Improved Statistical Fault Detection Technique and Application to Biological Phenomena Modeled by S-Systems

Area of Science:

• Statistical Process Control
• Machine Learning
• Systems Biology

Background:

• Linear Principal Component Analysis (PCA) methods struggle with nonlinear systems.
• Previous work established the effectiveness of PCA-based Moving Window-Generalized Likelihood Ratio Test (MW-GLRT) for fault detection.
• Real-world systems often exhibit nonlinear dynamics, necessitating advanced detection methods.

Purpose of the Study:

• To develop a nonlinear fault detection method using Kernel Principal Component Analysis (KPCA).
• To enhance the MW-GLRT technique with Exponentially Weighted Moving Average (EWMA) for improved performance.
• To combine KPCA and EWMA-GLRT for superior fault detection in nonlinear biological systems.

Main Methods:

• Application of KPCA to handle nonlinear data and extract accurate principal components.
• Extension of the MW-GLRT technique to incorporate EWMA for residual weighting.
• Development of the KPCA-based EWMA-GLRT fault detection algorithm.

Main Results:

• The KPCA-based EWMA-GLRT method demonstrated superior fault detection performance.
• The new method achieved lower False Alarm Rates (FAR) and missed detection rates.
• Improved Average Run Length (ARL1) values were observed compared to traditional methods like GLRT, EWMA, Shewhart, and MW-GLRT.
• Effective application in monitoring key variables of the E. coli Cad System.

Conclusions:

• The KPCA-based EWMA-GLRT method offers significant improvements in fault detection for nonlinear systems.
• This approach enhances the monitoring of biological phenomena and process means.
• The developed method provides a robust tool for identifying faults with greater accuracy and reduced error rates.