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Quality-related Fault Detection Based on Approximate Kernel Partial Least Squares Method

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Abstract

The kernel partial least squares (KPLS) method has been widely used in quality-related fault detection since it can acquire the features of the object under investigation in the detection process. However, this method has high computational requirements and storage costs. In order to address these problems, in this paper, a novel quality-related fault detection method, namely, the approximate kernel partial least squares (AKPLS) based on the truncated singular value decomposition (TSVD) has been proposed. In this method, a mapping of the process variables onto a feature space is done via AKPLS. A linear PLS is then performed on the basis of the TSVD in the feature space, owing to which the proposed AKPLS method can be scaled to approximate the kernel matrix with limited memory storage. Therefore, the proposed AKPLS method can be used for handling real-time quality-related fault detection and large-scale quality-related detection. The RMSEP obtained by the AKPLS model was significantly smaller than that obtained by the eLW-KPLS and LW-KPLS models. As the number of samples increases, the RMSEP of AKPLS is observed to become smaller and gradually tends to a constant value. Therefore, the proposed AKPLS is observed to be well suited for a mass-dependent prediction model. The AKPLS model achieved a larger R2 compared to the PLS, KPLS, eLW-KPLS and LW-KPLS models. The relatively large coefficient of determination R2 indicates that the variables selected by the AKPLS model have a strong influence on the predicted values. The statistics of the root mean squared error (RMSE) and the determination coefficients R2 have been constructed in order to monitor the quality-related fault detection. The effectiveness of the proposed method has been illustrated using a numerical example and the penicillin fermentation process.

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Data Availability

The experimental data used to support the findings of this study are available from the corresponding author upon request.

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Acknowledgements

The authors would like to thank the anonymous reviewers and editors for their valuable suggestions that greatly improved the quality of this presentation.

Funding

This work was sponsored in part by the National Natural Science Foundation of China (61772020).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Xidian University, Xi’an, 710071, Shaanxi, China

    Xiling Liu & Shuisheng Zhou

  2. Zhengzhou University of Economics and Business, Zhengzhou, 451191, Henan, China

    Xiling Liu

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The experimental data used to support the findings of this study are available from the corresponding author upon request.

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Correspondence to Shuisheng Zhou.

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Liu, X., Zhou, S. Quality-related Fault Detection Based on Approximate Kernel Partial Least Squares Method. J Grid Computing 21, 29 (2023). https://doi.org/10.1007/s10723-023-09670-1

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