Multi-lag latent variable models for industrial process monitoring in dynamic and static states

Process data collected in modern complex industries have both static and dynamic features, and current process monitoring algorithms only focus on analyzing the two features individually, ignoring the coupling between the two features. This paper proposes a multi-lag latent variable model (MLVM) capable of monitoring both static and dynamic features of industrial processes and addressing the shortcomings of multi-lag slow feature analysis in applications. Firstly, the slow features with multi-lag autocorrelation are extracted separately using slow feature analysis, and the autocorrelation coefficients of the slow features are calculated. Multi-lag dynamic and static features are obtained by setting thresholds, and the static characteristics are further analyzed using independent component analysis. Finally, multi-lag dynamic, static, and global statistics are obtained using Bayesian inference. In addition, the averaging process under online monitoring is proposed to reduce the noise impact on MLVM. The reconstruction-based contribution index for the MLVM is derived to diagnosis after a fault. Based on the Tennessee Eastman process, the superiority of MLVM over the known algorithm is verified, and the validity and interpretability of MLVM are proved.