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This paper proposes a boosting vine copula-based dependence description (BVCDD) method for multivariate and multimode process monitoring. The BVCDD aims to improve the standard vine copula-based dependence description (VCDD) method by establishing an ensemble of submodels from sample directions based on a boosting strategy. The generalized Bayesian inference-based probability (GBIP) index is introduced to assess the degrees of a VCDD model (submodel) to depict different samples, which means how likely an observation is under the probabilistic model for the system. Every sample is weighted individually according to the depiction degree. The weights are then used to choose a certain number of samples for each succeeding submodel. In this way, the samples with large error in the preceding model can be selected for training the next submodel. Moreover, the number of submodels as well as the number of training samples chosen for every submodel are determined adaptively in the ensemble learning process. The proposed BVCDD method can not only solve weak sample problems but also remove redundant information in samples. To examine the performance, empirical evaluations have been conducted to compare the BVCDD method with some other state-of-the-art methods in a numerical example, the Tennessee Eastman (TE) process, and an acetic acid dehydration process. The results show that the developed BVCDD models are superior to those obtained by the counterparts on weak samples in both accuracy and stability.

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We propose a novel algorithm for supervised dimensionality reduction named manifold partition discriminant analysis (MPDA). It aims to find a linear embedding space where the within-class similarity is achieved along the direction that is consistent with the local variation of the data manifold, while nearby data belonging to different classes are well separated. By partitioning the data manifold into a number of linear subspaces and utilizing the first-order Taylor expansion, MPDA explicitly parameterizes the connections of tangent spaces and represents the data manifold in a piecewise manner. While graph Laplacian methods capture only the pairwise interaction between data points, our method captures both pairwise and higher order interactions (using regional consistency) between data points. This manifold representation can help to improve the measure of within-class similarity, which further leads to improved performance of dimensionality reduction. Experimental results on multiple real-world data sets demonstrate the effectiveness of the proposed method.