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OUTPUT-ONLY MODAL ANALYSIS: DEVELOPMENT OF A GUI FORMATLAB

Bart Peeters, Bart Van den Branden, Alexander Laquiere, Guido De RoeckDepartment of Civil Engineering, Katholieke Universiteit Leuven

W. de Croylaan 2, B-3001 Heverlee, BELGIUME-mail: Bart. Peeters@ bwk.kuleuven.ac.be

ABSTRACTIn this paper the development of a Graphical User Interface(GUI) for Matlab is described. The simple peak-picking methodas well as the more advanced stochastic subspace method areimplemented in a user-friendly way. By pushing buttons theuser is guided through the whole process of output-only modalanalysis: converting measurements to engineering units,preprocessing the data, system identification, extracting modalparameters from a stabilisation diagram, "gluing" mode shapeparts together (typically for output-only modal analysis),animating mode shapes, . . .NOMENCLATUREf~

ANPSDDOF(s)OFTFRF(s)GUIMACECppSIMCESSSISVD

frequencydamping ratiostandard deviation of variable xdiscrete time instantnumber of outputsnumber of DOFssampled measurements ( EIR1x1 )state vector ( EIR2n2x1 )state matrix, discrete time model ( EIR2n2x 2n2 )output matrix ( EIR1x2n2 )process noise ( EIR2n,xl)measurement noise ( EIR1x 1 )Averaged Normalized Power-Spectral DensityDegree(s) Of FreedomDiscrete Fourier TransformFrequency Response Function(s)Graphical User InterfaceModal Analysis on Civil Engineering ConstructionsPeak PickingSystem Identification to Monitor Civil Eng. Struct.Stochastic Subspace IdentificationSingular Value Decomposition

1 INTRODUCTIONSystem identification is one of the tasks of the BRITE-EURAMproject SIMCES. In the context of the project civil engineeringstructures such as bridges are the considered systems andidentification means the extraction of modal parameters(eigenfrequencies, damping ratios and mode shapes) fromdynamic measurements. These modal parameters will serveas input to model updating and damage identificationalgorithms in order to detect and locate possible damage inthe structure. In this paper -as in the SIMCES project- attentionis focussed on output-only modal analysis: the input isunmeasured ambient excitation and by consequence no inputmeasurements are available.There exist many modal analysis software packages. Originallydeveloped in mechanical engineering for identification basedon input/output data (FRFs), today some of these packageshave also modules for output-only modal analysis (e.g. recentrevision of LMS CADA-X [2]). However most commercialdedicated software packages have some drawbacks in aresearch environment: it is impossible to view how analgorithm has been implemented and it is often notstraightforward to add own developments to these packages.Matlab [3] on the other hand is a program that offerscomputation, visualization and programming tools. The basicpackage has a lot of building blocks that can be used to makemore application-specific toolboxes. Most of the functions areaccessible ASCII-files which are compiled at their first call ina session; so the user can learn from their implementation oreven modify it. Some existing toolboxes in the field of systemidentification and modal analysis will be briefly reviewed.Both the System Identification Toolbox [4] and the FrequencyDomain System Identification [5] offer data preprocessing,identification and model validation tools. The first fits timedomain models to the data whereas the latter operates in thefrequency domain. These toolboxes have been written by

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people with an electronic engineering background, but sincethey can identify any linear dynamic system frommeasurements, they can also be used in civil engineering (abridge is assumed to be a linear dynamic system). Howeverboth toolboxes only offer a mathematical model that best fitsthe data but the need remains to extract the modal parametersfrom the model and to plot them in stabilisation diagrams forincreasing model order to allow the user to select stable poles.Further it is necessary to combine different setups sincebridges are large structures that cannot be measured in onesetup and finally a visualization of the structures geometry andits mode shapes is essential.Next to official toolboxes supported and distributed by TheMathWorks, there exist also many toolboxes in a connectionprogram [6] for Matlab-related third party products. One ofthese products is the Structural Dynamics Toolbox [7], thatoffers possibilities in experimental modal analysis, finiteelement analysis and updating. The toolbox has geometry andmode shape visualization possibilities. However identificationis based on FRFs and therefore not suitable for output-onlymodal analysis.

2 DEVELOPMENT2.1 HistoryFrom the previous section it is clear that the need arose todevelop an own program for output-only modal analysis. Lastyears some stochastic system identification and modalanalysis algorithms were tried out and implemented in Matlabat the department of civil engineering, K.U.Leuven. Thesealgorithms can be executed by typing in the Matlab commandwindow the name of the function together with the input andoutput variables. For instance:

[ a , k , c , r ] = s s i { y , i , n ) ; (1)applies the stochastic subspace identification algorithm(section 3.2) to the data matrix y, according to someparameters i and n, resulting in the stochastic state spacemodel a, k, c , r . The difficulty with all these functions is thatone has to know the syntax and keep track of all variables.Therefore a MSc-project [8] was set up in order to build aGraphical User Interface (GUI) incorporating most of theexisting functions for data conversion, system identificationand adding functions for mode shape animation. In stead oftyping in commands, the user just has to click buttons. (1) isreplaced by clicking the Apply button:

There might exist better environments to create a GUI (e.g.Delphi), but none of these have the efficient computation andpowerful 20 and 30 visualization possibilities of Matlab. Also

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algorithm development is very easy in Matlab, because of theinteraction between the function under development and theworkspace: the programmer can always control the state of thevariables. A disadvantage of using Matlab for developing aGUI could be that the result is not a stand-alone program butthat the user needs Matlab to run it.2.2 GUis in Matlab [9)The first step in building a GUI is its design. The principles ofgood design are universal and not restricted to theenvironment used to build the GUI. The design of the GUI assuch will not be treated. The second step is theimplementation. It divides into screen layout and Callbackhandling. [9]: "This is the difference between how the screenlooks versus what it does when you interact with it." To explorethe possibilities concerning screen layout, it is useful todiscuss shortly Matlabs Handle Graphics object hierarchy(figure 1 .RootF ItgureAxes Uicontrol UimenuImage Light Line PatchFigure 1: Handle Graphics object hierarchy.

Surface Text

Every object on the screen has a unique identifier, called ahandle that allows to modify the object at any time. The Rootobject (figure 1) is the screen and a Figure object is a window.Every Figure can consists of Axes, Uicontrols and Uimenus.The Uimenus are the classical menus and submenus at thetop of a window (e.g. file, !;dit, . . . !::!elp). Uicontrols can beplaced anywhere on a window. There exist 9 styles ofUicontrols: pushbuttons, radio buttons, sliders, etc. Althoughthe number of available Uicontrols is rather limited (probablydue to the fact that the applications built within Matlab shouldrun on different platforms: Windows, Unix, Mac), it is possibleto create quite advanced GUis. Finally the Axes can visualizedata; they consist of Images, Lines, Text, etc. Since version 5,Matlab has a tool to create graphically a GUIIayout. It is in facta GUI to create a GUI and is called GUIDE (Graphical UserInterface Development Environment) [9].2.3 Design and implementation of MACECAfter the more general discussion of previous section, theimplementation of MACEC is discussed here. MACEC standsfor Modal Analysis on Civil Engineering Constructions. Thepossibilities and features will be discussed later. Twoquestions are very important when designing a GUI [9]:1. Do the users always know where they are?2. Do they always know where to go next?In order to get positive answers to these questions MACEC isconstructed around one main window (figure 2), that is divided

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into three main tasks: preprocessing - system identification -visualization. To perform each of these tasks a new window isopened and after the user has gone through all desiredfeatures of the task, the window is closed and the user returnsto the main window.

Figure 2: MACEC main window.

To implement MACEC Matlabs GUIDE (section 2.2) was notused. It was the authors' experience that it became too slow asthe complexity of the interface increased. Also it was difficultto keep control of every detail of the implementation withGUIDE. Therefore the screen layout was programmed on alow-level (e.g. manually typing of coordinates of buttons).Further the implementation was inspired by chapter 6 of [1 0].For every window of MACEC only one function was writtenincorporating the screen layout as well as the Callbackhandling (the Callbacks of the Uicontrols recall the samefunction that created the Figure but with different inputarguments). Every function consists of three parts (see [8, 10]for more details):1. Initialization (if the Figure does not already exist):

A Figure is created together with Uimenus, Uicontrols andAxes. The handles to all these objects are stored in theUserData - property of the Figure.

2. Retrieve all handles (if the Figure already exists):By executing the Callbacks (part 3), some of the objectsof the Figure may change and hereto the handles of theobjects are required. These were stored in the FiguresUserData (part 1).

3. Writing Callbacks (a Callback defines what happens if forinstance a button is pushed):Switchyard programming is used [9] to be able to defineall Callbacks in one function.

To make the user more familiar with the toolbox, someattention was paid to give it a "Windows 95/NT4-Iook": Some of the pushbuttons have standard Windows images

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Frames that group a set of Uicontrols and/or axes areembossed.

Typical dialog boxes are used:

If a Figure is resized, only the Axes are resized and notthe Uicontrols (buttons, . . . .

3 OUTPUT-ONLY MODAL ANALYSISBefore giving an overview off all possibilit ies of MACEC, sometheory behind the core of the toolbox (i.e. system identification)is explained. Currently two identification methods that can dealwith the output-only case are implemented. The first is the verysimple peak-picking method. It has some theoreticaldrawbacks, but it is very practical: the method is very fast andcan be used on site allowing a quality check of the acquireddata. The second method is complementary; it is thestochastic subspace method: slower than peak-picking butyielding more accurate results so that it can be usedafterwards, back at the office, to analyse the data into moredetail.Common to all output-only identification methods is theassumption that the system is excited by a white noise input.Violation of this assumption will lead to identification ofadditional modes which are not due to the system but due tothe non-white noise character of the input. Also because theinput remains unknown, it is not possible to obtain an absolutescaling of the identified mode shapes (e.g. mass-normalization).3.1 Peak-Picking {PP)In this method the natural frequencies are determined as thepeaks of the Averaged Normalized Power-Spectral Densities(ANPSDs). The ANPSDs are basically obtained by convertingthe measured accelerations to the frequency domain by aDiscrete Fourier Transform (OFT). The coherence functioncomputed for two simultaneously recorded output signals hasvalues close to one at the natural frequencies [11]. This factalso helps to decide which frequencies can be considered asnatural. The components of the mode shapes are determinedby the values of the transfer functions at the naturalfrequencies. Note that in the context of ambient testing,transfer function does not mean the ratio of response overforce, but rather the ratio of response measured by a rovingsensor over response measured by a reference sensor. Soevery transfer function yields a mode shape componentrelative to the reference sensor. Here it is assumed that thedynamic response at resonance is only determined by one

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mode. The validity of this assumption increases as the modesare better separated and as the damping is lower.In spite of the drawbacks of the method (picking the peaks isoften a subjective task; operational deflection shapes areobtained in stead of mode shapes and the damping estimatesare unreliable), it is often used in civil engineering practicebecause it is fast and easy to apply.3.2 Stochastic subspace identif ication (SSI}It is beyond the scope of this paper to explain in full detail thestochastic subspace identification method. The interestedreader is re ferred to li terature ([12] for the theory and [13, 14]for civil engineering applications). Here only the main ideasbehind the method are given.The method assumes that the dynamic behaviour of astructure excited by white noise can be described by astochastic state space model (this statement can be justified[13]):

xk+1 = Axk + wkYk = Cxk + vk (2)

(The symbols are explained in the nomenclature at thebeginning of the paper). The subspace method than identifiesthe state space matrices based on the measurements and byusing robust numerical techniques such as OR-factorization,SVD and least squares. Loosely said, the OR results in asignificant data reduction, whereas the SVD is used to rejectthe noise (assumed to be represented by the higher singularvalues). Once the mathematical description of the structure(the state space model) is found, it is straightforward todetermine the modal parameters (by an eigenvaluedecomposition): natural frequencies, damping ratios and modeshapes. SSI is a time domain method that directly works withtime data, without the need to convert them to correlations orspectra.

4 FUNCTIONS OF MACECThe main functions of MACEC are reviewed. Some of them willbe illustrated with Z24-bridge vibration data (section 5). Thefunctions can be divided into three categories: preprocess ing-system identification - visualization.4.1 PreprocessingThe raw time data can be imported into the program in ASCII-format or a more efficient binary format. Before further analysisthe data is converted into an internal format (*.sit: SystemIdentification Toolbox-format): if the data was stored in Volts[V], it is scaled to obtain accelerations [m/sec2]. The scaling isvery easy, once the user has created an ASCII-file containingthe sensitivities of all his sensors (figure 3).

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Figure 3: Scaling data from Volt to accelerations, by selecting theused sensor and specifying the amplification.

It is also possible to incorporate the physical locations of themeasurement points and axis (node numberand DOF) into thesit-format. If the sensitivity axis of a sensor does not coincidewith one of the global axis, it can be defined with two angles:ar=]-180,180], the angle in the xy-plane; and E [ -90 ,90c],the angle perpendicular to the xy-plane (figure 4).

Figure 4: Definition of a sensitivity axis.Next the true preprocessing can begin. Preprocessing is thedata treatment before system identification and it highlyinfluences the identification result. Following possibilities areimplemented: Decimate: the data is low-pass filtered and decimated; the

identification can concentrate on a limited frequency band. Detrend: the best straight line fit is removed from the data.

This removes the DC-component that can badly influencethe identification results.

No E/ec: removal of spurious frequencies (e.g. at 50 Hzdue to AC power supply). This operation is not the sameas stopband filtering, but it really removes only thecomponent at a certain frequency.

Delete channel: removal of a complete channel. Forinstance a very noisy channel can be better removed toimprove the identification result.Time window: a certain high-quality time segment can beselected for further analysis.

The effect of the preprocessing can be seen immediately , bothin time and frequency domain (figure 5).

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Figure 5: Time and frequency domain representation of channel10(setup 2) of the Z24-bridge test (section 5). Application ofpreprocessing tools.

4.2 System identificationAs already mentioned (section 3), two complementarymethods are implemented. If the user selects the Peak-Picking(PP) method, a window with the ANPSD is opened, the mousepointer changes into a cross-hair and the user can pick thepeaks (figure 6). Approximated mode shapes (operationaldeflection shapes) are determined at the selected frequencies.

Figure 6: The peak-picking process applied to Z24-bridge data.

The second method is the Stochastic Subspace Identification(SSI) method. First the user can specify some input-parameters of the algorithm: selection of channels, orderrange, . . . (figure 7).After some computations (OR, SVD), a stabilisation diagramis constructed, according to the input parameters of the SSI-algorithm (figure 8). Stabilisation diagrams show the stabilityof the poles as function of increasing model order. Spuriousmodes can be distinguished from physical ones. The user canchange the stabilisation criteria (default is 1% foreigenfrequencies, 5% for damping ratios and 1% for modeshape vectors). The better the quality of the data, the stricter

these tolerances can be set. The diagram is representedtogether with the ANPSD to stress the fact that the timedomain subspace identification algorithm found indeedeigenfrequencies at the peaks of the spectrum. The selectionof stable poles can be done graphically.

Figure 7: Specification of input parameters of SSI-algorithm.

Figure 8: Stabilisation diagram for pole selection in the SSI-methodapplied to Z24-bridge data.

4.3 VisualizationEvery setup of simultaneously measured channels yields afteridentification a part of the global mode shape. These parts areglued together with the aid of reference sensors, common toall setups. Least Squares approximation is used to determinethe scaling factor of a certain mode between two setups(figure 9).The DOFs were already attributed to the channels in thepreprocessing step (figure 4). Before visualization the locationof the nodes (grid) and the connection between the nodes(beams/surfaces) need to be defined. This is realized byloading two ASCII-files into the program: a grid-file and abeam- or surface-file. The grid-file contains 4 columns: nodenumber and coordinates. The beam-file contain 2 columns: aMatlab Line object is defined by 2 nodes; whereas the surface-

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file has 4 columns: 4 nodes define a Matlab Patch object(figure 1 . These files can easily be generated in MACEC withthe "beam/surface-generator'' [8]. Visualization of DOFs whichwere not measured can be done in a "slaving"-procedure: theunmeasured slave DOFs are related to measured masterDOFs.

ReferenceAmplitudes of modeX in setup 2

ReferenceAmplitudes ofmode X in setup 1Figure 9: Use of reference sensors toglue mode shape parts.

Now we are ready to visualize the mode shapes (Figure 10).The visualization window offers a lot of possibilities: scrollingthrough all modes, representation of undeformed structure andnode numbers, 3D-view with possibility to change theviewpoint, animation of mode shape, . . .

Moiie 1 f= 3.933Hz = 1 1%

Figure 10: First mode shape of Z24-bridge. The nodes areconnected with beams.

5 EXAMPLE: Z24-BRIDGEMACEC was not only tested with simulated or laboratory data,but also with real-life data from an ambient vibration test on abridge. The Z24-bridge is situated in Switzerland overpassingthe national highway A1 between Bern and Zurich. Moredetails on this bridge and how it was measured can be foundin [1, 15]. The data was sampled at a rate of 80 Hz and theanti-aliasing filter had a cut-off frequency at 20 Hz. A total of65536 samples (13 min, 39.2 sec) were acquired for eachchannel and each setup. 9 setups were necessary to scan thewhole surface of the bridge. The ambient excitation sources ofthe bridge were wind and traffic on the highway.

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This data was already used in previous sections (figures 5-1 0)to illustrate the functions of MACEC. Here only the estimatedmodal parameters are given (Table 1 . The statistics are basedon 9 samples: there were 9 setups and each resulted in onevalue for an eigenfrequency and a damping ratio. Figure 10represented already the first mode; the other identified modesare represented in figures 11-16.Table 1: Mean values and standard deviations (a xl ofeigenfrequencies and damping ratios obtained with stochasticsubspace identification (SSI).

mode2 6 7

SSI f [Hz] 3.93 5.22 10.10 10.75 12.8 13.7 19.7a 1 [Hz] 0.03 0.02 0.04 0.03 0.1 0.2 0.1

[%] 1.1 1.4 1.4 1.2 2.1 3.0 1.9[%] 0.5 0.3 0.4 0.3 0.6 1.3 0.4

6 CONCLUSIONSIn this paper the development of a GUI for Matlab wasdescribed. The goal was a complete and user-friendly packagefor output-only modal analysis (with civil engineeringapplications in mind). Matlab was used as developmentenvironment because of the large amount of computation andvisualization tools that are already present and also becauseit is a very open programming environment with access tomost of the code, allowing the programmer to easily modifyimplementations or add new features. The toolbox haspreprocessing, system identification and visualizationpossibilities that allow both a fast quality check of the data onsite (PP method) and a more accurate analysis afterwards(SSI method). The use of MACEC was demonstrated with real-life data from an ambient vibration test on a bridge.

ACKNOWLEDGEMENTSSven Vranckx is gratefully acknowledged for sharing hisexperience in Matlab GUI development.Part of the research has been carried out in the framework ofthe BRITE-EURAM Programme CT96 0277, SIMCES with afinancial contribution by the European Commission. Partnersin the project are: K.U.Leuven, Aalborg University, EMPA, LMSInternational, WS Atkins, Sineco, T.U.Graz.

REFERENCES[1] KRAMER, C. AND DE SMET, C.A.M. Brite-EuRam project

S/MCES (CT96-0277}, task A1: bridge testing, 2'd systemidentification of Z24 bridge. Technical Report 168'349/6,EMPA, Dubendorf, Switzerland, 1997.

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[2] LMS INTERNATIONAL. LMS GADA-X, modal analysismanual, revision 3.5. Leuven, Belgium, 1998.

[3] THE MATHWORKS. Using MATLAB, version 5.2. Natick,MA, USA, 1998.

[4] LJUNG L. System identification toolbox user's guide,version 4. The MathWorks, Natick, MA, USA, 1995.[5] KOLLAR, I. Frequency domain system identification toolbox

user's guide, version 2. The MathWorks, Natick, MA, USA,1995.

[6] THE MATHWORKS. MATLAB Connections. Available fromhttp : / /www-europe.mathworks.com/connect ions,Natick, MA, USA, 1998.

[7] BALMES, E. Structural dynamics toolbox user's guide,version 3. Scientific Software Group, Sevres, France,1997.

[8] LAOUIERE, A. AND VAN DEN BRANDEN, B. Multivariabelestochastische systeemidentificatie. MACEC, modalanalysis on civil engineering constructions. In Dutch, MSc-thesis, Dept. of Civil Eng., K.U.Leuven, Belgium, 1998.

[9] THE MATHWORKS. Building GUis with MA TLAB, version 5.Natick, MA, USA, 1997.

z

y

[10] MARCHAND, P. Graphics and GUis with MATLAB. CRCPress, Boca Raton, FL, USA, 1996.

[11] BENDAT, J.S. AND PIERSOL, A.G. Engineering applicationsofcorrelation and spectral analysis. 2"d edition, JohnWiley& Sons, New York, NY, USA (1993).

[12] VAN 0VERSCHEE, P. AND DE MOOR, B. Subspaceidentification for linear systems: theory- implementation -applications. Kluwer Academic Publishers, Dordrecht, TheNetherlands, 1996.

[13] PEETERS, B. AND DE ROECK, G. Stochastic subspacesystem identification of a steel transmitter mast. InProceedings of I MAC 16, the International Modal AnalysisConference, pp. 130-136, Santa Barbara, CA, USA(1998).

[14] PEETERS, B., DE ROECK, G., HERMANS, l. , WAUTERS, T.,KRAMER, C., DE SMET, C.A.M. Comparison of systemidentification methods using operational data of a bridgetest. In Proceedings of ISMA 23, the InternationalConference on Noise and Vibration Engineering, pp. 923-930, K.U.Leuven, Belgium, September 1998.

[15] KRAMER, C., DESMET, C.A.M., PEETERS, B. Comparison ofambient and forced vibration testing of civil engineeringstructures. In Proceedings of IMAC 17, the InternationalModal Analysis Conference, Kissimmee, FL, USA (1999).

.z .z

y y

Figure 11: 2nd mode (881). Figure 12: 3"' mode (8SI). Figure 13: 4'h mode (8SI).

,z

y y

Figure 14: S'h mode (SSI). Figure 15: 6'h mode (SSI). Figure 16: 71h mode (S81).

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