基于λ-PDF和一次二阶矩的不确定性反求方法

Uncertain Inverse Method Based on λ-PDF and First Order Second Moment

为了有效评价测量响应中不确定性对结构参量识别结果的影响,提出一种基于λ概率密度函数(Probability distribution function,PDF)和一次二阶矩的不确定性计算反求方法。采用二次衍生λ-PDF对待识不确定性参量的PDF进行建模。内层通过对参量呈λ-PDF的功能函数采用一次二阶矩法进行正问题求解,得到计算响应的概率分布;外层通过最小化测量响应与计算响应之间的概率分布特征量将不确定性反问题转化为确定性的最优化问题,并用隔代映射遗传算法识别未知参量λ-PDF的参数。本方法不仅有效地实现了结构未知参量PDF的估计,而且与传统基于抽样的统计方法相比,计算效率较高。数值算例和工程应用验证了本方法的可行性和有效性。

An inverse method based on λ-probability distribution function（PDF） and first order second moment is developed to effectively evaluate the influence of the uncertainty of measured response on the identified results of structural parameters. The quadric derivative of λ-PDF is used to model the PDF of the identified uncertain variable. The method includes a double-loop procedure. In the inner-loop the performance function is solved by first older second moment method to obtain the computational PDFs of the responses. In the outer-loop the uncertain inverse problem is transformed into an optimization problem by minimizing the moment errors of the measured and computational responses, and the optimization problem is solved by intergeneration projection genetic algorithm. The method proposed can not only effectively estimate the PDFs of the unknown structure variables, but also have a higher computational efficiency compared with the traditional statistical method. Two numerical examples and an engineering problem are used to demonstrate the feasibility and effectiveness of the proposed method.