Copula entropy-based PCA method and application in process monitoring

Abstract

As an effective unsupervised data feature extraction algorithm, principal component analysis (PCA) has been successfully applied in multivariate statistical process monitoring. The PCA algorithm obtains the principal components through the maximum variance criterion, which is limited to the linear correlation between feature variables. Therefore, it cannot accurately measure the strength of the correlation between the nonlinearly related feature variables. Based on this, a method of Copula entropy-based PCA (CEPCA) is proposed and applied to process monitoring. Compared to the traditional PCA feature extraction approach, the Copula entropy method is used to calculate the mutual information between the feature variables. The covariance matrix is derived from the mutual information matrix, then the corresponding statistics can be constructed in the principal component space and the residual subspace, respectively. The effectiveness and superiority of CEPCA in process monitoring is verified with the Tennessee Eastman (TE)process.