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    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.