An identification approach for linear and nonlinear time-variant structural systems via harmonic wavelets

A novel identification approach for linear and nonlinear time-variant systems subject to non-stationary excitations based on the localization properties of the harmonic wavelet transform is developed. Specifically, a single-input/single-output (SISO) structural system model is transformed into an equivalent multiple-input/single-output (MISO) system in the wavelet domain. Next, time and frequency dependent generalized harmonic wavelet based frequency response functions (GHW-FRFs) are appropriately defined. Finally, measured (non-stationary) input–output (excitation–response) data are utilized to identify the unknown GHW-FRFs and related system parameters. The developed approach can be viewed as a generalization of the well established reverse MISO spectral identification approach to account for non-stationary inputs and time-varying system parameters. Several linear and nonlinear time-variant systems are used to demonstrate the reliability of the approach. The approach is found to perform satisfactorily even in the case of noise-corrupted data.

► A novel harmonic wavelets based system identification approach is developed. ► Time and frequency dependent wavelet based frequency response functions are defined. ► The approach can account for non-stationary data and nonlinear time-variant systems. ► Non-Gaussian random processes can be handled in a straightforward manner.