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Saddlepoint approximation based line sampling method for uncertainty propagation in fuzzy and random reliability analysis

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Science china(Technological Sciences) 2010年第8期53卷 2252-2260页

作者： li luyi,lu zhenzhou &song shufang school of aeronautics,northwestern polytechnical university,xi’an 710072,china school of aeronautics Northwestern Polytechnical University Xi’an China

For structural system with random basic variables as well as fuzzy basic variables,uncertain propagation from two kinds of basic variables to the response of the structure is investigated.A novel algorithm for obtaining membership function of fuzzy reliability is presented with saddlepoint approximation(SA)based line sampling *** the presented method,the value domain of the fuzzy basic variables under the given membership level is firstly obtained according to their membership *** the value domain of the fuzzy basic variables corresponding to the given membership level,bounds of reliability of the structure response satisfying safety requirement are obtained by employing the SA based line sampling method in the reduced space of the random *** this way the uncertainty of the basic variables is propagated to the safety measurement of the structure,and the fuzzy membership function of the reliability is *** to the direct Monte Carlo method for propagating the uncertainties of the fuzzy and random basic variables,the presented method can considerably improve computational efficiency with acceptable *** presented method has wider applicability compared to the transformation method,because it doesn't limit the distribution of the variable and the explicit expression of performance function, and no approximation is made for the performance function during the computing ***,the presented method can easily treat the performance function with cross items of the fuzzy variable and the random variable,which isn't suitably approximated by the existing transformation *** examples are provided to illustrate the advantages of the presented method.

关键词： membership function fuzzy reliability fuzzy variable random variable saddlepoint approximation based line sampling method

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Reliability Sensitivity Algorithm Based on Stratified Importance Sampling Method for Multiple Failure Modes Systems

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Chinese Journal of aeronautics 2010年第6期23卷 660-669页

作者： Zhang Feng lu zhenzhou Cui lijie song shufang school of Mechanics and Civil and Architecture Northwestern Polytechnical University Xi 'an 710072 China school of aeronautics Northwestern Polyteehnical University. Xi 'an 710072 China

Combining the advantages of the stratified sampling and the importance sampling, a stratified importance sampling method （SISM） is presented to analyze the reliability sensitivity for structure with multiple failure modes. In the presented method, the variable space is divided into several disjoint subspace by n-dimensional coordinate planes at the mean point of the random vec- tor, and the importance sampling functions in the subspaces are constructed by keeping the sampling center at the mean point and augmenting the standard deviation by a factor of 2. The sample size generated from the importance sampling function in each subspace is determined by the contribution of the subspace to the reliability sensitivity, which can be estimated by iterative simulation in the sampling process. The formulae of the reliability sensitivity estimation, the variance and the coefficient of variation are derived for the presented SISM. Comparing with the Monte Carlo method, the stratified sampling method and the importance sampling method, the presented SISM has wider applicability and higher calculation efficiency, which is demonstrated by numerical examples. Finally, the reliability sensitivity analysis of flap structure is illustrated that the SISM can be applied to engineering structure.

关键词： multiple failure modes reliability sensitivity Monte Carlo simulation stratified sampling method importance sam-piing method stratified importance sampling method (SISM)

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Reliability and Sensitivity Analysis of Transonic Flutter Using Improved line Sampling Technique

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Chinese Journal of aeronautics 2009年第5期22卷 513-519页

作者： song shufang lu zhenzhou Zhang Weiwei Ye Zhengyin school of aeronautics Northwestern Polytechnical University Xi'an 710072 China National Key Laboratory of Aerodynamic Design and Research Northwestern Polytechnical University Xi'an 710072 China

The improved line sampling （LS） technique, an effective numerical simulation method, is employed to analyze the probabilistic characteristics and reliability sensitivity of flutter with random structural parameter in transonic flow. The improved LS technique is a novel methodology for reliability and sensitivity analysis of high dimensionality and low probability problem with implicit limit state function, and it does not require any approximating surrogate of the implicit limit state equation. The improved LS is used to estimate the flutter reliability and the sensitivity of a two-dimensional wing, in which some structural properties, such as frequency, parameters of gravity center and mass ratio, are considered as random variables. Computational fluid dynamics （CFD） based unsteady aerodynamic reduced order model （ROM） method is used to construct the aerodynamic state equations. Coupling structural state equations with aerodynamic state equations, the safety margin of flutter is founded by using the critical velocity of flutter. The results show that the improved LS technique can effectively decrease the computational cost in the random uncertainty analysis of flutter. The reliability sensitivity, defined by the partial derivative of the failure probability with respect to the distribution parameter of random variable, can help to identify the important parameters and guide the structural optimization design.

关键词： flutter aeroelastic line sampling technique Monte Carlo simulation uncertainty reduced order model

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随机样本数据的概率表征方法

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高等数学研究 2024年第1期27卷 51-57页

作者：宋述芳王家辉吕震宙员婉莹西北工业大学航空学院陕西西安710072

本文通过算例分析了参数概率表征方法的适用性和有效性.对于非参数概率密度估计,介绍了几种拟合变量概率密度函数的方法,通过算例对比了不同方法的拟合效果.

关键词：随机试验样本概率表征参数估计假设检验概率密度函数

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概率论课程中蕴含的数学文化

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高等数学研究 2020年第3期23卷 70-76页

作者：李璐祎宋述芳吕震宙王燕萍西北工业大学航空学院陕西西安710072

数学文化是概率论课程的重要组成部分,因此在概率论课程教学中非常有必要展示所蕴含的数学文化,才能使概率论课程教学在培养学生的工程数学学习与应用技能的同时,又能形成良好的数学思维与素养.从概率论的发展历程、概率论的数学思想与... 详细信息

数学文化是概率论课程的重要组成部分,因此在概率论课程教学中非常有必要展示所蕴含的数学文化,才能使概率论课程教学在培养学生的工程数学学习与应用技能的同时,又能形成良好的数学思维与素养.从概率论的发展历程、概率论的数学思想与方法,概率实际应用案例等几方面阐明概率论中蕴含的数学文化.概率论课程教学与数学文化的融合能够解读枯燥的概率知识,降低概率知识的抽象性,用数学文化自身的魅力吸引学生,培养学生的创新应用等综合素质.

关键词：数学文化概率论二项分布正态分布中心极限定理古典概型

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多元函数在某点偏导数的若干解法

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高等数学研究 2022年第2期25卷 28-31,34页

作者：宋述芳祁会治吕震宙西北工业大学航空学院陕西西安710072

针对多元函数在某点偏导数的计算,本文归纳总结了四种求解方法,分别给出了各解法的原理并举例说明其实现步骤.

关键词：多元函数偏导数极限有限差分

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