Weighted preliminary-summation-based principal component analysis for non-Gaussian processes |
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Affiliation: | 1. College of Information and Control Engineering, China University of Petroleum, Qingdao 266580, UK;2. Electronics and Computer Science, University of Southampton, Southampton SO17 1BJ, UK;3. King Abdulaziz University, Jeddah 21589, Saudi Arabia |
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Abstract: | For industrial chemical process, preliminary-summation-based principal component analysis (PS-PCA), an amended PCA method was recently provided for coping with both Gaussian and non-Gaussian characteristics. By summing the training and monitoring data respectively, PS-PCA is capable of resolving the issue of non-Gaussian processes and achieves higher fault detection rate than the traditional PCA. However, in the PS-PCA summation operation, all data samples are regarded as the same weight, which results in the fault information of newly-samples may be diluted, leading to significant detection delays. To address this challenge, in this paper, we propose a novel weighted PS-PCA (WPS-PCA) method that employs an exponential weighting scheme to put more emphasis on recent information. Subsequently, a mathematical argument demonstrates that when the number of variables is enough plentiful, the obtained summation combined with the generalized central limit theorem conforms to approximately a Gaussian distribution. The kurtosis relationships indicate this conversion will bring out well-pleasing feasibility for conventional PCA. Ultimately, the proposed technique verifies detection performance using the Tennessee Eastman process, which is compared with the existing PCA and PS-PCA schemes, in terms of the fault detection time and fault detection rate. The simulation studies reveal that the proposed method is efficient and superior. |
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Keywords: | Process monitoring Preliminary-summation-based PCA (PS-PCA) Generalized central limit theorem (CLT) Gaussian verification Weighted preliminary-summation-based PCA (WPS-PCA) |
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