Interpretable Fault Detection using Projections of Mutual Information Matrix

TL;DR

This paper introduces a novel fault detection method based on a mutual information matrix that effectively identifies root variables causing faults with high interpretability, improved detection rates, and robustness to hyper-parameters.

Contribution

The paper proposes the PMIM methodology using matrix-based Rénnyi's entropy to estimate MI, enhancing fault detection interpretability and performance in industrial processes.

Findings

PMIM achieves higher fault detection rate (FDR)

PMIM maintains lower false alarm rate (FAR)

PMIM is less sensitive to hyper-parameters

Abstract

This paper presents a novel mutual information (MI) matrix based method for fault detection. Given a $m$-dimensional fault process, the MI matrix is a $m \times m$ matrix in which the $(i,j)$-th entry measures the MI values between the $i$-th dimension and the $j$-th dimension variables. We introduce the recently proposed matrix-based R\'enyi's $\alpha$-entropy functional to estimate MI values in each entry of the MI matrix. The new estimator avoids density estimation and it operates on the eigenspectrum of a (normalized) symmetric positive definite (SPD) matrix, which makes it well suited for industrial process. We combine different orders of statistics of the transformed components (TCs) extracted from the MI matrix to constitute the detection index, and derive a simple similarity index to monitor the changes of characteristics of the underlying process in consecutive windows. We term the overall methodology "projections of mutual information matrix" (PMIM). Experiments on both synthetic data and the benchmark Tennessee Eastman process demonstrate the interpretability of PMIM in identifying the root variables that cause the faults, and its superiority in detecting the occurrence of faults in terms of the improved fault detection rate (FDR) and the lowest false alarm rate (FAR). The advantages of PMIM is also less sensitive to hyper-parameters. The advantages of PMIM is also less sensitive to hyper-parameters. Code of PMIM is available at https://github.com/SJYuCNEL/Fault_detection_PMIM