Development of New Discrete Wavelet Families for Structural Dynamic Analysis

Wavelet analysis is a powerful method for analyzing the time histories of signals. A discrete wavelet family is developed for structural dynamics by using the dilation equation to calculate scaling function coefficient values for arbitrary waveforms. The performance of this formula is verified by analyzing the scaling functions of multiple Daubechies wavelets. To assure the new discrete wavelet families have the characteristics of a specific system, the formula is applied to analytical and experimental response data. The relationship between the number of coefficients and their ability to successfully capture the characteristics of the signal is studied and a method is developed for determining the number of coefficients to be used when applying the formula. The resulting new families of discrete wavelets are based upon the nominal characteristics of a given system for use in signal processing and model discretization applications. The impulse response of a structure is proposed as a tuned baseline for structural health monitoring applications; the corresponding Wavelet Analysis of Structural Anomalies using Baseline Impulse-Response (WASABI) method is presented and discussed in the context of the wavelet development.