System Identification by Subdomain Reduction Method

Abstract

A number of approximate techniques have been developed to determine primary degrees of freedom ( DOF ) of the reduced eigenvalue problem . These schemes approximate the lower eigenvalues that represent the g lobal behavior of the structures. In general, sequential elimination can be used with reliability. But it takes excessively large amount of time to construct a reduced system. To reduce computational time and resources, two -level selection scheme combined with sub -structuring method are used . Especially, in the three - dimensional problem with relatively large number of degrees of freedom on the interface area, conventional sub -structuring techniques are not efficient because the large number of interface deg rees of freedoms is included in the final degrees of freedom in the reduction process. Therefore, to reduce computer resources and computing time, an improved sub - domain reduction method is used. In the present study, nonlinear inverse perturbation method is used to solve inverse problem. In the system reduction process, nonlinear inverse perturbation equations are derived for full system because damage effects are distributed to the whole system. This formulation is the form of optimal design problem with the objective function which is the residual error of dynamic equilibrium equations. In the traditio nal inverse problem, all the perturbation quantities of element matrices belong to the design variables. However, in the present study, design variables are limited not to all the perturbed quantities of the elements in the global domain but only to the perturbed quantities in the particular sub -domain which is expected to possess damages. The present sub -domain system identification method can provide effici ent tool in inverse problems because it requires only small number of design variables and convergence in nonlinear problem is much faster than tha t of a single global system.