# Unsupervised Deep Anomaly Detection for Industrial Multivariate Time Series Data
## 1 Introduction  
With the rapid development and widespread adoption of the Industrial Internet of Things (IIoT), which involves the real-time collection of large volumes of industrial environmental data through sensors, devices, and other IoT devices for data gathering, analysis, and automated control in industrial environments [1, 2, 3, 4], there has been an explosive growth in time-series data. This presents significant challenges for information mining and processing in modern industry [5, 6]. The Industrial Internet of Things is a crucial driver for the digital transformation of traditional manufacturing, energy, and power industries into Industry 4.0. Any abnormal behavior in devices within the Industrial Internet of Things nodes can lead to a series of errors, potentially causing major production accidents and significant economic losses. Implementing automatic and accurate anomaly detection can contribute to reducing such events. However, time-series anomaly detection remains a complex task and continues to be a subject of significant research and attention [7]. Industrial time-series anomaly detection faces the following challenges. While deep learning shows promise in industrial anomaly detection, the multivariate time-series data anomaly detection field still encounters significant challenges. In real industrial production environments, the data generated often lack labels. Labeling theextensive data collected from sensors and smart devices requires substantial human and material resources. Additionally, the challenge of data imbalance arises because the probability of actual device anomalies is extremely low. Improving model anomaly detection capabilities in the absence of sufficient anomaly data samples is difficult. This poses a substantial challenge to model training, necessitating research into how to train models to recognize anomaly data in unbalanced datasets to achieve the desired outcomes. Furthermore, anomalies often result from the combined effects of multiple variables rather than a single variable. Therefore, the inter-variable correlations cannot be ignored. However, as the feature dimensions increase, it becomes more challenging to grasp the correlations between variables [8; 9]. To address these challenges, this paper proposes a multivariate time-series anomaly detection method. Essentially, it extracts features through a convolutional autoencoder as a characterization network to obtain reconstruction errors. It then utilizes an attention-based prediction network to capture the time-dependent relationships of the reconstruction errors. Finally, the two subnetworks are jointly optimized to minimize both reconstruction and prediction errors, significantly enhancing the model's anomaly detection performance. The contributions of this paper are summarized as follows:  
1. Introduction of the AT-DCAEP, a model that characterizes spatiotemporal patterns by simultaneously performing reconstruction and prediction analyses. In the characterization network, we construct a convolutional autoencoder to extract spatial features from multivariate time-series data. In the prediction network, we build an externally attention-based prediction model to capture time dependencies. 2. Addition of multi-head attention between the convolutional encoder and decoder to focus on crucial information in low-dimensional space. The inclusion of multi-head attention is intended to model the distribution of low-dimensional feature space, enhancing the characterization network's reconstruction capabilities. Experimental results show the effectiveness of this method in improving model accuracy. 3. Performance benchmarking of the AT-DCAEP against state-of-the-art anomaly detection methods on six publicly available datasets. Experimental results demonstrate that AT-DCAEP significantly outperforms baseline methods, with a 5.68% improvement in \(F1\) score. Additionally, the AT-DCAEP achieves the optimal balance between anomaly detection performance and computational cost.