REMOVING DISTURBING HARMONICS IN OPERATIONAL MODAL ANALYSIS

Bart Peeters, Bram Cornelis, Karl Janssens, Herman Van der Auweraer

LMS International, Leuven, Belgium

bart.peeters@lms.be

Abstract In Operational Modal Analysis applications, it is assumed that the structure is excited by white noise. However, in some cases, the operational vibration data are acquired while rotating equipment is active in the background or while it is even the main source of excitation. The structural responses will then consists of a broadband response from which the structural modes can be determined and additional harmonic response at discrete frequencies, which are disturbing the parameter identification process. Sometimes, the harmonic response is dominating and the Operational Modal Analysis methods only find poles at these harmonic frequencies.

Therefore, it is desired to try to remove the disturbing harmonics from the data before applying Operational Modal Analysis. In this paper, a method that serves this purpose will be discussed. If the fundamental frequency of the disturbing harmonics is not known, it will be estimated by applying a “tacho-less rpm extraction” procedure. Using the (possibly fluctuating) rpm, the data can be converted to the angle domain and, then time (or better: angle) synchronous averaging is applied to remove the harmonics. This procedure will be illustrated using simulated data as well as real industrial operational data from an in-flight helicopter test and from a running large diesel engine.

1 Introduction Operational Modal Analysis (OMA) is used to derive an experimental dynamics model from vibration measurements on a structure in operational conditions (as opposed to dedicated laboratory testing). Cases exist where it is rather difficult to apply an artificial force and where one has to rely upon available ambient excitation sources. It is practically impossible to measure this ambient excitation and the outputs are the only information that can be passed to the system identification algorithms. In this case one speaks of Operational Modal Analysis. 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.

The number of applications is constantly increasing, and recently a considerable interest was raised in the application of OMA in the presence of rotating machinery. Two cases can be distinguished:

• The engine is running through its operational rotation speed (rpm) range. In this case the different engine orders (harmonics) are sweeping through a broad frequency band and can be considered as unknown, but useful excitation and there is no need to apply any kind of filtering. In some cases, one has to be careful in the interpretation of certain modes as some of them are so-called “end-of order” effects. More details on this approach can be found in [1]. An example can be found in Figure 1.

• The engine is running at fixed (or slowly varying) rotation speed. In this case, the best excitation is at the fixed harmonic frequencies. However, these represent only a few spectral lines and do not contain sufficient information to base OMA curve-fitting on. So the modal parameter estimation also relies on the broadband excitation that is supposed to be present next to the harmonics. Unfortunately, the harmonics hamper considerably the identification process since the modal estimators will preferably find harmonics instead of structural modes. Therefore they should be removed from the data. An example can be found in Figure 2.

The paper discusses the second case by presenting a method to remove the disturbing harmonics from the data before applying Operational Modal Analysis (Section 2). In Section 3, a simulated example is discussed and in Section 4, some industrial examples are given.

Figure 1: Example of sweeping harmonics: sound pressure measurements inside a car while the engine is running up. The engine orders excite the acoustic resonances (vertical lines).

Figure 2: Example of fixed harmonics: in flight helicopter vibration data with main and tail rotor harmonics.

2 Theory Different methods exist in trying to separate discrete harmonic components from broadband random response. In [2] some of these are discussed, including synchroneous averaging [3], adaptive noise cancellation (ANC) [4] and the so-called Discrete-random separator (DRS) [5], which can be used in case of stationary signals (non-varying rpm) and is more efficient and robust than ANC. The difference compared with synchronous averaging is that the discrete frequency components are not required to have harmonic relationships. In [6], a method is discussed to remove order domain content in rotating equipment signals by double resampling. Double resampling refers to the fact that the time signal is first resampled in angle domain, after which the order content can be removed and then a second resampling takes place to convert the signal back to time domain. In [7], such an adaptive resampling procedure is discussed. Figure 3 shows the resampling principle. Figure 4 compares the same signal represented in frequency domain and order domain. In the angle or order domain, it will be possible to remove the disturbing chirping harmonics.

Figure 3: Illustration of resampling in angle domain after upsampling the time data [6].

Figure 4: Chirp from 2 – 10 Hz in 10s with also 2nd harmonic) represented (Left) in frequency-domain and (Right) in Order domain [6].

Based on the ideas found in the above-cited literature, and after carrying out numerous evaluations [8], the following 4-step method (called “harmonic filter”) was found to be practical and reliable for removing harmonic disturbances in Operational Modal Analysis:

1. Measure (preferred) or estimate the fundamental harmonic / rpm of the rotational phenomenon.

2. Resample the data in angle domain (after upsampling)

3. Apply sliding window (angle) synchroneous averaging for separating discrete (harmonic) and random (broadband response) components (see also Figure 5).

4. Restore the signal in time domain

Note that after the procedure, a time signal is obtained with the same length and sampling frequency as the original signal. Therefore it is possible to apply also time-domain OMA methods.

It is also worth noting that in [9] an alternative approach was developed consisting in the reformulation of some classical modal parameter estimation algorithms to account for the presence of undamped harmonics, i.e. the modal equations were complemented by harmonics with fixed and known frequencies, but amplitudes and phases which are estimated together with the modal parameters.

Figure 5: Equivalent filter characteristic of synchroneous averaging.

3 Simulated example A 6 Degree-of-Freedom (DOF) system was excited by white noise. A disturbing harmonic was added to the excitation. In order to make it challenging, the frequency did not remain constant, but was constructed as an FM-modulated 12 Hz component of which the frequency could vary with about ± 4 %. Moreover, the carrier frequency (12 Hz) of the disturbance coincides with a mode of the system. Figure 6 shows the simulation results. When the disturbing component is not removed from the data, the modes could be identified, but in addition, much more modes around 12 Hz showed up in the stabilization diagram. Also the mode shape estimation is seriously compromised by the disturbing high-amplitude peaks in the spectra. When removing the disturbance using the 4-step approach outlined in Section 2, the PolyMAX modal parameter estimation results correspond very well to the true values.

Figure 6: Simulation example. (Top) results without removal of modulated harmonic; (Bottom) results after removing disturbance using the method described in Section 2. (Left) PolyMAX stabilization diagram; (Right) MAC matrix indicating the correlation between estimated and true mode shapes.

4 Industrial examples In this section, the procedure outlined in Section 2 will be applied to real industrial operational data from an in-flight helicopter test and from a running large diesel engine (Figure 7). Key to the method is the knowledge of the fundamental frequency of the disturbing harmonics. It is always a good idea to measure it during the operational test using a tacho probe. However, when it is not available, the “tacho-less rpm extraction” procedure developed in [10] can be applied to a response signal which is “close” to the harmonic excitation source. Also the Hilbert transform is useful to verify the stationarity and phase of these signals: Figure 8 shows the envelope of two helicopter roof acceleration signals which were band-pass filtered around the blade-pass frequency. It is clear that in this 30s recording, the harmonic amplitude is not constant (non-stationary signal). Figure 9 shows the phase of the Hilbert transform from which the instantaneous pulsation can be obtained by derivation (Figure 10). In this way, also an estimate of the rpm can be obtained. The 2 signals seem to agree well, except for some spikes in the signal, which indicate a bad estimate of the instantaneous pulsation in the signal due to low amplitudes (spikes in Figure 10 correspond to low

envelope values in Figure 8. Using the measured or estimated (possibly fluctuating) rpm, the data can be converted to the angle domain and, then time (or better: angle) synchronous averaging is applied to remove the harmonics. Such a filtered spectrum is shown in Figure 11. A typical in-flight helicopter mode shape is shown in Figure 7.

Figure 7: Examples of typical OMA applications in the presence of disturbing harmonic: a running engine and a helicopter in flight.

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Figure 8: Bandpass filtered signal envelope estimation as the magnitude of Hilbert transform of 2 helicopter roof accelerations.

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Figure 9: Bandpass filtered signal angle estimation as the phase of the Hilbert transform of 2 helicopter roof accelerations.

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Figure 10: Signal instantaneous frequency estimation as the derivative of the phase in Figure 9.

Figure 11: Helicopter in-flight acceleration spectrum before and after applying the harmonic filter.

Figure 12: Stationary running large engine. (Top) spectrum and stabilization diagram before filtering. (Bottom) spectrum and stabilization diagram after applying the harmonic filter.

In case of the helicopter, it was still possible to find some modes; even without filtering the harmonics from the data. This is confirmed by another case in literature [11]. In case of the stationary running large engine, the magnitude of the engine harmonics and the spacing between them was such that the OMA methods could only detect these harmonics and no single structural

mode was found (Figure 12 – Top). After filtering the harmonics from the time series, OMA could be successfully applied (Figure 12 – Bottom). Moreover, it was found that the OMA modal parameters were in good agreement with the modal parameters identified using impact test and classical modal analysis (the engine was not running during impact testing).

5 Conclusions This paper introduced the “harmonic filter”, a method which is able to filter disturbing harmonics from broadband time data. The envisaged application is Operational Modal Analysis, where it was observed that the applicability to certain industrial problems was hampered by the presence of these harmonics. It was shown that the harmonic filter successfully filters the measured time signals so that the, originally hidden, structural modes can be identified using e.g. Operational PolyMAX.

Acknowledgements This work was carried out in the frame of the EUREKA project E! 3341 FLITE2. The financial support of the Institute for the Promotion of Innovation by Science and Technology in Flanders (IWT) is gratefully acknowledged.

References [1] K. JANSSENS, Z. KOLLAR, B. PEETERS, S. PAUWELS, H. VAN DER AUWERAER. Order-based

resonance identification using operational PolyMAX. In Proceedings of IMAC 24, the International Modal Analysis Conference, Saint Louis (MO), USA, 30 January – 2 February 2006.

[2] R.B. RANDALL. State of the art in monitoring rotating machinery. In Proceedings of the ISMA 2002, Leuven, Belgium, September 2002.

[3] P.D. MCFADDEN. A revised model for the extraction of periodic waveforms by time domain averaging. Mechanical Systems and Signal Processing, 1(1): 83-95, 1987.

[4] G.K. CHATURVEDI AND D.W. THOMAS. Bearing fault detection using adaptive noise cancelling. Transactions of the ASME, 104: 280-289, 1982.

[5] J. ANTONI AND R.B. RANDALL. Unsupervised noise cancellation for vibration signals: part II – a novel frequency-domain algorithm. Mechanical Systems and Signal Processing, 18(1): 103-117, 2004.

[6] C.L. GROOVER, M.W. TRETHEWEY, K.P. MAYNARD AND S.M. LEBOLD. Removal of order domain content in rotating equipment signals by double resampling. Mechanical Systems and Signal Processing, 19(3): 483-500, 2005.

[7] F. LEMBREGTS, J. TOP, AND F. NEYRINCK. Adaptive resampling for off-line signal processing. In Proceedings of IMAC 14, the International Modal Analysis Conference, Dearborn (MI), USA, 12-15 February 1996.

[8] B. CORNELIS. Verwijdering van vaste frequentiecomponenten uit meetdata bij Operationele Modale Analyse. Industrial internship report, Dept. ESAT, K.U.Leuven, 2006.

[9] P. MOHANTY. Operational Modal Analysis in the presence of harmonic excitations. PhD thesis, T.U.Delft, The Netherlands, 2005.

[10] I. BELGHIT, A. VECCHIO AND K. JANSSENS. Plausibility check of RPM measurements. ICSV Conference, St. Petersburg, Russia, July 2004.

[11] C. CAVAGNINO. Operational modal analysis of a lightweight helicopter tail. LMS Conference Europe, München, Germany, 22-23 March 2006.