## 1 Introduction  
Deflection plays a vital role in bridge structural health monitoring systems [1]. It is a direct indicator of the overall vertical stiffness and load-carrying capacity of the bridge structure. To a certain extent, it can reflect the change in the bridge line shape. When the deformation exceeds the allowable range of its deflection, it is often prone to collapse, so deflection monitoring in bridge projects is necessary [2]. With the rapid rise of large structures, the safety and reliability of bridges have become an increasing concern [3]. In general, establishing a structural health monitoring system is the primary method for understanding the operational status of a bridge [4]. However, due to various unfavorable factors, such as sensor failures and environmental influences, the monitoring data from bridge structural health systems often face issues like data distortion and abnormal offsets [5], making it difficult to assess the health of bridgespromptly. Therefore, preprocessing the signals collected from the static components of bridges to improve data quality has become an important issue [6]. Study [7] described the sliding average method to reduce noise by smoothing and filtering, which is simple to implement and computationally efficient. However, the method may introduce bias when processing signal boundaries, potentially distorting transient features in bridge deflection monitoring. Study [8] used the least squares method to smooth the signal and identified the signal singularities from the monitoring data by wavelet transform to obtain the characteristics of the real signal. Although this method can effectively identify singularities and perform preliminary denoising, it may be insufficient in dealing with complex noise environments, non-smooth signals, and dynamic noise characteristics. Study [9] applied Gaussian smoothing to filter noise in vibration signals, which preserves the overall trend and reduces high-frequency noise. However, it may misclassify important short-term fluctuations as anomalous, resulting in the loss of critical information. Study [10] employed an exponential smoothing method for rapid identification of the fundamental frequency of bridge ties, adjusting smoothing coefficients for non-smooth signals. However, it only performs simple exponential weighting and cannot accommodate multiscale features, limiting its ability to capture both short-term and long-term changes, which affects accurate bridge health monitoring. On the other hand, developing an effective bridge deflection prediction model remains a challenge [11]. At present, the primary focus is on statistical and data-driven approaches to predicting bridge health. Regarding statistics, study [12] analyzed the time-series signals of bridges using autoregressive integrated moving averages (ARIMAs), which effectively isolated the trend component of the data. However, this method only applies to linear models and cannot capture nonlinear features in the time series. Study [13] designed a seasonal differential autoregressive sliding average method with seasonal factors to address this limitation. However, this approach demands high data smoothness and suffers from low computational efficiency. On the data-driven side, study [14] obtains spatial information within the same period using convolutional neural networks (CNNs), but this method can only obtain features within the size of its convolutional kernel, and it cannot capture temporal features at the same time for long distances. Study [15] used a bidirectional long short-term memory network (BiLSTM) to input historical signals, focusing on connections between different time steps, but the method ignores the spatial information within each segment. In study [16], to focus on the time-space information simultaneously, the CNN and Gated Recurrent Unit (GRU) are united to predict the deflection value by using the bridge deflection data as the input to the CNN-GRU.