## 1 Introduction  
With the continuous development of urban rail transit, subway lines have developed rapidly in many cities. With the increasing demand for transportation facilities construction, a large amount of measured data in terms of subway evaluation, field testing, experimental verification, and simulation have been collected. Due to the sensor used for data acquisition being affected by vibration, some sensors are damaged, and the data is lost during the collection process, leading to a large amount of data waste. The data waste can be significantly reduced if the lost data can be recovered based on the existing normal data from adjacent channels. Research on lost data recovery is usually based on historical data to build a data recovery model [1]. At present, the research methods for data recovery can be roughly divided into three categories: The first is traditional mathematical models, including the moving average method, historical trend method, residual grey model, and interpolation method [2, 3, 4, 5, 6]. The second is intelligent recovery methods, including nonparametric regression and neural networks [7, 8]. The third is combination models [9, 10], which refers to a combination of two or more data processing methods. Although conventional methods can achieve the accurate recovery of single missing datasets, important information in long-term time series data is often ignored in addition to a prolonged estimation time, which causes missing data and distortion and has a greater impact on subsequent data analysis. The intelligent recovery method, especially the use of a neural network, can identify the characteristics, trends, and development laws of the variable changes from the time series, thereby achieving the effective prediction and recovery of the missing data. The intelligent recovery method mainly employs machine learning algorithms to identify and recover abnormal and lost data, and it is currently widely used for data recovery. With the advancement of machine learning, it is possible to predict future multi-epoch data by quantifying the relationship between current data and historical data through the characteristic trend in the data over time. [PERSON] et al. and [PERSON] et al. [11; 12] tried to use deep learning to monitor abnormal bearing data, and the results showed that deep learning achieved very high accuracy and robustness in monitoring the future state of things with the historical data. As the data have characteristics in the format of time series, learning temporal dependencies from sequence data poses challenges to classical machine learning techniques and standard neural networks. The long short-term memory (LSTM) network addresses this problem by introducing memory units into the network architecture. The LSTM network has great advantages in analyzing large-scale data [13; 14], and it has high prediction accuracy for time-series data such as atmospheric and ocean temperature, traffic flow, and vibration signals [15; 16]. For example, [PERSON] et al. applied the LSTM model to the temperature prediction of pavement roads [17]. Based on the excellent performance of the LSTM model, [PERSON] et al. [18] considered the influence factors of historical air quality and meteorological data and realized the fast and accurate prediction of PM2.5 by analyzing the long-term historical process of time-series data. [PERSON] et al. [19] applied a one-dimensional convolutional neural network (1-D CNN) and an LSTM to analyze vibration signals for bearing fault diagnosis. [PERSON] et al. [20] proposed a CNN-LSTM model for the accurate point-by-point prediction of high-speed railway car body vibration. LSTM networks perform well in extracting knowledge from sequence data over time spans, as has been shown in previous studies. Nowadays, an LSTM neural network is mainly used for the prediction of single-channel time-series data based on historical data.