Inverse Analysis Method Using a Set of Solutions and A Priori Information.
Kenji AMAYA, Shigeru Aoki · TRANSACTIONS OF THE JAPAN SOCIETY OF MECHANICAL ENGINEERS Series A · 1995
A new analysis method for nonlinear inverse problems was developed. 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 null space. 3. The solution is obtained by fuzzy reasoning using the set of solutions and a priori information which are expressed as fuzzy membership functions. Since the solution is identified by taking into account a priori information, the iteration converges quickly and stably, and oscillatory solutions can be avoided. Example problems were solved by this method in order to demonstrate its accuracy and applicability.