“…This relationships are often employed to achieve fault detection, e.g., using the auto-regressive moving average model (ARMA) or canonical correlation analysis (Chen et al, 2020a;2020b), etc. Fault monitoring signals, generated in practical industrial systems, tend to pose some new challenges, such as nonlinearity, dynamics, variability, and limited labels in nonstationary and stationary hybrid processes, which leads to the fact that the traditional, linear, and stationary common trend analysis methods are difficult to implement in fault detection (Zhirabok and Shumsky, 2018;Byrski et al, 2019). Therefore, considering the diversity of nonstationary and stationary industrial process faults and the fact that most of them are nonlinear or even strongly nonlinear, it is necessary to combine multiple variable analysis to explore relationships between many monitored variables, and then to describe the dynamic system behaviors (Worden et al, 2016;Ma et al, 2018;Zhang and Zhao, 2017;Zhang et al, 2018;Yan et al, 2016).…”