INDUSTRIAL RELEVANCE OF OPERATIONAL MODAL ANALYSIS – CIVIL, AEROSPACE AND AUTOMOTIVE CASE

HISTORIES

Bart Peeters, Herman Van der Auweraer, Steven Pauwels, Jan Debille

LMS International, Belgium bart.peeters@lms.be

Abstract During the last 15 years or so, Operational Modal Analysis developed and reached a mature state with advanced parameter estimation algorithms, commercial software implementations, and very relevant industrial applications. This paper will discuss some case histories. A first application is structural health monitoring in civil engineering: in order to assess the health of structures by means of vibration measurements, the dynamic characteristics of the structure need to be identified from measurements. For monitoring purposes, it is evident that the structure has to be tested in its operational conditions, being excited by wind or traffic, and that artificial measurable excitation is often no option.

The second part of the paper focuses on aerospace applications with a case on using operational modal analysis during a satellite vibration qualification test and a case involving flight flutter testing. Aircraft in-flight vibration tests allow the validation of the analytical models under various real flight conditions and, more important, allow to assess the aero-elastic interaction between the structure and the aerodynamic forces as they may lead to a sudden unstable behaviour known as flutter. During these tests, the trends of eigenfrequencies and damping ratios of the critical modes as a function of airspeed are carefully studied. The present paper will concentrate on the cases where the aircraft is excited by natural turbulences only.

A final case study is operational automotive testing: in troubleshooting, competitive benchmarking, or target setting projects, it is common to acquire a lot of vibration data while the car is driven on the road or tested on a roller bench. We will discuss the use of these data for Operational Modal Analysis.

1 Civil engineering applications In Cunha et al. [1], it is shown how the analysis of dynamic measurements can play a role during the complete lifetime of civil engineering structures: from design and construction, via long-term monitoring to rehabilitation. Evidently, it is very difficult and expensive to artificially excite constructions such as bridges and buildings with a hammer or shaker to obtain induced vibration levels that exceed the natural vibrations due to traffic or wind. Therefore, Operational Modal Analysis (OMA), where experimental dynamic models are determined based on ambient or operational vibrations, proved to be very useful.

1.1 The Z24-Bridge

Data from an extensive study on the Z24-Bridge, a Swiss highway overpass, is used to illustrate Operational Modal Analysis. The bridge was tested in the frame of the European research project SIMCES. In this project the use of vibration measurements for Structural Health Monitoring

(SHM) was demonstrated [2]. The bridge was excited by unknown ambient excitation such as wind and traffic passing underneath. Figure 1 compares the stabilisation diagrams from stochastic subspace identification and PolyMAX. More information about these two system identification methods and the concept “stabilisation diagram” can be found in another paper of these proceedings [3]. Although both methods are known to yield accurate modal parameter estimates, it is obvious that PolyMAX considerably facilitates the identification process; in the sense that it is much easier to pick the stable poles from the diagram. A clear diagram also opens the door to a fully automatic data processing [4], which is very relevant for monitoring applications. Figure 2 shows some typical mode shapes of the Z24-Bridge identified with PolyMAX.

Figure 1: Stabilisation diagram obtained by applying stochastic subspace identification (Top) and the new PolyMAX method (Bottom) to the Z24-Bridge data.

Figure 2: Typical mode shapes of the Z24-Bridge obtained with PolyMAX.

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Figure 3: Measured spectrum (full line) and identified spectrum (‘+’).

Figure 3 compares a measured half spectrum (Fourier transform of the correlations) with the spectrum that is synthesised from the identified modal parameters. The very good correspondence indicates that all major dynamic properties have been extracted from the data.

1.2 Monitoring of a football stadium

For more than a year, the University of Sheffield monitored the Midland Road Stand at the Bradford and Bingley Stadium, home of Bradford City Football Club. These data serve to study the effects of crowd occupation on the dynamic performance of a grandstand [5]. Figure 4 presents a 4-hours recording that is analysed in this subsection. The data acquisition started about 1 hour before the football game and includes different events, with different crowd-structure interaction scenarios.

As discussed in [3] and [6], the main advantage of PolyMAX is that it yields extremely clear stabilisation diagrams. This makes an automation of the parameter identification process rather straightforward and enables a continuous monitoring of the dynamic properties of a structure. An overview and discussion on automatic modal analysis techniques can be found in [4]. Here, PolyMAX has been used in combination with a method, which is able to autonomously interpret stabilisation diagrams based on a set of heuristic rules [7]. The autonomous monitoring results are represented in Figure 5. Generally, the frequencies of the structure are decreasing when the number

of people is increasing (added mass) and the damping ratios are increasing. More details about the analysis can be found in [8].

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Figure 4: Typical acceleration time history and “sliding” RMS value with an indication of the events during the game.

Figure 5: Unusual stabilisation diagrams representing automatic PolyMAX modal analysis results: the y-axis is not the model order, but represents the time. The background image is the normalised 1st singular value (CMIF) of the spectrum matrix computed for each segment. The curves on the Left represent the sliding RMS values (Figure 4).

2 Aerospace applications

2.1 INTEGRAL vibration qualification test

Space hardware development programs typically foresee 2 phases requiring laboratory tests. First a so-called modal survey test is carried out to obtain an experimental model of the structure or to update a Finite Element (FE) model. These models are essential in planning the second phase, namely the qualification test. Here, the structure is subjected to environments that are representative for flight or launch conditions. If the structure survives the qualification test, there is a high probability that it will also survive the launch. In [9] is has been shown that a significant amount of expensive space program time can be saved by doing the hardware validation cycle with only one test set-up: the one from the vibration qualification test.

The data set of the Alenia-Spazio INTEGRAL satellite has been measured during a base-driven sine qualification test, executed in the IABG laboratories. The test set-up is shown in Figure 6 and consisted of 350 degrees of freedom (DOFs) that were measured in a 5-100 Hz frequency band. As no input forces were measured, the output-only (or operational) version of PolyMAX was applied. The stabilisation diagram is shown in Figure 6.

Figure 6: (Left) Alenia-Spazio INTEGRAL satellite during testing at IABG. (Right) PolyMAX stabilisation diagram from base-driven test.

Figure 7 shows some typical measured cross spectra when compared with spectra synthesised from the modal parameters. It is clear that PolyMAX is able to perform an accurate identification of the satellite structural dynamics based on vibration qualification data. Figure 8, finally, shows 2 mode shapes resulting from the PolyMAX analysis.

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Figure 7: Comparison of measured (red/black) cross spectra with cross spectra synthesised from the identified modal parameters (grey/green). (Top-Left) point on the payload module; (Top-Right) point on a solar panel, (Bottom-Left) point on the service module and (Bottom-Right) point on the antenna.

Figure 8: PolyMAX mode shapes. (Left) Symmetric bending of the 2 payload modules at 18.5 Hz; (Right) Anti-symmetric bending at 23.3 Hz.

2.2 In-flight vibration testing

The development cycle of a new aircraft consists of several modelling and testing stages: structural finite element (FE) modelling, ground vibration testing (GVT), computational fluid dynamics (CFD) modelling, wind tunnel testing, and in-flight tests. These flight (vibration) tests allow the validation of the analytical models under various real flight conditions and, more important, allow to assess the aero-elastic interaction, as a function of airspeed and altitude, between the structure and the aerodynamic forces as they may lead to a sudden unstable behaviour known as flutter. Flutter shows up in the vibration signals as apparent negative damping and corresponding sudden increase of the vibration amplitudes. For economic and safety reasons (i.e. to avoid a loss of the aircraft), it is evidently avoided that an aircraft goes into flutter during an in-flight test, but it has to be certified that it has sufficient flutter margin when flying at the different points of the flight envelope where it is designed for. To determine this margin, typically, the trends of eigenfrequencies and damping ratios of the critical modes as a function of airspeed are carefully studied. This explains the need to perform a modal analysis during the flight. More background information on flight flutter testing can be found in [10][11].

This section explores the possibilities to enhance the flight data exploitation by using Operational Modal Analysis. The reason for using modal analysis techniques that do not require input information is that it is difficult to measure the forces from the artificial excitation devices and that these techniques also allow the use of natural turbulences as input. Real turbulent flight data from a business jet is used to investigate the problem. Please note that the figures’ axes have been rescaled and/or omitted for confidentiality reasons. Figure 9 shows a typical response signal and the applied data pre-processing. The time data are converted to correlations and the spectra are computed as the Fourier transforms of the positive time lags of the correlation functions. By doing so, even the auto spectra have phases different from zero. Figure 10 shows the sum of the cross spectra and gives a rough idea about the location of the modes.

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Figure 9: (Top-Left) Aircraft response to turbulence excitation; (Top-Right) autocorrelation computed from time response; (Bottom) auto spectrum.

Figure 11 compares the stabilisation diagrams of stochastic subspace identification with PolyMAX. When using stochastic subspace identification, a larger number of non-physical poles are identified at higher model order. Figure 12 shows some typical measured cross spectra when compared with spectra synthesised from the modal parameters. This comparison shows that PolyMAX is able to perform an accurate identification of the structural dynamics from in-flight output-only data.

Figure 10: Sum of cross spectra of in-flight data and frequency band of interest.

Figure 11: (Left) stochastic subspace stabilisation diagram; (Right) operational PolyMAX stabilisation diagram.

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Figure 12: Comparison of a measured (red/black) power spectrum with a spectrum synthesised from the identified modal parameters (grey/green). (Left) at the aircraft body; (Right) at the wing tip.

3 Automotive applications A final case study is operational automotive testing: in troubleshooting, competitive benchmarking, or target setting projects, it is common to acquire a lot of vibration data while the car is driven on the road or tested on a roller bench (Figure 13). We will discuss the use of these data for Operational Modal Analysis.

Figure 13: Acquisition of operational data during road (Left) or roller bench testing (Right).

A typical automotive case, where operational modal analysis is applied, is to study the behaviour of the suspension system. By design, a suspension system is non-linear and hence it reacts differently to a low-level vibration test and real operational conditions. The vibration data discussed here

originates from a rear suspension of a car tested on a roller bench with a bump on the rollers. This causes a highly repeatable impact-like excitation with a broad frequency range. Another advantage is that the excitation in different runs is similar, allowing the data of different measurement runs to be analysed simultaneously. Figure 14 shows the time data and the power spectrum of one of the reference acceleration channels. From this graph it is clear that he excitation is very consistent between the test runs. Figure 15 shows the PolyMAX stabilisation diagram and Figure 16 a typical mode shape. Figure 17 compares measured and synthesised cross spectra at several components of the suspension.

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Figure 14: (Left) Reference output time series; (Right) Power spectrum of reference output during two different runs.

Figure 15: PolyMAX stabilisation diagram from roller-bench data.

Figure 16: Suspension mode shape: bending of the twist beam.

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Figure 17: Comparison of measured (red/black) suspension cross spectra with spectra synthesised from the identified modal parameters (grey/green).

4 Conclusions This paper showed that Operational Modal Analysis has developed and reached a mature state with advanced parameter estimation algorithms, high-quality data acquisition systems, commercial

software implementations, and very relevant industrial applications. This paper gave an overview of industrially-relevant case histories in civil, aerospace and automotive engineering.

Acknowledgements The work was conducted in the framework of the EC 6-FWP research project NMP2-CT-2003-501084 “INMAR” (Intelligent Materials for Active Noise Reduction, www.lbf.fhg.de/inmar) and the EC 5-FWP research network “SAMCO” (www.samco.org). The support of the EC is gratefully acknowledged.

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measurements on bridges: design, rehabilitation and monitoring, Bridge Engineering, 156(3), 135-148, 2003.

[2] B. PEETERS AND G. DE ROECK, One-year monitoring of the Z24-Bridge: environmental effects versus damage events, Earthquake Engineering and Structural Dynamics, 30(2), 149-171, 2001.

[3] B. PEETERS AND H. VAN DER AUWERAER, PolyMAX: a revolution in Operational Modal Analysis, In Proceedings of IOMAC, the 1st International Operational Modal Analysis Conference, Copenhagen, Denmark, 26-27 April 2005.

[4] H. VAN DER AUWERAER AND B. PEETERS, Discriminating physical poles from mathematical poles in high order systems: use and automation of the stabilization diagram, In Proceedings of IMTC 2004, the IEEE Instrumentation and Measurement Technology Conference, Como, Italy, 18-20 May 2004.

[5] Z. IBRAHIM, P. REYNOLDS, AND A. PAVIC, The effects of crowd occupation on the dynamic performance of a grandstand, In Proceedings of ISMA 2004, the International Conference on Noise and Vibration Engineering, Leuven, Belgium, 20-22 September 2004.

[6] B. PEETERS, H. VAN DER AUWERAER, P. GUILLAUME, AND J. LEURIDAN, The PolyMAX frequency-domain method: a new standard for modal parameter estimation? Shock and Vibration, Special Issue dedicated to Professor Bruno Piombo, 11, 395-409, 2004.

[7] J. LANSLOTS, B. RODIERS, AND B. PEETERS, Automated pole-selection: proof-of-concept & validation. In Proceedings of ISMA 2004, the International Conference on Noise and Vibration Engineering, Leuven, Belgium, 20-22 September 2004.

[8] B. PEETERS, F. VANHOLLEBEKE, AND H. VAN DER AUWERAER, Operational PolyMAX for estimating the dynamic properties of a stadium structure during a football game, In Proceedings of IMAC 23, Orlando, FL, USA, 31 January - 3 February 2005.

[9] B. PEETERS, H. VAN DER AUWERAER, AND P. GUILLAUME, The integration of operational modal analysis in vibration qualification testing, In Proceedings of IMAC 20, pp. 977-983, Los Angeles (CA), USA, February 2002.

[10] M.W. KEHOE, A historical overview of flight flutter testing, NASA TM-4720, www.dfrc.nasa.gov/DTRS, 1995.

[11] C.R. PICKREL AND P.J. WHITE, Flight flutter testing of transport aircraft: in-flight modal analysis, In Proceedings of IMAC 21, Kissimmee (FL), USA, 2003.