r bulletin 96 — november 1998

Modern Modal-Identification Analysis

P. Deloo, G. PrietoAtos BV, Leiden, The Netherlands

M. KleinStructures Division, ESA Directorate of Technical and Operational Support,ESTEC, Noordwijk, The Netherlands

J. MerletIntespace, Toulouse, France

IntroductionThe identification of the modal properties ofstructures has gained significant importance inrecent years because it constitutes an essentialstep in the updating and correlation of themathematical models used for the design andverification of aerospace structures. For theseactivities, representative mathematical modelsare indispensable and modal identification isusually the first step in the updating procedurefor such models. The possibility of performingmodal identification using shaker-test resultsenables one to integrate this activity within astandard shaker sine qualification test withminimal impact on the project schedule.

The previous software implementation of theoriginal ISSPA method consists of variousFortran programs and was used for thecharacterisation of space structures such asthe SUMER and SGSS instruments currentlybeing flown on ESA’s SOHO scientific satellite.The software’s performance in terms of thequality of modal identification was excellent, butthe handling of all of the data involved wascumbersome due to the ‘old fashioned’ natureof the user interface then available. Theintegration of ISSPA into DynaWorks hassimultaneously enhanced DynaWorks with amodal identification capability and eased thetask of the ISSPA user by providing a state-ofthe-art interface.

Tool descriptionAs with the original ISSPA program, the task ofmodal identification consists of sessionscorresponding to the processing of the resultsfrom one test with a specific excitation axis.Each session is composed of sequences ofidentification calculations for one or morefrequency bands. The latter are user-selectedsub-domains of the overall frequency range ofthe test responses. For each sequence, modalcharacteristics (e.g. frequency, modes anddamping) are derived, as well as variousphysical matrices (e.g. inverse mass matrix,inverse stiffness matrix and damping matrix).Modal information from several sequences of a session can then be combined to form themodal base at session level. Synthesisedresponses can be calculated from the modalbase of a sequence or a session of sequences.

The various stages of an identificationsequence are as follows:– initialisation– curve-fitting and residual correction– identification– mode deletion and matrix assembly– calculation of equivalent proportional

damping

The ISSPA computer program allowing the modal identification ofstructures from sine-vibration-test data has been integrated intoDynaWorks 4.0 and applied successfully for the characterisation ofseveral space structures. Its integration into a system such asDynaWorks provides increased capabilities within the modal-identification process as well as greater flexibility and user-friendliness.

This article describes the user interface that was specificallydeveloped to handle the ISSPA module in terms of data selection,management of identification sequences and all of the graphicaldisplays which are so indispensable if one is to work efficiently onpractical applications. A practical application of the new tool to acomplete satellite, performed at ESTEC and Intespace in early 1997, isalso reported.

Identification of Structural System Parameters(ISSPA) is a modal identification method thathas been developed at the University of Kassel,in Germany. It is based on the identification ofthe physical and modal mass, stiffness anddamping matrices of a structure in the case ofan ‘incomplete excitation’. The latter meansthat the number of excited modes is lower thanthe number of measurement degrees offreedom needed to describe the test item’sstructural dynamic behaviour in physicalcoordinates.

modern modal-identification analysis

Figure 2. Frequency-band selection window

Figure 1. Initialisation window

– The type of excitation and correspondingparameters:• constant-force excitation (i.e. modal-

survey test results normalised to aconstant excitation)

• constant-base excitation (i.e. shaker testresults normalised to a constant excitation);this option is currently not active, but shakertest results can be processed as modal-survey test results using the constant-forceexcitation option, provided the rigid-bodymovement imposed by the shaker issubtracted from the responses.

– Spectral line reduction: an option to reducethe number of frequency points of responsecurves with a minimal impact onidentification quality; it is useful in caseswhere data is voluminous and/or computerresources are limited.

Last but not least, descriptive informationfacilitating the management of the identificationsequences can be specified.

Once the initialisation window is defined, agraphical window presenting the graphicalreference is opened. One or more frequencyband(s) can be defined graphically by movingvertical cursors with the mouse, or typedexplicitly in the columns located on the right-hand side of the window (Fig. 2). Theidentification process can now start for theselected frequency band(s).

– combination of sequences– response synthesis.

Modal identification stepsSelection of the ISSPA identification optionopens a window listing the various stages ofthe identification procedure and the windowsshowing the available information.

InitialisationThe initialisation is an important step in anyidentification sequence because it defines themain parameters of the process. Theinitialisation window presented in Figure 1allows the definition of:

– The responses used in the identification: theselection is made in the first sequence andcannot be modified for subsequentsequences in the session.

– The graphical reference: this is the curve thatwill be plotted in the graphical windows forthe selection of the frequency bands andresponse peaks, and three options areavailable:• selected response: particular responses

selected by the user as graphicalreference

• envelope of all responses’ imaginary partsused in the identification session

• phase resonance criterion: curve derivedfrom all responses used in the identificationsession that clearly show resonance peaks.

r bulletin 96 — november 1998 bull

Figure 3. Damping and modal mass iteration curves

Figure 4. Identification RMS errors

Figure 5. Ratio of singular values

Curve fitting and residual correctionThe next step is a multiple degree of freedom(MDOF) curve-fit and a residual correction ofthe data to eliminate the effects of modesoutside the selected frequency band.

The response peak frequencies are selectedusing the graphical reference in a similarmanner to the frequency-band selection. At thisstage, modal results such as frequency, mass,damping and mode shape are already availablefor modes within the frequency band(s).

The quality and validity of these intermediateresults can be assessed by displaying twocurves (Fig. 3):– the Damping Iteration curve– the Modal Mass Iteration curve.

The calculation of effective modal massesrequires the vector of inertia forces as input. Ifnot defined explicitly by the user, a unit vectoris used. Of course, the modal masses are notthen correct, but the convergence informationcan still be used. The number of curve pairscorresponds to the number of selected peaks.

ISSPA identificationOnce a satisfactory MDOF identification isachieved, the modal results can be refinedusing the ISSPA method itself. It allows thecomputation of: – number of effective modes in the selected

frequency band(s)

– modal parameters of these modes– eigen-shapes of these modes– contribution of these modes to the inverse

mass, stiffness and damping matrices.

The effective number of modes corresponds tothe number of modes effectively excited in thetest within the selected frequency band(s) andis given by the number of non-negligiblesingular values.

At the end of the calculation, information aboutthe identification accuracy within the frequencyband(s) is displayed in terms of RMS errors (Fig.4). In this message, the wording ‘condensationof 2 effective dofs’ actually means ‘assembly ofsubstitute measurement matrices from 2effective vectors of the singular valuedecomposition’.

The number of effective modes within thefrequency band(s) can be verified by inspectingthe ratio of singular-value curves (Fig. 5).

The most suitable number of effective modescorresponds to the number of modes with non-negligible singular values for the real andimaginary parts (a recommended thresholdvalue is 0.1). Selecting too few modes for theISSPA identification results in large RMS errors,while selecting too many modes results in noiseor numerical modes. At this stage, a goodengineering judgement is necessary.

3

4

5

modern modal-identification analysis

Figure 6. Control window

Figure 7. Status window

The purpose of this step is to create a modalbase containing all the retained modes from thedifferent sequences of the session that the userwants to use for a subsequent responsesynthesis.

Response synthesisThe purpose of the response-synthesis step isto validate the computed modal characteristicsby comparing the analytical responsescomputed using the identified modalparameters with the original test responses(Figs. 10 and 11). The response synthesis canbe performed for the current sequence or forthe modal base of the session resulting fromthe combination of sequences.

Additional related toolsThree tools in the DynaWorks system that areindependent of the modal-identification moduleare also useful in a modal-identification exercise:

Display of mode shapesIf a computer model of the test specimen isavailable in the database, plots of the identifiedmode shape can be visualised. If needed,superimposition with analytical model modeshapes is possible for visual comparison (Figs.8 and 9).

Mode deletion and matrix assemblyThis step is essential if the current sequence isto be combined with other sequences at a laterstage. It allows the removal of unwantedmodes and performs the assembly of physicalmatrices for the system corresponding tomodes within the frequency band(s). Onceagain, the decision to keep or reject a mode inthe modal base requires good engineeringjudgement.

Calculation of equivalent proportional dampingThis step is only possible after matrix assembly.It enables a refinement of the estimate of thediagonal elements of the damping matrix byresolution of the system of equations of motionaround the modal frequencies, since thedamping values are the only unknowns of thesystem.

Combination of sequencesFurther to the processing of a sequence, theabove steps can be repeated for newsequences and other modes identified in otherfrequency band(s). Sequences can easily becombined just by specifying their names. To aid in this task, a control and a status windoware available to help the user to remember thecontent of each sequence (Figs. 6 and 7).

r bulletin 96 — november 1998 bull

Figure 8. Antenna mode at53 Hz

Figure 9. Torsion mode at 37 Hz

MAC calculationThe calculation of the MAC (Modal AssuranceCriterion) is available as a DynaWorks stand-alone function. It uses a pairing table to allowcomputation of the MAC between modes oftwo different models. A specific tool is alsoavailable to create the pairing table in the mostautomated manner possible, but preservinguser control over the pairings defined. Theresults of the MAC calculation can be displayedin a DynaWorks 3D window for a visualassessment of the quality of the corres-pondence between modes.

Test animation/mode animationThe test animation facility allows one to replay avibration test on the screen using a topologicalmodel of the test item. Animateddisplacements are computed from measuredexperimental acceleration responses (harmonicor transfer functions). The real movement of thestructure during the test, corresponding to thesuperposition of all individual modal responsesof the specimen, is reproduced at eachfrequency.

The mode animation facility helps inunderstanding the various modes identified andtheir comparison with analytical modes.

Management of identification sessionsThe current state of an identification sessioncan be saved at any time, restored to continueworking, modified and saved again. There is nolimit to the number of sessions that can besaved, other than the available computerresources.

In addition, the main results such as modalparameters, matrices and synthesisedresponses can be saved selectively to thedatabase for archiving or future use with otherDynaWorks tools.

Practical applicationA DynaWorks implementation of ISSPA hasbeen used at ESTEC to perform a modalidentification for ESA’s MTP satellite (MeteosatTransition Programme) based on low-level sinetests performed at Aerospatiale in Cannes (F).This work was necessary to allow a goodcorrelation and updating of the mathematicalmodel of the spacecraft destined for a coupledload analysis by Arianespace.

Base excitation tests were performed in thethree axes, delivering the Frequency ResponseFunctions (FRFs) via about 32 accelerometers(60 DOFs). The FRFs were imported intoDynaWorks, and the Elastic Transfer Functions(ETFs) required as input for the modalidentification derived by removing the rigid-body movement imposed by the vibrationtable. This identification task constituted achallenging test for DynaWorks/ISSPA sincethe test responses were quite noisy and oftenrepresented degenerated modes.

ResultsThree identification sessions – one for eachexcitation axis – were performed in thefrequency range 5 to 65 Hz. For each session,DynaWorks delivered a modal base consistingof:

modern modal-identification analysis

Figure 12. Z-excitation, measurement point 290:- Z

– mode shapes– frequencies– dampings.

An experimental model was used to plot eachidentified mode’s shape for visual inspectionand comparison with analytical mode shapes.Figure 8 is a superposition of deformed andundeformed shapes, whilst Figure 9 presents atorsion mode where displacements are shownas vectors. Damping values were obtained foreach mode of each of the three modal bases.

Synthesised responses for each modal baseand each measurement point were computedin the frequency range of interest andcompared to test responses to assess thequality of the modal identification. Figures 10-12 present a comparison of original test andsynthesised responses. Test animations werealso performed to further assess the quality ofthe identification process.

Present limitations and on-goingimprovementsDuring the practical application describedabove, a number of potential furtherimprovements were identified and the softwareis currently being updated in order toimplement them.

One limitation that was noted was theimpossibility of combining the modal bases ofdifferent sessions. Indeed, modes that arepoorly excited in one direction are normally notfound within the modal identification sessioncorresponding to that direction. This mode can,however, be identified in another sessioncorresponding to an axis in which the mode isproperly excited. The possibility of combining

modal bases of different sessions will allowmore complete and meaningful checks.Indeed, modes that are weakly excited (i.e.lateral modes in an axial test) may be replacedby modes of another session corresponding toa test in which these modes are stronglyexcited. In this way, it will soon be possible toselect the best set of modes for the calculationof the synthesised response of a given session.

r

Figure 10. X-excitation, measurement point 520: +Y Figure 11. Y-excitation, measurement point 520:+Y