This paper presents an application of the multi-resolution wavelet-based methodology to uncover thermal effects from bridge responses based on the distinguished frequency bandwidths. First, periods of daily and seasonal temperature effects are verified using field-measured mid-span deflections of a cable-stayed bridge. Then, the formula to determine the decomposition level is derived on the basis of its capability in dividing the total bandwidth of signals. Moreover, simulated signals on two scales (i.e., minutely and hourly) are applied to validate the effectiveness of the proposed formula. Meanwhile, wavelet basis function ‘coif5′ is selected for thermal response separation due to its more stable performance compared to other functions. In-situ measured mid-span deflections of Xihoumen bridge are taken as an example to validate the effectiveness of the method through the similarity of daily vehicle gross mass and daily mean reconstructed deflection signals (without effects of temperature actions). As a result, the trends of daily mean deflections and vehicle gross mass are generally similar, except for the beginning and end of the time window. In conclusion, it is of practicality to determine the parameters by following the suggestion in this paper when using multi-resolution wavelet-based method to separate temperature responses.

中文翻译：

---

基于多分辨率小波的方法对桥梁长期监测系统的热响应分离

本文提出了一种基于多分辨率小波方法的应用程序，该方法基于可分辨的频率带宽从桥响应中发现热效应。首先，使用实测斜拉桥的中跨挠度来验证每日和季节性温度影响的周期。然后，基于其分解信号总带宽的能力，得出确定分解级别的公式。此外，在两个刻度（即，分钟和小时）上使用模拟信号来验证所提出公式的有效性。同时，由于与其他函数相比，小波基函数“ coif5”具有更稳定的性能，因此选择它来进行热响应分离。以西侯门大桥的实测跨距挠度为例，通过每天车辆总质量和日均重构挠度信号的相似性（无温度作用的影响）验证了该方法的有效性。结果，除了时间窗口的开始和结束之外，日平均挠度和车辆总质量的趋势通常相似。总之，采用多分辨率小波方法分离温度响应时，按照本文的建议确定参数是可行的。时间窗口的开始和结束除外。总之，采用多分辨率小波方法分离温度响应时，按照本文的建议确定参数是可行的。时间窗口的开始和结束除外。总之，采用多分辨率小波方法分离温度响应时，按照本文的建议确定参数是可行的。