Multivariate Time Series (MTS) analysis is crucial to understanding and managing complex systems, such as traffic and energy systems, and a variety of approaches to MTS forecasting have been proposed recently. However, we often observe inconsistent or seemingly contradictory performance findings across different studies. This hinders our understanding of the merits of different approaches and slows down progress. We address the need for means of assessing MTS forecasting proposals reliably and fairly, in turn enabling better exploitation of MTS as seen in different applications. Specifically, we first propose BasicTS+, a benchmark designed to enable fair, comprehensive, and reproducible comparison of MTS forecasting solutions. BasicTS+ establishes a unified training pipeline and reasonable settings, enabling an unbiased evaluation. Second, we identify the heterogeneity across different MTS as an important consideration and enable classification of MTS based on their temporal and spatial characteristics. Disregarding this heterogeneity is a prime reason for difficulties in selecting the most promising technical directions. Third, we apply BasicTS+ along with rich datasets to assess the capabilities of more than 30 MTS forecasting solutions. This provides readers with an overall picture of the cutting-edge research on MTS forecasting.

Multivariate time series long-term prediction, which aims to predict the change of data in a long time, can provide references for decision-making. Although transformer-based models have made progress in this field, they usually do not make full use of three features of multivariate time series: global information, local information, and variables correlation. To effectively mine the above three features and establish a high-precision prediction model, we propose a double sampling transformer (DSformer), which consists of the double sampling (DS) block and the temporal variable attention (TVA) block. Firstly, the DS block employs down sampling and piecewise sampling to transform the original series into feature vectors that focus on global information and local information respectively. Then, TVA block uses temporal attention and variable attention to mine these feature vectors from different dimensions and extract key information. Finally, based on a parallel structure, DSformer uses multiple TVA blocks to mine and integrate different features obtained from DS blocks respectively. The integrated feature information is passed to the generative decoder based on a multi-layer perceptron to realize multivariate time series long-term prediction. Experimental results on nine real-world datasets show that DSformer can outperform eight existing baselines.

Spatial-Temporal Graph Neural Networks (STGNNs) have been widely utilized in multivariate time series forecasting (MTSF), but they rely on the assumption of data completeness. In practice, due to factors such as natural disaster, STGNNs frequently encounter the challenge of missing data resulting from numerous malfunctioning data collectors. In this case, on the one hand, due to the presence of missing values, STGNNs easily generate incorrect spatial correlations, leading to the performance degradation. On the other hand, STGNNs require separate training of models for different missing rates, limiting their robustness. To address these challenges, we first propose two important components (interpolation attention and adaptive graph convolution), which utilize normal values to recover missing values into reliable representations and reconstruct spatial correlations. Then, we replace the fully connected layers in simple recursive units with these two components and propose Graph Interpolation Attention Recursive Network (GinAR), aiming to recursively correct spatial correlations and achieve end-to-end MTSF with missing values. Finally, we use data with different missing rates as positive and negative data pairs. By employing contrastive learning to train GinAR, we propose GinAR+ and enhance its robustness to data with different missing rates. Experiments validate the superiority of GinAR+ and our motivation.

This paper reviews the current research status of rolling bearing fault diagnosis technology for railway vehicles. Several domains are covered, including vibration fault diagnosis, acoustic signal fault diagnosis, and temperature prediction diagnosis methods on train rolling bearing test principles and related research. The application scenarios, system diagnosis accuracies, and model structures of various studies in the literature are also compared and analyzed. Furthermore, the main technical points to be improved and the analysis of the possible research directions are proposed, which provide new research ideas for subsequent fault diagnosis methods and system innovation research and development.