Identification of MIMO Nonlinear Gaussian Time-Varying System Based on Multi-Dimensional Taylor Network Multi-Level Approximation

Jiefei Li; Shaolin Hu

doi:doi:10.11648/j.ijdst.20241002.12

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Identification of MIMO Nonlinear Gaussian Time-Varying System Based on Multi-Dimensional Taylor Network Multi-Level Approximation

Jiefei Li

, Shaolin Hu^*

Published in International Journal on Data Science and Technology (Volume 10, Issue 2)

Received: 25 June 2024 Accepted: 11 July 2024 Published: 29 July 2024

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Abstract

Aiming at the problems of identification difficulties and low identification accuracy in modelling and identification of multiple-input multiple-output (MIMO) nonlinear Gaussian time-varying systems, this paper proposes an identification scheme based on the step-by-step approximation of multidimensional Taylor network (MTN). The aim of this paper is to improve the modelling of complex nonlinear systems so as to improve the prediction performance and control effect of the system. Different from the traditional multidimensional Taylor network identification method, this method adopts an order-by-order approximation strategy, which seeks its parameters sequentially from the lower order to the higher order, and continuously optimises the parameter weights during the parameter seeking process. Firstly, the nonlinear function model is approximated as a polynomial form by the order-by-order Taylor expansion, and then the weight parameters of each order of the Taylor expansion are calculated and updated step by step by using the algorithm based on the Variable Forgetting Factor Recursive Least Squares (VFF-RLS) method. Through iterative optimized of these parameters, dynamic weight assignment to each order of the Taylor expansion is achieved. A parameter-identified nonlinear function model is finally obtained, which can more accurately describe the dynamic behaviour and characteristics of the system. Finally, an arithmetic simulation is carried out through an example to verify the effectiveness of the proposed method.

Published in	International Journal on Data Science and Technology (Volume 10, Issue 2)
DOI	10.11648/j.ijdst.20241002.12
Page(s)	26-37
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Gaussian Nonlinear Time-Varying System, Multi-Dimensional Taylor Network, Gradual Approximation, Variable Forgetting Factor Recursive Least Squares Algorithm

References

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APA Style

Li, J., Hu, S. (2024). Identification of MIMO Nonlinear Gaussian Time-Varying System Based on Multi-Dimensional Taylor Network Multi-Level Approximation. International Journal on Data Science and Technology, 10(2), 26-37. https://doi.org/10.11648/j.ijdst.20241002.12

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ACS Style

Li, J.; Hu, S. Identification of MIMO Nonlinear Gaussian Time-Varying System Based on Multi-Dimensional Taylor Network Multi-Level Approximation. Int. J. Data Sci. Technol. 2024, 10(2), 26-37. doi: 10.11648/j.ijdst.20241002.12

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AMA Style

Li J, Hu S. Identification of MIMO Nonlinear Gaussian Time-Varying System Based on Multi-Dimensional Taylor Network Multi-Level Approximation. Int J Data Sci Technol. 2024;10(2):26-37. doi: 10.11648/j.ijdst.20241002.12

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@article{10.11648/j.ijdst.20241002.12,
  author = {Jiefei Li and Shaolin Hu},
  title = {Identification of MIMO Nonlinear Gaussian Time-Varying System Based on Multi-Dimensional Taylor Network Multi-Level Approximation},
  journal = {International Journal on Data Science and Technology},
  volume = {10},
  number = {2},
  pages = {26-37},
  doi = {10.11648/j.ijdst.20241002.12},
  url = {https://doi.org/10.11648/j.ijdst.20241002.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijdst.20241002.12},
  abstract = {Aiming at the problems of identification difficulties and low identification accuracy in modelling and identification of multiple-input multiple-output (MIMO) nonlinear Gaussian time-varying systems, this paper proposes an identification scheme based on the step-by-step approximation of multidimensional Taylor network (MTN). The aim of this paper is to improve the modelling of complex nonlinear systems so as to improve the prediction performance and control effect of the system. Different from the traditional multidimensional Taylor network identification method, this method adopts an order-by-order approximation strategy, which seeks its parameters sequentially from the lower order to the higher order, and continuously optimises the parameter weights during the parameter seeking process. Firstly, the nonlinear function model is approximated as a polynomial form by the order-by-order Taylor expansion, and then the weight parameters of each order of the Taylor expansion are calculated and updated step by step by using the algorithm based on the Variable Forgetting Factor Recursive Least Squares (VFF-RLS) method. Through iterative optimized of these parameters, dynamic weight assignment to each order of the Taylor expansion is achieved. A parameter-identified nonlinear function model is finally obtained, which can more accurately describe the dynamic behaviour and characteristics of the system. Finally, an arithmetic simulation is carried out through an example to verify the effectiveness of the proposed method.
},
 year = {2024}
}

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TY  - JOUR
T1  - Identification of MIMO Nonlinear Gaussian Time-Varying System Based on Multi-Dimensional Taylor Network Multi-Level Approximation
AU  - Jiefei Li
AU  - Shaolin Hu
Y1  - 2024/07/29
PY  - 2024
N1  - https://doi.org/10.11648/j.ijdst.20241002.12
DO  - 10.11648/j.ijdst.20241002.12
T2  - International Journal on Data Science and Technology
JF  - International Journal on Data Science and Technology
JO  - International Journal on Data Science and Technology
SP  - 26
EP  - 37
PB  - Science Publishing Group
SN  - 2472-2235
UR  - https://doi.org/10.11648/j.ijdst.20241002.12
AB  - Aiming at the problems of identification difficulties and low identification accuracy in modelling and identification of multiple-input multiple-output (MIMO) nonlinear Gaussian time-varying systems, this paper proposes an identification scheme based on the step-by-step approximation of multidimensional Taylor network (MTN). The aim of this paper is to improve the modelling of complex nonlinear systems so as to improve the prediction performance and control effect of the system. Different from the traditional multidimensional Taylor network identification method, this method adopts an order-by-order approximation strategy, which seeks its parameters sequentially from the lower order to the higher order, and continuously optimises the parameter weights during the parameter seeking process. Firstly, the nonlinear function model is approximated as a polynomial form by the order-by-order Taylor expansion, and then the weight parameters of each order of the Taylor expansion are calculated and updated step by step by using the algorithm based on the Variable Forgetting Factor Recursive Least Squares (VFF-RLS) method. Through iterative optimized of these parameters, dynamic weight assignment to each order of the Taylor expansion is achieved. A parameter-identified nonlinear function model is finally obtained, which can more accurately describe the dynamic behaviour and characteristics of the system. Finally, an arithmetic simulation is carried out through an example to verify the effectiveness of the proposed method.

VL  - 10
IS  - 2
ER  -

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Author Information

Jiefei Li

School of Information and Control Engineering, Jilin Institute of Chemical Technology, Jilin, China

Contact Email

http://orcid.org/0009-0005-4832-499X
Shaolin Hu

School of Automation, Guangdong University of Petrochemical Technology, Maoming, China

Contact Email

http://orcid.org/0000-0003-0565-7450

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Plain Text BibTeX RIS

APA Style

Li, J., Hu, S. (2024). Identification of MIMO Nonlinear Gaussian Time-Varying System Based on Multi-Dimensional Taylor Network Multi-Level Approximation. International Journal on Data Science and Technology, 10(2), 26-37. https://doi.org/10.11648/j.ijdst.20241002.12

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ACS Style

Li, J.; Hu, S. Identification of MIMO Nonlinear Gaussian Time-Varying System Based on Multi-Dimensional Taylor Network Multi-Level Approximation. Int. J. Data Sci. Technol. 2024, 10(2), 26-37. doi: 10.11648/j.ijdst.20241002.12

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AMA Style

Li J, Hu S. Identification of MIMO Nonlinear Gaussian Time-Varying System Based on Multi-Dimensional Taylor Network Multi-Level Approximation. Int J Data Sci Technol. 2024;10(2):26-37. doi: 10.11648/j.ijdst.20241002.12

Copy | Download

@article{10.11648/j.ijdst.20241002.12,
  author = {Jiefei Li and Shaolin Hu},
  title = {Identification of MIMO Nonlinear Gaussian Time-Varying System Based on Multi-Dimensional Taylor Network Multi-Level Approximation},
  journal = {International Journal on Data Science and Technology},
  volume = {10},
  number = {2},
  pages = {26-37},
  doi = {10.11648/j.ijdst.20241002.12},
  url = {https://doi.org/10.11648/j.ijdst.20241002.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijdst.20241002.12},
  abstract = {Aiming at the problems of identification difficulties and low identification accuracy in modelling and identification of multiple-input multiple-output (MIMO) nonlinear Gaussian time-varying systems, this paper proposes an identification scheme based on the step-by-step approximation of multidimensional Taylor network (MTN). The aim of this paper is to improve the modelling of complex nonlinear systems so as to improve the prediction performance and control effect of the system. Different from the traditional multidimensional Taylor network identification method, this method adopts an order-by-order approximation strategy, which seeks its parameters sequentially from the lower order to the higher order, and continuously optimises the parameter weights during the parameter seeking process. Firstly, the nonlinear function model is approximated as a polynomial form by the order-by-order Taylor expansion, and then the weight parameters of each order of the Taylor expansion are calculated and updated step by step by using the algorithm based on the Variable Forgetting Factor Recursive Least Squares (VFF-RLS) method. Through iterative optimized of these parameters, dynamic weight assignment to each order of the Taylor expansion is achieved. A parameter-identified nonlinear function model is finally obtained, which can more accurately describe the dynamic behaviour and characteristics of the system. Finally, an arithmetic simulation is carried out through an example to verify the effectiveness of the proposed method.
},
 year = {2024}
}

Copy | Download

TY  - JOUR
T1  - Identification of MIMO Nonlinear Gaussian Time-Varying System Based on Multi-Dimensional Taylor Network Multi-Level Approximation
AU  - Jiefei Li
AU  - Shaolin Hu
Y1  - 2024/07/29
PY  - 2024
N1  - https://doi.org/10.11648/j.ijdst.20241002.12
DO  - 10.11648/j.ijdst.20241002.12
T2  - International Journal on Data Science and Technology
JF  - International Journal on Data Science and Technology
JO  - International Journal on Data Science and Technology
SP  - 26
EP  - 37
PB  - Science Publishing Group
SN  - 2472-2235
UR  - https://doi.org/10.11648/j.ijdst.20241002.12
AB  - Aiming at the problems of identification difficulties and low identification accuracy in modelling and identification of multiple-input multiple-output (MIMO) nonlinear Gaussian time-varying systems, this paper proposes an identification scheme based on the step-by-step approximation of multidimensional Taylor network (MTN). The aim of this paper is to improve the modelling of complex nonlinear systems so as to improve the prediction performance and control effect of the system. Different from the traditional multidimensional Taylor network identification method, this method adopts an order-by-order approximation strategy, which seeks its parameters sequentially from the lower order to the higher order, and continuously optimises the parameter weights during the parameter seeking process. Firstly, the nonlinear function model is approximated as a polynomial form by the order-by-order Taylor expansion, and then the weight parameters of each order of the Taylor expansion are calculated and updated step by step by using the algorithm based on the Variable Forgetting Factor Recursive Least Squares (VFF-RLS) method. Through iterative optimized of these parameters, dynamic weight assignment to each order of the Taylor expansion is achieved. A parameter-identified nonlinear function model is finally obtained, which can more accurately describe the dynamic behaviour and characteristics of the system. Finally, an arithmetic simulation is carried out through an example to verify the effectiveness of the proposed method.

VL  - 10
IS  - 2
ER  -

Copy | Download