On the development of a neural network based orthogonal nonlinear principal component algorithm for process data analysis

New Nonlinear Approach for Process Monitoring: Neural Component Analysis

“…O-NLPCA algorithm develops orthogonal components directly from an autoassociative neural network using the Gram–Schmidt orthogonalization process . O-NLPCA adopts the cascade control strategy to incorporate the orthogonalization procedure into NLPCA.…”

“…Using the cumulative percent variance method, NCA picks five uncorrelated components for process monitoring; PCA also picks five principal components. For O-NLPCA, the number of principal components is determined as the method in ref taking 4.…”

“…However, NLPCA does not have restrictions on principal components during the training stage, the obtained principal components are not uncorrelated and they do not contain the maximum amount of variability in the process data. Then, Chessari et al adopted the Gram–Schmidt method for principal component orthogonalization, which is termed as orthogonal NLPCA (O-NLPCA). Many improved versions of O-NLPCA have been proposed: Doymaz et al added several schemes to O-NLPCA, such as the tandem filtering technique, fault isolation technique, and sensor reconstruction technique; Maulud et al , utilized the optimal wavelet decomposition to extract the deterministic features of the process variables, then applied O-NLPCA to extract the nonlinearity characteristics, and finally applied PCA to orthogonally transform the nonlinearity characteristics to a score matrix; Maulud et al applied O-NLPCA in batch/semi-batch process monitoring; and Doymaz et al − extended O-NLPCA’s network structure to partial least squares regression (PLS).…”

A Fault Detection and Diagnosis Strategy for Batch/Semi-Batch Processes

“…Another important characteristic of linear PCA is that the first principal component always captures the highest variance of the input data followed by the second and so on. In NLPCA, the data information tends to be evenly distributed among the principal components (Chessari, Barton et al 1995). In view of this drawback, a training algorithm using Gram-Schmidt process for NLPCA was proposed, in which the nonlinear scores produced were orthogonal at the end of training session (Chessari, Barton et al 1995).…”

“…In NLPCA, the data information tends to be evenly distributed among the principal components (Chessari, Barton et al 1995). In view of this drawback, a training algorithm using Gram-Schmidt process for NLPCA was proposed, in which the nonlinear scores produced were orthogonal at the end of training session (Chessari, Barton et al 1995). Although the Gram-Schmidt scheme conceptually can provide some meaningful remedies for orthogonality, in practice it suffers a constraint of a trade-off between the main objective (overall convergence) and the secondary objective (orthogonal principal components).…”