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.

在土木工程结构以及其他结构（如机械或飞机结构）的结构健康监测中遇到的一个关键问题是如何令人信服地分析即将上线的非平稳数据，如何减少高维特征以及如何提取有用的信息与破坏推断结构条件有关的特征。由于其独特的特性，小波变换已被证明是一种用于处理和分析非平稳数据的有效技术。但是，在确保小波变换在分析来自土木工程结构的大量非平稳数据以及结构健康诊断中的有效性时，经常遇到的最大挑战是如何选择正确的小波。哪种小波函数适合用于处理和分析土木工程结构中的非平稳数据的问题尚未得到明确解决，并且文献中也没有报告明确的准则或规则来说明如何选择正确的小波。因此，本研究旨在通过提出一个新的框架来选择合适的小波，从而解决这一重要问题，该小波可以针对大量的非平稳数据分析，干扰分离以及与损伤相关的信息特征的提取进行定制。所提出的方法考虑了数据类型，数据和小波特征，相似性，共享信息和数据恢复精度。这项研究的新颖之处在于整合了多个标准，这些标准与与损坏造成的结构变化良好相关的特征直接相关，包括诸如能量，熵，线性相关指数和方差之类的通用标准。此外，它介绍并考虑了新提出的措施，例如基于小波的非线性相关（例如cosh光谱距离和互信息），基于小波的能量波动，基于措施的恢复精度（例如敏感特征提取，降噪等）。评估各种基本小波的功能能力，以适当地分解和重建结构动力响应。实验和仿真数据验证了该方法的有效性。