基于响应面法的结构有限元模型静动力修正理论及应用

Static and dynamic finite element model updating of structures based on response surface method:theory and application

将响应面法引入到有限元模型的静动力修正,通过合适的实验设计和回归分析,建立反映参数与响应量之间关系的响应面模型,代替初始有限元模型进行优化。为了验证该方法的可行性和准确性,首先选择一简支梁作为数值算例,分别基于静、动力分析的挠度及模态频率及同时利用挠度及模态频率结果构建目标函数,在假设的损伤工况下修正了初始有限元模型,修正结果表明,基于三种目标函数修正后的参数取值均与损伤的预设值基本一致,但同时利用挠度及模态频率结果修正后的参数取值更接近于预设值。然后利用一座刚构-连续组合梁桥的现场静、动力测试数据,对该桥的初始有限元模型进行了修正,修正后有限元模型的挠度和频率计算值与实测值更加吻合,表明修正后的有限元模型能更准确地反映实际结构的力学性能,可以作为后期进行状态评估的基准有限元模型。

In this paper, response surface method is adopted to update the finite element model of the structure based on static and dynamic test data simultaneously. Using the reasonable experiment design and regression tech- niques, a response surface model is formulated to approximate the relationships between the parameters and re- sponse values instead of the initial finite element model for further updating. In order to investigate the feasibility and accuracy of this approach, a numerical example of a simply supported beam is taken as case study and finite el- ement model of the beam with assumed damage is updated first. The objective function is built based on deflections and modal frequencies from static and dynamic analysis simultaneously. The objective functions based on deflec- tions and modal frequencies separately are also built for comparison. Updated results show that updated parameters from all three objective functions are close to the assumed values and updated parameters based on deflections and modal frequencies simultaneously are more accurate than the others. Furthermore, this approach is applied to up- date the finite element model of a prestressed reinforced concrete rigid frame-continuous girders bridge based on the in-situ static and dynamic measurement results. The numerical modal frequencies and deflections from the updatedmodel are in good agreement with the in-situ measurements. This indicates that the updated finite element model can accurately represent the mechanical properties of the bridge and it can serve as a benchmark model for further damage detection and condition assessment of the bridge.