The Research Of Finite Element Model Updating Methods Based On First-order Optimization Algorithm And The Response Surface Method

Although in the past 20 years the FEM correction technology has been widely researched and applied, so far, for the reason that people’s knowledge level, measurement technology and the actual conditions, some problems appeared in the process of the finite element model updating, such as slow convergence speed, too many fixed parameters, large amount of calculation, etc. Based on this, exploring the method of finite element model updating that is more reliable and efficient still has far-reaching significance. In this paper, the method of finite element model updating of bridge structure was studied, the main work includes:(1) Using first-order optimization algorithm of ANSYS, the finite element model updating process was carried out. Stiffness reduction method were used to simulate the damaged beam structure, which was regarded as an actual beam. Making approximation between the modal frequency obtained by the "actual beam" and the modal frequency calculated with a nondestructive beam, the optimized results including convergence curve of objective function and correction parameter value were obtained. In the process of correction parameters’ selection, sensitivity analysis module of ANSYS were used to select out the correction parameter that has guiding significance, which avoid the large amount of calculation problems and excessive correction parameters, due to the selection that depended on experience. A frame beam UCF of the university of Florida was choosed to verify the reliability of first-order optimization algorithm in application, and the reason why this frame beam is selected is that the bridge’s test model test results have been widely recognized by many scholars. On the basis of UCF beam test model, the corresponding finite element model is established. By implementing the process of correction parameters selection and the process of sensitivity analysis and the process of model modification proved the reliability and effectiveness of the first-order optimization algorithm.(2) The response surface method which combines mathematical method with statistical method was chosen to explore the finite element model updating method that has fast convergence speed and small amount of calculation. Selecting the numerical beam and UCF beams model were used to realize the correction process, which same as the first-order optimization algorithm. The factorial design table was established by using the response eigenvalue calculated by ANSYS. By analyzing the design table the pareto chart was obtained,which determined the correction parameter. The results were consistent with the first-order optimization algorithm, which verified the reliability of the response surface method. The response surface model is established by using MINITAB software, and the iterative optimization of the response surface model is obtained by using the optimization theory.(3) For the numerical beam and UCF beam, the results calculated by the first-order optimization algorithm were compared with the results calculated by the response surface method. In term of the determination of correction parameters the results were consistent with the two methods. From the convergence graph of the objective function it can be seen that the convergence speed based on response surface method of finite element model updating is more efficient and faster than the correction based on first-order optimization algorithm.To sum up, the practicability of two methods in terms of finite element model updating is reliable and can be used in practical engineering application. The response surface method has more advantages on convergence speed and efficiency, it can effectively reduce the amount of calculation and shorten the convergence time, so it can be used for complex large engineering structure.