Robust identification of the mechanical properties of viscoelastic non-standard materials

This work presents an identification procedure for the constitutive model of viscoelastic non-standard materials, such as Functionally Graded Materials (FGM). A generalized Kelvin model of arbitrary order is selected, making it possible to define the material constitutive relationship by means of the ratio of polynomials in the frequency domain. Since ill-conditioning may occur at the numerical identification stage of high model order parameters, a novel approach, mainly employing a orthogonal polynomial basis, to identify the model optimal order and parameters is proposed in this paper. Least square error fitting techniques employing a classic monomial and a Forsythe orthogonal polynomial basis are compared starting from numerically estimated measurements with noise.