Modal parameter estimation based on the wavelet transform of output data

Abstract

The paper presents the results of the research on modal parameter estimation based alone on output measurements. A system is excited randomly and random decrement functions are used to separate the random responses from the determination free vibrations. It is shown that on estimation of the natural frequencies and damping ratios of the system is possible using the wavelet transform of the system's free response. A particular form of the son wavelet function improves the results compared to those obtained with the Morlet wavelet function. An optimal son wavelet function is obtained by minimisation of the wavelet transform entropy. The accuracy of this new technique is confirmed in a numerical example and by applying it to ambient vibration measurements of a bridge excited by traffic.Keywords Wavelet transform, Modal parameters, Ambient vibration transform entropy, Random decrement technique IntroductionModal analysis is an important tool in a wide variety of engineering applications including structural vibrations and acoustics. The information obtained by it describes the natural frequencies and damping associated with structural modes of a system. It can be used then to determine properties of the system such as safe operating condition, dynamic response behaviour, material damage or to conduct active vibration control of the system [2, 3, 6]. In general, the experimental identification of structural modes of vibration is carried out by measuring the input, or the excitation, of the structure under test and the resulting response due to this input. There are situations, however, where controlled excitation cannot be used. For example, if the structure to be tested is in operation, applying any kind of external force may cause undesirable effect. Other examples are mechanical or civil engineering systems such as offshore structures, bridges, [2, 6], towers [3], tall buildings and aircraft in flight which are under ambient vibrations and the excitation is not available. To identify the modal parameters only acceleration responses of the system are available, measured under ambient conditions. System identification using ambient vibration measurements presents a challenge, requiring the use of special identification techniques, which can deal with very small magnitudes of ambient vibration contaminated by noise. In such cases, a promising technique is the use of the random decrement technique, [3,4], which is a special averaging procedure to obtain, free responses.The aim of this paper is to show how the wavelet analysis of the free response of a system allows the estimation of modal parameters. The paper is organised as follows. The theoretical background of the wavelet transform with its properties is presented in Sec. 2. In Sect. 3, we minimise the entropy of the wavelet transform to obtain a parameter which improves the time and frequency resolutions. It is shown in Sect. 4 that the modulus and phase of the wavelet transform are directly related to eigenfrequencies and damping coefficients of vibrating systems...

Analysis of wave slam induced hull vibrations using continuous wavelet transforms

“…(10) is always smaller than 1.2 Â 10 À 3 . Moreover, recent studies of mechanical fault detection, impact and singularity detection have used the Morlet function, (see Ruzzene et al, 1997;Staszewski, 1997;Jordan et al, 1998;Hajj et al, 1998;Weggel et al, 1999;Kelley et al, 2000;Teisseire et al, 2000;Patsias and Staszewski, 2002;Lardies et al, 2004;Liu and Babanin, 2004;Ren, 2004 andTse, 2005).…”

“…Using asymptotic techniques, (see Delprat et al, 1992;Carmona et al, 1997;Staszewski, 1997;Ruzzene et al, 1997;Brenner and Lind, 1998;Piombo et al, 2000;Boltezar, 2004;Lardies et al, 2004;Yan et al, 2006a;Meo et al, 2006;Erlicher andArgoul, 2007 andTan et al, 2008), the wavelet transform can be expressed approximately as:…”

New modal identification method under the non-stationary Gaussian ambient excitation

“…It has seen a surge of such activities in the last decade. The most extensively employed techniques involve the short-time Fourier transform (STFT), WignerVille distribution (WVD), wavelet transform, and Hilbert-Huang transform (HHT) and their enhanced derivatives [2][3][4][5] . However, the non-parametric T-F methods suffer from various limitations respectively.…”

Modal parameter identification based on ARMAV and state–space approaches

“…In the time domain [7][8][9][10] correlation functions or covariance matrices between output responses are used to obtain a companion matrix or a transition matrix and extract modal parameters from eigen decomposition of these matrices. In the time-frequency domain [11,12] the wavelet transform of the free response of the structure is used. The wavelet transform of a signal results in a complex valued form and it is shown that the modulus of the wavelet transform is related to damping ratios and its phase to eigenfrequencies.…”