大跨桥梁参数识别响应面方法中的近似函数及样本选取

以某大跨斜拉桥实验室物理模型设计参数与动力特性之间复杂的隐式关系为对象,分析响应面模型中近似函数和试验样本对回归模型精度的影响。首先推导多项式和径向基函数响应面模型的建模方法,然后基于斜拉桥三维空间模型的有限元动力分析,比较分析完全二阶多项式与几种径向基函数模型在设计域和扩展设计域内以及噪声污染情况下的回归精度。最后对几种少量样本的试验设计方法和响应面试验设计方法进行了分析。结果表明,径向基函数模型各方面性能优于多项式模型,响应面实验设计方法优于其他方法,少量样本可采用D优化设计,较多样本情况下以中心复合设计较佳。

Study on approximate functions and sample selection of response surface method for parameters identification of long-span bridges

The modeling and sample selection of response surface method (RSM) are investigated in this study by using numerical simulation based on the 3D Finite Element model of a laboratorial bridge model.The implicit expression and complicated relationship between design parameters and dynamic characteristics are selected to establish the response surface model.RSMs with different approximate functions of radial basis function (RBF) and full quadratic polynomial are discussed,and several methods of design of experiment (DOE) are investigated to study the sample selection for RSM modeling.The comparative analysis indicates that RSMs based on RBFs are better than the quadratic polynomial model.Methods of response surface design are better than the conventional experimental design methods,and the optimal method of DOE discussed above is central composite design