Reducing smearing effect in contribution plots and improving fault detection via polynomial approximated isomap embeddings

Abstract

AbstractDimension reduction is an essential method used in multivariate statistical process monitoring for fault detection and diagnosis. Principal component analysis (PCA) and independent component analysis (ICA) are the most frequently used linear dimensional reduction tools, and the contribution plot is the most popular fault isolation method in the absence of any prior information on the faults. These methods, however, come with their shortcomings. The fault detection capability of linear methods may not be sufficient for non‐linear processes, and smearing effect is known to deteriorate the diagnostics obtained from contribution plots. While the fault detection rate may be increased by kernelized methods or deep artificial neural network models, tuning data‐dependent hyperparameter(s) and network structure with limited historical data is not an easy task. Furthermore, the resulting non‐linear models often do not directly possess fault isolation capability. In the current study, we aim to devise a novel method named ICApIso‐PCA, which offers non‐linear fault detection and isolation in a rather straightforward manner. The rationale of ICApIso‐PCA mainly involves building a non‐linear scores matrix, composed of principal component scores and high‐order polynomial approximated isomap embeddings, followed by implementation of the ICA‐PCA algorithm on this matrix. Applications on a toy dataset and the Tennessee Eastman plant show that the I2 index from ICApIso‐PCA yields a high fault detection rate and offers accurate contribution plots with diminished smearing effects compared to those from traditional monitoring methods. Easy implementation and the potential for future research are further advantages of the proposed method.