Citation: Shahzad, F.; Huang, Z.;
Memon, W.H. Process Monitoring
Using Kernel PCA and Kernel
Density Estimation-Based SSGLR
Method for Nonlinear Fault
Detection. Appl. Sci. 2022, 12, 2981.
https://doi.org/10.3390/
app12062981
Academic Editors: João Carlos de
Oliveira Matias and Paolo Renna
Received: 18 January 2022
Accepted: 11 March 2022
Published: 15 March 2022
Publisher’s Note: MDPI stays neutral
with regard to jurisdictional claims in
published maps and institutional affil-
iations.
Copyright: © 2022 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
Article
Process Monitoring Using Kernel PCA and Kernel Density
Estimation-Based SSGLR Method for Nonlinear Fault Detection
Faisal Shahzad
1
, Zhensheng Huang
1,
* and Waqar Hussain Memon
2
1
Department of Statistics and Financial Mathematics, School of Sciences, Nanjing University of Science and
Technology, Nanjing 210094, China; faisalshahzad@njust.edu.cn
2
Department of Mechanical Engineering, School of Sciences, Nanjing University of Science and Technology,
Nanjing 210094, China; waqarmemon@njust.edu.cn
* Correspondence: zshuang@njust.edu.cn
Abstract:
Fault monitoring is often employed for the secure functioning of industrial systems. To
assess performance and enhance product quality, statistical process control (SPC) charts such as
Shewhart, CUSUM, and EWMA statistics have historically been utilized. When implemented to
multivariate procedures, unfortunately, such univariate control charts demonstrate low fault sensing
ability. Due to some limitations of univariate charts, numerous process monitoring techniques
dependent on multivariate statistical approaches such as principal component analysis (PCA) and
partial least squares (PLS) have been designed. Yet, in some challenging scenarios in industrial
chemical and biological processes with notably nonlinear properties, PCA works poorly, according to
its presumption that the dataset generally be linear. However, Kernel Principal Component Analysis
(KPCA) is a reliable and precise nonlinear process control methodology, but the interaction mainly
through upper control limits (UCLs) dependent on the Gaussian distribution may weaken its output.
This article introduces time-varying statistical error tracking through Kernel Principal Component
Analysis (KPCA) based on Generalized Likelihood Ratio statistics (GLR) using a sequential sampling
scheme named KPCA-SSGLR for nonlinear fault detection. The main issue of employing just T
2
and Q statistic in KPCA is that they cannot correctly give practitioners the change point of the
system fault, preventing practitioners from diagnosing the issue. Based on this perspective, this
study attempts to incorporate KPCA with sequential sampling Generalized Likelihood Ratio (SSGLR)
for monitoring the nonlinear fault in multivariate systems. The KPCA is utilized for dimension
reduction, while the SSGLR is employed as a tracking statistic. The kernel density estimation (KDE)
was employed to approximate UCLs for variational system operation relying on KPCA. The testing
efficiency of the corresponding KPCA-KDE-SSGLR technique was then analyzed and competed
with KPCA and kernel locality preserving projection (KLPP), the UCLs of which were focused on
the Gaussian distribution. The purpose of this analysis is to enhance the development of KPCA-
KDE-SSGLR to accomplish future enhancements and to advance the practical use of the established
model by implementing the sequential sampling GLR approach. The fault monitoring efficiency is
demonstrated through different simulation scenarios, one utilizing synthetic data, the other from
the Tennessee Eastman technique, and lastly through a hot strip mill. The findings indicate the
applicability of the KPCA-KDE-based SSGLR system over the KLPP and KPCA-KDE methods by its
two T
2
and Q charts to recognize the faults.
Keywords:
generalized likelihood ratio chart; multivariate statistics; kernel principal component analysis;
kernel density estimation; fault detection and identification; kernel locality preserving projections
1. Introduction
Fault assessment serves a pivotal part in maintaining the consistency of manufacturing
as well as factory enrichment. Several factors are monitored in different working units
within newly constructed industrial process units, and these factors are captured at several
Appl. Sci. 2022, 12, 2981. https://doi.org/10.3390/app12062981 https://www.mdpi.com/journal/applsci
