Multimode Process Monitoring Based on Modified Density Peak Clustering and Parallel Variational Autoencoder

Clustering algorithms and deep learning methods have been widely applied in the multimode process monitoring. However, for the process data with unknown mode, traditional clustering methods can hardly identify the number of modes automatically. Further, deep learning methods can learn effective features from nonlinear process data, while the extracted features cannot follow the Gaussian distribution, which may lead to incorrect control limit for fault detection. In this paper, a comprehensive monitoring method based on modified density peak clustering and parallel variational autoencoder (MDPC-PVAE) is proposed for multimode processes. Firstly, a novel clustering algorithm, named MDPC, is presented for the mode identification and division. MDPC can identify the number of modes without prior knowledge of mode information and divide the whole process data into multiple modes. Then, the PVAE is established based on distinguished multimode data to generate the deep nonlinear features, in which the generated features in each VAE follow the Gaussian distribution. Finally, the Gaussian feature representations obtained by PVAE are provided to construct the statistics $H^2$, and the control limits are determined by the kernel density estimation (KDE) method. The effectiveness of the proposed method is evaluated by the Tennessee Eastman process and semiconductor etching process.