基于试验数据的大跨度拱桥有限元模型修正

为了获取菜园坝长江大桥的基准有限元模型，结合Kriging代理模型和一种改进的粒子群优化算法，利用荷载试验数据对其初始有限元模型进行修正。首先，叙述模型修正和Kriging模型基本理论，在基本粒子群算法中引入交叉变异计算，提出一种改进的粒子群算法，并通过测试函数对改进的粒子群算法进行验证；其次，简要介绍菜园坝长江大桥荷载试验、荷载试验结果及初始有限元模型；最后，根据敏感性分析选定6个待修正参数，通过试验设计得到频率和位移关于修正的参数的样本，并建立有限元模型的Kriging代理模型以预测结构响应；以频率和位移的试验值和计算值残差为目标函数，分别利用基本粒子群算法和改进的粒子群算法在修正参数的设计空间内寻找目标函数的最小值，并对比分析模型修正的结果。结果表明：测试函数表明改进的粒子群算法具有较好的稳定性和成功率，并能获得更为精确的优化结果；建立的Kriging代理模型均方根误差较小，可以替代有限元模型预测结构频率和位移；经过模型修正，菜园坝长江大桥前5阶频率计算值与试验值相对误差均控制在5%之内；除个别测点外，位移相对误差均控制在10%以内；相比基本粒子群算法，改进的粒子群算法获得了更小的目标函数值，修正后的频率和位移的相对误差更小。

Finite Element Model Updating of Large-span Arch Bridge Based on Experimental Data

In order to develop the baseline finite element model of the Caiyuanba Yangtze River Bridge, model updating based on data obtained from load tests using the Kriging model and an improved particle swarm optimization (IPSO) technique was implemented. First, the fundamental theory of model updating and the Kriging model were summarized. Then, an IPSO technique was proposed by introducing crossover and mutation operations in the standard particle swarm optimization (PSO) technique. The proposed IPSO was verified by two test functions. Then, the load test of Caiyuanba Yangtze River bridge, the test results and the initial finite element model are briefly presented. Finally, six updating parameters were chosen based on the sensitive analysis. The data samples of the chosen updating parameters and the corresponding frequency/displacement responses were obtained through design experiments. The Kriging model was established using the data samples, and it served as a surrogate for the finite element model in predicting the analytical responses. The objective function was constructed using the error functions between the experimental and analytical values of frequencies and displacements. The PSO and IPSO were employed to search the design space for updating parameters to minimize the objective function. The updating results of PSO and IPSO were analyzed and compared. The results indicate that the IPSO has higher stability and success rate, as shown by test functions. The updated Kriging model shows very small mean squared errors, and hence can be used as a surrogate for the finite element model in predicting the analytical responses. It was observed that the first five frequencies of the bridge are closer to the experimental values after model updating. The relative errors of frequencies are all under 5%. Except in an isolated case, the relative errors of displacements are approximately 10% after model updating. Hence, compared to PSO, the proposed IPSO can achieve a smaller objective function value, and the relative errors of frequencies/displacements are also smaller.