Analysis of swept-sine runs during modal identification

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Abstract

Experimental modal analysis of large aerospace structures in Europe combine nowadays the benefits of the very reliable but time-consuming phase resonance method and the application of phase separation techniques evaluating frequency response functions (FRF). FRFs of a test structure can be determined by a variety of means. Applied excitation signal waveforms include harmonic signals like stepped-sine excitation, periodic signals like multi-sine excitation, transient signals like impulse and swept-sine excitation, and stochastic signals like random. The current article focuses on slow swept-sine excitation which is a good trade-off between magnitude of excitation level needed for large aircraft and testing time. However, recent ground vibration tests (GVTs) brought up that reliable modal data from swept-sine test runs depend on a proper data processing. The article elucidates the strategy of modal analysis based on swept-sine excitation. The standards for the application of slowly swept sinusoids defined by the international organisation for standardisation in ISO 7626 part 2 are critically reviewed. The theoretical background of swept-sine testing is expounded with particular emphasis to the transition through structural resonances. The effect of different standard procedures of data processing like tracking filter, fast Fourier transform (FFT), and data reduction via averaging are investigated with respect to their influence on the FRFs and modal parameters. Particular emphasis is given to FRF distortions evoked by unsuitable data processing. All data processing methods are investigated on a numerical example. Their practical usefulness is demonstrated on test data taken from a recent GVT on a large aircraft. The revision of ISO 7626 part 2 is suggested regarding the application of slow swept-sine excitation. Recommendations about the proper FRF estimation from slow swept-sine excitation are given in order to enable the optimisation on these applications for future modal survey tests of large aerospace structures.

Introduction

The European aircraft industry plans to extend their product offer towards high-capacity aircraft. The prototypes of these aircraft are dynamically characterised by a high modal density in the very low frequency range. This requires a high effort on the part of the experimental modal analysis. On the other hand, the test time should be reduced to a minimum in order to reduce costs. A new test strategy was proposed, developed, and applied during the ground vibration tests (GVTs) of the recently built, new aircraft prototypes [1], [2] in order to meet these requirements.

An essential part of the improved test strategy is the combination of the classical phase resonance test method (sine dwell) with phase separation techniques which, in turn, are based on the evaluation of measured frequency response functions (FRFs). Several excitation types (see also [3]) were investigated with regard to their suitability for the modal identification of large aircraft during a research GVT in 1999 [2]. The slow swept-sine excitation emerged from the investigation as the most promising excitation signal. The tests also revealed that reliable FRFs depend on the proper signal processing of the measured data.

In 1986, the international organisation for standardisation published guidelines with ISO 7626 part 2 [4] for the application of slowly swept sinusoids. They are referred to in the standard issue on modal testing [5], where the recommendation is given “to check that progress through the frequency range is sufficiently slow to check that the steady-state response conditions are attained before measurements are made. If an excessive sweep rate is used, then distortions of the FRF plot are introduced, ...”.

This article investigates the source of these so-called FRF distortions. The standards on swept-sine excitation are reviewed and the theoretical background of sweep excitation is given. Furthermore, the methods of the correct estimation of FRFs are elucidated and compared with those that produce FRF distortions. The energy of swept-sine waveforms is investigated and the effect of swept-sine excitation on the FRF is studied using a single degree-of-freedom (sdof) system. Finally, experimental data acquired during the vibration tests of large aerospace structures are presented.

Section snippets

Review of the standards

The standard for the experimental determination of mobility is defined in the International Standard ISO-7626 [4] which was published in its first issue in 1986. Mobility is defined there as an FRF which is a phasor of the motion (acceleration, velocity, or displacement) at a structural point due to a unit force excitation. The FRF is exclusively determined by the dynamics of the structure which, in turn, are usually described by modal parameters. This implies linearity.

FRFs can be determined

Theoretical background

The effect of swept-sine excitation on the identification of the FRFs can be best studied in a sdof system. Its dynamic behaviour can be described in general by the FRF of the system:H(ω)=U(ω)P(ω),where U(ω) and P(ω) are the spectra of the response and excitation, respectively. The FRF is exclusively determined by the dynamics of the structure.

FRF estimation

The effect of swept-sine excitation on the FRF by means of different estimation methods is investigated in this section. A typical corner case for large aerospace structures is taken as a numerical example. The sdof system and its excitation is determined by

  • eigenfrequency: fr=1Hz

  • damping: ζ=1% and ζ=2%

  • logarithmic sweep

  • different sweep rates: S=0.25–2oct/min

  • frequency range of excitation: f=0.7–1.4Hz

Experimental results of large aircraft

Typical swept-sine test data acquired during the GVT of a four-engine aircraft are presented here in order to investigate the effect of the different evaluation methods on real test data. The aircraft is dynamically characterised by a high modal density (≈4modes/Hz) in the low-frequency range. A photo of a typical GVT test set-up is shown in Fig. 11.

The sweep test run investigated here is defined by the following parameters:

  • frequency band from 0.5 to 32Hz

  • logarithmic sweep, velocity 0.5oct/min

Summary and conclusion

The European aircraft industry is constantly calling for a reduction of the testing time of prototypes without diminishing the accuracy of the data. As a consequence, substantial changes in the testing strategy have been introduced in past ground vibration tests of European aircraft. This test strategy is mainly based on the combination of the benefits of the very reliable but time-consuming phase resonance method and the use of phase separation techniques on data stemming from swept-sine

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