Selecting optimum levels of wavelet multi‐resolution analysis for time‐varying signals in structural health monitoring

Although the effectiveness of discrete wavelet transform (DWT) for analyzing time-varying measurements has been studied for mechanical and civil engineering applications, a few fundamental questions still need to be answered, such as how to choose an optimal decomposition level (DL) for a specific task. Selection of the optimal DL still remains a question that has not been adequately explored and not thoroughly investigated. Vast majority of wavelet based methods in mechanical and civil engineering applications have been associated with nonstationary measurements and do not offer detail information on how DL should be selected or linked to useful features that can identify anomalies in a structure. This study proposes a new detailed framework for choosing the optimal DL to guarantee an effective wavelet analysis for time-varying structural responses. The approach proposed in this paper uses various wavelets and theoretical levels to decompose the signal and to identify those aspects that interact to affect the DL, such as data characteristics, frequency band features, noise reduction, similarity, sharing information, and reconstruction quality. To show the effectiveness of our proposed method, we considered a comparative study using various mother wavelets on El Centro earthquake and acceleration responses from shaking table results of physical experiment. Experimental results show that the optimal DL for El Centro earthquake is 4 and for the acceleration data is 6. These results obviously demonstrate the stability and the robustness of the proposed method in the analysis of contaminated time-varying signals.