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Parameter estimation for the generalized fractional element network Zener model based on the Bayesian method

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  • Fan, Wenping
  • Jiang, Xiaoyun
  • Qi, Haitao

Abstract

In the present study, an inverse problem to estimate parameters in the Zener model of viscoelasticity based on the generalized fractional element (GFE) network is studied. The Bayesian method is proposed to obtain the optimal estimation of the viscoelastic parameters. Three examples are performed to certify the validity of the method. All numerical results lead to an excellent fitting between the calculative results and experimental data. It is shown that the Bayesian method is feasible in the inverse problem of parameter estimation for the fractional constitutive equation, and the GFE network Zener model is efficient in the modeling of the viscoelastic behavior.

Suggested Citation

  • Fan, Wenping & Jiang, Xiaoyun & Qi, Haitao, 2015. "Parameter estimation for the generalized fractional element network Zener model based on the Bayesian method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 427(C), pages 40-49.
    • Handle: RePEc:eee:phsmap:v:427:y:2015:i:c:p:40-49
    DOI: 10.1016/j.physa.2015.02.037
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    Citations

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    Cited by:

    1. Zhang, Hui & Jiang, Xiaoyun & Yang, Xiu, 2018. "A time-space spectral method for the time-space fractional Fokker–Planck equation and its inverse problem," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 302-318.
    2. Duan, Jun-Sheng & Qiu, Xiang, 2018. "Stokes’ second problem of viscoelastic fluids with constitutive equation of distributed-order derivative," Applied Mathematics and Computation, Elsevier, vol. 331(C), pages 130-139.
    3. Francisco J. Ariza-Hernandez & Martin P. Arciga-Alejandre & Jorge Sanchez-Ortiz & Alberto Fleitas-Imbert, 2020. "Bayesian Derivative Order Estimation for a Fractional Logistic Model," Mathematics, MDPI, vol. 8(1), pages 1-9, January.
    4. Lei, Dong & Liang, Yingjie & Xiao, Rui, 2018. "A fractional model with parallel fractional Maxwell elements for amorphous thermoplastics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 465-475.
    5. Carrera, Y. & Avila-de la Rosa, G. & Vernon-Carter, E.J. & Alvarez-Ramirez, J., 2017. "A fractional-order Maxwell model for non-Newtonian fluids," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 482(C), pages 276-285.

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