Several Identification Method On The Structure Fault Diagnosis

The theory of inverse problems of a partial differential equation is used for the structure fault diagnosis in this paper. A set of identification models of a differential stiffness and of an integral equation on the additional stiffness are given to identify the small stiffness of a variational structure which is caused by the fault in the structure, thus may to the crack of occurrence, development carry on the online examination.This paper through the Fourier transformation, transforms the differential equation of parameter question from the time domain to the frequency domain, then utilizes the small perturbance theory to solve inverse problem. The question is transformed to solve the first kind of Fredholm integral equation. At first, this paper takes the first kind of integral equation to discrete, and takes the Landweber method to improve. Because Landweber method is a well stable solution method, but the computational burden is big. This paper utilizes the knowledge of matrix to reduce greatly the computational burden of the Landweber method. Secondly, this paper imitates Landweber method to structure one kind regularization strategy which is suit in having the symmetric Kernel about the first kind of integral equation and has made the effective improvement to it, which improve computational efficiency obviously. Finally, this paper uses the regularization homotopy method to solve the first kind of integral equation. The most main merit of homotopy method is a wide range convergence method, but regarding to the ill-posed question, it can not overcome ill-posedness of the operator equation. In conquering ill-posed aspect of inverse problem, Tikhonov regularization method is without doubt most famous and the most effective method. The first kind of integral equation with the regularization homotopy method to solve is possible to unify both the merits.