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Gaussian process regression combined with dynamic data reconciliation for improving the performance of nonlinear dynamic systems

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Abstract

Process data are generally subjected to noise during the measuring, transmission and processing procedures, which may lead to the deterioration and even failure of the process supervision and control. Although Kalman filters are widely used to estimate the true states of linear or linearized systems, their applications are limited to state–space models that can be mathematical or empirical. Neural networks are satisfactory solutions to model unknown nonlinear dynamic systems. However, there is no valid confidence evaluation about the model prediction of neural networks. In this paper, Gaussian process regression (GPR) complementarily advantages dynamic data reconciliation (DDR) to form a novel data-driven filtering scheme named GPR–DDR. DDR is served as an alternative filter, which is suitable for a broader class of process models compared with Kalman filters, while GPR is employed to predict system outputs with their associate uncertainty, which makes parameters of the DDR needless to online tune and adaptive for varying inputs. The effectiveness of GPR–DDR is demonstrated by its implementations on a classical mathematical example and a dynamic chemical process. The simulation results show that the proposed method can further improve the output response and is robust to changes of the noise level.

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The data that support the findings of this study are available from the authors upon reasonable request.

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Acknowledgements

This work was supported in part by the National Natural Science Foundation of China (No. 62071363) and the Key R&D program of Shaanxi Province (2021LLRH-06).

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Authors and Affiliations

  1. School of Aerospace Science and Technology, Xidian University, Xi’an, 710126, Shaanxi, China

    Guiting Hu & Luping Xu

  2. The National and Local Joint Engineering Research Center of Electrical Digital Design Technology, Wenzhou University, Wenzhou, 325000, Zhejiang, China

    Zhengjiang Zhang

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  1. Guiting Hu
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  2. Luping Xu
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Correspondence to Luping Xu or Zhengjiang Zhang.

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Hu, G., Xu, L. & Zhang, Z. Gaussian process regression combined with dynamic data reconciliation for improving the performance of nonlinear dynamic systems. Nonlinear Dyn 111, 15145–15163 (2023). https://doi.org/10.1007/s11071-023-08624-2

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