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Identification of MISO Hammerstein system using sparse multiple kernel-based hierarchical mixture prior and

Xiaolong Chen1, Yi Chai1, Qie Liu1

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This study introduces a Bayesian sparse multiple kernel method for identifying Hammerstein systems. The novel approach effectively estimates parameters and selects model orders for nonlinear dynamical systems.

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Area of Science:

  • Systems Engineering
  • Control Theory
  • Signal Processing

Background:

  • Hammerstein systems, a cascade of nonlinear and linear subsystems, are crucial for modeling complex dynamical behaviors.
  • Identifying Hammerstein systems presents challenges in selecting model structure and achieving sparse representation of nonlinear components.

Purpose of the Study:

  • To propose a novel Bayesian sparse multiple kernel-based identification method (BSMKM) for multiple-input single-output (MISO) Hammerstein systems.
  • To address challenges in model parameter estimation, nonlinear function sparsity, and linear subsystem order selection.

Main Methods:

  • Utilized a basis-function model for the nonlinear part and a finite impulse response model for the linear part.
  • Developed a hierarchical prior distribution using Gaussian scale mixture and sparse multiple kernels for joint sparsity and correlation structure.
  • Employed a full Bayesian approach with variational Bayesian inference for parameter estimation.

Main Results:

  • Successfully estimated Hammerstein system parameters, including FIR coefficients, hyperparameters, and noise variance.
  • Achieved indirect nonlinearity order selection and model order selection for the linear dynamical system.
  • Demonstrated the effectiveness of the BSMKM method through numerical simulations and real-world data.

Conclusions:

  • The proposed BSMKM offers a robust framework for Hammerstein system identification.
  • The method effectively handles parameter estimation and model order selection in complex nonlinear systems.
  • BSMKM shows promise for applications involving real-world nonlinear dynamical system analysis.