Development of correlation-based process characteristics visualization method and its application to fault detection

Although process monitoring is important for maintaining safety and product quality, it is difficult to understand process characteristics particularly when they are changing. Since the correlation among variables changes due to changes in process characteristics, process data visualization based on the correlation among variables helps process characteristic understanding. In the present work, a new correlation-based data visualization method is proposed by integrating joint decorrelation (JD) and stochastic proximity embedding (SPE). JD is a blind source separation (BSS) method that can separates sample based on the correlation, and SPE is a self-organizing algorithm that can map high-dimensional data to a two-dimensional plane. The proposed method, referred to as JD-SPE, separates samples based on the correlation using JD and the separated samples are visualized in the two-dimensional plane by SPE. Correlation matrices have to be constructed before sample separation for JD; however how to construct them is not clear. The present work also proposes a correlation matrix construction method for JD by using nearest correlation spectral clustering (NCSC), which is a correlation-based clustering method. In addition, a new process monitoring method based on multivariate statistical process control (MSPC) which is a well-known process monitoring algorithm and JD-SPE. This monitoring method is referred to as JD-SPE-T
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. The proposed JD-SPE-T
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can detect a fault that can not detected by the conventional MSPC. The usefulness of the proposed methods is demonstrated through numerical examples.