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<p>This paper addresses a parameter identification problem for the Wiener nonlinear system with mixed Gaussian measurement noises by integrating correlation analysis with variational Bayesian methods. The Wiener system developed is composed of two blocks, i.e., a dynamic block modeled by an autoregressive moving average (ARMA) process and a static nonlinear block represented by a neuro fuzzy model (NFM), and a probabilistic model of Gaussian mixed measurement noises is constructed. To estimate the Wiener system unknown parameters, Gaussian signals are introduced. Firstly, the correlation function of the linear block is analyzed under Gaussian input, then the ARMA model parameters are estimated using correlation analysis method. Subsequently, in the NFM identification, the variational Bayesian technique, combining prior knowledge with observation data, is introduced for updating the weights and noise precision. By updating the noise precision, the noise variance is dynamically adjusted, thereby reducing the impact of noise on the Wiener system. Studies with a numerical simulation and a nonlinear process demonstrate the efficiency. In the numerical simulation, when the SNR decreases from 16.54 dB to 6.59 dB, the ARMA model parameters begin to converge and remain stable when <i>t</i> reaches 2000. Furthermore, for fitting nonlinear block, the proposed method reduces the mean square error by 5.99% compared to adaptive Kalman filtering identification method. For continuous stirred tank reactor nonlinear process, when the concentration set value is 0.1, the rise time for the proposed method is 0.0078&#xa0;h, which is 48.34% shorter than the 0.0151&#xa0;h of traditional PI control method.</p>

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Parameters Identification of Wiener Nonlinear Systems with Gaussian Mixed Measurement Noises

  • 期刊论文

  • 发表日期：

    2025年8月26日

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  • Feng Li,
  • Yanzong Zhu,
  • Shengyi Qian,
  • Ya Gu

摘要

This paper addresses a parameter identification problem for the Wiener nonlinear system with mixed Gaussian measurement noises by integrating correlation analysis with variational Bayesian methods. The Wiener system developed is composed of two blocks, i.e., a dynamic block modeled by an autoregressive moving average (ARMA) process and a static nonlinear block represented by a neuro fuzzy model (NFM), and a probabilistic model of Gaussian mixed measurement noises is constructed. To estimate the Wiener system unknown parameters, Gaussian signals are introduced. Firstly, the correlation function of the linear block is analyzed under Gaussian input, then the ARMA model parameters are estimated using correlation analysis method. Subsequently, in the NFM identification, the variational Bayesian technique, combining prior knowledge with observation data, is introduced for updating the weights and noise precision. By updating the noise precision, the noise variance is dynamically adjusted, thereby reducing the impact of noise on the Wiener system. Studies with a numerical simulation and a nonlinear process demonstrate the efficiency. In the numerical simulation, when the SNR decreases from 16.54 dB to 6.59 dB, the ARMA model parameters begin to converge and remain stable when t reaches 2000. Furthermore, for fitting nonlinear block, the proposed method reduces the mean square error by 5.99% compared to adaptive Kalman filtering identification method. For continuous stirred tank reactor nonlinear process, when the concentration set value is 0.1, the rise time for the proposed method is 0.0078 h, which is 48.34% shorter than the 0.0151 h of traditional PI control method.