A Guaranteed-Superset Fusion of PCA and Slow Feature Analysis for Robust Fault Detection in the Tennessee Eastman Process

Principal Component Analysis (PCA)-based monitoring, via Hotelling's T² and Squared Prediction Error (SPE), remains the yardstick most fault-detection work in the chemical process industry is measured against. Its known weakness is faults that creep in as slow drifts rather than sharp variance jumps: faults 3, 9, and 15 in the Tennessee Eastman Process (TEP) benchmark are the standard examples. Slow Feature Analysis (SFA) takes a different angle, searching for latent directions that evolve as slowly as possible rather than ones with high variance, though alone it does not consistently beat PCA on the faults that matter most. Combining the two helps: flagging a sample whenever either the PCA or SFA limit is crossed guarantees a fault detection rate (FDR) no lower than PCA's by construction — a deterministic property that distinguishes this fusion from the heuristic, weight-tuned evidence-combination schemes (Bayesian, Dempster–Shafer, weighted voting) more commonly used to merge heterogeneous fault detectors — and empirically it proved meaningfully higher on faults 3, 9, and 15, with non-overlapping 95% bootstrap intervals throughout. We also layered a series of supervised meta-classifiers onto the PCA/SFA statistics with progressively more temporal structure: exponential smoothing, then per-dimension features, then CUSUM accumulation. The CUSUM variant wins on one of the three hard faults, but no learned model beats PCA on all three, itself a useful result showing how much a guaranteed detector can be worth against one whose edge is only empirical. Repeating the core comparison on a fully separate resample of TEP runs, untouched during detector construction, gave the same result, and we report the false-alarm cost honestly rather than showcasing detection gains alone. Fusing two linear detectors this way, one provably no worse than the baseline, is a sound, defensible upgrade to classical PCA monitoring wherever slow, hard-to-catch drifts matter operationally.