Optimum wavelet selection for nonparametric analysis toward structural health monitoring for processing big data from sensor network: A comparative study

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.