## 1 Introduction  
The structural performance of immersed tunnels built on soft soil will degrade with time due to the uneven settlement of foundations and the repeated action of external loads (such as vehicle flow, tidal force, and sedimentation loads). These potential problems may affect the operation and normal use of the tunnel, and even cause safety incidents such as structural damage [1; 2; 3; 4]. Establishing a health monitoring system for immersed tunnels is an effective way to solve this problem; thus, the dynamic changes of the tunnel structure can be monitored to assist the operation and management of the tunnel [5; 6; 7; 8]. This is of great significance for improving the reliability of the structure, ensuring its operational safety, reducing maintenance costs, preventing disasters, and improving operating service levels.  
Some immersed tunnels have been built with health monitoring systems, such as the Yongjiang Immersed Tunnel [9], the Zhoutouzui Immersed Tunnel [10], and the Nanchang Honggu Tunnel [11] in China. Additionally, the structural health monitoring systems, condition evaluation methods and data analysis methods have been presented in detail for the Nanchang Honggu Tunnel [12] and the Hong Kong-Zhuhai-Macao Bridge [13]. The establishment of a health monitoring system provides strong support for the infrastructure's operation and maintenance. However, in the process of data collection, the health monitoring system will inevitably be affected by factors such as stochastic vibrations, weak connections between devices, aging lines, unstable wireless transmission signals, and channel failures of collection devices, etc., resulting in a decline in the quality of collected data [14]. Such noise in data is not caused by the structure itself or state changes, but by the real-time health monitoring system. The noise contained in the monitoring sequence will interfere with structural damage identification and health state assessment, as the real structural response may be overwhelmed by the noise. Therefore, it is necessary to look for suitable methods to eliminate the noise.  
Experience has shown that these monitoring data inevitably contain a lot of noise [15]. For the problem of denoising health monitoring data, a lot of research points to the wavelet analysis method. These methods include the Bayesian discrete wavelet packet transform denoising approach [16], an adaptive wavelet packet denoising algorithm [17], an improved wavelet threshold denoising method [18], and discrete wavelet transform (DWT)-based denoising techniques [19]. These wavelet analysis-based methods each have their own characteristics and advantages, but they also have some limitations. For example, it is still an open issue about how to choose the best wavelet basis for the wavelet decomposition, since different wavelet bases have a great impact on the separation results [18]. On the other hand, there are various evaluation indicators of wavelet decomposition effects, such as the root mean square error (RMSE), the signal-to-noise ratio (SNR), the correlation coefficient (R), and smoothness (SMOT); thus, a comprehensive evaluation indicator needs to be developed.  
To solve the problems mentioned above in the preprocessing of health monitoring data of immersed tunnels, this study proposed an improved wavelet threshold denoising method. Firstly, it adopts a quantitative factor, namely the sparse index, to assist in selecting the most suitable wavelet basis. Then, the optimal wavelet basis, decomposition layer, and threshold are evaluated by the variation coefficient method. Finally, the concrete strain health monitoring data of the Hong Kong-Zhuhai-Macao Bridge (HZMB) immersed tunnel is used to verify the effectiveness of the proposed method.