小失效概率情况下的全局可靠性灵敏度分析的高效方法

针对目前很多算法都无法准确、高效地计算小失效概率（10^-4,甚至更小）情况下的全局可靠性灵敏度问题,本文提出了一种高效求解小失效概率情况下的全局可靠性灵敏度新算法。所提算法通过扩大标准差构造重要抽样密度函数来进行空间分割（SP）,再与无迹变换（UT）结合,利用函数在分割后的子空间内非线性程度的降低和无迹变换方法可以高效计算低非线性程度函数的前二阶矩,来高效准确地计算小失效概率情况下的全局可靠性灵敏度。所提算法的优点有：重要抽样密度函数的选择可以使得空间分割时向重要区域偏移,并且在分割区域内功能函数的复杂性被降低,从而可以利用无迹变换方法高效计算失效概率,进而高效求得全局可靠性灵敏度。与已有的算法相比,算例说明了本文所提方法的优势。     

基于乏信息失效数据的可靠性评估方法

基于乏信息失效数据,提出了机械产品可靠性的最大熵评估模型.根据可靠性经验值公式,获得失效数据的可靠性经验值向量,并逆推出离散失效频率向量即获得统计直方图;基于区间映射的牛顿迭代方法获得具有最大熵的概率密度函数,对其积分获得失效概率分布函数,进而得到可靠性估计真值函数.仿真案例和试验案例研究证明该方法可以很好地评估已知分布的可靠性并有效地解决只有失效数据而没有概率分布任何先验信息的可靠性评估问题.在寿命给定时,最大熵方法获得的可靠性取值与已知分布获得的可靠性取值之间的差值非常小仅为3.40%.      

可靠性灵敏度分析的一种新方法

基于极限状态函数矩估计的失效概率计算,提出一种新的可靠性灵敏度分析方法。推导极限状态函数的矩对基本变量分布参数的偏导数,并进而利用失效概率与极限状态方程矩的关系,推导失效概率对基本变量分布参数的偏导数,从而得到可靠性灵敏度。与改进一次二阶矩可靠性灵敏度分析方法相比,所提方法不用求极限状态方程的设计点,因而不需用到极限状态函数对基本变量的梯度函数,适用于隐式极限状态方程的可靠性灵敏度分析,算例结果也充分显示所提方法的合理性和精度。     

小样本下分位数函数的Bootstrap置信区间估计

航空产品试验一般为小样本试验,为了分析小样本情况下的试验数据,结合以概率加权矩为约束条件的最大熵法和求解置信区间及置信带的Bootstrap方法,提出了一种估计小样本试验件母体分位数函数置信区间的方法。最大熵法在矩约束下能够估计样本的密度函数,而以概率加权矩为约束条件的最大熵法能够针对小样本直接给出分位数的无偏估计,无需由密度函数积分得到累积分布函数,再进行转化得到分位数函数。Bootstrap方法求解置信区间具有不依赖于数据分布的优点,具有广泛的应用范围。     

对偶型最大熵概率密度函数模型及其优化解法

针对经典型最大熵概率密度函数模型及其计算目前存在的非线性程度高,优化不收敛,求解效率低等问题,提出了一种对偶型最大熵概率密度函数模型+逐次优化的方法.根据优化过程不稳定,重新推导了拉格朗日系数的线性变换公式.针对几种常见及一种复杂的概率密度函数,采用经典型与对偶型最大熵概率密度函数模型分别计算概率密度及可靠度的对比表明:与经典型最大熵概率密度函数模型相比,对偶型最大熵概率密度函数模型优化函数形式简单,非线性程度低.逐次优化法求解拉格朗日系数不仅克服了初始值敏感性问题,而且计算效率高.对偶型最大熵概率密度函数模型+逐次优化法与其他方法相比,计算精度最高,且能很好的应用于复杂概率分布及可靠性问题.      

渐变结构系统模糊可靠性灵敏度分析的矩方法(英文)

For a degradable structural system with fuzzy failure region, a moment method based on fuzzy reliability sensitivity algorithm is presented. According to the value assignment of performance function, the integral region for calculating the fuzzy failure probability is first split into a series of subregions in which the membership function values of the performance function within the fuzzy failure region can be approximated by a set of constants. The fuzzy failure probability is then transformed into a sum of products of the random failure probabilities and the approximate constants of the membership function in the subregions. Furthermore, the fuzzy reliability sensitivity analysis is transformed into a series of random reliability sensitivity analysis, and the random reliability sensitivity can be obtained by the constructed moment method. The primary advantages of the presented method include higher efficiency for implicit performance function with low and medium dimensionality and wide applicability to multiple failure modes and nonnormal basic random variables. The limitation is that the required computation effort grows exponentially with the increase of dimensionality of the basic random vari- able; hence, it is not suitable for high dimensionality problem. Compared with the available methods, the presented one is pretty competitive in the case that the dimensionality is lower than 10. The presented examples are used to verify the advantages and indicate the limitations.     

Scatter factor confidence interval estimate of least square maximum entropy quantile function for small samples

Classic maximum entropy quantile function method (CMEQFM) based on the probabil-ity weighted moments (PWMs) can accurately estimate the quantile function of random variable on small samples, but inaccurately on the very small samples. To overcome this weakness, least square maximum entropy quantile function method (LSMEQFM) and that with constraint condition (LSMEQFMCC) are proposed. To improve the confidence level of quantile function estimation, scatter factor method is combined with maximum entropy method to estimate the confidence inter-val of quantile function. From the comparisons of these methods about two common probability distributions and one engineering application, it is showed that CMEQFM can estimate the quan-tile function accurately on the small samples but inaccurately on the very small samples (10 sam-ples); LSMEQFM and LSMEQFMCC can be successfully applied to the very small samples;with consideration of the constraint condition on quantile function, LSMEQFMCC is more stable and computationally accurate than LSMEQFM; scatter factor confidence interval estimation method based on LSMEQFM or LSMEQFMCC has good estimation accuracy on the confidence interval of quantile function, and that based on LSMEQFMCC is the most stable and accurate method on the very small samples (10 samples).     

基于交叉熵和空间分割的全局可靠性灵敏度分析

基于失效概率的全局灵敏度分析可以度量各个基本随机变量的不确定性对失效概率的影响程度,对如何降低结构的失效概率具有指导意义。基于交叉熵方法和空间分割提出一种新全局可靠性灵敏度分析方法。该方法采用交叉熵法自适应的确定重要抽样密度函数,有效地回避了传统重要抽样中设计点位置和个数求解的困难。基于评估失效概率所使用的样本,利用空间分割方法计算各个输入随机变量的全局可靠性灵敏度指标,能够提高样本的利用率和计算效率。文中利用一个数值算例和两个工程算例验证了所提方法的计算效率和精度。     

飞机整体驱动发电机可靠性与维修策略探究

针对飞机整体驱动发电机可靠性分析手段缺乏、故障样本小且维修策略相对保守的问题,提出了以历史故障数据为驱动的贝叶斯和马尔可夫链融合的可靠性分析方法。首先,利用蒙特卡洛方法对故障数据预处理以增大样本空间,并通过最大信息熵法求解飞机整体驱动发电机的先验分布;其次,利用马尔可夫链方法对复杂后验分布进行解算;最后,以可靠性为中心给出飞机IDG的维修建议。经过数值仿真软件计算后得IDG的累计失效函数参数估计误差分别为0.121 3和0.001 3,误差较小。仿真结果表明,提出的可靠性分析方法适用于小样本空间的飞机IDG可靠性分析,并根据结果给出了维修建议。     

定向结晶涡轮叶片可靠性分析

本文在正交异性材料定向结晶涡轮叶片的应力有限元分析的基础上, 以一种简单的破坏模式列出了可靠度的计算方法。首先利用 Hill准则建立临界函数 (破坏函数 ), 对于多随机变量及非线性破坏函数利用二阶矩方法及 Hasofer-Lind方法找出破坏点和这种破坏模式的可靠度。并用Monte-Carlo方法予以验证。      

某型发动机无失效数据的Bayes可靠性分析

在定时截尾试验中,有时会遇到无失效数据,特别是在高可靠性、小样本问题中更容易产生无失效数据。对某型发动机的无失效数据,在失效概率服从不完全Beta分布时,给出了失效概率的Bayes估计,并在引进失效信息后,给出了失效概率的Bayes估计和综合估计,从而可以得到该型发动机可靠度的估计。     

截断分布下广义失效概率的可靠性分析方法

提出基于随机变量为截断分布和失效域模糊下的结构可靠性分析方法。由于常规的可靠性分析方法不能直接用于截断分布情况下广义失效概率的计算,因此,先将截断分布情况下的可靠性分析模型转化为非截断分布情况下的多模式并联系统模型,在此基础上引入模糊失效域的隶属函数,将截断分布情况下的模糊可靠性分析问题转化为一般的随机可靠性问题,利用Monte Carlo法和重要抽样法求得广义失效概率。给出了方法的实现步骤和原理,并用不同算例验证了方法的合理性与可行性。     

Reliability and reliability sensitivity analysis of structure by combining adaptive linked importance sampling and Kriging reliability method

The application of reliability analysis and reliability sensitivity analysis methods to complicated structures faces two main challenges: small failure probability (typical less than 10⁻⁵) and time-demanding mechanical models. This paper proposes an improved active learning surrogate model method, which combines the advantages of the classical Active Kriging – Monte Carlo Simulation (AK-MCS) procedure and the Adaptive Linked Importance Sampling (ALIS) procedure. The proposed procedure can, on the one hand, adaptively produce a series of intermediate sampling density approaching the quasi-optimal Importance Sampling (IS) density, on the other hand, adaptively generate a set of intermediate surrogate models approaching the true failure surface of the rare failure event. Then, the small failure probability and the corresponding reliability sensitivity indices are efficiently estimated by their IS estimators based on the quasi-optimal IS density and the surrogate models. Compared with the classical AK-MCS and Active Kriging – Importance Sampling (AK-IS) procedure, the proposed method neither need to build very large sample pool even when the failure probability is extremely small, nor need to estimate the Most Probable Points (MPPs), thus it is computationally more efficient and more applicable especially for problems with multiple MPPs. The effectiveness and engineering applicability of the proposed method are demonstrated by one numerical test example and two engineering applications.     

Study on segmented distribution for reliability evaluation

In practice, the failure rate of most equipment exhibits different tendencies at different stages and even its failure rate curve behaves a multimodal trace during its life cycle. As a result, traditionally evaluating the reliability of equipment with a single model may lead to severer errors. However, if lifetime is divided into several different intervals according to the characteristics of its failure rate, piecewise fitting can more accurately approximate the failure rate of equipment. There-fore, in this paper, failure rate is regarded as a piecewise function, and two kinds of segmented dis-tribution are put forward to evaluate reliability. In order to estimate parameters in the segmented reliability function, Bayesian estimation and maximum likelihood estimation (MLE) of the seg-mented distribution are discussed in this paper. Since traditional information criterion is not suit-able for the segmented distribution, an improved information criterion is proposed to test and evaluate the segmented reliability model in this paper. After a great deal of testing and verification, the segmented reliability model and its estimation methods presented in this paper are proven more efficient and accurate than the traditional non-segmented single model, especially when the change of the failure rate is time-phased or multimodal. The significant performance of the segmented reli-ability model in evaluating reliability of proximity sensors of leading-edge flap in civil aircraft indi-cates that the segmented distribution and its estimation method in this paper could be useful and accurate.     

相关变量模糊可靠性灵敏度分析的线抽样方法

 依据失效域具有模糊性时模糊失效概率的定义,提出了相关变量模糊可靠性灵敏度的分析方法。针对线性功能函数、正态基本变量和正态型隶属函数情况,推导了相关变量的模糊可靠性灵敏度计算的解析表达式。对于工程中的一般情况,给出了可靠性灵敏度分析的数字模拟方法。尽管数字模拟法适用范围广,但该方法的效率较低,尤其是针对高维和小失效概率问题。为了解决数字模拟方法效率低的问题,提出了相关变量模糊可靠性灵敏度分析的线抽样方法。通过离散模糊失效概率积分区域,建立了相关变量模糊可靠性灵敏度与离散区域随机可靠性灵敏度的关系,进而可以利用相关变量随机可靠性灵敏度分析的线抽样方法求得模糊可靠性灵敏度。相关变量模糊可靠性灵敏度分析线抽样方法的基本原理、计算公式及实现步骤被详细给出,文中算例充分验证了其精度高、收敛快及适用于高维和小失效概率等优点。     

翼盒结构的可靠性分析及基于系统可靠性的优化设计

 本文研究了翼盒结构的可靠性分析及基于系统可靠性的结构优化设计方法。采用发展了的优化准则法枚举系统的主要失效模式,和Feng的高精度法计算系统破坏概率,提出两个迭代公式进行元件尺寸的优化设计。算例结果表明本文方法是中、大型结构系统可靠性分析及优化设计的有效方法。     

基于树形马氏链模型的可靠性分析方法

复杂系统的极限状态函数非线性程度较高，在进行可靠性分析时，易导致失效概率的计算误差大、效率低，针对上述问题，提出了树形马氏链（TMC）算法和基于该算法的可靠性分析方法。树形马氏链是对原始马尔可夫链的改进，其状态转移过程更加灵活，具备局部多链并行和自适应探索失效域边界的特性。树形马氏链通过多候选状态点扩大对失效域信息的收集，生成能充分反映失效分布特征的样本，对该样本进行自适应核密度估计得到近似最优的重要抽样分布密度函数，从而提高计算结果的准确度。文末的数值算例和工程算例验证了算法性能，计算结果表明算法对设计点、抽样起点的位置不敏感，处理强非线性及复杂串联系统问题时，能在少样本量下得到相对高准确度的计算结果，且在样本量改变时，计算结果相对稳定可靠；工程算例给出了所提方法在实际问题下的效率，体现了所提方法的工程应用价值。     

Efficient adaptive Kriging for system reliability analysis with multiple failure modes under random and interval hybrid uncertainty

In the field of the system reliability analysis with multiple failure modes, the advances mainly involve only random uncertainty. The upper bound of the system failure probability with multiple failure modes is usually employed to quantify the safety level under Random and Interval Hybrid Uncertainty(RI-HU). At present, there is a lack of an efficient and accurate method for estimating the upper bound of the system failure probability. This paper proposed an efficient Kriging model based on nume...     

An Optimum First-Order Time Delay Tracker

The key to the general estimation problem is the computation ofthe posterior probability density function (PDF) of the desiredparameter, or PDF conditioned on knowing all availableobservations. Any optimum estimate can be computed from this PDF. The theory and implementation of a numerical solution ispresented for the computation of the posterior PDF in real time fortime delay tracking with a first-order Markov assumption. Benefitsinclude a lack of threshold effects usually associated with nonlineartrackers as well as theoretically optimum performance.     

最大熵准则识别材料疲劳寿命分布

疲劳寿命具有很大的分散性,是工程结构设计中必须考虑的因素。为了降低主观不确定性的引入,得到更合理的疲劳寿命分布类型,提出一种用于识别疲劳寿命概率分布类型的一般计算方法。该方法首先根据疲劳试验样本信息确定疲劳寿命的前四阶统计矩;基于统计矩信息,利用最大熵准则确定疲劳寿命的概率分布类型。在基于最大熵准则识别疲劳寿命分布时,利用Lagrange乘子法求解最大熵分布。采用已有的航空铝合金2024-T351板件疲劳裂纹扩展试验数据验证所提计算方法的合理性和有效性。结果表明:所提方法能够高效地识别材料疲劳寿命分布类型,并且不局限于单峰标准分布类型。