Optimising kernel-based multivariate statistical process control

Kernel-based multivariate statistical process control (K-MSPC) extends classical MSPC by capturing nonlinear dependence through kernel principal component analysis (K-PCA). In practice, however, K-MSPC performance depends strongly on the choice of kernel and hyperparameters, which are often selected using non-procedural and time-consuming searches (e.g., grid/line search) that do not scale to richer parameterisations. We propose a fully procedural kernel-learning framework for K-MSPC inspired by Kernel Flows, in which kernel parameters are learned using stochastic subsampling and gradient-based optimisation. Because MSPC relies on a truncated K-PCA subspace, we optimise kernel parameters through an intermediate kernel principal component regression (K-PCR) discrimination objective that is structurally aligned with the latent-variable representation used by monitoring statistics. Building on this framework, we demonstrate extensions that become computationally feasible: learning variable-wise (additive) kernel parameters and learning kernel combinations to adapt the kernel family to data. The approach is evaluated on the Tennessee Eastman Process benchmark. Results show improved fault detection, including difficult faults that are poorly detected by standard K-PCA baselines, while providing diagnostic insights via variable contribution and attribution analyses. The proposed optimisation requires access to faulty (or simulated faulty) data and thus represents a supervised/semi-supervised calibration strategy complementary to classical unsupervised MSPC. • Kernel MSPC is performant to detect challenging faults, if optimisation is done right. • Kernel MSPC optimisation can be achieved through optimising Kernel PCR. • A Kernel Flows-inspired procedure is appropriate for optimising individual-parameter kernels. • Fitting individual kernel parameters brings performance improvement and diagnostics.