改进响应面法在桥梁结构有限元模型修正中的应用

Application of Improved Response Surface Method in Modification of Bridge Structure FE Model

为了获得精确的桥梁结构有限元计算模型,提供健康监测和受力性能再分析的基准有限元模型,对桥梁结构有限元模型修正方法进行研究,提出以二阶多项式与径向基函数相结合的改进响应面法。将该方法应用到一座系杆拱桥的有限元模型修正中,选择该桥的铺装层厚度、拱肋、主梁、横梁及吊杆的弹性模量和密度作为待修正参数,采用D-最优试验设计方法进行试验设计,对试验设计得到的一系列样本点进行方差分析。以F检验法筛选出对各测点挠度和各阶频率影响显著的参数,建立改进后的响应面模型,并计算出关于设计参数的响应值。结合现场试验得到的静动力测试数据构造目标函数,对目标函数进行优化求解得到各参数的最优解,代入到初始有限元模型中,完成对初始有限元模型的修正。结果表明:各构件的弹性模量及其二次项和铺装层厚度对挠度影响高度显著,一些构件的弹性模量和密度对频率影响显著,以显著性较高的参数拟合的响应面模型具有较高的精度,修正后的有限元模型的计算值与现场试验实测值的误差显著降低。修正后的系杆拱桥有限元模型与实际结构更加吻合,可作为基准有限元模型,对今后桥梁结构的健康监测、静动力性能分析、损伤识别具有重要意义和实用价值。

In order to obtain the accurate finite element calculation models of bridge structures and provide the benchmark finite element models for health monitoring and re-analysis of mechanical performance,the modification methods of bridge structure finite element models are studied,and an improved response surface method combining second-order polynomial and radial basis function is proposed.This method is applied to the modification of the finite element model of a tied arch bridge.Selecting the pavement thickness,the elastic moduli and densities of arch ribs,main girder,beams and hangers of the bridge as the parameters to be corrected,the test design is conducted by using D-optimal test design method,and the analysis of variance on a series of sample points obtained from the experimental design is conducted.The parameters that significantly affect the deflection of each measuring point and the frequency of each order are screened out by F test method,the improved response surface model is established,and the response values about design parameters are calculated.The objective function is constructed based on the static and dynamic test data obtained from the field test.The objective function is optimized and solved to obtain the optimal solution of each parameter,which is substituted into the initial finite element model to complete the modification of the initial finite element model.The result shows that(1)The elastic modulus of each member and its quadratic term and the thickness of the deck pavement have a highly significant influence on the deflection.The elastic modului and the densities of some members have a significant influence on the frequency.The response surface model fitted with more significant parameters has higher accuracy.The error between the calculated value of the modified finite element model and the measured value of the field test is significantly reduced.(2)The modified finite element model of the tied arch bridge is more consistent with the actual structure,and can be used as a reference finite element model.It can be used as a benchmark finite element model,which is of great significance and practical value for future health monitoring,static and dynamic performance analysis,and damage identification of bridge structures.