Dynamic Principal Component Analysis (DPCA) Method for Serially Correlated Data

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To effectively monitor production processes, short sampling intervals are required to capture subtle changes, making serial correlation a common characteristic of real-world process data. Exploring Dynamic Principal Component Analysis (DPCA) methods suitable for serially correlated data is essential, involving time-lagged variable expansions and covariance matrix adaptations for dynamic feature extraction.

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To better monitor production processes, short sampling intervals are necessary to capture subtle changes in the process. However, since serial correlation is prevalent in actual process data, traditional Principal Component Analysis (PCA) methods may lead to information loss or distortion. To overcome this issue, we need to explore Dynamic Principal Component Analysis (DPCA) methods suitable for serially correlated data. DPCA is a time-evolution based PCA technique that captures dynamic characteristics in process data while remaining robust to serial correlations. The implementation typically involves constructing an augmented data matrix with time-lagged variables, followed by eigen decomposition of the expanded covariance matrix to extract dominant dynamic modes. By introducing DPCA, we can more comprehensively understand variations in production processes and take corresponding measures to improve production efficiency and quality.

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