assoc prof dr pelin gundes bakirassoc. prof. dr. pelin ...web.itu.edu.tr/~gundes/introduction to...

ERASMUS Teaching (2008), Technische Universität Berlin

Vibration monitoringVibration monitoring

Assoc Prof Dr Pelin Gundes BakirAssoc. Prof. Dr. Pelin Gundes BakirIstanbul Tecnical University

[email protected] @y

ReferencesERASMUS Teaching (2008), Technische Universität Berlin

References• Pete Avitable’s web page• Pete Avitable s web page

http://faculty.uml.edu/pavitabile/22.515/ME22515_PDF_downloads.htm

• Safak E., ‘Structural monitoring, what is it, why is it done, how is it done, and what is it worth?’ Sixth National Conference on Earthquake Engineering 16 20 Octoberit worth?’,Sixth National Conference on Earthquake Engineering, 16-20 October 2007, Istanbul, Turkey

• Celebi M. ‘Seismic instrumentation of buildings’, USGS Open-File Report 00-157, 20002000.

• Heylen W., Lammens S. And Sas P., ‘Modal Analysis Theory and Testing’, Katholieke Universiteit Leuven, 1997.

• Ewins D.J., ‘Modal Testing, Theory, Practice, and Application’ (Mechanical Engineering Research Studies Engineering Design Series), Research Studies Pre; 2 edition (August 2001) ISBN-13: 978-0863802188 ( g )

• Maia, N. M. M. and Silva, J. M. M.Theoretical and Experimental Modal Analysis Research Studies Press Ltd,, Hertfordshire, 1997, 488 pp.,ISBN 0863802087

P. Gundes Bakir, Vibration based structural health monitoring 2

Vibration monitoringVibration monitoringERASMUS Teaching (2008), Technische Universität Berlin

Th i f ib ti it i i t d ib t t i t f it

Vibration monitoringVibration monitoring• The aim of vibration monitoring is to describe a structure in terms of its

modal parameters which are the frequency, damping and mode shapes. • If we explain modal analysis in terms of the modes of vibration of a simple

plate:

• Suppose we apply a sinusoidal force. We will change the rate of oscillation of the frequency but the peak force will always be the same. We will also

th f th l t d t th it ti ithmeasure the response of the plate due to the excitation with an accelerometer attached to one corner of the plate.



Vibration monitoringVibration monitoringIf th f th• If we measure the response of the plate, we will notice that the amplitude changes as we change the rate of oscillation of the inputthe rate of oscillation of the input force. There will be increases as well as decreases in amplitude at different points as we sweep in titime.

• The response amplifies as we l f ith t fapply a force with a rate of

oscillation that gets closer and closer to the natural frequency (or resonant frequency) of the systemresonant frequency) of the system and reaches a maximum when the rate of oscillation is at the resonant frequency of the system.


Modal analysisERASMUS Teaching (2008), Technische Universität Berlin

Th i d id f l i f i B if k h

Modal analysis• The time data provides very useful information. But if we take the

time data and transform it to the frequency domain using the Fast Fourier Transform then we can compute something called the frequency response function.

• Now, there are some very interesting items to note. We see that there are peaks in this function which occur at the resonantthere are peaks in this function which occur at the resonant frequencies of the system. Now, we notice that these peaks occur at frequencies where the time response was observed to have maximum response corresponding to the rate of oscillation of themaximum response corresponding to the rate of oscillation of the input excitation.


Modal analysisERASMUS Teaching (2008), Technische Universität Berlin

N if l h i i h h f h

Modal analysis• Now, if we overlay the time trace with the frequency trace what we

will notice is that the frequency of oscillation at the time at which the time trace reaches its maximum value corresponds to the frequency where peaks in the frequency response function reach a maximum.

• So we can see that we can either use the time trace to determine• So we can see that we can either use the time trace to determine the frequency at which the maximum amplitude increases occur or the frequency response function to determine where these natural f i Cl l th f f ti i ifrequencies occur. Clearly the frequency response function is easier to evaluate.



Vibration monitoringVibration monitoring• The figure shows the deformation patterns that will result when the

excitation coincides with one of the natural frequencies of the system.



Vibration monitoringVibration monitoring• We see that when we dwell at the first natural frequency, there is a first q y

bending deformation pattern in the plate shown in blue. When we dwell at the second natural frequency, there is a first twisting deformation pattern in the plate shown in red.p



Vibration monitoringVibration monitoring• When we dwell at the third and fourth natural frequencies, the second bending and q , g

second twisting deformation patterns are seen in green and magenta, respectively.

These deformation patterns are referred to as the mode shapes of the structure.



Vibration monitoringVibration monitoring• Now these natural frequencies and mode shapes occur in all structures that

we design. Basically, there are characteristics that depend on the weight and stiffness of my structure which determine where these natural frequencies and mode shapes will existfrequencies and mode shapes will exist.

• As a design engineer, I need to identify these frequencies and know how they might affect the response of my structure when a force excites the y g p ystructure.

• Understanding the mode shape and how the structure will vibrate when excited helps the design engineer to design better structuresexcited helps the design engineer to design better structures.

• Now we can better understand what modal analysis is all about-it is the study of the natural characteristics of structures. Both the natural frequencystudy of the natural characteristics of structures. Both the natural frequency and mode shape (which depends on the mass and stiffness distributions in my structure) are used to help design my structural applications.


How many points are enough for a vibration How many points are enough for a vibration ERASMUS Teaching (2008), Technische Universität Berlin

measurement?measurement?

F l f 45 i h h• For a total of 45 measurement points, we can see that there are sufficient number of points to describe the mode shape for each mode.


How many points are enough for a vibration How many points are enough for a vibration ERASMUS Teaching (2008), Technische Universität Berlin

y p gy p gmeasurement?measurement?

• For a total of 5 measurement points along one edge of the plate, ifFor a total of 5 measurement points along one edge of the plate, if we compare mode 1 and 3, we see that there are not enough points to adequately describe the mode shape for each mode. The same conclusion can be drawn from the comparison of modes 2 and 4conclusion can be drawn from the comparison of modes 2 and 4.


How many points are enough for a vibrationHow many points are enough for a vibration


How many points are enough for a vibration How many points are enough for a vibration measurement?measurement?

• If we increase the number of measurement points to 15, we see that the modes can be measured well only if the measurement points are selected with care If we select the points as shown in thepoints are selected with care. If we select the points as shown in the figure, then it will be very hard to distinguish between modes 1 and 3. The mode shapes look almost the same.


How many points are enough for a vibrationHow many points are enough for a vibrationERASMUS Teaching (2008), Technische Universität Berlin


• If we only take measurements along the front and back edges of the plate, then it would be very hard to distinguish between the first rigid body mode and the first flexural mode.

• From all these simple examples above, it becomes obvious that we need a distribution of points located appropriately such that each mode shape can be uniquely distinguished.


mode shape can be uniquely distinguished.



• If I am only interested in characterizing modes 1 and 2, then possibly I could get a fairly good decription with only 6 points as shown but fewer points than that would be difficult especially if we p p yneeded to distingish the flexible modes from the rigid body modes.




• If the only accessible surfaces are the 3 exterior surfaces and we can notIf the only accessible surfaces are the 3 exterior surfaces, and we can not get any measurement from inside, modes 2 and 4 or modes 5 and 6 can not be distinguished. The second storey beams are in phase for these two modes but the first storey beams are out of phase.modes but the first storey beams are out of phase.


What is the difference between time domainWhat is the difference between time domainERASMUS Teaching (2008), Technische Universität Berlin

What is the difference between time domain What is the difference between time domain and the frequency domain and the modal and the frequency domain and the modal

space?space?space?space?

• First let’s consider a simple cantilever beam and imaginecantilever beam and imagine that the beam is excited by a pulse at the tip of the beam.

• The response at the tip of the beam will contain the response

f ll th d f th tof all the modes of the system (shown in the black time response plot); notice that there appears to response at se eralappears to response at several different frequencies.





• The time response at the tip of the beam can be converted to thebeam can be converted to the frequency domain by performing a Fourier Transform of the signal. Th f d i• The frequency domain representation of this converted time signal is often referred to as the frequency response functionthe frequency response function, or FRF for short (shown in the black frequency plot); notice that there are peaks in the plot whichthere are peaks in the plot which correspond to the natural frequencies of the system.





• We know that the cantilever beam will have many natural frequencieswill have many natural frequencies of vibration. At each of these natural frequencies, the structural deformation will take on a verydeformation will take on a very definite pattern, called a mode shape. For this beam, we see that there is a first bending modethere is a first bending mode shown in blue, a second bending mode shown in red, and a third bending mode shown in green.bending mode shown in green.

• Of course there are also other higher modes not shown but only three modes will be discussed


three modes will be discussed here.



space?space?space?space?• Now, the physical beam could

also be evaluated using an analytical lumped mass model oranalytical lumped mass model or finite element model (shown in black in the upper right part of the figure)figure).

• This model will generally be evaluated using some set of equations where there is anequations where there is an interrelationship, or coupling, between the different points, or degrees of freedom used to modeldegrees of freedom used to model the structure. This means you pull on one of the dofs in the model, the other dofs are also affected


and also move.



space?space?space?space?• This coupling means that the

equations are more complicated in order to determine how theorder to determine how the system behaves. As the number of equations used to describe the system get larger and larger thesystem get larger and larger, the complication in the equations become more involved. We often use matrices to help organize all p gof the equations of motion describing how the system behaves which looks like:





• Usually, the mass is a diagonal matrix and the damping and thematrix and the damping and the stiffness matrices are symmetric with off-diagonal terms indicating the degree of coupling betweenthe degree of coupling between the different equations or dofs describing the system.

• The size of the matrices depend on the number of equations that

e se to describe o r s stemwe use to describe our system.





• Mathematically, we perform something called an eigensolutionsomething called an eigensolution and use the modal transformation equation to convert these coupled equations into a set of uncoupledequations into a set of uncoupled single degree of freedom systems described by diagonal matrices of modal mass modal damping andmodal mass, modal damping and modal stiffness in a new coordinate system called modal space described as:space described as:





• We can see that the transformation from physicaltransformation from physical space to modal space using the modal transformation equation is a process whereby we convert aprocess whereby we convert a complicated set of coupled physical equations into a set of simple uncoupled single dofsimple uncoupled single dof systems.





• And we see in the figure that the analytical model can be brokenanalytical model can be broken down into a set of single dof systems where the single dof describing mode 1 is shown indescribing mode 1 is shown in blue, mode 2 is shown in red and mode 3 is shown in green.

• Modal space allows us to describe the system easily using simple single dof s stemssingle dof systems.




space?space?space?space?• Now let’s go back to the time and

frequency responses shown in black We know that the totalblack. We know that the total response can be obtained from the contribution of each of the modes The total response shownmodes. The total response shown in black comes from the summation of the effects of the response of the model shown in pblue for mode 1, red for mode 2, and green for mode 3. This applies whether I describe the ppsystem in the time domain or the frequency domain. Each domain is equivalent and just presents the


data from a different viewpoint.



space?space?space?space?• So we can see that the total time

response is made up of the time response due to the contributionresponse due to the contribution of the time response of mode 1 shown in blue, mode 2 in red and mode 3 in greenmode 3 in green.

• We can also see that the total FRF is made up of the part of theFRF is made up of the part of the FRF due to the contribution of the FRF of mode 1 shown in blue, mode 2 in red and mode 3 inmode 2 in red and mode 3 in green.

.




space?space?space?space?• Please note that we have only

shown the magnitude part of the FRF here this function is actuallyFRF here, this function is actually complex which is correctly displayed using both magnitude and phase or real and imaginaryand phase or real and imaginary parts of the FRF.

• Since we can break the analytical model up into a set of single dofmodel up into a set of single dof systems, we could determine the FRF for each of the single dof systems as shown with mode 1 insystems as shown with mode 1 in blue, mode 2 in red, and mode 3 in green.




space?space?space?space?• We could also determine the time

response for each of these single dof systems due to the pulse inputdof systems due to the pulse input

• Or we could simply inverse Fourier transform the FRF for each of the single dof systemseach of the single dof systems.

• Or we could also measure the response of the beam at the tip due to the pulse and filter thedue to the pulse and filter the response of each modes of the system, and we we would see the response of each of the modes ofresponse of each of the modes of the system with mode 1 in blue, mode 2 in red, and mode 3 in green


green.



space?space?space?space?• As a result, we see that there is no

difference between the time domain frequency domain modaldomain, frequency domain , modal space and physical space. Each domain is just a convenient way for presenting or viewing the datafor presenting or viewing the data.

• However, sometimes one domain is much easier to see things than another domain For instance theanother domain. For instance, the total time response does not clearly identify how many modes there are contributing to thethere are contributing to the response of the beam.





• But the total FRF in the frequency domain is much clearer in showingdomain is much clearer in showing how many modes are activated and the frequency of each of the modesmodes.

• So often, we transform one d i t th d i i ldomain to another domain simply because the data is much easier to interpret.



Single degree of freedom Single degree of freedom systemssystemssystemssystems

System equation and transferSystem equation and transferERASMUS Teaching (2008), Technische Universität Berlin

System equation and transfer System equation and transfer functionfunction

• The force equilibrium for a viscously damped SDOF structure:

)()()()( tftKxtxCtxM =++ &&&

• Transforming this time domain equation into the Laplace domain:

)()()( 2 pFpXKCpMp =++

)()()(

)()()(

pFpXpZor

pFpXKCpMp

=

++

where Z is the dynamic stiffness. Inverting Z gives the transfer function:

)()()( ppp

)/()/(/1

)()()( 2 MKpMCp

MpFpXpH

++==


System poles, naturalSystem poles, naturalERASMUS Teaching (2008), Technische Universität Berlin

System poles, natural System poles, natural frequencies, damping ratiosfrequencies, damping ratios

Th d i t f th ti• The denominator of the equation

)/()/(/1

)()()( 2 MKpMCp

MpFpXpH

++==

is referred to as the system characteristic equation. Its roots are called the system poles which are given by:

)/()/()( MKpMCppF ++

system poles which are given by:

If h i d i h d id i i i

)/()2/()2/( 22,1 MKMCMC −±−=λ

• If there is no damping, the system under consideration is a conservative system (C=0).The undamped natural frequency (rad/s) is then defined as:

MK /Ω MK /1 =Ω


System poles naturalSystem poles naturalERASMUS Teaching (2008), Technische Universität Berlin


• The critical damping Cc is the damping value that makes the term under the square root of the equation

)/()2/()2/( 2CCλ

equal to zero:

)/()2/()2/( 22,1 MKMCMC −±−=λ

MKMC /2=• Fraction of critical damping or damping ratio is:

MKMCc /2=

CC /=ξ

• The first equation yields in the time domain a solution to the homogeneous system equation:

cCC /1 =ξ

system equation:tt exextx 21

21)( λλ +=




• Depending on the value of the damping ratio, the systems are classified as overdamped (ζ1>1), critically damped (ζ1=1) or underdamped (ζ1<1) systems.

• The response of overdamped systems consist of a decay only. They have no tendency to oscillation.

• The response of underdamped systems is a decaying oscillation.

• Critically damped systems form the border case between over and underdamped systems. For real world systems, the damping ratio is rarely larger than ten percent unless the system contains some active damping mechanisms.

• Here only the underdamped case will be considered.



System poles, natural System poles, natural frequencies, damping ratiosfrequencies, damping ratiosq p gq p g

• The equation

)/()2/()2/( 2CCλ

• Yields two complex conjugate roots

)/()2/()2/( 22,1 MKMCMC −±−=λ

• Yields two complex conjugate roots

111111 * ωσλωσλ jj −=+=

• Where σ1 is the damping factor and ω1 is the damped natural frequency

12

111 )1( Ω−+−= ζζλ j 1111


ResiduesResiduesERASMUS Teaching (2008), Technische Universität Berlin

ResiduesResidues• With the knowledge of the equationg q

the equation for the transfer function

111111 * ωσλωσλ jj −=+=

the equation for the transfer function

)/()/(/1

)()()( 2 MKpMCp

MpFpXpH

++==

becomes:)/()/()( MKpMCppF ++

))((/1)( *

1 1λλ −−

=pp

MpH

Applying the theory of partial fraction expansion yields:*

1 /1 MAA

In this formula A1 and A1* are the residues.

11*

11

1

2/1with

)()()( 1

ωλλ jMA

ppApH =

−+

−=


1 1

Frequency response functionERASMUS Teaching (2008), Technische Universität Berlin

Frequency response function• The previous section discussed the relation between input (force) and

output (displacement) of a single degree of freedom system in the Laplace domain.

• This relation can also be expressed in the frequency domain. The transfer function evaluated along the frequency axis (jω) is called the frequency response function (FRF).

)()()()( *

1

*

1

1 1

λωλωω

ω −+

−==

= jA

jAHpH

jp

• The FRF is a subset of the transfer function. The contribution of the complex conjugate part (or negative frequency part) is negligible around resonance Therefore the FRF for SDOF system is often approximated by:resonance. Therefore, the FRF for SDOF system is often approximated by:

)()( 1

λωω

−=

jAH


)( 1λωj

Impulse response functionERASMUS Teaching (2008), Technische Universität Berlin

Impulse response function• Inverse Laplace transforming the expression for the transfer functionInverse Laplace transforming the expression for the transfer function

)()()()( *

1

*

1

1 1

λωλωω

ω −+

−==

= jA

jAjHpH

jp

yields the expression in the time domain: the impulse response function.

)()( 11 λωλω jj

)()( 111*11 ** tjtjttt AAAAh ωωσλλ −

The residue A1 is the real part of the pole which defines the initial amplitude σ is the imaginary part of the pole which defines the decay rate

)()( 1

1

111

1

111

tjtjttt eAeAeeAeAth ωωσλλ +=+=

amplitude, σ1 is the imaginary part of the pole which defines the decay rate and ω1 is the frequency of oscillation.

Th i l f t i th t t Di• The impulse response of a system is the system response to a Dirac impulse at time t=0.



Multi degree of freedom Multi degree of freedom systemssystemssystemssystems

System equation and the transferSystem equation and the transferERASMUS Teaching (2008), Technische Universität Berlin

System equation and the transfer System equation and the transfer functionfunction

Th ti f ti i• The equation of motion is:

{ } { } { } { }fxKxCxM =++ ][][][ &&&

• If we transform this time domain equation into the Laplace domain (variable p), assuming the initial displacements and velocities are zero yields:

[ ] [ ] [ ] { } { }[ ]{ } { })()()(

)()()( 2

pFpXpZpFpXKCpMp

==++

where [Z(p)] is the dynamic stiffness matrix. The inverse of [Z(p)] is [H(p)]

[ ]{ } { })()()( ppp

{ } [ ]{ }{ } [ ]{ })()()( pFpHpX =




• Standard calculus proves that the inverse of a matrix can be calculated from its adjoint matrix:

[ ] [ ] [ ])(

)()()( 1

pZpZadjpZpH == −

• Where adj([Z(p)]) is the adjoint matrix of [Z(p)] which can be expressed as.

column and row without )],([ oft determinan the:

][)])(([

jipZZ

ZpZadj

ji

tjiij= ε

)]([ oft determinan the:)(

odd is if -1even; is if ,1

pZpZ

jijiij +=+=ε




• The frequency response function can be written as:

][][)]([)]([*kk

m AAjHH ∑• The individual term can be written as:

)(][

)(][)]([)]([ *

1 k

k

k

k

kjp jj

jHpHλωλω

ωω −+

−== ∑

==

The individual term can be written as:

)()()( *

*

1 k

ijk

k

ijkm

kij j

a

ja

jhλωλω

ω−

+−

=∑=

• hij(ω) means a particular output response at point i due to an input force at point j. Since [M], [C], [K] are symmetric, [H(j ω)] is also symmetric. This implies that hij=hji which is called reciprocity. This means that you can measure the FRF byhij hji which is called reciprocity. This means that you can measure the FRF by impacting point i and measuring the response at point j and get exactly the same FRF as impacting point j and measuring the response at point i. This is what is meant by reciprocity.



ResiduesResidues• The residues are directly related to mode shapes and a scaling factor as:

• This shows that the frequency response function can be written in terms of idresidues.

• When written as a mode shape, then it becomes very clear that if the value p , yof the mode shape at the reference point is zero (or almost zero) then that mode will not be seen in the frequency response function.

• Always select a reference point where all the modes can be seen all the time from that reference point.



ResiduesResidues• Never select the reference point at the node of a mode!


The big pictureThe big pictureERASMUS Teaching (2008), Technische Universität Berlin

The big pictureThe big picture• FRFs can be generated from residues and poles. The residues are directly

related to the mode shapes and the poles are the frequency and dampingrelated to the mode shapes and the poles are the frequency and damping of the system.



The big pictureThe big picture• First let's start with an analytical

representation such as the finiterepresentation such as the finite element model shown. Basically, we use the FEM to approximate a lumped mass system that islumped mass system that is interconnected by springs to represent the physical system.

• Since the analytical approximation is described in terms of a force balance for each mass that isbalance for each mass that is described in the system, we end up with one equation for each mass (or degree of freedom) used todegree of freedom) used toapproximate the system.



The big pictureThe big picture• Since we need many small little

finite elements to accuratelyfinite elements to accurately describe the system, I end up with many equation and unknowns.

• Right away, it becomes convenient to describe all these equations

i t i N I husing matrices. Now once I haveassembled all these equations, a mathematical routine called aneigensolution is used to representeigensolution is used to represent the system in simpler terms - the system's frequencies and mode shapes This is what we do in theshapes. This is what we do in the finite element process.



The big pictureThe big picture• I can take those same equations

and transform them into theand transform them into the Laplace domain.

• Now in the Laplace domain, we have, [B(s)], the system equation and its inverse,[Hs)], the system t f f ti N k th ttransfer function. Now we know that this inverse is the adjoint of the system matrix (or the cofactors ofthe system matrix) divided by thethe system matrix) divided by the determinant of the system matrix. This inverse is described in all vibrations text booksvibrations text books



The big pictureThe big picture• It turns out that the adjoint matrix

contains the modal vectors and wecontains the modal vectors and we call this the Residue Matrix.

• The determinant of [B(s)] contains the roots, or poles of the system. Well, this is the same basici f ti th t i bt i d f thinformation that is obtained from the analytical model.

• So we could determine the system dynamic characteristics from eitherthe analytical model or from the Laplace domain representation -they both will give the same results.

• .



The big pictureThe big picture• Now another important relationship p p

is the Frequency ResponseFunction, FRF. This is the system transfer function evaluated along the jω axis. The FRF is actually a matrix of terms, [H(jω)].

• Well, since we are dealing with a matrix, it is convenient to identify input-output measurements with ap psubscript. So a particular output response at point 'i' due to an input force at point 'j' is called hij(jω).p j (j )

• .



The big pictureThe big picture• Now what we need to realize is that

those FRFs that were generated (synthesized) contain information relative to the system characteristics.

• Remember that the FRFs can beRemember that the FRFs can begenerated from residues and poles. And that the residues are directly related to the mode shapes and the ppoles are the frequency and damping of the system.

..



The big pictureThe big picture



The big pictureThe big picture• Up until now we have only discussed p y

using the mass, damping and stiffness approximations to compute system characteristics from the finite element model or from the Laplace domain representation of the system.

• Both these approaches use approximations of the physical parameters of mass, damping and p , p gstiffness to describe the system and sothey will both provide the same basic information.

.



The big pictureThe big picture• If there were some other way to y

estimate those FRFs without assumingphysical properties then I could employ the modal parameter estimation techniques to extract the desired information. This is where modal testing comes in.

• Basically, my structure is excited with some measured force. The response of the system due to the applied force is measured along with the force. Nowthis time data is transformed to the frequency domain using the FFT and basically a ratio of output response to input force is computed to form an approximation of the FRF.

P. Gundes Bakir, Vibration based structural health monitoring 56.


The big pictureThe big picture• So we could measure one input-output p p

FRF based on this approach. If we used a shaker to excite the structure and move the accelerometer to many points then we could measure acolumn of the FRF matrix. So the big advantage of making measurements is that I measure the response of the system due to the applied force – Idon't ever make any assumptions as to th d i d tiff f ththe mass, damping and stiffness of the system - and I avoid any erroneousapproximations I may make. Ofco rse I need to make s re that Icourse, I need to make sure that I make very good measurements otherwise I will distort my system characteristics


characteristics.

.


Vib ti it i iVib ti it i iVibration monitoring in Vibration monitoring in buildingsbuildingsbuildingsbuildings

Seismic behaviour and performanceSeismic behaviour and performanceERASMUS Teaching (2008), Technische Universität Berlin

Seismic behaviour and performance Seismic behaviour and performance of structural systemsof structural systems

There are three main approaches to evaluate seismic behavior and performance of structural systems (Celebi et al ):and performance of structural systems (Celebi et al.):

1. Laboratory Testing

2. Computerised analysis

3. Natural Laboratory of the Earth:Integral to the “natural laboratory” approach is the advance instrumentation of selected structures so that their responses can be recorded during futurestructures so that their responses can be recorded during future earthquakes.


Structural responseStructural responseERASMUS Teaching (2008), Technische Universität Berlin

Structural responseStructural responseThe methods used in studying structural response records are quite diverse:

(a) Mathematical modeling (finite element models varying from crude to very ( ) g ( y g ydetailed, subjected to timehistory, response spectrum or modal analyses). The procedure requires the blueprints of the structures which may not be readily accessible;

(b) System identification techniques: single input/single output or multi input/multi output. In these procedures, the parameters of a model are adjusted for consistency with input and output data (Ljung 1987);adjusted for consistency with input and output data (Ljung, 1987);

(c) Spectral analyses: response spectra, Fourier amplitude spectra, autospectra Sx or Sy cross spectral amplitudes Sxy and coherenceautospectra, Sx or Sy, cross-spectral amplitudes Sxy, and coherence functions ( γ) [using the equation : γ2

xy (f) = S2xy (f)/ Sx (f)Sy (f)] and

associated phase angles


Why do we instrument buildings?Why do we instrument buildings?ERASMUS Teaching (2008), Technische Universität Berlin

Why do we instrument buildings?Why do we instrument buildings?

• Improve our understanding of the behavior and potential for damage in structures under the dynamic loads of earthquakes.dynamic loads of earthquakes.

• Emergency response : A detailed real time hazard analysis i b i tin urban environments

• Improvement in mathematical models: An instrumentationmodels: An instrumentation program should provide enough information to reconstruct the response of the structure in enough detail to compare with theenough detail to compare with the response predicted by mathematical models and those observed in laboratories.




• Damage detection: Explain the reasons for any damage to structures• Damage detection: Explain the reasons for any damage to structures

• Quantify the interaction of the soil and the structure: The nearby free-field and ground-level time history should be known in order to quantify thefield and ground level time history should be known in order to quantify the interaction of soil and structure.

• Determine the importance of nonlinear behavior on the overall and local f th t tresponse of the structure,




• Follow the spreading nonlinear behavior throughout the structure• Follow the spreading nonlinear behavior throughout the structure as the response increases and determine the effect of this nonlinear behavior on the frequency and damping

• Correlate the damage with inelastic behavior

• Determine the ground motion parameters that correlate well with• Determine the ground-motion parameters that correlate well with building response damage

• Make recommendations to improve the building codes• Make recommendations to improve the building codes

• Facilitate decisions to retrofit/strengthen the structural system as well as securing the contents within the structureswell as securing the contents within the structures




• Determine whether the structure has to be retrofitted or not in an• Determine whether the structure has to be retrofitted or not in an objective way following big earthquakes and aftershocks

• Determining the structural members and parts that have to be• Determining the structural members and parts that have to be retrofitted in the structure

• Determine the best retrofit technique• Determine the best retrofit technique

• Evaluating whether the intended benefit from retrofitting is obtained or notobtained or not

• Determine the maximum interstory drifts in the structure

• Providing an early warning system for traffic closure when the bridges are subjected to excessive wind loading




• Prediction of the behaviour of the buildings under future earthquakes• Prediction of the behaviour of the buildings under future earthquakes by monitoring their behaviour under small magnitude earthquakes or ambient vibrations.

• Real time assessment of the performance level of the structure following catastrophic earthquakes and aftershocks.

•• Immediate occupancy?Immediate occupancy?

•• Life safety performance level?Life safety performance level?•• Life safety performance level?Life safety performance level?

•• Collapse prevention?Collapse prevention?

•• Collapse??Collapse??




Th id l d d i h• The most widely used code in the United States, the Uniform Building Code (UBC-1997 and prior editions), recommends, for seismic zones 3 and 4 a minimum of three accelerographs be g pplaced:

in every building over six stories with– in every building over six stories with an aggregate floor areas of 5500m2 or more

– in every building over ten stories regardless of the floor area.




• UBC Code type instrumentation is• UBC-Code type instrumentation is illustrated in Figure.

• Experiences from past earthquakes show that the UBC minimum guidelines do not ensure

ffi i t d t t fsufficient data to perform meaningful model verifications.

• As an example, three horizontal accelerometers are required to define the horizontal motion of a floor (two translations and torsion).




• Rojahn and Matthiesen (1977) concluded that the predominant response of apredominant response of a high-rise building can be described by the participation of the first fourparticipation of the first four modes of each of the three sets of modes (two translations and torsion).translations and torsion).

• Therefore, a minimum of 12 accelerometers would beaccelerometers would be necessary to record these modes.



Why do we instrument buildings?Why do we instrument buildings?• If vertical motion and rocking are expected to be significant and

need to be recorded at least three vertical accelerometers areneed to be recorded, at least three vertical accelerometers are required at the basement level.

Thi f i i h i ll d h id l i• This type of instrumentation scheme is called the ideal extensive instrumentation scheme herein and is illustrated in the Figure.



Why do we instrument buildings?Why do we instrument buildings?• Diaphragm effects are best captured by adding sensors at the• Diaphragm effects are best captured by adding sensors at the

center of the diaphragm as well as the edges.

• Performance of base-isolated systems and effectiveness of the isolators are best captured by measuring tri-axial motions at top and bottom of the isolators as well as the rest of the superstructure.




Engineers se free field motions as inp t motion at the fo ndation• Engineers use free-field motions as input motion at the foundation level, or they obtain the motion at foundation level by convoluting the motion through assumed or determined layers of strata to base rock and deconvoluting the motion back to foundation leveldeconvoluting the motion back to foundation level.

• To confirm these processes requires downhole instrumentation near or di l b h D h l d i lldirectly beneath a structure. Downhole data are especially scarce, although a few such arrays have been developed outside of the United States. These downhole arrays will serve to yield data on:

(1) the characteristics of ground motion at bedrock at a defined distance from a source

(2) the amplification of seismic waves in layered strata.



Steps in instrumenting Steps in instrumenting structuresstructuresstructuresstructures

Selection of Structures to beERASMUS Teaching (2008), Technische Universität Berlin

Selection of Structures to be Instrumented

1. Structural parameters: the construction material, structural system geometry discontinuity and agestructural system, geometry, discontinuity, and age

2 Site-related parameters:2. Site related parameters:

a. Severity-of-shaking factor to be assigned to each a Se e ty o s a g acto to be ass g ed to eacstructure on the basis of its closeness to one or more of the main faults within the boundaries of the area considered (e g for the San Francisco Bay area the Sanconsidered (e.g. for the San Francisco Bay area, the San Andreas, Hayward, and Calaveras faults are considered).




b. Probability of a large earthquake (M = 6.5 or 7 occurring on the fault(s) within the next 30 years was obtained. The purpose of this parameter is to consider the regions where there is strong chance ofparameter is to consider the regions where there is strong chance of recording useful data within an approximately useful life of a structure.

c. Expected value of strong shaking at the site, determined as the product of a and b.

3. Building usage, functionality, occupancy and relevance to life safety requirements following damaging earthquakes.

4. Other parameters of interest to owners or public officials.




Once the particular structure to be instrumented is identified, the engineering staff

• obtains instrumentation permits for selected structures

• gathers information relative to the project including structural plans and design and model informationstructural plans and design and model information

• directs structural evaluation and if necessary performsdirects structural evaluation and if necessary performs ambient response studies.




• study of available design and analysis information after permission• study of available design and analysis information after permission for instrumenting is granted by the owner,

• site visit• site visit

• required analytical studies and tests, if feasible and necessary.

• In general, the following information, if available, will be required:

(1) relevant blueprints and design calculations

(2) dynamic analysis (mode shapes and frequencies)( ) y y ( p q )

(3) if available, forced-vibration test results, and ambient-vibration test results.




• Seldom is all this information available for any structure.

• The collected set of data is then used as a basis for determining transducer locations that ill adeq atel define the response of the str ct re d ring alocations that will adequately define the response of the structure during a strong earthquake.

• After the sensor locations have been agreed upon by the engineering staffAfter the sensor locations have been agreed upon by the engineering staff, the installation team, a representative of the owner of the structure, and an electrical contractor is called in to plan placement of the data cable.

Th i ll i k i h h d i hi h d• The installation team works with the contractor during this phase and subsequently calibrates and installs sensors and recording systems. A final step is a complete documentation of each transducer location and orientation, characteristics of total system response, and any peculiarities of y p y pthe instrumentation or access to required sites.


Importance of Building Specific Free-ERASMUS Teaching (2008), Technische Universität Berlin

Importance of Building Specific FreeField Station

• If physically feasible, it is advisable to include into the instrumentation scheme, a building specific free-field station.

• Such a free-field station is usually deployed at a distance greater than 1.5-2 times the height of the nearest/tallest building. This is due to the desire that motions recorded by a free-field station should not be influenced by the shaking of the buildingsnot be influenced by the shaking of the buildings.

• In general, free-field and ground-level motions should be known in order to quantify the interaction of the soil and the structureorder to quantify the interaction of the soil and the structure.

• However, data recorded at building specific free-field stations can be used to augment data bases used for structural response studies asused to augment data bases used for structural response studies as well as ground motion studies including development of attenuation relationships and quantification of site response transfer functions and characteristics.


Tests on Existing Structures toERASMUS Teaching (2008), Technische Universität Berlin

Tests on Existing Structures to Determine Dynamic Characteristics

• Although it is possible to obtain a satisfactory understanding of a structure's expected dynamic behavior by preliminary analytical studies, an ambient-vibration and/or a forced vibration test on an existing structure can be performed to identify mode shapes andexisting structure can be performed to identify mode shapes and frequencies.

• Ambient vibration tests can be performed efficiently using portable• Ambient vibration tests can be performed efficiently using portable recorders at three to five locations that are expected (from analytical studies or other information) to have maximum amplitudes during the first three to four vibrational modes.

• Thus, elastic properties of the structure can be determined. If the subject structure experiences nonlinear behavior during a strong j p g gshaking, it will be much easier to evaluate the nonlinear behavior once linear behavior is determined before the nonlinear behavior occurs during the strong shaking.


Tests on Existing Structures toERASMUS Teaching (2008), Technische Universität Berlin

Tests on Existing Structures to Determine Dynamic Characteristics

• Compared to ambient vibration test a forced vibration test is• Compared to ambient-vibration test, a forced-vibration test is more difficult to perform. The required equipment (vibration generator with control consoles, weights, recorders, accelerometers, and cables) is heavier, and the test takes longer than the ambient-) , gvibration test.

• State-of-the-art vibration generators do not necessarily have the g ycapability to excite to resonance all significant modes of all structures (Çelebi and others, 1987).

• Dynamic Analysis• A simplified finite-element model can be developed to obtain the

elastic dynamic characteristics.

• This is performed with any one of the several tested computer programs available (e.g. SAP2000, ANSYS, and STRUDL).



Selection and installation of Selection and installation of instrumentsinstrumentsinstrumentsinstruments

Selection and installation of instrumentsSelection and installation of instrumentsERASMUS Teaching (2008), Technische Universität Berlin

Selection and installation of instrumentsSelection and installation of instruments

• In selection and defining an• In selection and defining an instrumentation scheme, an optimum list of hardware is developed after careful pconsideration of cost and data requirements.

• While developing the instrumentation scheme within the budgetary constraints, it is best to consider the maximum availableconsider the maximum available channels for each recording system. Most recording systems have maximum of 12 or 18 channels of recording capability.




• The following general approach is followed• The following general approach is followed to install seismic instruments:

1. After an instrumentation scheme is developed and approximate sensordeveloped and approximate sensor locations are chosen, monitoring team and the owner's representative review the site to determine exact sensor locations and routing of cableslocations and routing of cables satisfactory to both parties.

This is important from viewpoint of long-term accessibility potential interferenceterm accessibility, potential interference with the occupant's space, placement of data cable runs, and aesthetic requirements of the owner.

Figure exhibits a sample schematic showing locations of sensors, routing of cables, location of junction boxes and recording units.


g



2 N t t h i i h ld i t th ti t t l h2. Next a technician should inspect the entire structural scheme with an electrical contractor who will install the data cable, junction boxes at key locations and terminal boxes (if required) t h it Th d di t tat each sensor site. The modern recording systems may not

require terminal boxes as they have internal terminals. Actual cabling by the contractor is monitored by the monitoring team and the owner's representative to be sure the cable is installedand the owner s representative to be sure the cable is installed as desired and that all building code regulations are followed.

3. The cable-termination box includes data circuits, batteries and battery charges. This box is normally mounted on the wall above the recorder. The recorder location is selected on the basis of

it t i ll i t l h l t i l it h d isecurity, typically in a telephone or electrical switch room, and in some circumstances is enclosed with separate fencing in an open area.




4 Th i t t ti d li i4. The instrumentation undergoes a preliminary calibration in the strong-motion laboratory and is then installed in the structure with appropriate test

d i l di t ti tilt iti it t t fprocedures including a static tilt sensitivity test for each component and determination of direction of motion for upward trace deflection on the record.

For modern digital systems, this information is entered into the recorder data section and is stored in ainto the recorder data section and is stored in a general database.

Other documentation includes precise sensor location, period and damping of each unit, location of cable runs, access information, and circuit diagrams.


, , g

Sensor locationsSensor locationsERASMUS Teaching (2008), Technische Universität Berlin

Sensor locationsSensor locations• The number of required sensors and sensor locations depend on the• The number of required sensors and sensor locations depend on the

condition that whether 2 dimensional or 3 dimensional motions of the structure are going to be monitored.

• In 2 dimensions, the degrees of freedom are 2 translations and one rotation.

• A typical example to such a structure is a multistorey building with shear ll d i id di hwalls and a rigid diaphragm.

• In order to determine these two translations and one rotation, three measurements are neededmeasurements are needed.

• These three measurements have to satisfy the following conditions:

– The measurements have to be taken from two separate locations– The three measurement directions should not be parallel.– The three measurement directions should not intersect each other.



Sensor locationsSensor locations• In 3 D space the vibrations of the structure can be fully described by• In 3 D space, the vibrations of the structure can be fully described by

3 translations and 3 rotations.

• In such a structure we need at least 6 measurements which have to• In such a structure, we need at least 6 measurements which have to satisfy the following conditions in order to solve for the 3 rotations and 3 translations from the dynamic equilibrium equations:

– The measurements have to be taken at least from 3 separate locations.

– The measurement locations should not be on a straight line.The measurement locations should not be on a straight line.

– The 6 measurement directions should not be parallel.

– The 6 measurement directions should not intersect each other.



Sensor locationsSensor locations• Sensor locations should not be determined based on the locations of• Sensor locations should not be determined based on the locations of

maximum displacements, because that displacement can be dominated by a single mode. That means, if you put a sensor there you would only identify that mode. The location you should search for is the one whose displacement has contrib tions from a ma im m n mber of modes Thatdisplacement has contributions from a maximum number of modes. That way you can identify more modes (Şafak,2009).

• For typical multi-story buildings there is no reason to put a vertical sensor inFor typical multi story buildings, there is no reason to put a vertical sensor in the middle of floor slab, unless it has a huge span with no beams and columns to support it. Even then, it would record only the local behavior of the floor slab, not the global behavior of structural system, which is more important when matching analytical models (Şafak 2009)important when matching analytical models (Şafak,2009).

• For torsion, the larger the distance between the two parallel horizontals, the more accurate the calculated torsion (i e the better the signal to noise ratiomore accurate the calculated torsion (i.e., the better the signal to noise ratio in the torsional signal) (Şafak,2009).

P. Gundes Bakir, Vibration based structural health monitoring 88•


Sensor locationsSensor locationsI l h d f l iIn general the order for placing sensors:• Roof• Ground floorGround floor• Basement• Any location where stiffness and/or mass changes significantly• Any location where the curvature of the deformed shape is expected

to change.


Sensor locations in buildingsSensor locations in buildingsERASMUS Teaching (2008), Technische Universität Berlin

Sensor locations in buildingsSensor locations in buildings1 The first group of sensors should be located on the roof of structures1. The first group of sensors should be located on the roof of structures.2. The second group of sensors should be placed on the top of the

foundations (in the ground floor or basement).3. The third group of sensors should be placed at the locations where the3. The third group of sensors should be placed at the locations where the

rigidity and the mass of the structure change. 4. The rest of the sensors should be placed on locations where the

amplitudes of the vibration modes of the structure are expected to be largelarge.


Optimal sensor placementOptimal sensor placementERASMUS Teaching (2008), Technische Universität Berlin

Optimal sensor placementOptimal sensor placement

1. Effective Independence Technique

2. Optimum Driving Point Based Method

3. Non-optimum driving point based method

4 EFI Driving point residue method4. EFI- Driving point residue method


Effective IndependenceEffective IndependenceERASMUS Teaching (2008), Technische Universität Berlin

Effective Independence Effective Independence TechniqueTechniqueTechniqueTechnique





where Q is the Fisher information matrix



The best state estimate can be obtained by maximizing Q which results in the minimization of the covariance matrix For simplicity it is assumedthe minimization of the covariance matrix. For simplicity, it is assumed that the measurement noise is uncorrelated and possesses identical statistical properties of each sensor. The Fisher Information Matrix can then be simplified as:then be simplified as:


Effective Independence Effective Independence TechniqueTechnique


Non-Optimum driving point based method


Optimum driving point based method


Effective Indepence Driving Point Residue Technique


MaintenanceMaintenanceERASMUS Teaching (2008), Technische Universität Berlin

MaintenanceMaintenance• It is essential to have periodic and consistent maintenance of instruments in• It is essential to have periodic and consistent maintenance of instruments in

order to have a successful program. Unless maintenance arrangements are made, successful recording of data cannot be accomplished. Therefore, routine maintenance is conducted every 3-12 months if circumstances and e perience so alloexperience so allow.

• This maintenance includes the following:

1. Remote calibration of period and damping.

2. Inspection of battery terminals, load voltage, and charge rate (batteries are p y g g (replaced every 3 years).

3. Measurement of threshold of triggering system and length of recording cycle.

• As a final maintenance procedure, a calibration record is obtained and then examined for the desired characteristics. All inspection procedures are recorded in the permanent station file at the laboratory.


GPS unitsGPS unitsERASMUS Teaching (2008), Technische Universität Berlin

GPS unitsGPS unitsUntil recently in general only accelerometers (single• Until recently, in general, only accelerometers (single, biaxial or triaxial) were used to instrument structures.

• However, observations of damages during the 1994 Northridge and 1995 Kobe earthquakes, have forced engineers and scientists to focus on performanceengineers and scientists to focus on performance based seismic design methods and to find new techniques to control drift and displacements.

• To verify these developments, sensors directly measuring displacements or relative displacements g p p(transducers, laser devices and GPS units) are now being considered.


assoc prof dr pelin gundes bakirassoc. prof. dr. pelin ...web.itu.edu.tr/~gundes/introduction to...

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