on modal strain energy was developed by Stubbs et al. (1995) and had been successfully applied to beam-type (one-dimensional) structures for damage localization. However, its applications to two- and three-dimensional frame type structures were shown to be not as promising (Farrar and Jauregui, 1996). To avoid these shortcomings of the methods mentioned

above, an effective damage localization method, modal strain energy decomposition (MSED) method, is developed by Yang et al. (2004) for three-dimensional frame structures. The MSED method defines two damage indicators, axial damage indicator and transverse damage indicator, for each member. Analyzing the joint information of the two damage indicators greatly improves the accuracy of localizing damage elements. The appealing features of the modal strain energy decomposition method are: (1) it requires only a few incomplete mode shapes identified from damaged and undamaged structures under ambient excitation which don't include structural rotational degree of freedoms (DoFs), and (2) it can locate local damages in the 3-D frame structures, such as offshore platforms. For validating the damage detection method, a physical platform model was manufactured and several damage cases including single damage location and double damage locations were simulated. Modal strain energy decomposition method was applied to localize the damages. Results demonstrates that the proposed method is effective for the structural damage detection and achieves satisfactory precision.

2 Modal Strain Energy Decomposition Method In this paper, the structural modal strain energy was assigned into two parts: One is axial modal strain energy; the other is flexural modal strain energy. In order to detect damage location in the offshore platform, two damage indicators were defined; axial modal strain energy change can be obtained as following:

( )[ ]( )[ ]∑

= ΦΦΦΦ+ΦΦ

ΦΦΦΦ+ΦΦ=

NM

i icT

iicT

iicj

Ti

icT

iicT

iicj

Tic

jKKk

KKk

1**

****

β j=1, 2,…e (1)

And flexural modal strain energy change is given as:

( )[ ]( )[ ]∑

= ΦΦΦΦ+ΦΦ

ΦΦΦΦ+ΦΦ=

NM

i ifT

iifT

iifj

Ti

ifT

iifT

iifj

Tif

jKKk

KKk

1**

****

β j=1, 2,…e (2)

where iΦ , *iΦ are the structural undamaged mode shapes and damaged mode

shapes, respectively. cjk is the element stiffness, which contains structural

compression information, only; fjk is the element stiffness, which contains

structural flexuosity information only; and NM is the identified mode shapes.

Two normalized damage localization indicators: axial modal strain energy change ratio (Axial damage Indicator) is obtained as follows:

( ) cccj

cjZ βσββ −= (3)

Flexural modal strain energy change ratio (Transverse damage indicator) is obtained as follows:

( ) fffj

fjZ βσββ −= (4)

where cβ , fβ represent the mean of the damage indices, and cβσ , f

βσ represent the standard deviation of the damage indices.

3 Verification Using Modal Testing Data

3-1 Description of the Offshore Platform Model

The structure studied here is a jacket-type offshore platform model, as shown in Fig.1. The platform model is a welded-steel space frame with four primary legs, braced with horizontal and diagonal members. All the members are welded with steel pipes except that the top deck is a steel plate (deck). The essential geometrical and material properties of the frame structure are given below. Young’s modulus E is a constant equal to 2.07×1011 Pa for all members. The primary legs of the first story of the model had a diameter of 18 mm with its pipe thickness 2.5mm. The primary legs of other three stories of the model had a diameter of 14 mm with its pipe thickness 2.5mm. All the horizontal braces had a diameter of 10mm(thickness 2mm). All the diagonal braces in vertical plane had a diameter 8mm(thickness 1.5mm) and all the diagonal braces in horizontal planes are solid bar with diameter 10mm. The deck is a steel plate of 20mm thickness. Other geometrical dimensions are shown in figure 2.

3-2 Experimental Set-up and Modal Testing

Totally 32 accelerometers are installed to monitor the whole physical model, with each joint two sensors to record the response in x and y directions, respectively. The model is fixed to concrete foundation at the bottom and excited by an impact hammer which horizontally hits the center of the platform deck. First tests are performed on the undamaged structure. Then the tests are repeated in the same way for the damaged structure after some structural member(s) is/are broken.

Damages were simulated in the way as shown in Fig.3. Damage occurs when the bolts and metal spacer are removed. When refitting the spacer and settling the screws, damage disappear. Throughout the test, the sampling frequency is 500Hz.

Several damage scenarios are simulated in the tests, as listed in table 1. The damage scenarios include single damage cases and double damage cases, damaged diagonal braces in different levels and in different directions. As stated in section 2, damage detection based on modal strain energy requires the stiffness matrix of each element of the undamaged structure. According to the specifications of the platform structure, numerical model of the tested structure is modeled by finite element method, as shown in figure 2. And each element was assigned with a number.

Fig. 1 Physical model under test Fig. 2 Description of the model

spacer

bolt

brace

Fig. 3 damage simulation

3-3 System Identification

Eigensystem realization algorithm with natural excitation technique was verified to be effective for modal identification based on output-only responses(Wang and Li, 2005) and was used to extract modal frequencies and mode shapes of the undamaged and damaged structure. The first two modal frequencies of the undamaged structure and other damage cases are listed in table 2. The first mode vibrates dominantly in y (short-span) direction and 2nd mode dominantly in x (long-span) direction.

Table 1 Damage cases of the model and the first two modal frequencies

Frequencies (Hz) Damage cases

Damaged element 1st mode 2nd mode

Undamaged FEM --- 17.0120 24.0110

Undamaged physical model

--- 17.0335 24.725

Damage case 1 brace 30 14.5168 24.9822

Damage case 2 brace 34 14.7063 24.3354

Damage case 3 brace 43 16.9225 23.4138

Damage case 4 brace 39 brace 34

15.0785 21.6580

3-4 Damage Location Results

Applying the damage detection procedure of the modal strain energy decomposition method using the first two identified mode shapes, the damage detection for each damage case is shown in figure 4 to figure 7, respectively.

Damage cases 1 to 3 investigate the damage detection for single damage location. For damage case 1, the damage member is a diagonal brace 30 in the fourth story in the long-span direction. The results are shown in Fig.4. The top panel of Fig.4 is the axial damage indicator and the bottom panel is the transverse damage indicator. From the axial damage indicator, it can be obviously seen that element 30 is damaged. The transverse indicator proves the above conclusion by indicating vertical elements 2 and 3 are affected by true damaged diagonal brace 30.

In damage case 2, the damaged member is the diagonal brace 34 in the third story in short-span direction and the damage member is the diagonal brace in the first story in long-span direction in damage case 3. The results are shown in Fig.5 and Fig.6. Same conclusion can be drawn as from damage case 1.

Damage case 4 investigates the damage detection of double damage locations and result is shown in figure 7. The damaged locations are diagonal brace 39 of floor 2 in long-span direction and diagonal brace 34 of floor 3 in short-span direction. From figure 7, one can see that modal strain energy decomposition method can localize the damage locations correctly.

Fig. 4 Damage case1: brace 30 is damaged

Fig. 5 Damage case2: brace 34 is damaged

Fig. 6 Damage case3: brace 43 is damaged

Fig. 7 Damage case4: brace 34 and 39 are damaged

4 Concluding Remarks Modal strain energy decomposition method for detecting damages of an offshore jacket structures is investigated. This newly proposed damage localization algorithm defines two damage indices: axial damage indicator and transverse damage indicator, for each member based on the change of modal strain energy

associated with structural elements before and after damage occurred.. Analyzing the joint information of the two damage indicators greatly improves the accuracy of localizing damage elements. For validating the damage detection method, a physical platform model was manufactured and several damage cases including single damage location and double damage locations were simulated by the physical model. Modal strain energy decomposition method was applied to localize the damages. In applying the procedure, only the first two identified modes are used for damage localization. And partial information, with each node (joint) two identified components are utilized. Results demonstrates that the proposed method is effective for the structural damage detection and achieves satisfactory precision.

5 References Doebling, S.W., C.R. Farrar, M.B. Prime and D.W. Shevitz. A Review of Damage Identification Methods that Examine Changes in Dynamic Properties, Shock and Vibration Digest, 30 (2), pp. 91-105, 1998.

Farrar, C.R. and D.V. Jauregui. Damage Detection Algorithms Applied to Experimental and Numerical Modal Data from the I-40 Bridge, Los Alamos National Laboratory Report, LA-13074-MS, 1996.

Rytter, A.. Vibration Based Inspection of Civil Engineering Structures, Ph. D. Dissertation, Department of Building Technology and Structural Engineering, Aalborg University, Denmark, 1993.

Stubbs N., J.T. Kim and C.R. Farrar. Field Verification of a Nondestructive Damage Localization and Severity Estimation Algorithm, Proc. of IMAC, Connecticut, USA, Society of Experimental Mechanics, pp. 210-218, 1995.

Wang Shuqing and Huajun Li. Output-based Modal Parameters Identification of a Three Dimensional Structure, Proceedings of the Second International Structural Health Monitoring of Intelligent Infrastructure, Vol.2, 1209-1214, 2005.

Yang H.Z. and H.J. Li. Modal Parameter Identification of Offshore Platform under Ambient Excitation, High Technology Letters, 10(1), pp.80-84, 2004.

Yang H.Z. and H.J. Li. Damage Localization of Offshore Platform under Ambient Excitation, China Ocean Engineering, 17(4), pp. 307-316, 2003.