基于Monte Carlo法的结构动力学模型确认

提出一种蒙特卡洛模拟(MCS)与多元回归分析相结合的有限元模型确认方法。采用基于动态响应面法生成的代理模型改进直接MCS,用一种逐步迭代的方式改进代理模型保证模型确认的精度。传统欧氏距离/马氏距离从不同方面描述了两点间距离,然而如果在距离准则中能够同时考虑两者则会更全面。在相关性分析过程中,综合欧氏/马氏距离的特点,采用了一种欧氏/马氏距离相结合的不确定量化方法(距离判别方法),并给出了基于此指标的迭代收敛判断准则。算例仿真结果表明:所提出的有限元模型确认方法和此距离判别方法的使用,能比较大地降低MCS的计算量并能得到满意的模型确认结果,迭代收敛的稳定性和精度都有了提高。

The Structural Dynamics Model Validation based on Monte Carlo Method

A statistical method based on Monte Carlo Simulation (MCS) and multiple regression analysis is presented for FEM model validation. An agent model created by Response Surface Method with dynamic response is used to improve direct MCS, which has guaranteed the accuracy of model validation. The traditional Euclidean/ Mahalanobis Distance describe the distance of two points in different aspects,if the two can be both considered in Uncertainty Quantification it might be more Comprehensive. Incorporating the features (advantages) of Euclidean/Mahalanobis Distance in the aspect of correlation measure, a method which the two distance are used for Uncertainty Quantification (a distance criterion) with its Iteration convergence judgment criteria is employed. Simulation results show that the presented method with the distance criterion can greatly reduce the time spend on calculation and can get satisfactory results of model validation; And can provide a more stable approximation process and enhance the accuracy of the result.