Efficient slope reliability analysis under soil spatial variability using maximum entropy distribution with fractional moments

Spatial variability of soil properties imposes a challenge for practical analysis and design in geotechnical engineering.The latter is particularly true for slope stability assessment,where the effects of uncertainty are synthesized in the so-called probability of failure.This probability quantifies the reliability of a slope and its numerical calculation is usually quite involved from a numerical viewpoint.In view of this issue,this paper proposes an approach for failure probability assessment based on Latinized partially stratified sampling and maximum entropy distribution with fractional moments.The spatial variability of geotechnical properties is represented by means of random fields and the Karhunen-Loève expansion.Then,failure probabilities are estimated employing maximum entropy distribution with fractional moments.The application of the proposed approach is examined with two examples:a case study of an undrained slope and a case study of a slope with cross-correlated random fields of strength parameters under a drained slope.The results show that the proposed approach has excellent accuracy and high efficiency,and it can be applied straightforwardly to similar geotechnical engineering problems.

SAMPLING INSPECTION OF RELIABILITY IN (LOG)NORMAL CASE WITH TYPE I CENSORING

This article proposes a statistical method for working out reliability sampling plans under Type I censored sample for items whose failure times have either normal or lognormal distributions. The quality statistic is a method of moments estimator of a monotonous function of the unreliability. An approach of choosing a truncation time is recommended. The sample size and acceptability constant are approximately determined by using the Cornish-Fisher expansion for quantiles of distribution. Simulation results show that the method given in this article is feasible.

Sensitivity of Sample for Simulation-Based Reliability Analysis Methods

In structural reliability analysis,simulation methods are widely used.The statistical characteristics of failure probability estimate of these methods have been well investigated.In this study,the sensitivities of the failure probability estimate and its statistical characteristics with regard to sample,called‘contribution indexes’,are proposed to measure the contribution of sample.The contribution indexes in four widely simulation methods,i.e.,Monte Carlo simulation(MCS),importance sampling(IS),line sampling(LS)and subset simulation(SS)are derived and analyzed.The proposed contribution indexes of sample can provide valuable information understanding the methods deeply,and enlighten potential improvement of methods.It is found that the main differences between these investigated methods lie in the contribution indexes of the safety samples,which are the main factors to the efficiency of the methods.Moreover,numerical examples are used to validate these findings.

IMPROVED STRATIFIED SAMPLING MONTE CARLO METHOD TO ANALYZE RELIABILITY OF STRUCTURAL SYSTEMS

A stratified sampling Monte Carlo method to analyze the reliability of structural systems is presented. Introducing a small exploratory simulation, this method overcomes the difficulties for getting the systematic sampling probability of all the strata. Several useful and efficient stratification methods are given and the strategies of stratification and simulation are studied. A general conclusion has been presented corresponding to actual engineering structures. The strict theoretical proof has been given,and it is especially effective to solve probabilistic integration. Statistic error of evaluating failure probability is reduced obviously. Especially in highly non-linear and nonreonvex problems, it is more accurate than other methods. Compared with other variance reduction techniques, this method can obtain a more obvious variance reduction and an increased sampling efficiency. Moreover, without strict limiting condition, it is convenient to use. This method is especially suitable to solve the reliability problem of structural systems with multiple failure modes and highly non-linear safety margin equations.

Reliability analysis method for slope stability based on sample weight

The single safety factor criteria for slope stability evaluation, derived from the rigid limit equilibrium method or finite element method （FEM）, may not include some important information, especially for steep slopes with complex geological conditions. This paper presents a new reliability method that uses sample weight analysis. Based on the distribution characteristics of random variables, the minimal sample size of every random variable is extracted according to a small sample t-distribution under a certain expected value, and the weight coefficient of each extracted sample is considered to be its contribution to the random variables. Then, the weight coefficients of the random sample combinations are determined using the Bayes formula, and different sample combinations are taken as the input for slope stability analysis. According to one-to-one mapping between the input sample combination and the output safety coefficient, the reliability index of slope stability can be obtained with the multiplication principle. Slope stability analysis of the left bank of the Baihetan Project is used as an example, and the analysis results show that the present method is reasonable and practicable for the reliability analysis of steep slopes with complex geological conditions.

Sample-data Decentralized Reliable H∞ Hyperbolic Control for Uncertain Fuzzy Large-scale Systems with Time-varying Delay

这份报纸学习样品数据的问题为有变化时间的延期的不明确的连续时间的模糊大规模系统的可靠 H 夸张控制。第一，模糊夸张模型( FHM )被用来为某些复杂大规模系统建立模型，然后根据 Lyapunov 指导方法和大规模系统的分散的控制理论，线性 matrixine 质量( LMI )基于条件 arederived toguarantee H 性能不仅当所有控制部件正在操作很好时，而且面对一些可能的致动器失败。而且，致动器的精确失败参数没被要求，并且要求仅仅是失败参数的更低、上面的界限。条件依赖于时间延期的上面的界限，并且不依赖于变化时间的延期的衍生物。因此，获得的结果是不太保守的。最后，二个例子被提供说明设计过程和它的有效性。

Adaptive Radial Based Sampling for Reliability and Reliability Sensitivity Analysis Involving Truncated Correlated Normal Variables

The reliability and reliability sensitivity （ RS ） models are presented for the engineering problem involving truncated correlated normal variables （CNV）, and in the case an adaptive radial based sampling is used to analyze the reliability and the RS. In the presented models, the truncated CNV is transformed to general CNV, and the value domains of the truncated CNV are treated as multiple failure modes, then the reliability and the RS with the truncated CNV are transformed to the general cases, on which an e^cient radial based sampling is used to analyze the trans- formed reliability and RS. An adaptive strategy is employed to search for the optimal radial in the sampling, by which the robustness of the method is improved. After the model concepts and the detailed implementation are given, several examples are presented to demonstrate the feasibility of the model and the efficiency of the solutions.

Reliability-Based Optimization:Small Sample Optimization Strategy

The aim of the paper is to present a newly developed approach for reliability-based design optimization. It is based on double loop framework where the outer loop of algorithm covers the optimization part of process of reliability-based optimization and reliability constrains are calculated in inner loop. Innovation of suggested approach is in application of newly developed optimization strategy based on multilevel simulation using an advanced Latin Hypercube Sampling technique. This method is called Aimed multilevel sampling and it is designated for optimization of problems where only limited number of simulations is possible to perform due to enormous com- putational demands.

最大熵试验法对切割器功能可靠性的评估

针对切割器设计裕度大且刺激能量服从正态分布的特点,提出采用最大熵试验法对切割器的功能可靠性进行评估。以某型切割器为实例,通过临界药量摸底试验、升降法试验及成败型试验对其功能可靠性进行了评估。结果表明:运用最大熵试验法,采用46个试验样本即可完成切割器在置信度γ=0.95下,可靠性指标不小于0.999 995的可靠性评估试验,为航天火工装置(尤其是切割器)的小样本量高可靠性评估提供了技术途径。

基于生成对抗网络数据增强的舰炮可靠性分析

舰炮故障数据不足会导致其可靠性分析变得极其困难。为解决故障数据不足这一问题,采用生成式对抗网络(generative adversarial network,GAN)对故障样本进行数据增强。建立GAN数据增强深度神经网络的舰炮可靠性分析模型,并与原始数据进行可靠性分析获得的指标进行了对比。结果表明,利用GAN数据增强后的扩充样本得到的指数分布拟合精度及威布尔分布拟合精度分别提高了5.40%和11.90%,相较于原始数据有了显著提升。为实现舰炮故障数据可靠性分析提供了方法和思路。

一种新型可靠性抽样设计方法——基于经济优化视角

混合截尾可以看作是一型截尾及二型截尾的拓展,常用于可靠性试验。然而,在规定时间上限内,当产品失效数远小于截尾数时,现有的可靠性抽样方案可能存在推断偏误。因此,结合已有研究,立足混合截尾,基于经济视角设计出混合截尾下一种新型可靠性抽样方案。通过一系列对比分析,发现新方案可在保留原方案小样本量优点的同时增强判定的可靠性。从缩减企业检验成本的角度出发,应在试验前使检验时间上限尽可能小、截尾度尽可能大。从科学性及实用性角度综合考虑,该方案展现出较优的性质,值得推广使用。

小样本加速寿命试验设计与评估方法

针对工程上加速寿命试验仍然存在时间长、试样多的问题,提出一种小样本加速寿命试验设计与评估方法。该方法只需在两个加速应力水平下进行加速寿命试验,即可对产品在正常使用应力水平下高置信度、高可靠度的可靠寿命进行评估。文中首先利用工程上常用的线性加速模型(如阿伦尼斯模型、逆幂律模型和指数模型等)建立了正常使用应力水平下可靠寿命的单侧置信下限与两个加速应力水平下的可靠寿命置信限之间的数学关系式,给出了正常使用应力水平下高置信度、高可靠度的可靠寿命单侧置信下限评估方法。然后分别对指数分布、两参数Weibull分布和对数正态分布的定数截尾加速寿命试验情况进行了详细讨论,给出了相应的正常使用应力水平下高置信度、高可靠度的可靠寿命单侧置信下限计算公式。该方法计算简单,而且对完全数据、不完全数据以及各种分布均适用。大量工程算例和Monte Carlo模拟验证表明,与需要在多个加速应力水平下进行寿命试验的传统方法相比,本文方法不但可以节省大量试样和试验时间,而且理论上更加严谨,精度更高。

小样本积木式可靠性评估与更新方法

针对工程上只能进行极少甚至无法进行整机寿命试验,导致可靠性评估精度不高的情况,提出一种小样本积木式可靠性评估与更新方法。首先建立了能够根据机电产品子系统当前试验、以往试验和以往服役寿命数据,对其整机高置信度、高可靠度的可靠寿命进行评估的方法,从而解决了机电产品无法进行整机寿命试验时的可靠性评估难题,为其外场使用提供了科学依据。然后给出了能够根据该机电产品整机试验寿命数据和外场服役寿命数据对上述可靠寿命评估结果进行更新的方法,从而增大了信息量,显著提高其可靠性评估精度。文中针对工程上常用的指数分布、Weibull分布和对数正态分布情况进行了详细讨论,给出了相应的整机高置信度、高可靠度的可靠寿命评估与更新公式。

串联系统小样本可靠度直接评估方法

建立了一种串联系统小样本可靠度直接评估方法,能够根据子系统的可靠度置信限直接给出串联系统的可靠度置信限,解决了目前常用的LM法和MML法等传统方法需将信息量较大的连续型分布的子系统试验数据转换为信息量较小的成败型数据,造成试验信息大量丢失,导致可靠度评估精度不高或偏于危险的问题。在此基础上,针对工程上许多成败型试验转计量型试验的机构都是正态分布串联系统的情况,建立了正态分布串联系统小样本可靠度直接评估方法,该方法能够根据子系统的小样本计量型数据对串联系统可靠度进行高精度评估。大量的Monte Carlo模拟验证和实例计算结果表明,传统方法在小样本情况下误差较大,甚至无法满足置信度要求,本文方法则不仅能够满足置信度要求,而且评估精度更高。此外,本文方法对工程上常用的指数分布、 Weibull分布和正态分布等连续分布均适用。

多应力小样本加速寿命试验设计与评估方法

针对目前多应力加速寿命试验需要的组合应力水平多、时间长、费用高的问题,提出一种多应力小样本加速寿命试验设计与评估方法。该方法建立了正常使用应力水平下可靠寿命的单侧置信下限与加速应力水平下的可靠寿命置信限之间的数学关系式,给出了正常使用应力水平下高置信度、高可靠度的可靠寿命单侧置信下限计算公式。文中首先针对工程上最常用的双应力情况,分别建立了无耦合和有耦合的双应力小样本加速寿命试验设计与评估方法,它只需在三个(无耦合)或四个(有耦合)组合应力水平下进行加速寿命试验,即可对产品在正常使用应力水平下高置信度、高可靠度的可靠寿命进行评估。然后针对一般的m种应力情况,建立了基于多应力线性加速模型的小样本加速寿命试验设计与评估方法,它只需在m+1个组合应力水平下进行加速寿命试验,即可求得产品在正常使用应力水平下高置信度、高可靠度的可靠寿命单侧置信下限。该方法计算简单,而且对完全数据、不完全数据以及各种分布均适用。大量工程算例和Monte Carlo模拟验证表明,与传统多应力加速寿命试验方法相比,本文方法不但可以节省大量试样和试验时间,而且理论上更加严谨,精度更高。

Weibull和正态分布不完全数据可靠性评估方法

提出一种两参数Weibull分布和正态分布定数截尾数据可靠性评估方法,建立了其高置信度下的可靠寿命和可靠度单侧置信限计算公式。同时,给出一种能够充分开发利用以往试验数据,并与当前试验数据有机融合进行可靠性评估的方法,由于增大了信息量,从而可以显著提高当前产品可靠性评估精度。在此基础上,还进一步将上述方法推广用于两参数Weibull分布和正态分布的定时截尾数据、无失效数据以及一般不完全数据的可靠性评估,从而实现了不完全数据情况机电产品高精度小样本可靠性评估。与传统的需查表计算的BLUE和BLIE等方法相比,本文方法不但理论上更加严谨,而且评估精度更高,工程计算也更加便捷。

基于支持向量回归的Bootstrap数据扩充方法及其在小子样可靠性评估中的应用

针对航空发动机小子样特性下的可靠性评估问题,提出一种基于支持向量回归(Support Vector Regression, SVR)的Bootstrap数据扩充方法:建立并训练SVR模型,采用邻域抽样法构造输入集,输入训练好的模型中获得扩充样本。仿真结果表明,采用该方法获得的扩充样本较传统Bootstrap方法更接近真实分布,且有效拓展了样本取值区间。以某航空发动机涡轮盘小子样疲劳寿命试验数据为例:(1)非参数方法,采用两种方法获得的平均疲劳寿命十分接近,但新方法获得的置信区间更大,这与样本取值区间的拓展相关;(2)参数方法,对新方法扩充的样本进行参数估计得到的结果与参考值更为接近,最大相对偏差为-1.290 2%,而传统方法的最大相对偏差达到了29.477 6%,两种方法下计算得到的平均疲劳寿命与参考值均较接近,但新方法得到的置信区间与参考区间更为接近。综合来看,所提出的方法能够有效实现样本扩充,具有一定的应用价值。

小样本情形集中供热系统元件失效率估计方法研究

对国内3个典型城市集中供热系统失效事件进行了调查统计,并对元件失效率进行了估计。针对直接估计模型存在的限制,引入了Bayes(贝叶斯)理论,融合历史信息,提出了一般Bayes模型和分层Bayes模型。比较了3种模型的精度,管道、阀门和补偿器3类元件的分层Bayes模型精度分别为0.31、0.32、0.29,在3种模型中精度最高;最终通过改变样本量,得出3种模型精度随样本量增加均呈现上升趋势,且相互差距逐渐缩小,验证了Bayes模型在小样本情形的适用性。

高置信水平结构逆可靠度分析与优化方法研究进展

不确定性客观存在于工程结构生产制造以及服役等各环节之中并对结构的承载性能影响显著.特别是对于服役条件苛刻的航空航天承载装备,在设计阶段考虑多源不确定性的影响对于结构安全至关重要.在众多不确定性分析方法中,逆可靠度分析方法在效率和稳健性方面具有一定优势.为此,国内外学者在高置信水平结构逆可靠度分析与优化方法方面开展了大量研究并取得了长足进步,包括自适应迭代控制算法、先进可靠度优化策略与非充分样本下的高置信水平设计方法等.本文首先对国内外逆可靠度分析与优化方法取得的进展进行了系统梳理与总结,特别是逆可靠度分析方法的发展历程以及面临的挑战问题,主要包括强非线性功能函数、多设计点以及低失效概率问题.进一步,针对长期困扰可靠度方法实际应用的小样本问题,重点从结构高置信水平可靠度分析与优化理论角度开展系统介绍,详细论述了小样本诱发的认知不确定性到可靠度置信水平的传播链条.最后,基于现有成果和国家重大前沿需求,重点围绕航天装备可重复使用需求对结构可靠度未来研究方向进行了思考与展望,期望相关研究成果能够进一步助力我国航空航天结构实现高可靠性与极致轻量化设计.

时变可靠性分析的高效近似最大可能轨迹法

现有的时变可靠性分析方法在处理飞行器复杂时变可靠性分析问题时,具有求解效率过低的缺点。在基于近似最大可能轨迹的时变可靠性分析方法的基础上,根据时间离散所得串联系统瞬时可靠度最小的组件决定整个系统可靠度的特点,在最大可能轨迹自适应建模过程中同时考虑轨迹模型的预测误差和预估值增加样本,提出时变可靠性分析的高效近似最大可能轨迹法;采用解析算例验证最大可能轨迹法的有效性,并将该可靠性分析方法应用于水动力涡轮叶片和航天飞机机翼的时变可靠性分析。结果表明:在精度相近的情况下,所提方法对极限状态函数调用次数不高于基于时间离散的可靠性分析方法的3%。