基于二阶泰勒级数展开和风驱动优化算法的结构有限元模型修正

为得到结构响应与修正参数之间的函数关系、简化参数迭代过程，通过推导结构响应关于修正参数的一阶与二阶泰勒级数展开，并选用具有寻优效率高、全局搜索能力强的风驱动优化算法，建立了基于二阶泰勒级数展开和风驱动优化算法的结构有限元模型修正方法。同时，为求解响应关于修正参数的二阶泰勒级数展开，采用差分法近似求得响应关于修正参数的一阶和二阶偏导数。利用该方法对算例模型进行了修正，并对比了一阶和二阶泰勒级数展开的修正效果。结果表明：二阶泰勒级数展开的修正效果明显优于一阶泰勒级数展开，增加二阶偏导数项可以更好地反映响应与修正参数之间的函数关系。基于该方法，采用实桥的静动力测试数据对青林湾大桥的有限元模型进行了修正，修正后的有限元模型能够较好地反映大桥的实际状况。

Updating of finite element model of structures using second-order Taylor expansions and wind driven optimization

In the updating of finite element model (FEM), in order to obtain the functional relationship between structural responses and updating parameters, and to simplify the process of parameter iteration, this paper proposes an updating method for FEM which adopts second-order Taylor expansions and wind driven optimization. This method was developed through deriving first-order and second-order Taylor expansions of structural responses of updating parameters and selecting a wind driven optimization algorithm with high searching efficiency and global searching ability. In addition, to obtain the second-order Taylor expansions of structural responses of update parameters, the difference method was used to get approximate first-order and second-order partial derivatives. Then, a numerical example was updated using this FEM updating method and the updating effects of first-order Taylor expansions and second-order Taylor expansions were compared. It was found that the updating effects of second-order Taylor expansions is obviously superior to those of the first-order Taylor expansions, and that increasing the number of second-order partial derivative terms can better express the functional relationship between structural responses and updating parameters. Lastly, based on the proposed method and the static and dynamic field measurement data of an actual bridge, the FEM of Qinglin Bay bridge was updated, and it can be concluded that the actual structural responses of the bridge can be better simulated and reflected by the updated FEM.