一种新的体系可靠度的近似计算方法

提出了一种新的体系可靠度的近似计算方法。首先将一个线性失效模式在另一线性失效模式失效前提下的条件失效模式近似为一个等价的线性失效模式,然后利用条件概率的基本原理并结合所推导的等价失效模式的理论表达式,提出了一种并联体系可靠度的近似计算方法,从而将求解一组失效模式交集失效概率的复杂问题转化为求解一组线性等价失效模式失效概率乘积的简单问题。由于串联体系以及串并联混合体系均可表示为一系列失效模式交集的线性组合,因此方法可以很方便地应用于串联体系以及串并联混合体系的体系可靠度计算。此算法计算过程简单、计算量小、计算精度高,适合于大型结构体系的体系可靠度计算。     

Automatic generation of stochastically dominant failure modes in frame structures for reliability studies

Structural system design for reliability requires failure probability prediction as bounds or as a unique value. The analysis here refers to plane frame, both steel and reinforced concrete (RC), modelled as a combination of series and parallel systems from the reliability standpoint. Using the concept of failure path probability, stochastically dominant failure modes are identified heuristically taking into account the infinite and limited rotation capacity of steel and RC sections. This paper highlights the advantage of using this strategy as it does away with regeneration of failure modes for RC frames as has been attempted earlier. The heuristic also ensures that no failure mode with a reliability level that can be chosen during the analysis is missed, which contributes significantly to system failure probability.     

Structural reliability analysis under evidence theory using the active learning kriging model

Structural reliability analysis under evidence theory is investigated. It is rigorously proved that a surrogate model providing only correct sign prediction of the performance function can meet the accuracy requirement of evidence-theory-based reliability analysis. Accordingly, a method based on the active learning kriging model which only correctly predicts the sign of the performance function is proposed. Interval Monte Carlo simulation and a modified optimization method based on Karush–Kuhn–Tucker conditions are introduced to make the method more efficient in estimating the bounds of failure probability based on the kriging model. Four examples are investigated to demonstrate the efficiency and accuracy of the proposed method.     

响应面法在结构体系可靠度分析中的应用

一个失效模式由许多的失效单元构成,它是一个并联系统;而所有的失效模式构成一个串联系统。整个结构体系可看成是许多并联系统(失效模式)组成的一个串联系统。首先,利用基于响应面的随机有限元法来获得失效模式中各个单元的极限状态方程,这些方程都是二次多项式;第二步,利用结构可靠度分析中的几何法得到这些方程的等效线性化方程从而可逐步得到该失效模式的等效线性化方程;第三步,计算各失效模式间的相关系数;最后,由Ditlevsen界限法来计算结构的体系可靠度。算例表明,利用该方法来获得大型、复杂结构的体系可靠度具有高效、实用的特点。     

多失效模式典型结构系统可靠性稳健设计方法研究

应用随机摄动技术与二阶矩方法,结合概率网络估算法（Probability Network Evaluation Technique）,讨论了多失效模式下结构系统的可靠性和可靠性灵敏度问题,并进一步对结构系统的可靠性稳健设计进行了分析。获得了不同失效模式间的相关统计特性,应用概率网络估算法确定了系统的代表失效模式,得出了...     

基于最终层失效的复合材料舱体稳健性协调优化

传统可靠性设计难以符合现代设计要求,对舱体进行稳健性优化设计,可提高其综合可靠性。基于基体破坏和纤维断裂两种失效模式,采用验算点法求解复合材料单层可靠度。基于最终层失效假设,提出把结构看作由串联子系统组成的并联系统的思想,结合材料刚度比率退化准则和单层可靠度理论,采用概率逐步失效分析方法,计算出主要失效链,从而得出结构的失效概率。复合材料舱体设计变量复杂,提出二级优化方法思想：一级为系统级布局优化,对加强筋截面形状、位置确定等参数进行优化;二级为子系统级尺寸优化,对筋截面尺寸、复合材料各铺层厚度等参数进行优化。采用自适应随机搜索遗传算法,以复合材料舱体质量最小为目标函数,以可靠度要求为约束条件,采用稳健性协调优化方法,对存在初始缺陷的复合材料舱体进行稳健性优化,为复合材料结构优化设计提供参考。     

噪声方差自适应修正的混合系统故障诊断方法

针对混合系统故障诊断问题,提出了一种模型噪声方差自适应修正的多模态故障诊断方法。首先,在粒子滤波的框架内将混合系统故障诊断建模为最优状态估计与跟踪问题,利用实时观察信息和各个模态先验的转移概率,估计最优的故障模态,并针对估计结果进行单独的建模分析;接着,根据平滑估计值和当前观测信息之间的相关性,建立噪声方差在线自适应检测机制,对模态噪声方差进行自适应更新,有效克服了模型噪声统计特性时变对滤波精度的影响,提升了算法的鲁棒性。最后,针对多种模态估计跟踪进行了充分的仿真分析,验证了本文方法的有效性和鲁棒性。     

Methodology for the optimal component selection of electronic devices under reliability and cost constraints

The objective of this paper is to present an efficient computational methodology for the reliability optimization of electronic devices under cost constraints. The system modeling for calculating the reliability indices of the electronic devices is based on Bayesian networks using the fault tree approach, in order to overcome the limitations of the series–parallel topology of the reliability block diagrams. Furthermore, the Bayesian network modeling for the reliability analysis provides greater flexibility for representing multiple failure modes and dependent failure events, and simplifies fault diagnosis and reliability allocation. The optimal selection of components is obtained using the simulated annealing algorithm, which has proved to be highly efficient in complex optimization problems where gradient‐based methods can not be applied. The reliability modeling and optimization methodology was implemented into a computer program in Matlab using a Bayesian network toolbox. The methodology was applied for the optimal selection of components for an electrical switch of power installations under reliability and cost constraints. The full enumeration of the solution space was calculated in order to demonstrate the efficiency of the proposed optimization algorithm. The results obtained are excellent since a near optimum solution was found in a small fraction of the time needed for the complete enumeration (3%). All the optimum solutions found during consecutive runs of the optimization algorithm lay in the top 0.3% of the solutions that satisfy the reliability and cost constraints. Copyright © 2007 John Wiley & Sons, Ltd.     

Error-based stopping criterion for the combined adaptive Kriging and importance sampling method for reliability analysis

Metamodel-based method is a wise reliability analysis technique because it uses the metamodel to substitute the actual limit state function under the predefined accuracy. Adaptive Kriging (AK) is a famous metamodel in reliability analysis for its flexibility and efficiency. AK combined with the importance sampling (IS) method abbreviate as AK–IS can extremely reduce the size of candidate sampling pool in the updating process of Kriging model, which makes the AK-based reliability method more suitable for estimating the small failure probability. In this paper, an error-based stopping criterion of updating the Kriging model in the AK–IS method is constructed and two considerable maximum relative error estimation methods between the failure probability estimated by the current Kriging model and the limit state function are derived. By controlling the maximum relative error, the accuracy of the estimate can be adjusted flexibly. Results in three case studies show that the error-based stopping criterion based AK–IS method can achieve the predefined accuracy level and simultaneously enhance the efficiency of updating the Kriging model.     

基于Copula函数的并联结构系统可靠度分析

不完备概率信息条件下变量联合分布函数的确定及其对结构系统可靠度的影响还缺少系统地研究,该文目的在于研究表征变量间相关性的Copula函数对结构系统可靠度的影响规律。首先,简要介绍了变量联合分布函数构造的Copula函数方法。其次,提出了并联系统失效概率计算方法,并推导了相应的计算公式。最后以几种典型Copula函数为例研究了Copula函数类型对结构并联系统可靠度的影响规律。结果表明:表征变量间相关性的Copula函数类型对结构系统可靠度具有明显的影响,不同Copula函数计算的系统失效概率存在明显的差别,这种差别随构件失效概率的减小而增大。当并联系统的失效区域位于Copula函数尾部时,Copula函数的尾部相关性对系统可靠度有明显的影响,计算的失效概率比没有尾部相关性的Copula函数的失效概率大。当组成并联系统的两构件功能函数间正相关时,系统失效概率随相关系数的增大而增加;当构件功能函数间负相关时,系统失效概率随相关系数的增大而减小。此外,无论构件失效概率和变量间相关系数如何变化,Copula函数计算的失效概率都位于系统失效概率的上下限内。     

Reliability analysis of structures based on a probability‐uncertainty hybrid model

The traditional reliability analysis method based on probabilistic method requires probability distributions of all the uncertain parameters. However, in practical applications, the distributions of some parameters may not be precisely known due to the lack of sufficient sample data. The probabilistic theory cannot directly measure the reliability of structures with epistemic uncertainty, ie, subjective randomness and fuzziness. Hence, a hybrid reliability analysis (HRA) problem will be caused when the aleatory and epistemic uncertainties coexist in a structure. In this paper, by combining the probability theory and the uncertainty theory into a chance theory, a probability‐uncertainty hybrid model is established, and a new quantification method based on the uncertain random variables for the structural reliability is presented in order to simultaneously satisfy the duality of random variables and the subadditivity of uncertain variables; then, a reliability index is explored based on the chance expected value and variance. Besides, the formulas of the chance theory‐based reliability and reliability index are derived to uniformly assess the reliability of structures under the hybrid aleatory and epistemic uncertainties. The numerical experiments illustrate the validity of the proposed method, and the results of the proposed method can provide a more accurate assessment of the structural system under the mixed uncertainties than the ones obtained separately from the probability theory and the uncertainty theory.     

Multivariate performance reliability prediction in real-time

This paper presents a technique for predicting system performance reliability in real-time considering multiple failure modes. The technique includes on-line multivariate monitoring and forecasting of selected performance measures and conditional performance reliability estimates. The performance measures across time are treated as a multivariate time series. A state–space approach is used to model the multivariate time series. Recursive forecasting is performed by adopting Kalman filtering. The predicted mean vectors and covariance matrix of performance measures are used for the assessment of system survival/reliability with respect to the conditional performance reliability. The technique and modeling protocol discussed in this paper provide a means to forecast and evaluate the performance of an individual system in a dynamic environment in real-time. The paper also presents an example to demonstrate the technique.     

非正态变量情况下基于杂交SAPSO-SFLA的多目标稳健协同优化

为解决非正态变量空间中复杂多变的隐式非线性功能函数的可靠性及灵敏度的问题,融合鞍点估计与线抽样法的优点,结合二分法的特点与黄金分割法的求解效率,提出基于黄金分割二分法的鞍点线抽样法,即可沿重要线抽样方向利用黄金分割点的二分法快速找到各样本点对应于功能函数的零点,将结构失效概率转化为一系列线性功能函数失效概率的平均值,求出相关变量的可靠性灵敏度,从而导出失效概率对变量均值与方差的可靠性灵敏度及结构轻量化的多目标优化问题,并阐明了多目标协同优化的思想。同时,针对可靠性灵敏度作为目标函数因误差导致多目标协同优化难以收敛的问题,提出了利用误差的思想与方法;为提高算法的收敛性,对粒子群优化(Particle Swarm Optimization,PSO)算法与混合蛙跳算法(Shuffled Frog-Leaping Algorithm,SFLA)进行改进以后,再将两者进行杂交,提出杂交自适应粒子群优化-混合蛙跳算法(Self-Adaptive PSO-SFLA,SAPSO-SFLA),并用来求解上述多目标优化问题。算例表明:1) 基于黄金分割二分法的鞍点线抽样法在求解复杂非线性功能函数的可靠性及灵敏度时精度高,速度快;2) 与粒子群优化和混合蛙跳算法相比,所提杂交SAPSO-SFLA不仅具有更快的收敛速度,其鲁棒性还能使盾构行星减速器箱体体积减小8.42%。     

A double-loop relevant vector machine-based system reliability analysis method with Meta-IS idea and active learning strategy

This paper proposes a double-loop relevant vector machine (RVM) model for system reliability analysis. To reduce the computational load, an adaptive RVM is constructed, which is built by minority initial samples and K-folds clustering. The candidate sample pool constructed by this rough adaptive RVM model improves the computational efficiency. Based on the idea of active learning, another adaptive RVM is established. By combining two adaptive RVMs, the proposed model has the advantages of both active learning and importance sampling, which is called DLRVM. In this model, the failure probability is expressed as a product of the augmented failure probability and the correction factor. From the characteristics of RVM, this model under the Bayesian framework has significant generalization ability which avoids the limitations of many machine learning models. The accuracy and high efficiency are verified via four academic examples and an implicit engineering problem. The results also indicate that RVM is appropriate for system reliability analysis.     

Probability of infancy problems for space launch vehicles

This paper addresses the treatment of ‘infancy problems’ in the reliability analysis of space launch systems. To that effect, we analyze the probability of failure of launch vehicles in their first five launches. We present methods and results based on a combination of Bayesian probability and frequentist statistics designed to estimate the system's reliability before the realization of a large number of launches. We show that while both approaches are beneficial, the Bayesian method is particularly useful when the experience base is small (i.e. for a new rocket). We define reliability as the probability of success based on a binary failure/no failure event. We conclude that the mean failure rates appear to be higher in the first and second flights (≈1/3 and 1/4, respectively) than in subsequent ones (third, fourth and fifth), and Bayesian methods do suggest that there is indeed some difference in launch risk over the first five launches. Yet, based on a classical frequentist analysis, we find that for these first few flights, the differences in the mean failure rates over successive launches or over successive generations of vehicles, are not statistically significant (i.e. do not meet a 95% confidence level). This is true because the frequentist analysis is based on a fixed confidence level (here: 95%), whereas the Bayesian one allows more flexibility in the conclusions based on a full probability density distribution of the failure rate and therefore, permits better interpretation of the information contained in a small sample. The approach also gives more insight into the considerable uncertainty in failure rate estimates based on small sample sizes.     

Small sample reliability growth modeling using a grey systems model

ABSTRACT

When performing system-level developmental testing, time and expenses generally warrant a small sample size for failure data. Upon failure discovery, redesigns and/or corrective actions can be implemented to improve system reliability. Current methods for estimating reliability growth, namely the Crow (AMSAA) growth model, stipulate that parameter estimates have a great level of uncertainty when dealing with small sample sizes. For purposes of handling limited failure data, we propose the use of a modified GM(1,1) model to predict system reliability growth parameters and investigate how parameter estimates are affected by systems whose failures follow a poly-Weibull distribution. Monte-Carlo simulation is used to map the response surface of system reliability, and results are used to compare the accuracy of the modified GM(1,1) model to that of the AMSAA growth model. It is shown that with small sample sizes and multiple failure modes, the modified GM(1,1) model is more accurate than the AMSAA model for prediction of growth model parameters.     

The interval estimation of reliability for probabilistic and non-probabilistic hybrid structural system

The aim of this paper is to improve evaluation of the reliability of probabilistic and non-probabilistic hybrid structural system. Based on the probabilistic reliability model and interval arithmetic, a new model of interval estimation for reliability of the hybrid structural system was proposed. Adequately considering all uncertainties affecting the hybrid structural system, the lower and upper bounds of reliability for the hybrid structural system were obtained through the probabilistic and non-probabilistic analysis. In the process of non-probabilistic analysis, the interval truncation method was used. In addition, a recognition method of the main failure modes in the hybrid structural system was presented. A five-bar statically indeterminate truss structure and an intermediate complexity wing structure were used to demonstrate the new model is more suitable for analysis and design of these structural systems in comparison with the probabilistic model. The results also show that the method of recognition of main failure modes is effective. In addition, range obtained through interval estimation is shown to be more credible than certain results of other reliability models.     

岩质边坡稳定的体系可靠度分析及工程应用

对岩质边坡存在多个滑动面时的体系可靠度进行分析,可以对边坡的稳定性作出更加合理的评价。采用非线性有限单元法,通过降低岩体的强度参数,寻找边坡的潜在滑动面,并定义滑动面上所有单元同时破坏时,作为边坡的失稳模式;针对岩体破坏的特点,按Druker-Prager屈服准则和单轴抗拉强度准则构建失稳模式中单元的功能函数,再采用响应面法和蒙特卡罗法计算单元的可靠指标和相关系数;单一失稳模式是由滑动面上的单元组成的并联体系,为此,研究了一种逐步等效线性化求交法用于计算单一失稳模式的可靠指标;最后,用Ditlevsen窄界限公式估算由各失稳模式组成的串联体系的可靠指标。上述方法得到的可靠指标可用于边坡的稳定性评价。作为工程实例,对某水电站左岸坝肩边坡的体系可靠度进行了分析和评价,验证了本方法的合理性和可行性。     

A time-variant reliability analysis method for structural systems based on stochastic process discretization

In this paper, we propose a new method for analyzing time-variant system reliability based on stochastic process discretization, which provides an effective tool for reliability design of many relatively complex structures considering the whole lifecycle. Within a design lifetime, the stochastic process is discretized into a series of random variables, and meanwhile, we can derive a time-invariant limit-state function in each time interval; the discretized random variables from the stochastic processes and the original random variables are transformed to the independent normal space, and a conventional time-invariant system reliability problem is derived through the linearization to each discretized limit-state functions; by solving this time-invariant system reliability problem, we can obtain the structural reliability or failure probability within the design lifetime. Finally, in this paper, we provide four numerical examples to verify the effectiveness of the method.     

考虑土质边坡多失效模式的区域概率风险分析方法

针对现有边坡风险分析仅考虑单一失效模式及风险分析结果难以被工程师理解等问题,提出了考虑边坡多失效模式的区域概率风险分析方法。首先给出了区域概率的概念,建立了以区域概率定量表征边坡稳定性的方法,推导了基于区域概率的边坡系统风险评价公式,探讨了该公式的适用性。在此基础上采用直接蒙特卡罗模拟计算边坡区域失效概率。最后以一不排水黏性土坡为例阐明了所提方法的有效性。结果表明:区域概率风险分析方法为表征边坡的关键失效区提供了一种简单、直接的可视化工具,为工程师制定合理的边坡加固设计方案提供了参考依据。基于区域概率风险分析方法的边坡系统风险评价公式不仅能够有效地回避边坡风险评价中多滑面间安全系数及滑块体积之间相关性计算问题,而且能够准确地量化边坡多破坏模式的系统风险。传统的风险评价方法可能显著低估边坡系统风险,使得边坡设计方案偏危险。边坡失效概率最大的滑面不一定是边坡失效风险最大的滑面,在边坡加固设计中,失效风险较大的滑面也应该予以关注。