TC-GATN: Temporal Causal Graph Attention Networks With Nonlinear Paradigm for Multivariate Time-Series Forecasting in Industrial Processes

Multivariate time-series (MTS) forecasting plays an important role in industrial process monitoring, control, and optimization. Usually, hierarchical interactive behaviors among industrial MTS have formed complex nonlinear causal characteristics, which greatly hinders the applications of the existing predictive models. It is found that graph attention networks (GATs) provide technical ideas to meet this challenge. However, the unknown directed graph and linear conversions of node information make conventional GATs less popular for the industrial fields. In this article, we propose a novel prediction model termed as temporal causal graph attention networks with nonlinear paradigms (TC-GATN) to adequately capture inherent dependencies on industrial MTS. Specifically, the graph learning algorithm concerning the Granger causality is exploited to extract potential relationships among multiple variables for guiding directional edge connections of the hierarchy. Then, parallel gated recurrent unit encoders located in the graph neighborhood space are introduced to perform the nonlinear interaction of node features, which accomplishes the adaptive transformation and transmission. The self-attention mechanism is further employed to aggregate encoder hidden states across all the stages. Finally, a temporal module is supplemented to process information from the graph layer, achieving satisfactory predictions. The feasibility and effectiveness of the TC-GATN are validated by two actual datasets from the methanol production and the chlorosilane distillation