PurposeThis paper attempts to develop an efficient algorithm to solve the inverse problem of identifying constitutive parameters in VFG (viscoelastic functionally graded) materials/structures.Design/methodology/approachAn adaptive recursive algorithm with high fidelity is developed to acquire the derivatives of displacements with respect to constitutive parameters, which are required for the accurate and stable gradient based inverse analysis. A two-step strategy is presented in the process of identification, by which the unknown parameters can be separately identified and the scale and complexity of the inverse VFG problem are reduced. At each step, the process of identification is treated as an optimization problem that is solved by the Levenberg–Marquardt method.FindingsThe solution accuracy of forward problems and derivatives of displacements can be stably achieved with different step sizes, and constitutive parameters of homogenous/regional-inhomogeneous VFG materials/structures can be effectively and accurately identified. By examining the reliability, resolution, impacts of reference information and noisy data, the effectiveness of the proposed approach is numerically verified via three numerical examples.Originality/valueAn adaptive recursive algorithm is developed for derivatives computing with high fidelity, providing a solid platform for the sensitivity analysis and thereby a two-step strategy in conjunction with Levenberg–Marquardt method is presented in the process of identification. Consequently, an effective algorithm is developed to identify constitutive parameters of homogenous/regional-inhomogeneous VFG materials/structures.
An Inverse Problem Involving a Viscous Eikonal Equation with Applications in Electrophysiology
