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Hierarchical Parameter Estimation for the Frequency Response Based on the Dynamical Window Data

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  • Control Theory and Applications
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Abstract

This paper studies the problem of parameter estimation for frequency response signals. For a linear system, the frequency response is a sine signal with the same frequency as the input sine signal. When a multi-frequency sine signal is applied to a system, the system response also is a multi-frequency sine signal. The signal modeling for multi-frequency sine signals is very difficult due to the highly nonlinear relations between the characteristic parameters and the model output. In order to obtain the parameter estimates of the multi-frequency sine signal, the signal modeling methods based on statistical identification are proposed by means of the dynamical window discrete measured data. By constructing a criterion function with respect to the model parameters to be estimated, a hierarchical multi-innovation stochastic gradient estimation method is derived through parameter decomposition. Moreover, the forgetting factor and the convergence factor are introduced to improve the performance of the algorithm. The simulation results show the effectiveness of the proposed methods.

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Author information

Authors and Affiliations

  1. School of Internet of Things Technology, Wuxi Vocational Institute of Commerce, Wuxi, 214153, P. R. China

    Ling Xu

  2. School of Internet of Things Engineering, Jiangnan University, Wuxi, 214122, P. R. China

    Ling Xu & Weili Xiong

  3. NAAM Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia

    Ahmed Alsaedi & Tasawar Hayat

Authors
  1. Ling Xu
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  2. Weili Xiong
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  3. Ahmed Alsaedi
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  4. Tasawar Hayat
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Corresponding author

Correspondence to Weili Xiong.

Additional information

Recommended by Associate Editor Yongping Pan under the direction of Editor Duk-Sun Shim. This work was supported by the Science Research of Colleges Universities in Jiangsu Province (No. 16KJB120007, China), and sponsored by Qing Lan Project, and the National Natural Science Foundation of China (No. 61773182), and sponsored by Postdoctoral Science Foundation of Jiangsu Province (No. 1701020A), the 111 Project (B12018), and the Natural Science Foundation of Jiangsu Province (No. BK20160162 and No. BK20140164). The first author is grateful to Professor Feng Ding at the Jiangnan University for his helpful suggestions and the main idea of this work comes from him and the series papers in the Journal of Qingdao University of Science and Technology, 2017.

Ling Xu was born in Tianjin, China. She received the Master and Ph.D. degrees from the Jiangnan University (Wuxi, China) in 2005 and 2015. She has been an Associate Professor since 2015. She is a Colleges and Universities “Blue Project” Young Teacher (Jiangsu). Her research interests include process control, parameter estimation and signal modeling.

Weili Xiong received her Ph.D. degree in School of Communication and Control Engineering from Jiangnan University (Wuxi, China) in 2007. She has been a professor in the School of Internet of Things Engineering at the Jiangnan University. She was a visiting scholar in Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Canada from 2013 to 2014. Her research interests include system identification, soft sensor of industry processes and optimization.

Ahmed Alsaedi obtained his Ph.D. degree from Swansea University (UK) in 2002. He has a broad experience of research in applied mathematics. His fields of interest include dynamical systems, nonlinear analysis involving ordinary differential equations, fractional differential equations, boundary value problems, mathematical modeling, Newtonian and Non-Newtonian fluid mechanics. He served as the chairman of the mathematics department at KAU and presently he is serving as director of the research program at KAU.

Tasawar Hayat was born in Khanewal, Punjab, Distinguished National Professor and Chairperson of Mathematics Department at Quaid-I-Azam University is renowned worldwide for his seminal, diversified and fundamental contributions in models relevant to physiological systems, control engineering. He has a honor of being fellow of Pakistan Academy of Sciences, Third World Academy of Sciences (TWAS) and Islamic World Academy of Sciences in the mathematical Sciences.

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Xu, L., Xiong, W., Alsaedi, A. et al. Hierarchical Parameter Estimation for the Frequency Response Based on the Dynamical Window Data. Int. J. Control Autom. Syst. 16, 1756–1764 (2018). https://doi.org/10.1007/s12555-017-0482-7

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