Sequential exploration-exploitation with dynamic trade-off for efficient reliability analysis of complex engineered systems

A new sequential sampling method, named sequential exploration-exploitation with dynamic trade-off (SEEDT), is proposed for reliability analysis of complex engineered systems involving high dimensionality and a wide range of reliability levels. The proposed SEEDT method is built based on the ideas of two previously developed sequential Kriging reliability methods, namely efficient global reliability analysis (EGRA) and maximum confidence enhancement (MCE) methods. It employs Kriging-based sequential sampling to build a surrogate model (i.e., Kriging model) that approximates the performance function of an engineered system, and performs Monte Carlo simulation on the surrogate model for reliability analysis. A new acquisition function, referred to as expected utility (EU), is developed to sequentially locate a computationally efficient set of sample points for constructing the Kriging model. The SEEDT method possesses three technical contributions: (i) defining a new utility function with several desirable properties that facilitates the joint consideration of exploration and exploitation over the course of sequential sampling; (ii) introducing a new exploration-exploitation trade-off coefficient that dynamically weighs exploration and exploitation to achieve a fine balance between these two activities; and (iii) developing a new convergence criterion based on the uncertainty in the prediction of the limit-state function (LSF). The effectiveness of the proposed method in reliability analysis is evaluated with several mathematical and practical examples. Results from these examples suggest that, given a certain number of sample points, the SEEDT method is capable of achieving better accuracy in predicting the LSF than the existing sequential sampling methods.     

Adaptive-sparse polynomial chaos expansion for reliability analysis and design of complex engineering systems

This paper presents an adaptive-sparse polynomial chaos expansion (adaptive-sparse PCE) method for performing engineering reliability analysis and design. The proposed method combines three ideas: (i) an adaptive-sparse scheme to build sparse PCE with the minimum number of bivariate basis functions, (ii) a new projection method using dimension reduction techniques to effectively compute the expansion coefficients of system responses, and (iii) an integration of copula to handle nonlinear correlation of input random variables. The proposed method thus has three positive features for reliability analysis and design: (a) there is no need for response sensitivity analysis, (b) it is highly efficient and accurate for reliability analysis and its sensitivity analysis, and (c) it is capable of handling a nonlinear correlation. In addition to the features, an error decomposition scheme for the proposed method is presented to help analyze error sources in probability analysis. Several engineering problems are used to demonstrate the three positive features of the adaptive-sparse PCE method.     

Monte Carlo simulation for reliability evaluation of complex systems

A complex system of s-dependent and s-independent units is considered in this paper for system reliability evaluation. It is also assumed that failure of any unit in the dependent set increases the failure probabilities of the remainder in the set. A general ease of partial redundant subsystems is considered. A computational algorithm to compute effective failure rates of the remaining components which fail sequentially, is explained for programme implementation. Fault-tree logic for the system failure is used as one of the subprogrammes. The advantage of this approach is that it can be used for a large complex system without any difficulty, besides many advantages normally associated with the fault-tree technique.     

Sequential approach to reliability analysis of multidisciplinary analysis systems

The goal of this study is to present an efficient strategy for reliability analysis of multidisciplinary analysis systems. Existing methods have performed the reliability analysis using nonlinear optimization techniques. This is mainly due to the fact that they directly apply multidisciplinary design optimization (MDO) frameworks to the reliability analysis formulation. Accordingly, the reliability analysis and the multidisciplinary analysis (MDA) are tightly coupled in a single optimizer, which hampers the use of recursive and function-approximation-based reliability analysis methods such as the first-order reliability method (FORM). In order to implement an efficient reliability analysis method for multidisciplinary analysis systems, we propose a new strategy named sequential approach to reliability analysis for multidisciplinary analysis systems (SARAM). In this approach, the reliability analysis and MDA are decomposed and arranged in a sequential manner, making a recursive loop. The key features are as follows. First, by the nature of the recursive loop, it can utilize the efficient advanced first-order reliability method (AFORM). It is known that AFORM converges fast in many cases and requires only the value and the gradient of the limit-state function. Second, the decomposed architecture makes it possible to execute concurrent subsystem analyses for both the reliability analysis and MDA. The concurrent subsystem analyses are conducted by using the global sensitivity equation (GSE). The efficiency of the SARAM method was verified using two illustrative examples taken from the literatures. Compared with existing methods, it showed the least number of subsystem analyses over the other methods while maintaining accuracy.     

复杂系统可靠性估计的模糊神经Petri网方法

针对复杂系统可靠性建模难问题,提出了一种新的适用于复杂系统可靠性估计的模糊神经Petri网(简称为FNPN)．文中首先给出了模糊神经Petri网的定义及其引发规则,然后给出了一种学习算法．该FNPN结合了模糊Petri网和神经网络各自的优点,既可以表示和处理模糊产生式规则的知识库系统又具有学习能力,可通过对样本数据学习调整模型中的参数以获得系统内部的等效结构,从而计算出非样本数据的系统的可靠度．最后以一无向网络为例说明该方法是可行的．     

Markov-chain based reliability analysis for distributed systems

In a typical distributed computing system (DCS), nodes consist of processing elements, memory units, shared resources, data files, and programs. For a distributed application, programs and data files are distributed among many processing elements that may exchange data and control information via communication link. The reliability of DCS can be expressed by the analysis of distributed program reliability (DPR) and distributed system reliability (DSR). In this paper, two reliability measures are introduced which are Markov-chain distributed program reliability (MDPR) and Markov-chain distributed system reliability (MDSR) to accurately model the reliability of DCS. A discrete time Markov chain with one absorbing state is constructed for this problem. The transition probability matrix is employed to represent the transition probability from one state to another state in a unit of time. In addition to mathematical method to evaluate the MDPR and MDSR, a simulation result is also presented to prove its correction.     

Analyzing reliability for systems with complex structure on multilevel models

We consider approaches to modeling reliability and technical efficiency of complex systems. We give a brief classification of models and approaches to system reliability analysis. We discuss decomposition and aggregation methods for static and dynamic models. As an example, we briefly characterize gas supply systems.     

大规模存储系统可靠性参数最优化分析

在大规模存储系统中,数据的可靠性越来越受到人们的关注。已有的研究分析了在系统规模已知的条件下,某些系统参数,如副本分布策略、存储对象数目等,对可靠性的粗略影响,但较少提及它们的最优值或者最优组合。提出了一种基于对象粒度恢复的可靠性新模型;基于该模型,在分析三种主流的副本分布策略的基础上,分别计算出了各个系统参数的独立最优值及其组合最优值。与已有模型相比,该模型更易于求解,且获得了更加综合实用的最优值,这些最优参数值能直接有效地指导系统设计者构建更可靠的大规模存储系统。     

Fuzzy Bayesian reliability and availability analysis of production systems

To have effective production planning and control, it is necessary to calculate the reliability and availability of a production system as a whole. Considering only machine reliability in the calculations would most likely result unmet due dates. In this study, a new modelling approach for determining the reliability and availability of a production system is proposed by considering all the components of the system and their hierarchy in the system structure. Components of a production system are defined as production processes; components of the processes are defined as sub-processes. In this hierarchical structure we could model all kinds of failures such as material and supply, management and personnel, and machine and equipment. In the analysis, a fuzzy Bayesian method is used to quantify the uncertainties in the production environment. The suggested modelling approach is illustrated on an example. In the example, also a separate reliability and availability analysis is conducted which only considered machine failures, and the results of both analyses are compared.     

Peaking demand factor-based reliability analysis of water distribution systems

Water demands vary and consideration of the probabilistic nature of the variations should lead to more instructive assessments of the performance of water distribution systems. Water consumption data for several households were analysed using the chi-square technique and it was found that distributions worth considering under certain circumstances include the normal and lognormal.Reliability values were calculated for a range of critical demand values and the corresponding confidence levels determined from the probability distributions. Water consumption was assumed to be pressure dependent and the modelling of the water distribution system was carried out accordingly. This peaking factor approach coupled with the statistical modelling of demands provides a more realistic way of incorporating variations in demands in the evaluation and reporting of system performance than the traditional single demand value approach in that the extent to which a network can satisfy any demand and the probability that the demand will occur can be recognized explicitly. The method is illustrated by an example.     

新的MOPSO及其在大型复杂系统可靠性优化中的应用

可靠性优化问题是大型复杂系统设计的一个关键问题。针对大型复杂系统多个指标(可靠度、造价和冗余数)同时进行最优分配的结果多样性不好的问题,提出了一种基于杂草克隆的多目标粒子群算法—IWMOP-SO(invasive weed multi-objective particle swarm optimization)的多指标分配方法。该分配方法通过引入杂草克隆机制来改善Pareto最优解的收敛性和多样性。通过对大型复杂系统多个指标进行分配,其分配效果与NSGA-Ⅱ相比,得到的Pareto非劣解集多样性和均匀性好,分布范围更广,更利于设计者进行决策,是一种更有效的复杂系统多指标分配方法。     

Pull and prune technique for complex structural reliability analysis

Based on the pull and prune technique proposed here for computing source-to-sink reliability, a very powerful 30-line Basic personal computer program reduces a complex reliability structure one node at a time by pruning return-loops from the evolving sink. Compared to the methodical application of the recursive pivotal decomposition technique, the proposed algorithm is particularly efficient for complex structures intertwined with many counter-directed components.     

Reachability analysis of complex planar hybrid systems

Hybrid systems are systems that exhibit both discrete and continuous behavior. Reachability, the question of whether a system in one state can reach some other state, is undecidable for hybrid systems in general. In this paper we are concerned with GSPDIs, 2-dimensional systems generalizing SPDIs (planar hybrid systems based on “simple polygonal differential inclusions”), for which reachability have been shown to be decidable. GSPDIs are useful to approximate 2-dimensional control systems, allowing the verification of safety properties of such systems.