離散逆問題の数値計算(<特集>逆問題)

抄録

After a brief description about the ill-posed inverse problems which are discretized with the finite element method etc., a method for solving such problems is presented with a practical example. This method consists of the following procedures. 1. The singular value decomposition of the coefficient matrix is performed, and then the rank is appropriately reduced. 2. A set of solutions is represented by Moore-Penrose's solution and the null space. 3. The solution is obtained by fuzzy reasoning using the set of solutions and sets of fuzzy priori information. Following three studies are presented: a study which the Kalman filtering technique is applied to estimate the material parameters of two nonlinear constitutive equations, A method for obtaining the optimal experimental/measurement procedure for general estimation problems, and a method (GA filter) for non-linear state space estimation using genetic algorithm.