材料パラメータ同定問題におけるガウスニュートン法の適用

抄録

In this study, the application of the Gauss-Newton method to several material parameter identification problems was investigated. The parameters of materials with complicated constitutive laws are determined to reproduce known physical quantities such as stiffness and natural frequency. The identification problem is usually formulated as a squared error minimization problem for the physical quantity. Gauss-Newton method is one of the important solution methods. In this method, the Hessian matrix is approximated using the first order differentiation of the physical quantity with respect to the parameters. Although this method obtains good convergence in the initial stage, it is observed that it becomes unstable in the final stage. We introduced a line search technique based on the Marquardt method to avoid the instability. We compared this method with the general gradient method and confirmed good convergence of this method.