A New Method of Determination Truncating Parameter in Spectral Decomposition

Despite of soft computing methods which makes an approximate answers of an inverse problem, hard computing methods makes more accurate answers. Therefore, the hard computing methods used more than soft computing mehods in this type of problems in engineering. Regularization tools is one of the methods to solve this type of problems. The purpose of regularization tools is replacing problem ill-conditioning with a well-posed problem, which can represent reliable responses. This methods are used in inverse problems and earthquake engineering because they did not need any prior information about fault and slip. In this research we proposed a new method for determination of suitable number of modes that involve in the final response that we call it truncating parameter. The method that we tried to examine its validity in this research was spectral decomposition of Green’s function. This method looks like singular value decomposition and can be categorize in regularization tools of solving inverse problems. Illustrative examples are solved to demonstrate the usefulness of the proposed inverse analysis method. Two examples are solved in two-dimensional faulting and one example solved in three-dimensional faulting. Using this proposed method, results of inverse analysis is satisfactory and shows that the proposed method is a reliable method and can be used for real cases. Thus the authors of this article suggest using this method in solving inverse problems of engineering.