Finite Element Model Updating For Cable-stayed Bridges Based On KRON Substructure Method

During the long-term monitoring of long-span cable-stayed bridges,damages are inevitable due to a variety of reasons such as earthquakes,typhoons,overloads and inappropriate maintenances.The aging issues have broadly been concerned in many cable-stayed bridges in our country,requiring proper health monitoring for the operational condition of such bridges.It is well known that in a cable-stayed bridge,a large number of structural members and great many designed parameters are involved,leading to a huge computational cost.Therefore,the efficiency of the finite element(FE)model updating is insufficient,especially for the traditional techniques,and this becomes among the crucial bottom necks in the field of structural health monitoring and damage detection applications.In the present work,the FE model updating is studied based on the Kron substructural technique.The method for the sensitivity analysis is proposed with respect to both the substructures and the entire structure.The proper selection of the updated parameters is discussed,and two types of subdivision schemes are proposed.The suitable substructural dividing schemes are recommended for coping with practical engineering requirements.The present thesis includes the following main works:(1)For long-span cable-stayed bridges,a large number of updated parameters are involved.This may lead to the illness of the algorithm which prevents the optimization from converging,and the FE model updating becomes inefficient.For this reason,the Kron substructural technique is proposed to be employed for the FE model updating of cable-stayed bridges.After introducing the principle of the Kron substructure,theoretical derivations have been performed.Since the Taylor’s expansion is included in the eigenvalue formulation,the errors are quantified by categorizing the residual flexibility into two parts according to the orders of the reserved residual terms.The finite element types and the modelling skills,being commonly used for bridges,are introduced.Based on the Kron substructures,the developed eigenvalue analysis has been proved to be effect through the numerical example of a simply supported beam.(2)In the substructural FE model updating,only a small part of the substructures,referring to the parameters to be updated,are necessary to be concerned,which is among the major advantages of the technique.It is therefore necessary to properly select the updated parameters for the key members in cable-stayed bridges based on the sensitivity point of view.In the present work,the closed-form formulae are derived for the evaluation of eigenvalue problems for both the substructures and the entire structure.Such formulae are then verified from the numerical model of a cable-stayed bridge,and the results further show that the sensitivities of the parameters are quite consistent between the substructures and the entire structure.For each structural member,the candidates for the parameters to be updated in the FE model can firstly be nominated referring to the parameter uncertainties in practical structures.For each candidate,its sensitivities to the substructures and the entire structure are then calculated,allowing to find a few “most sensitive” parameters for the FE model updating.(3)When the structure is divided inappropriately,the model updating procedure might be inefficient and inaccurate.In this study,two substructural dividing layouts are proposed based on the physical profile and the modal coordinates.By taking a set of dividing schemes,suitable schemes are recommended from the aspects of accuracy and efficiency according to different practical demands.From the number of elements involved,suitable dimensions of the substructures are recommended,where the accuracy and efficiency of the model updating are optimized.From the formulation of the connection matrix,the optimal substructural dividing points are recommended for practical cable-stayed bridges.Focusing on the model updating results of the cable-stayed bridge example,the techniques relying on the entire structural analysis and the substructural analysis are compared in detail,showing that the substructural technique is capable to significantly improve the computational efficiency without loss of accuracy.It can finally be concluded that the proposed substructural dividing and model updating methods for cable-stayed bridges offer an efficient and reliable approach for bridge FE model updating.