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.

中文翻译：

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结构健康监测中时变信号小波多分辨率分析的最佳水平选择

尽管离散小波变换 (DWT) 用于分析时变测量的有效性已经在机械和土木工程应用中得到了研究，但仍有一些基本问题需要回答，例如如何选择最佳分解级别 (DL)具体任务。最佳 DL 的选择仍然是一个尚未得到充分探索和彻底调查的问题。在机械和土木工程应用中，绝大多数基于小波的方法都与非平稳测量相关，并且没有提供有关如何选择 DL 或将其链接到可以识别结构异常的有用特征的详细信息。本研究提出了一个新的详细框架，用于选择最佳 DL 以保证对时变结构响应进行有效的小波分析。本文提出的方法使用各种小波和理论层次来分解信号并识别那些相互作用影响深度学习的方面，例如数据特征、频带特征、降噪、相似性、共享信息和重建质量。为了证明我们提出的方法的有效性，我们考虑了使用各种母小波对 El Centro 地震和物理实验振动台结果加速度响应的比较研究。实验结果表明，El Centro 地震的最佳 DL 为 4，加速度数据的最佳 DL 为 6。