A sparse PCA for nonlinear fault diagnosis and robust feature discovery of industrial processes

Abstract

Pearson's correlation measure is only able to model linear dependence between random variables. Hence, conventional principal component analysis (PCA) based on Pearson's correlation measure is not suitable for application to modern industrial processes where process variables are often nonlinearly related. To address this problem, a nonparametric PCA model is proposed based on nonlinear correlation measures, including Spearman's and Kendall tau's rank correlation. These two correlation measures are also less sensitive to outliers comparing to Pearson's correlation, making the proposed PCA a robust feature extraction technique. To reveal meaningful patterns from process data, a generalized iterative deflation method is applied to the robust correlation matrix of the process data to sequentially extract a set of leading sparse pseudoeigenvectors. For online fault diagnosis, the T 2 and SPE statistics are computed and analyzed with respect to the subspace spanned by the extracted pseudoeigenvectors. The proposed method is applied to two industrial case studies. Its process monitoring performance is demonstrated to be superior to that of the conventional PCA and is comparable to those of Kernel PCA and kernel independent component analysis at a lower computational cost. The proposed PCA is also more robust in sparse feature extraction from contaminated process data.

Chemical process fault diagnosis based on enchanted machine‐learning approach

“…Since the index of component G (XMEAS [35]) is regarded as product quality variable, process faults IDV (3,4), IDV (9,11), IDV (14,15), and IDV (19) have little impact on product quality, while other faults have a significant impact on quality variables, ie, faults IDV (1,2), IDV (5,6,7,8), IDV (12,13), and IDV (20,21) are more serious. [37] Detailed process monitoring charts of two typical faults IDV (8) and IDV (12) are given by Figures 4 and 5.…”

Integrated Numerical and Experimental Data-Driven Parameter Identification of Electrode Properties in All-Vanadium Redox Flow Batteries

“…The Kendall τ rank correlation coefficient [110] can instead be used to determine the correlations between the structural inputs and various electrochemical and fluid dynamic outputs. Unlike the Pearson correlation, the Kendall correlation is a robust calculation for non-linear data [111] with outliers [112]. The equation for the Kendall rank correlation coefficient is defined as [110]:…”

Data-Driven Electrode Parameter Identification for Vanadium Redox Flow Batteries Through Experimental and Numerical Methods

“…The Kendall τ rank correlation coefficient [110] can instead be used to determine the correlations between the structural inputs and various electrochemical and fluid dynamic outputs. Unlike the Pearson correlation, the Kendall correlation is a robust calculation for non-linear data [111] with outliers [112]. The equation for the Kendall rank correlation coefficient is defined as [110]: whereas, H e,− and k − decrease in correlative strength.…”