基于加权Kendall相关系数和序贯代理模型的有限元模型修正

为了提高桥梁结构有限元模型修正的效率和效果，提出基于加权Kendall相关系数和序贯代理模型的有限元模型修正方法。首先，建立基于目标响应误差和待修正设计参数灵敏度的加权Kendall相关系数指标，并采用凝聚层次聚类算法，合理确定待修正设计参数的数量和位置，保证待修正设计参数对目标响应具有合适的解耦能力；其次，为解决传统一次性代理模型法在构造代理模型过程中产生的欠采样或者过采样的问题，采用基于FLOLA-Voronoi通用序贯设计策略的序贯代理模型法，提高构造代理模型过程中试验设计样本的利用率和模型修正效率；最后，根据一座斜拉桥的静动力荷载试验数据进行有限元模型修正。结果表明：基于FLOLA-Voronoi算法的序贯代理模型能够合理地确定构造代理模型所需的样本数量和位置，使得在相同样本数量的情况下，序贯代理模型比一次性代理模型具有稍好的精度指标；采用加权Kendall相关系数指标的聚类方法可以得到具有合适解耦能力的待修正设计参数，使得修正前大误差目标响应的误差显著下降，小误差目标响应的误差基本都处于合理范围内，有效地降低了目标响应的整体误差；同时，有限元理论静动力响应与实测静动力响应的平均误差分别由5.56%、8.43%降低至1.87%、3.41%，并且相较于常规方法，修正精度更好，所提方法可以用于桥梁结构有限元模型修正，可得到准确的桥梁结构数值模型。

FEM Updating Based on Weighted Kendall Correlation Coefficient and Sequential Surrogate Model

To improve the efficiency and effect of the finite-element-model updating of bridge structures, a new method based on the weighted Kendall correlation coefficient and sequential surrogate model is proposed. Firstly, a weighted Kendall correlation coefficient index based on the target response error and the sensitivity of the design parameters to be modified was established, based on which the number and location of the design parameters were reasonably determined using the hierarchical clustering algorithm, ensuring that the selected parameters have proper decoupling ability to the target response. Secondly, the sequential surrogate model method based on the FLOLA-Voronoi general sequential design strategy was adopted to solve the problem of under sampling or oversampling in the process of constructing the surrogate model, which improves the utilization of experimental samples and the efficiency of model updating. Finally, the feasibility of the proposed method was validated through the model updating of a cable-stayed bridge. The results indicate that the sequential surrogate model based on the FLOLA-Voronoi algorithm can reasonably determine the number and location of samples, and the sequential surrogate model obtains slightly more precise result than the one-time surrogate model. With introducing the weighted Kendall correlation coefficient and hierarchical clustering algorithm, more proper updating parameters with appropriate decoupling capabilities can be obtained, thereby significantly decreasing the large error target response and maintaining the small error target response in a reasonable range, based on which the overall error of the target response are effectively reduced. For the utilized bridge, the average differences of the theoretical and measured static and dynamic responses between finite element model and real bridge decrease from 5.56% and 8.43% to 2.08% and 3.26%, respectively. Compared with the traditional method, the proposed method obtains better model updating results, indicating that the proposed method can be used to update the finite element model of the bridge structure and obtain an accurate numerical model.