Variable MWPCA for Adaptive Process Monitoring

Abstract

An adaptive process monitoring approach with variable moving window principal component analysis (variable MWPCA) is proposed. On the basis of recursively updating the correlation matrix in both samplewise and blockwise manners, the approach combines the moving window technique with the classical rank-r singular value decomposition (R-SVD) algorithm to construct a new PCA model. Compared with previous MWPCA algorithms, the method not only improves the computation efficiency but also reduces the storage requirement. Furthermore, instead of a fixed window size, a variable moving window strategy is described in detail for accommodating normal process changes with different changing rates. The proposed method is applied to an illustrative case and a continuous stirred tank reactor process, and the monitoring results show better adaptability to both a slow drift and a set-point change than the results of using the conventional MWPCA with a fixed window size.

Adaptive reference updating for vibration-based structural health monitoring under varying environmental conditions

“…As seen from the figure, the computational time of the APCA-based method (0.41-1.56 s) is much heavier than those of the CPCA-based method (0.0027-0.055 s), since the APCA-based method has the recursive framework to update the reference PC model. Considering that APCA in this study is based on singular value decomposition, its computational time can be significantly reduced by using rank-one modification [15][16][17][18]. It is also noted that the computational time of both methods is much smaller than those of the acquisition and modal identification (i.e., feature extraction).…”

“…It should be determined according to the change rate of the normal process which may not be known in advance. Instead of the fixed length of the moving window, He and Yang [17] proposed the variable MWPCA method which changes the length of the moving window adaptively in accordance with the rate of the system change. Once the optimal length of the moving window is adaptively selected, the additional challenging that there is not sufficient observed data may arise at the initial phase of monitoring.…”

“…In order to settle the limitation of CPCA, adaptive PCA (APCA) has been developed mainly in the field of process monitoring [15][16][17][18]. The main difference between APCA and CPCA is to update the reference PC model which represents the current system behavior by using the adaptive reference data set.…”

Polymerization Online Monitoring

“…These include recursive updating schemes [47] and moving window approaches [48,49] to reduce the amount of old data included that is often seen as more dissimilar to current batches. Adaptive updating schemes with forgetting factors can help deal with the presence of phases with fast as well as slow process changes [50].…”

An Improved Detection Statistic for Monitoring the Nonstationary and Nonlinear Processes

“…However, if the detection statistic is constructed based on rank reduction methods, then there are no analytical updating algorithms, because rank reduction methods usually involve singular value decomposition (SVD) and QR decomposition (QRD), for which there are only numerical updating algorithms, e.g. first-order perturbation (FOP) [4], data projection method (DPM) [20], recursive PLS (RPLS) [12,21], recursive PCA (RPCA) [16,8] and moving window PCA (MWPCA) [26,10].…”