High-Dimensional Statistical Process Control via Manifold Fitting and Learning

2025-09-24

AI Summary

Statistical process control (SPC) for high-dimensional dynamic industrial processes faces challenges due to nonlinear, time-varying underlying structures and the limitations of linear dimensionality reduction assumptions. Method: This paper proposes a distribution-free monitoring approach based on manifold fitting, explicitly modeling the intrinsic nonlinear low-dimensional manifold structure directly in the original high-dimensional space—contrasting with mainstream manifold learning paradigms that first embed data nonlinearly and then monitor in the latent space. Crucially, it constructs scalar control statistics enabling theoretically guaranteed Type-I error control. Results: Theoretical analysis and experiments on synthetic data, the Tennessee Eastman process, and armature images demonstrate superior fault detection sensitivity compared to PCA and KPCA-based methods. The approach achieves efficient online computation without distributional assumptions, offering a novel paradigm for anomaly detection in complex industrial systems.

Technology Category

• Machine Learning: Learning with Manifolds
• Data Mining & Knowledge Management: Anomaly/Outlier Detection
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

Abstract

We address the Statistical Process Control (SPC) of high-dimensional, dynamic industrial processes from two complementary perspectives: manifold fitting and manifold learning, both of which assume data lies on an underlying nonlinear, lower dimensional space. We propose two distinct monitoring frameworks for online or 'phase II' Statistical Process Control (SPC). The first method leverages state-of-the-art techniques in manifold fitting to accurately approximate the manifold where the data resides within the ambient high-dimensional space. It then monitors deviations from this manifold using a novel scalar distribution-free control chart. In contrast, the second method adopts a more traditional approach, akin to those used in linear dimensionality reduction SPC techniques, by first embedding the data into a lower-dimensional space before monitoring the embedded observations. We prove how both methods provide a controllable Type I error probability, after which they are contrasted for their corresponding fault detection ability. Extensive numerical experiments on a synthetic process and on a replicated Tennessee Eastman Process show that the conceptually simpler manifold-fitting approach achieves performance competitive with, and sometimes superior to, the more classical lower-dimensional manifold monitoring methods. In addition, we demonstrate the practical applicability of the proposed manifold-fitting approach by successfully detecting surface anomalies in a real image dataset of electrical commutators.

Problem

• Monitoring high-dimensional dynamic industrial processes via manifold techniques
• Developing two SPC frameworks using manifold fitting and learning approaches
• Ensuring controllable Type I error probability in fault detection

Innovation

• Manifold fitting approximates data in high-dimensional space
• Novel distribution-free chart monitors deviations from manifold
• Manifold learning embeds data into lower-dimensional space first