基于泰勒级数展开的区间反演方法

实际结构或构件的几何与材料参数总包含不确定性,在对结构计算模型进行精确分析时,有时需要对参数不确定性进行量化。本文提出了一种用于区间参数识别的反演方法,即基于泰勒级数展开式分别建立参数与响应的区间中值、区间半径的对应函数关系,并通过构建两个反演问题来分步识别参数区间中值和半径,以避免区间扩张现象和简化优化反演过程。通过数值质-弹系统初步验证了方法的可行性,然后基于一组钢板的动测数据,识别了钢板的几何及材料特性参数的区间范围。研究结果表明,本文方法具有良好的区间反演精度,能有效地避免区间扩张现象,可以用于实际工程区间问题的求解。

An interval inverse solution method based on Taylor series expansion

The geometric and material parameters of real-world structures always contain uncertainties.Sometimes such uncertainties should be quantified when precise analyses of structural computational models are required.An inverse problem for identifying interval parameters has been developed in this study.The relationships of mid-values and radii between interval parameters and responses were first established using Taylor series expansion.Then two inverse problems were formed to identify the mid-values and radii of parameters in a successive way.By this means the phenomenon of interval overestimation was maximally avoided and the process of inverse optimization was highly simplified.The proposed method has firstly been verified against a numerical mass-spring system.Subsequently using the measured modal data of a set of steel plates,the intervals of the geometric and material parameters of the plates were identified.The analysis results demonstrate that the method provides satisfactory accuracy and precision in solving interval inverse problems.Interval overestimation can be effectively restrained.Therefore,the method can be applied to solving practical engineering problems having interval uncertainties.