摘要
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.
作者
赵新攀
唐樟春
夏艳君
汪鹏
ZHAO Xinpan;TANG Zhangchun;XIA Yanjun;WANG Peng(Institute of Manned System Engineering, China Academy of Space Technology, Beijing 100094, China;School of Mechatronics Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China;Faculty of Mechanical Engineering ＆ Automation, Zhejiang Sei-Teeh University, Hangzhou 310018. China)
出处
《机械设计与研究》
CSCD
北大核心
2018年第3期22-25,29,共5页
Machine Design And Research
基金
国家自然科学基金(51405064,51405063,11602054)
机械设计及理论浙江省重中之重学科和浙江理工大学重点实验室开放基金(ZSTUME01A01)资助项目
关键词
可靠性
不确定性传递
概率密度函数
全因子数值积分
单变量降维法
reliability
uncertainty propagation
probability density function
full factorial numerical integration
univariate dimension reduction
