结构可靠性高效求解的两种近似解析方法研究

Two Approximate Analytic Methods for Efficiently Evaluating for Structural Reliability

针对具有多个不确定性参数的复杂结构,采用Pearson估计法及Johnson估计法确定输出响应解析的概率密度函数,而后基于概率密度函数进一步求解结构响应超越设定阈值的失效概率。在使用Pearson估计法及Johnson估计法时,需要事先确定输出响应的前四阶矩,分别采用蒙特卡洛法、全因子数值积分及单变元降维法求解前四阶矩。在求解前四阶矩时,这两种方法需要计算真实的功能函数,这是主要的计算量所在,尤其是对于工程上常见的需要调用有限元分析的隐式极限状态函数问题。数值算例结果显示,两种方法以少量的样本点即可得到高精度的响应概率密度函数及失效概率计算结果;而后进一步将方法应用到某涡轮叶片的不确定性传递及失效概率求解,验证了方法的工程适用性。

This paper employs Pearson method and Johnson method to obtain the analytic solution of the probability density function（ PDF） of the output response for complicated structures with many random input parameters,and the failure probability（ FP）,which defines the probability that the response exceeds the prescribed value,is further solved. The first four moments of the response need to be evaluated when utilizing the Pearson method and Johnson method,and they are assessed by Monte Carlo Simulation（ MCS）,full factorial numerical integration（ FFNI） and univariate dimension reduction（ UDR）. When solving the first four moments,the Pearson method and Johnson method need to compute the real performance function,which accounts for most of the computational cost,especially for the problem with implicit limit state function that is common in engineering and requires to perform the finite element analysis. A numerical example is employed to demonstrate that the Pearson method and Johnson method only need a few samples to obtain the good results for PDF and FP. Further,the two methods are applied to evaluate uncertainty propagation and FP for a turbine blade,which verifies the applicability of the two methods in practice.