基于响应面法和ARO算法的桥梁有限元模型修正

Finite Element Model Updating of Bridge Based on Response Surface Method and Artificial Rabbits Optimization

针对桥梁结构模型修正过程中计算量大、全局寻优难等问题,提出一种基于响应面法和人工兔优化算法(artificial rabbits optimization, ARO)的桥梁有限元模型修正方法。该方法通过F检验法明确对结构响应影响显著的参数并建立响应面模型作为桥梁有限元模型的代理模型进行迭代计算,然后通过静动力联合修正法基于特征响应的响应面模型计算值和试验值构建目标函数,并通过人工兔优化算法对目标函数进行迭代计算进而获得精确的有限元模型参数。采用该方法对变截面连续刚构黄河特大桥有限元模型进行修正,结果显示:基于显著性分析结果建立的桥梁响应面模型相关系数大于0.98,且平均绝对误差低于0.05;模型修正后主梁关键截面竖向位移最大相对误差由32.97%降至5.72%,平均相对误差由20.67%降至3.61%,桥梁前3阶竖向自振频率平均相对误差仅为0.18%。可见,采用所提方法修正的模型能用于评价桥梁结构实际受力性能。

Aiming at the problems of high computational complexity and difficultty in global optimization during the model updating process of bridge structure,a bridge finite element model updating method based on response surface method and artificial rabbits optimization(ARO)algorithm was proposed.The proposed method employed the F-test to identify parameters significantly affecting structural responses and constructed response surface models as surrogate models for the bridge finite element model for iterative calculations.Then,the static-dynamic combined updating method was used to establish an objective function of the calculated values and experimental values of the response surface model based on the characteristic response.The objective function was iteratively calculated by use of the ARO algorithm to obtain accurate finite element model parameters.The proposed method was applied to update the finite element model of the Huanghe Extra-Large Bridge,which was a continuous rigid-frame bridge with variable cross-sections.The results show that the correlation coefficient of the bridge response surface model established on the basis of the significance analysis results is greater than 0.98,with an average absolute error lower than 0.05.After model updating,the maximum relative error of vertical displacement at critical cross-sections of the main beam is reduced from 32.97%to 5.72%,and the average relative error is reduced from 20.67%to 3.61%.The average relative error of the bridge first three-order vertical natural frequencies is only 0.18%.Therefore,it can be seen that the model updated by the proposed method can be used to evaluate the actual stress performance of bridge structures.