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Probabilistic Multivariate Statistical Process Control via Kernel Parameter Uncertainty Propagation
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DOI：10.1109/ACCESS.2026.3706157.png)
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Abstract
En 中文
Kernel-based multivariate statistical process control (K-MSPC) extends classical latent-variable monitoring to nonlinear industrial processes, but its performance depends strongly on kernel parameters such as lengthscales and variance terms. In current practice, these parameters are typically selected using heuristic rules or deterministic optimisation and are then treated as fixed, despite being estimated from finite and noisy data. This may lead to overconfident control limits and unstable alarm behaviour when the kernel configuration is uncertain. This work proposes a probabilistic K-MSPC framework for quantifying and propagating kernel parameter uncertainty to process monitoring statistics and diagnostic contributions. The proposed method follows a two-stage workflow: first, kernel parameters are calibrated deterministically using supervised or unsupervised models; second, Bayesian inference is performed using Markov chain Monte Carlo to obtain posterior samples of the kernel parameters. These posterior samples are propagated through kernel principal component analysis to generate probabilistic Hotelling’s $T^{2}$ and squared prediction error control charts, together with uncertainty-aware contribution plots. The framework is evaluated using the Tennessee Eastman Process benchmark. The results show that posterior-mean monitoring improves fault detection compared with deterministic prior-mean charts for the squared exponential (SE) kernel in several fault scenarios. The bands remain narrow during normal operation and widen under faulty conditions, indicating that epistemic uncertainty is amplified in abnormal regimes. The automatic relevance determination (ARD) kernel performs better than the single-length SE kernel, reduces posterior uncertainty, whereas the unsupervised calibration route produces wider posterior bands while maintaining robust fault detection.
Keywords:
Kernel PCA
Bayesian inference
MCMC
uncertainty quantification
Tennessee Eastman process