Robust soft sensor modelling method for quality‐related data with mixed stationary and non‐stationary characteristics

Abstract Industrial process data typically exhibit mixed stationary and non‐stationary characteristics, with sensor sampling and noise interference often introducing outliers. Traditional stationary subspace analysis methods assume the entire process data to be non‐stationary, which can interfere with effective information extraction from stationary components. Moreover, the Gaussian distribution assumption often leads to severe performance degradation in the presence of outliers. To address these issues, this paper proposes a robust quality‐relevant soft sensor modelling method for mixed stationary and non‐stationary processes. Firstly, the process and quality data are decomposed into stationary and non‐stationary components using the augmented Dickey–Fuller test. Subsequently, the stationary components are decoupled into quality‐relevant stationary and quality‐irrelevant stationary latent variables, while the non‐stationary components are decoupled into quality‐relevant stationary, quality‐relevant non‐stationary, and quality‐irrelevant latent variables. A linear regression model is then constructed using the quality‐relevant stationary components from both the stationary and non‐stationary parts, along with the quality‐relevant non‐stationary components, as inputs, with the quality variable as the output. Furthermore, to enhance robustness against outliers, the Gaussian distribution assumption in the latent space is replaced with a Student's t‐distribution, whose time‐varying degrees of freedom allow for adaptive adjustment of tail heaviness. Experimental results based on numerical simulations and an industrial case study demonstrate that the proposed method achieves higher quality prediction accuracy for mixed data and exhibits strong robustness against outlier interference, providing a reliable online soft sensor solution for complex industrial processes.