Numerical Solutions Of Fractional Viscoelastic Inverse Problem Based On Kriging Surrogate Model

It has important application background in engineering and research value in theory to identify constitutive parameters of fractional viscoelastic problems. The Intelligent Optimization Algorithms, such as Ant colony Algorithm, are employed to solve the inverse fractional viscoelastic problems due to the difficulty of sensitivity analysis, but they are required to solve direct problem repeatedly which lead to a considerable amount of computing cost. In this paper, the Kriging surrogate model is applied to identify constitutive parameters of fractional viscoelastic problems, and the main academic contributions of this paper are:1. Developing a Kriging surrogate model based numerical method to solve direct fractional viscoelastic problems. The Kriging surrogate model is set up by making use of the displacement solution given by FEM and FDM at sample points, and sample points are selected via a Latin Hypercube sampling technique. The paper proposes a strategy of piecewise modeling in time domain for constructing Kriging surrogate model due to the temporal correlations. The computing accuracy and efficiency of the proposed method and strategy are tested via homogeneous/regionally inhomogeneous fractional viscoelastic numerical examples. The test indicates that the surrogate model is able to provide a reasonable computing accuracy, and is hopefully to save considerable amount of computing expense for large scale direct fractional viscoelastic problem which are required to solve repeatedly.2. Developing a Kriging surrogate model based numerical method to solve the inverse fractional viscoelastic problems. The established Kriging surrogate model is used as the solution model of direct problem and an improved Ant colony algorithm is employed as the solution model of inverse problem. The computing accuracy and efficiency of the proposed method are tested via numerical examples of combined identification for fractional viscoelastic parameters in cases of homogeneity and regionally inhomogeneity, and the effects of date noise are considered. The computing results demonstrate that the amount of computing expense is dramatically reduced as reasonable computing accuracy of inversion is maintained. This paper is hopefully to provide a valuable reference for improving computing efficiency of inverse/optimization fractional viscoelastic problems.