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

• The generalized fractional element network Zener model is considered.
• The Bayesian method to estimate parameter for GFE network Zener model is proposed.
• Three examples are performed to prove the validity of the Bayesian method.
• The Bayesian method is shown to be feasible for fractional constitutive equations.

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.