## 1 Introduction
However, this method cannot identify the importance of data features, and it is easy to obtain abnormal features, which reduces prediction accuracy. In addition, there are emerging technologies, such as those used by [PERSON] et al., to study the deformation of simply supported concrete girder bridges over time using the information content provided by satellite data and combining it with other available sources [17]. Subsequently, they proposed a GIS plug-in called Bridge Assessment System via MTInSAR (BAS-MTInSAR), which aims at assessing the deformation of existing simply supported concrete girder bridges by means of Multi-temporal Interferometric Synthetic Aperture Radar (MTInSAR) [18]. However, the limitations of the characterization of the information contained in the satellite data are such that the proposed method cannot replace the traditional monitoring methods. To solve the problems of ignoring short-term fluctuations and failing to extract temporal and spatial information at the same time in the current existing studies, this paper proposes a bridge deflection prediction method based on cascaded residual smoothing and multiscale spatiotemporal attention networks. Cascade residual smoothing solves the problem of inadequate access to short-term fluctuating trends with traditional smoothing methods and maintains the overall trend, improving data quality. Specifically, cascaded residual smoothing starts by initially removing high-frequency noise from the signal through Gaussian filtering, preserving the overall trend. Then, the raw signal and the residuals after initial smoothing are obtained to further highlight the short-period fluctuations in the signal, making it easy to capture detailed changes. Finally, quadratic exponential smoothing is used to extract short-term trends or small-period variations in the deflection data, ensuring that the predictions are stable and reflect subtle fluctuations. On the other hand, to simultaneously acquire spatiotemporal information between different periods and focus on the important features while ignoring the abnormal features, we designed the multiscale spatiotemporal attention network (MSSAN). The network first extracts spatial information of the deflection data at multiple scales using a Multiscale Convolutional Neural Network (MSCNN), which can capture both short-term fluctuations and long-term trends in the data. Then, the GRU effectively captures the time dependence of the bridge deflection data by using self-attention (SA) to focus on the important features, focusing on the critical time steps in the deflection data that greatly impact future deflection values. Finally, the predicted values are output by linear transformation. In this paper, the validity of the method is verified through experiments, and the data taken at several static levels shows good prediction results, and comparison with similar techniques, which reflects the superiority and advancement of the method proposed in this paper. The specific contributions of this paper are as follows:  
1. This paper designs a cascade residual smoothing method to solve the problem of ignoring short-term fluctuations that exists in traditional smoothing methods. The method separates the long-term trend and short-term fluctuations, and gradually denoises them by cascading them, and the cascading residual smoothing reduces the risk of over-smoothing the data. After Gaussian filtering treats the overall trend, quadratic exponential smoothing is applied only to the residual part, thus smoothing short-term fluctuations more gently and reducing strong interference with the original data. 2. This paper proposes a multiscale spatiotemporal attention network to solve the problem of not being able to obtain spatiotemporal information simultaneously, which exists in traditional prediction methods. The network has multi-level feature extraction and time-dependent modeling capabilities and screens important time-series features to improve prediction accuracy.