Although several works have been proposed for multi-channel profile monitoring, two additional challenges are yet to be addressed: (i) how to model complex correlations of multi-channel profiles when different profiles have different features (i.e., weakly or sparsely correlated); (ii) how to efficiently detect sparse changes occurring in only a small segment of a few profiles. To fill this research gap, our contributions are twofold. First, we propose a novel Sparse Multi-channel Functional Principal Component Analysis (SMFPCA) to model multi-channel profiles. SMFPCA can not only flexibly describe the correlation structure of multiple, or even high-dimensional, profiles with distinct features, but also achieve sparse PCA scores which are easily interpretable. Second, we propose an efficient convergence-guaranteed optimization algorithm to solve SMFPCA in real time based on the block coordinate descent algorithm. Third, as the SMFPCA scores can naturally identify sparse out-of-control (OC) patterns, we use the scores to construct a monitoring scheme which provides increased sensitivity to sparse OC changes. Numerical studies together with a real case study in a manufacturing system demonstrate the effectiveness of the developed methodology.
- Dimension reduction
- functional PCA
- multi-channel profiles
- sparse PCA
- statistical process control
ASJC Scopus subject areas
- Industrial and Manufacturing Engineering
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Weakly correlated profile monitoring based on sparse multi-channel functional principal component analysis
Zhang, C. (Contributor), Lee, S. (Contributor), Yan, H. (Contributor) & Shi, J. (Contributor), figshare Academic Research System, Oct 3 2018