Continuous wavelet analysis for system parameter identification

International audienceWavelets-based representations offer an important option for capturing localized effects in many signals. Over a period of several decades, wavelet analysis has been set on a rigorous mathematical framework and has been applied to quite diverse fields. The field of vibration analysis has benefited from this mathematical development in conjunction with vibration monitoring, system identification, damage detection and several other tasks. In order to overcome the weakness of the Fourier-based approach in providing indirect or incomplete information on capturing time-varying features of structure, wavelet transform can be developed to construct new frameworks for system identification and damage detection. Wavelet analysis really lends itself to system-identification applications. For instance, frequency localization properties allow detection and decoupling of each vibration modes of multi-degree-of-freedom linear systems. This lecture deals with the application of wavelet analysis for parameter identification from measured data of mechanical systems under vibration. The wavelet representation of the system response can be truncated to an appropriate scale parameter in order to filter measurement noise. It is divided into three parts. The first part has the restrictive objective of, on one hand, discussing concepts and properties of the continuous wavelet transform closely related to vibration analysis and, on the other hand, citing sources that can be readily available. The second part is devoted to the use of wavelet analysis for modal identification. Closedform expressions to compute the damping ratio, the natural frequency and the shape of each mode, based on ridges and skeletons of the wavelet transformed free vibration response are proposed. Two difficulties during the implementation of this technique are then highlighted: the edge effect and the choice of the time–frequency localization of the wavelet transform. The problem of the estimation of the instantaneous frequencies of two adjacent modes is finally illustrated and it is shown that a correct choice of the mother wavelet's parameters leads to an accurate identification of the modal parameters. Finally, a generalization of the use of wavelet analysis in the case of nonlinear systems is formulated in the third part. It allows to detect, localize and characterize the type of nonlinearities present within the system behaviour. Several application examples are presented such as free oscillations of a plexy-glass plate, response of a mechanism made of three pendulums under ambient excitations, free oscillations of a beam with a geometrical non-linearity, response of a stay-cable under shocks, response of a bridge-like structure under crossing loads