Finite Element Model Updating Of Bridges Based On Taylor Expansion And Wind Driven Optimization

There are often some deviations between initial finite element model calculated values and test values of the bridge structure responses. In order to make finite element model accurately reflect actual condition of the structure, it is necessary to update finite element model according to test values. Selecting updated parameters, constructing objective function of the difference between calculated values and test values and using optimization algorithm to minimize objective function by adjusting parameters are the basic processes of finite element model updating.For the complex bridge finite element model, it will take much time to calculate responses every time. A method which use the second-order Taylor expansion of responses about updated parameters to instead finite element model of calculating responses in parameters iterative is presented in this paper. In view of multivariable and nonlinear optimization problem in finite element model updating, Wind Driven Optimization is introduced.The main work and conclusions of this paper are as follows:(1) Firstly, the approximate functional relation between responses and updated parameters are fitted by cubic polynomial response surface. Combining with Sequential Quadratic Programming and Wind Driven Optimization respectively, a numerical example finite element model is updated. The parameters iterative process by Wind Driven Optimization is specifically introduced. The results show that Wind Driven Optimization has powerful ability of global optimization and can be used to solve multivariable and nonlinear optimization problem. The updated effect of combining use of frequency and static displacement is better than the use of frequency lonely, and it shows that combining dynamic and static information can not only make more response calculated values of updated finite element model agreement with test values but also contribute to update some parameters.(2) Secondly, the first-order and second-order Taylor expansions of responses about updated parameters are derived, and the approximate solution of first-order and second-order partial derivative are obtained by difference method. The updated effect of second-order Taylor expansion is much better than the first-order Taylor expansion. It illustrates that the second-order Taylor expansion can well represent functional relationship between responses and updated parameters by adding second-order partial derivative term. By comparing the updated effect of second-order Taylor expansion and cubic polynomial response surface, it can be found that the former can obtain more satisfactory updated effect in the case of less computational complexity.(3) Finally, an actual bridge finite element model is updated by second-order Taylor expansion and Wind Driven Optimization. The updated finite element model can well reflect actual condition of the bridge.