Constrained Substructure Model Updating Method Based on Local Mode

Modal updating is a crucial problem in Structure HealthMonitoring (SHM) and has strongly attracted researchers' attentions.Recently the structures have been becoming much huger and more complex, soit's getting harder to update the global structural model precisely usingthe classical model updating methods. In general, only some localsubstructure model is important and it is not necessary to update the wholestructure. Therefore the substructure technologies are important for thatthey require only few sensors and the local dynamic information toaccurately update the interested substructure model.Usually the updating of the element stiffness is enough to reflect thedamage and the structural dynamic performance. This paper proposes a conceptof the Isolated Substructure. It aims at updating local substructure elementstiffness only by the relative mode at the substructure location. Thepresent Isolated Substructure refers to a new structure formed by isolatingthe substructure from the global structure. Then the substructure can beupdated indirectly through updating the Isolated Substructure, such that theoptimizing variables become much less and the convergent speed is fastened.The key process of this method is to construct the flexibility matrix of theIsolated Substructure by measured data. First the lower order frequenciesand shape modes of the substructure are identified from the measured impulseresponse by utilizing Eigensystem Realization Algorithm (ERA), and therelative modal masses are estimated by Least Square Method (LSM); Second,according to its independence and convergence properties, the flexibilitymatrix corresponding to the substructure can be approximately constructed bythe identified lower order modes and be improved by the calculated higherorder modes from the theoretical model; and then utilizing the concept ofthe flexibility matrix, the substructure is isolated from the globalstructure through applying numerical supporting on the substructureboundary; synchronously the flexibility matrix of the Isolated Substructureis constructed from the advanced obtained flexibility matrix of the globalstructure, and is used to update the Isolated Substructure, that is, toequally update the substructure.The optimization method based on sensitivity idea is adopted, and therelative formulas are deduced. It makes the iteration and convergencefaster.A numerical example of a plane truss separately with 5% or 10% rmsGaussian measurement error validates that the substructure can be updatedeffectively by the Isolated Substructure model updating method.