A Kernel Sparse Representation Based Framework for Monitoring Nonlinear Multi-Mode Process

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  • Huang Zhenwei
    College of Mechanical Engineering, Zhejiang University of Technology
  • Zeng Jiusun
    College of Metrology and Measurement Engineering, China Jiliang University
  • Pan Guobin
    College of Mechanical Engineering, Zhejiang University of Technology
  • Xie Lei
    State Key Laboratory of Industrial Control Technology, Zhejiang University

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<p>The present paper proposes a monitoring framework for a nonlinear multi-mode process based on the kernel sparse representation based classifier (KSRC). In KSRC, samples from multiple modes are projected onto a high dimensional feature space using the kernel trick. In the kernel space, a test sample is regressed with the training samples using an l1 constraint sparse regression. The l1 constraint ensures that most of the regression coefficients corresponding to the training samples which are not from the same mode as the test sample shrink to zero. Mode assignment is then achieved by investigating the regression errors obtained from different modes. Comparing to other methods, KSRC considers the interrelationship between samples and can better capture the data generating mechanism. In order to reduce the scale of the l1 constraint regression problem, the present paper suggests to use kernel principal component analysis (KPCA) for dimension reduction. For the purpose of monitoring, two Bayesian monitoring statistics are constructed by integrating the monitoring results in different modes using the posterior probability of a test sample falling into each mode, which is calculated based on the regression error. The confidence limits of the monitoring statistics are obtained through kernel density estimation (KDE). Application studies to a simulation example and an ironmaking blast furnace show the advantages of the proposed monitoring strategy.</p>

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