EAAI Journal 2026 Journal Article
A Temporal-spatial Causal Variational Network for accurate sintering temperature forecasting in rotary kilns
- Kai Wang
- Hua Chen
- Xiaogang Zhang
- Qianyu Chen
- Yuqi Cai
- Lei Zhang
Accurate forecasting of sintering temperatures (ST) is pivotal to the high-efficiency, low-energy operation of rotary kilns. The complexity of coupled multivariable process data in industrial environments makes it difficult to uncover patterns and structures in the data, leading to unsatisfactory predictive performance. To accurately analyze temporal–spatial relationships among thermal process variables in rotary kilns, we analyze the causal association among variables and construct a causal graph of the sintering process according to the physicochemical mechanism of sintering. An autoregressive Causal Hidden Markov Model is introduced to model the causal relationships of variables and propagates to generate ST forecasting. In implementation, a generative recurrent neural network, Temporal–spatial Causal Variational Network (TCVN) is designed to generate the representation of hidden variables and extract ST-related features robustly. Each time step in TCVN is composed of a Causal Variational Module (CVM) that integrates a Graph Convolutional Network (GCN) with a Variational Autoencoder (VAE) based on the constructed causal graph. The experiments on real-world data demonstrate that the proposed approach effectively improves the forecasting accuracy of ST with horizons of 1, 3, 6, and 12 steps, confirming the superiority of the proposed model. • A TCVN is proposed for accurate sintering temperature forecasting in rotary kilns. • A causal graph according to the mechanism of sintering is designed. • A CVM is designed to learn the hidden variables in the causal graph. • Detailed experiments are conducted to validate the performance of the TCVN.