A critical problem facing data collection in structural health monitoring, for instance via sensor networks, is how to extract the main components and useful features for damage detection. A structural dynamic measurement is more often a complex time-varying process and therefore, is prone to dynamic changes in time-frequency contents. To extract the signal components and capture the useful features associated with damage from such non-stationary signals, a technique that combines the time and frequency analysis and shows the signal evolution in both time and frequency is required. Wavelet analyses have proven to be a viable and effective tool in this regard. Wavelet transform (WT) can analyze different signal components and then comparing the characteristics of each signal with a resolution matched to its scale. However, the challenge is the selection of a proper wavelet since various wavelets with varied properties that are to analyze the same data may result in different results. This article presents a study on how to carry out a comparative analysis based on analytic wavelet scalograms, using structural dynamic acceleration responses, to evaluate the effectiveness of various wavelets for damage detection in civil structures. The scalogram’s informative time-frequency regions are examined to analyze the variation of wavelet coefficients and show how the frequency content of a signal changes over time to detect transient events due to damage. Subsequently, damage-induced changes are tracked with time-frequency representations. Towards this aim, energy distribution and sharing information are investigated. The undamaged and damaged simulated comparative results of a structure reveal that the damaged structure were shifted from the undamaged structure. Also, the Bump wavelet shows the best results than the others.

A critical problem encountered in structural health monitoring of civil engineering structures, and other structures such as mechanical or aircraft structures, is how to convincingly analyze the nonstationary data that is coming online, how to reduce the high-dimensional features, and how to extract informative features associated with damage to infer structural conditions. Wavelet transform among other techniques has proven to be an effective technique for processing and analyzing nonstationary data due to its unique characteristics. However, the biggest challenge frequently encountered in assuring the effectiveness of wavelet transform in analyzing massive nonstationary data from civil engineering structures, and in structural health diagnosis, is how to select the right wavelet. The question of which wavelet function is appropriate for processing and analyzing the nonstationary data in civil engineering structures has not been clearly addressed, and no clear guidelines or rules have been reported in the literature to show how the right wavelet is chosen. Therefore, this study aims to address an important question in this regard by proposing a new framework for choosing a proper wavelet that can be customized for massive nonstationary data analysis, disturbances separation, and extraction of informative features associated with damage. The proposed method takes into account data type, data and wavelet characteristics, similarity, sharing information, and data recovery accuracy. The novelty of this study lies in integrating multi-criteria which are associated directly with features that correlated well with change in structures due to damage, including common criteria such as energy, entropy, linear correlation index, and variance. Also, it introduces and considers new proposed measures, such as wavelet-based nonlinear correlation such as cosh spectral distance and mutual information, wavelet-based energy fluctuation, measures-based recovery accuracy, such as sensitive feature extraction, noise reduction, and others to evaluate various base wavelets’ function capabilities for appropriate decomposition and reconstruction of structural dynamic responses. The proposed method is verified by experimental and simulated data. The results revealed that the proposed method has a satisfactory performance for base wavelet selection and the small order of Daubechies and Symlet provide the best results, especially order 3. The idea behind our proposed framework can be applied to other structural applications.