Operational Modal Analysis – Another Way of …

1 22 SOUND AND VIBRATION/AUGUST 2002 Operational Modal Analysis (often called output-only orambient Modal Analysis ) is described in this article. Modaltesting is performed on a plate structure with well-definedmodes, resonance frequencies and damping values. FrequencyDomain Decomposition (FDD) and Enhanced Frequency Do-main Decomposition (EFDD) concepts are presented and ap-plied to a plate structure. This article details the signal pro-cessing mathematical background and presents alternativecurve-fitting alternative Modal Analysis technique is presented in thisarticle. A typical Modal test of a structure is performed bymeasuring the input forces and output responses for a linear,time-invariant mechanical system.

2 The excitation is either tran-sient (impact hammer testing), random, burst-random or sinu-soidal (shaker testing). The advanced signal processing toolsused in Operational Modal Analysis techniques allow the inher-ent properties of a mechanical structure (resonance frequen-cies, damping ratios, mode patterns) to be determined by onlymeasuring the response of the structure without using an arti-ficial excitation. This technique has been successfully used incivil engineering structures (buildings, bridges, platforms, tow-ers) where the natural excitation of the wind is used to extractmodal , 2, 3 It is now being applied to mechanicaland aerospace engineering applications (rotating machinery,on-road testing, in-flight testing).

3 4,5,6 The advantage of this technique is that a Modal model canbe generated while the structure is under operating is, a model within true boundary conditions and actualforce and vibration levels. Another advantage of the techniqueis the ability to perform Modal testing in-situ, , without re-moving parts under test. The test can be performed with otherapplications or activities in parallel and does not affect or in-terrupt daily use of the machine. The measurement techniqueis identical to Operational Deflection Shape (ODS) measure-ment procedures where one accelerometer is used as a refer-ence and a series of accelerometers for the responses at all De-grees of Freedom (DOFs) of 1 shows a schematic description of an ambient re-sponse system.

4 The inputs to the system (that represent theexcitation forces) are assumed to have a Gaussian amplitudedistribution. In civil engineering applications, Gaussian exci-tation is typically provided by waves (offshore applications),wind or traffic load. In mechanical engineering, loads are typi-cally generated from bearings, vibration from the road or theair, rotating components or the engine. To define all modes, theexcitation should be broadband. Practically, this may involverunning up an engine or modifying the frequency of cases where the loading forces cannot be modified, the end-user needs to have at least some idea about the excitation fre-quencies that are generated to interpret the results and use theappropriate Modal extraction method.

5 For nonbroadband ex-citation, Modal extraction becomes difficult and would resultin poor model descriptions. The art of Operational Modal analy-sis is then to distinguish real structural behavior from noiseand other measured this study, measurements were made with a Br el & Kj rPULSE Multi-Analyzer System and the Modal Test Consult-ant (Type 7753) to create the test structure geometry, assignmeasurement points and capture the data. The Analysis wasperformed using the Br el & Kj r Operational Modal Analy-sis software (Type 7760) where advanced signal processingand Modal extraction procedures were ProcedureThe specimen used is a rectangular plate (29 cm 25 cm) rest-ing on a foam pad to simulate free-free boundary measurements were made using 4 accelerometers (1 for thereference and 3 roving accelerometers for the responses at 36 DOFs).

6 The data acquisition system was a portable PULSE Analysis platform (see Figure 2), composed of a 4-channel por-table front-end (4 inputs/2 outputs) and a laptop computer forthe tapping the plate for each set of measurements pro-vided enough energy to the structure. The PULSE Modal TestConsultant was used to set-up the hardware, create the ge-ometry and assign the measurements to each DOF. The refer-ence accelerometer was maintained at a well-chosen point onthe plate. The reference point selection has a significant effecton measurement results. It has to be placed such that all modescontribute to the reference accelerometer. A preliminary ideaof the mode shapes to be measured definitely helps in under-standing where to place the reference points.

7 Typically, pointsthat are not nodal or peak deflection points are good choices(atypical degrees of freedom). Each data set is then composedof the reference accelerometer signal and the 3 accelerometersmeasuring the responses at the specified DOFs. Twelve datasets were then collected for the plate. The raw time historieswere captured by a Time Capture Analyzer for each measure-ment set. A pretest measurement indicated that the lowest fre-quency of interest was about 350 Hz. In that case only 2 sec ofdata capture would be enough to represent more than 500cycles at the lowest frequency of interest. A sample data set isshown in Figure 4. This figure also shows a Short Time Fou- Operational Modal Analysis Another Way of Doing Modal TestingMehdi Batel, Br el & Kj r, Norcross, GeorgiaFigure 1.

8 Combined ambient 2. PULSE multi- Analysis portable system connected to testplate; hand-tapping excitation is Ambient SystemLoadingSystemStructural System(Linear, Time-Invariant) Unknown Excitation ForcesStationaryZero MeanGaussianWhite NoiseResponses23 SOUND AND VIBRATION/AUGUST 2002overlap of the windowed segments before averaging them to-gether. This technique minimizes spectral noise and the effectsof other artifacts. Using the averaged spectrum for frequencypeak-picking reduces possible misinterpretation of spectral density matrices are then calculated for all theseries of measurements. The size of the matrix is n n, n beingthe number of transducers (4 in this case, , 4 measuredDOFs). In this example, 12 matrices (of a size 4 4) were calcu-lated for each frequency.

9 Each element of those matrices is aspectral density function. The diagonal elements of the matrixare the magnitudes of the spectral densities between a responseand itself (power spectral densities). The off-diagonal elementsare the cross spectral densities between the 4 responses (Fig-ure 5). All those matrices are Hermitian (symmetric with com-plex conjugate elements around the diagonal).Each matrix is expressed in terms of power and cross spec-tral densities as follows:PSD(jw) denotes the power spectral density (magnitude of theauto spectral density) and CSD(jw) denotes the cross spectraldensity. Since the matrices calculated are Hermitian we haveThe * symbol denotes a complex conjugate value. The PSDpq(jw) are all real valued elements, and the CSDqp(jw) take com-plex values, carrying the phase information between the mea-surement and the reference degree of 6 shows the result obtained of the spectral densitycalculation between response 4 and the reference accelerom-eter at measurement 10 (cross spectral density).

10 Frequency Domain Decomposition Theory Background. Fre-quency Domain Decomposition (FDD) is an extension of theBasic Frequency Domain (BFD) technique or more often calledrier Transform (STFT) Analysis that provides a time/frequencyrepresentation of all the responses STFT Analysis is performed by a traveling Fast FourierTransform (FFT) window with user defined parameters. Fig-ure 4 exhibits straight lines showing up at specific frequenciesduring the entire capture that correspond to structural the raw time data, the geometry and the series of mea-surements are then directly exported from the data acquisitionsystem to the Operational Modal Analysis curve-fitter for sig-nal processing calculations and Modal Processing and DecompositionPreliminary Signal Processing.