## 1 Introduction  
Recently, with the continuous acceleration of industrialization, industrial sensors are used in all walks of life to obtain various data and are widely used in many fields such as weather forecasting, medical treatment, power statistics, and aerospace telemetry [1]. A time series is the data collected at a certain frequency of industrial physical quantities monitored by sensors, since multiple sensors in an industrial scene are often correlated and sampled from multiple industrial sensors to obtain a multidimensional time series. However, due to the problem of the hardware device, the multidimensional time series in the actual scene may have the problem of missing values. Not only that, but for some fields, such as weather forecasting and stock forecasting, multidimensional time series forecasting is also a very valuable research problem [2], both of which can be defined as imputation problems for missing data. For imputation of multidimensional time series, sufficient analysis of the time series is required. In order to deal with the imputation problem of multidimensional time series, researchers have provided many traditional algorithms, forming the initial solutions. For example, the autoregressive integrated moving average (ARIMA) treats the imputation of time series as the process of calculating the unknown dependent variable from the known independent variables [3]. [PERSON] applied the Markov chain Monte Carlo method (MCMC method) to data imputation for processing data with multivariate arbitrary missing patterns [4]. However, these methods often require some prior knowledge, such as the difference order and autocorrelation lag order of the ARIMA [5]. At the same time, for complex multidimensional time series with high missing rates, due to the incomplete utilization of time series characteristics, the performance of these methods is generally poor [6]. In recent years, many machine learning methods have been used for multidimensional time series imputation problems. [PERSON] et al. used the EM algorithm to combine the decision tree and build a decision forest. After classifying and merging the data, the EM algorithm was used to implement data imputation. Through experiments on six public datasets with missing values and three artificially made missing value datasets, as well as a comparison with the DMI and SiMI algorithms, the effectiveness of this method for the imputation of missing data in attribute classes was verified [7]. In 2015, [PERSON] et al. proposed applying a self-organizing map neural network (SOM) to the data imputation task to predict the physical and chemical parameters of water samples. An SOM uses a nonlinear method to automatically fill in missing values in the data matrix. [PERSON] verified the SOM method in data imputation through experiments on surface water data (17-39% missing rate) sampled from the Reconquista River in Argentina. Regarding task effectiveness [8], [PERSON] provided a review of the methods related to building prediction models for time series through deep learning. The two models that perform well in sequence modeling problems are based on self-attention mechanism models and recurrent neural network-based models [9]. DeepAR, proposed by [PERSON] et al., utilizes an encoder-decoder structure combined with an autoregressive RNN model for time series prediction [10]. These machine learning methods have all conducted valuable explorations for the multidimensional time series imputation problem. Inspired by [PERSON]'s review, we adopted a network model based on the self-attention mechanism to impute time series. The main contributions of this paper include the following two aspects:  
* We propose a model for multidimensional time series imputation, which is based on the WGAN-GP framework and uses the informer part of the network structure to form the generator and the discriminator. The networks proposed outperform the original informer model and the GAN-based AST model in both real-world datasets.