Discriminant diffusion maps based k‐nearest‐neighbour for batch process fault detection

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In this paper, a novel discriminant diffusion maps based k‐nearest‐neighbour rule (DDM‐kNN) is developed for the high‐dimensional data of batch process and nonlinear characteristics of the data, and the traditional multivariate statistical process control and monitoring methods is less effective. Firstly, a discriminant kernel parameter is applied to the framework of the diffusion maps, and the Gaussian kernel width is selected from the within‐class width and the between‐class width according to discriminating sample class labels, which can make kernel function effectively extract data correlation features and exactly describe the structure characteristics of data original space in the low‐dimensional feature. Subsequently, the adapted kNN rule is applied to the low‐dimensional manifold feature space for fault detection. The effectiveness of DDM for the performance of data dimension reduction and feature extraction is verified in 3 arm spiral test data experiments compared with other dimensionality reduction methods, and successfully shows the high‐dimensional data in the low‐dimensional space and optimally preserves the original intrinsic nonlinear structure of the dataset. In addition, DDM‐kNN is applied to penicillin fermentation process monitoring and fault detection, and results also verify the effectiveness of the proposed method by integrating discriminant diffusion maps with k‐nearest‐neighbour rule.