A Comparative Study of Linear vs. Nonlinear Data-Driven Modeling Accuracy and Fault Detection Sensitivity in Chemical Processes

Data-driven process monitoring frameworks depend on the quality of the underlying model to accurately represent normal operating behavior, as modeling errors propagate directly into fault detection residuals. In this paper, a two-stage comparative analysis is presented of three data-driven modeling approaches: Principal Component Analysis (PCA), Bayesian-Optimized Kernel PCA (BOKPCA), and Bayesian-Optimized Neural Networks (BONN). First, their prediction accuracy is evaluated at different noise levels and reduced dimensionalities, and then assessing how this accuracy translates into fault detection performance. Modeling accuracy is quantified using the mean squared error (MSE) relative to noise-free data across a range of signal-to-noise ratios. Fault detection performance is subsequently evaluated using the Maximum Multivariate Generalized Likelihood Ratio chart, augmented through interval data analysis. Three case studies are used: a nonlinear synthetic dataset, the Tennessee Eastman Process, and a bench-scale Fischer-Tropsch Gas-to-Liquid reactor. The modeling results show that BONN consistently achieves a lower MSE than PCA across noise levels, while BOKPCA's model selection accuracy degrades at higher noise. These trends carry through to fault detection, where BONN's modeling advantage translates into higher detection rates, particularly for mean-shift and slow-drift fault types in processes with strong nonlinear dynamics and limited training data.