This paper develops a trend line-based algorithm for signal decomposition in which the adjusted Savitzky–Golay filter is utilized to initiate the decomposition process. In this line, the proposed algorithm determines some special trend lines, mainly composed of the natural frequency of a bridge. An easy-to-implement algorithm is then provided to formulate this process and to decompose the given signal into its components in a systematic way. Additionally, a residual signal is generated by the proposed algorithm to store the detected noise and to reconstruct the original signal. To verify the proposed algorithm in the field of bridge health monitoring, a set of numerical and experimental examples are offered in which the proposed algorithm is employed to decompose the signal and provide the constituent components. Moreover, the application of the proposed algorithm in damage localization of the bridge is addressed in the appendix using a simply supported bridge under a moving vehicle. Finally, the bridge example is solved by empirical mode decomposition, as a promising benchmark method, to further illustrate the accuracy of the results and compare them in detail.

中文翻译：

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一种基于经验时域趋势线的基于Savitzky-Golay滤波器的桥式信号分解算法

本文开发了一种基于趋势线的信号分解算法，其中利用调整后的 Savitzky-Golay 滤波器来启动分解过程。在这条线上，所提出的算法确定了一些特殊的趋势线，主要由桥梁的固有频率组成。然后提供了一个易于实现的算法来制定这个过程，并以系统的方式将给定的信号分解为其组成部分。此外，所提出的算法会生成一个残差信号来存储检测到的噪声并重建原始信号。为了在桥梁健康监测领域验证所提出的算法，提供了一组数值和实验实例，其中使用所提出的算法来分解信号并提供组成成分。而且，所提出的算法在桥梁损伤定位中的应用在附录中使用移动车辆下的简支桥进行了讨论。最后，通过经验模态分解对桥梁实例进行求解，作为一种很有前景的基准方法，进一步说明结果的准确性并进行详细比较。