Inverse analysis by boundary element method with singular value decomposition

This paper describes an optimal design method by means of the singular value decomposition and fuzzy inference in stabilizing the coefficient matrix. We have already reported some optimal design methods with the boundary element method, and shown that an objective shape has been obtained with the iterative calculation that utilizes the least square method or the fuzzy inference method. Because most coefficient matrices of optimization methods are ill-posed matrices, the analyses accompany much difficulty. We investigate the coefficient matrix, and transform it into a well-posed one by using the singular value decomposition. In this method, the ambiguous regularization parameter is determined with fuzzy inference. As an example, singular value decomposition is applied to the ill-posed matrix of a synchrotron model for pole shape optimization.