Reliability Reallocation for Fuel Cell Vehicles Based on Genetic Algorithm

A fuel cell vehicle (FCV) is a type of alternative energy vehicle that could help resolve the energy crisis, mitigate environmental problems, and contribute to sustainable development. Developing an FCV with high reliability is an important goal for automobile factories and research institutions. Other key factors required by FCVs include mass production and customer approval. An FCV is a complex mechanism composed of many subsystems. During the development of the overall vehicle, steps should be taken to ensure that every subsystem is reliable. However, such development must also consider costs, which must be kept as low as possible. To ensure the reliability of FCV while operating under conditions that demand minimal cost, a genetic algorithm is employed to reallocate the reliability of the overall vehicle system. First, the growth factor of the reliability–feasibility of each subsystem is determined according to the complexity, importance, and technological level of the FCV subsystems. The FCV cost model is then established on the basis of such parameters as subsystem cost, reliability–feasibility growth factor, initial reliability, limit reliability, and so on. A genetic algorithm is then used to compute for the reliability of FCV subsystems. The rationality of reliability reallocation is verified according to the subsystem importance coefficient. This method considers the benefits for both enterprises and customers by applying principles of engineering and conducting a reliability study. Copyright © 2014 John Wiley & Sons, Ltd.     

Life-cycle reliability-based robust design optimization for GP model with response uncertainty

Reliability-based robust design optimization (RBRDO) is a crucial tool for life-cycle quality improvement. Gaussian process (GP) model is an effective alternative modeling technique that is widely used in robust parameter design. However, there are few studies to deal with reliability-based design problems by using GP model. This article proposes a novel life-cycle RBRDO approach concerning response uncertainty under the framework of GP modeling technique. First, the hyperparameters of GP model are estimated by using the Gibbs sampling procedure. Second, the expected partial derivative expression is derived based on GP modeling technique. Moreover, a novel failure risk cost function is constructed to assess the life-cycle reliability. Then, the quality loss function and confidence interval are constructed by simulated outputs to evaluate the robustness of optimal settings and response uncertainty, respectively. Finally, an optimization model integrating failure risk cost function, quality loss function, and confidence interval analysis approach is constructed to find reasonable optimal input settings. Two case studies are given to illustrate the performance of the proposed approach. The results show that the proposed approach can make better trade-offs between the quality characteristics and reliability requirements by considering response uncertainty.     

Belief rule-based dependence assessment method under interval uncertainty

Human reliability analysis (HRA) is of great significance for probabilistic risk assessment, and the technique for human error rate prediction (THERP) has been widely applied to assess the dependence among HRA. However, uncertainties in analyst's judgment and experts' knowledge, especially interval uncertainty in analyst's judgment, have been ignored by existing methods. To this end, the belief rule-based system is employed to model uncertainties in experts' knowledge in this paper, and the interval belief distribution is used to model interval uncertainty in analyst's judgment. Then, a new belief rule-based dependence assessment method is proposed, and two case studies are used to illustrate the effectiveness of the proposed method. Experimental results demonstrate that the proposed method could not only model uncertainty using belief rules and interval belief distributions, but also provide a novel and effective way for human reliability analysis.     

Research on multiple-state industrial robot system with epistemic uncertainty reliability allocation method

Reliability allocation of industrial robot (IR) system is one of the important means to improve its whole life cycle, reduce maintenance cost, and characterize weak subsystems. The IR system is not only very complex but also has strong customization; meanwhile, its sample data are small, resulting in unclear degeneration and failure. Based on the above two epistemic uncertainties, a new methodology called multiple-state IR system reliability allocation method with epistemic uncertainty (MIRS-RAM-EU) is proposed. First, the Dempster-Shafer (D-S) evidence theory is used to quantify the epistemic uncertainty. Then, the Kolmogorov differential equations of MIR's subsystems are calculated. The reliability index of MIRS is allocated based on Birnbaum importance degree theory, and the reliability allocation coefficient of each IR subsystem is clearly expressed by this method. Finally, compared with traditional importance allocation method, the MIRS-RAM-EU is more efficient and accurate. This method is usefully directive for reliability evaluation of IR.     

Accelerated Life Testing (ALT) Design Based on Computational Reliability Analysis

Accelerated life testing (ALT) design is usually performed based on assumptions of life distributions, stress–life relationship, and empirical reliability models. Time‐dependent reliability analysis on the other hand seeks to predict product and system life distribution based on physics‐informed simulation models. This paper proposes an ALT design framework that takes advantages of both types of analyses. For a given testing plan, the corresponding life distributions under different stress levels are estimated based on time‐dependent reliability analysis. Because both aleatory and epistemic uncertainty sources are involved in the reliability analysis, ALT data is used in this paper to update the epistemic uncertainty using Bayesian statistics. The variance of reliability estimation at the nominal stress level is then estimated based on the updated time‐dependent reliability analysis model. A design optimization model is formulated to minimize the overall expected testing cost with constraint on confidence of variance of the reliability estimate. Computational effort for solving the optimization model is minimized in three directions: (i) efficient time‐dependent reliability analysis method; (ii) a surrogate model is constructed for time‐dependent reliability under different stress levels; and (iii) the ALT design optimization model is decoupled into a deterministic design optimization model and a probabilistic analysis model. A cantilever beam and a helicopter rotor hub are used to demonstrate the proposed method. The results show the effectiveness of the proposed ALT design optimization model. Copyright © 2015 John Wiley & Sons, Ltd.     

钢筋混凝土柱的“强剪弱弯”可靠性区间分析

在钢筋混凝土结构抗震设计中,"强剪弱弯"是保证结构延性的一个重要设计概念。引进区间变量表达认知不确定性,对钢筋混凝土框架柱进行失效概率区间分析。通过结合代表认知不确定性的区间变量与代表偶遇不确定性的随机变量完成了对不确定性的数学描述。在此基础上,根据对基本事件的包含关系建立"强剪弱弯"区间可靠性概率模型,并从证据理论出发论证了该失效概率区间的上下界实质上等价于证据理论中的信任与似然函数。对于含有区间值不确定性参数的结构承载力计算,将Berz-Taylor模型引进计算过程中,减少由于区间扩张而导致的误差。在数值模拟计算中,运用模拟退火遗传算法(SAGA)确定了"强剪弱弯"的大致设计区间。根据该设计区间构造了特殊的采样函数进行重要性采样模拟从而得到了失效概率区间。误差分析表明该方法具有较好的精度。最后通过算例分析了各设计因素对"强剪弱弯"可靠性的影响,并提出了相应的设计建议。     

A nonprobabilistic reliability–based topology optimization method of compliant mechanisms with interval uncertainties

On account of the inevitable multisource uncertainty factors in compliant mechanisms, which seriously affect the accuracy of output motion, a nonprobabilistic reliability–based topology optimization (NRBTO) framework for compliant mechanisms with interval uncertainties is introduced. Combined with the solid isotropic material with penalization (SIMP) model and the set-theoretical interval method, the uncertainty quantification analysis is conducted to obtain mathematical approximations and boundary laws of considered mean compliance. By normalization treatment of the limit-state function, a new quantified measure of the nonprobabilistic reliability is then defined. The compliance-based NRBTO design method ensures the output motion realizing its target value accurately considering the uncertainty factors. The sensitivities of the nonprobabilistic reliability index with respect to design variables are calculated by the adjoint vector method. Two engineering examples are eventually presented to illustrate the applicability and the validity of the present problem statement as well as the proposed numerical techniques.     

Reliability analysis of multi‐state series systems with performance sharing mechanism under epistemic uncertainty

For real engineering systems, it is sometimes difficult to obtain sufficient data to estimate the precise values of some parameters in reliability analysis. This kind of uncertainty is called epistemic uncertainty. Because of the epistemic uncertainty, traditional universal generating function (UGF) technique is not appropriate to analyze the reliability of systems with performance sharing mechanism under epistemic uncertainty. This paper proposes a belief UGF (BUGF)‐based method to evaluate the reliability of multi‐state series systems with performance sharing mechanism under epistemic uncertainty. The proposed BUGF‐based reliability analysis method is validated by an illustrative example and compared with the interval UGF (IUGF)‐based methods with interval arithmetic or affine arithmetic. The illustrative example shows that the proposed BUGF‐based method is more efficient than the IUGF‐based methods in the reliability analysis of multi‐state systems (MSSs) with performance sharing mechanism under epistemic uncertainty.     

Fuzzy smart failure modes and effects analysis to improve safety performance of system: Case study of an aircraft landing system

Failure modes and effects analysis (FMEA) is a safety and reliability technique that is widely used to evaluate, design, and process a system against diverse possible ways through which the potential failure has a tendency to occur. In conventional FMEA, the risk evaluation is determined by risk priority number (RPN) obtained by multiplying of three risk factors—severity, occurrence, and detection. However, because of many shortages in conventional FMEA, the RPN scores have been widely criticized along issues bothering on ambiguity and vagueness, scoring, appraising, evaluating, and selecting corrective actions. In this paper, we propose a new integrated fuzzy smart FMEA framework where the combination of fuzzy set theory, analytical hierarchy process (AHP), and data envelopment analysis (DEA) is used, respectively, to handle uncertainty and to increase the reliability of the risk assessment. These are achieved by employing a heterogeneous group of experts and determining the efficiency of FMEA mode with adequate priority and corrective actions using RPN, time, and cost as indicators. A numerical example (aircraft landing system) is provided to exemplify the feasibility and effectiveness of the proposed model. The outputs of the proposed model compared with the conventional risk assessment technique results show its effectiveness, reliability, and propensity for real applications.     

需求和供应不确定下的选址研究

在需求不确定的同时,考虑了由于意外事件导致设施失灵而造成的供应不确定性,提出了这两个不确定因素下的设施选址模型.已知各个设施的失灵风险概率,通过情景规划描述需求不确定性,在保证供应系统的稳定性和鲁棒性不低于既定值的情况下,使得运输费用和设施失灵不能提供服务时的风险费用之和最小,提出了拉格朗日松弛算法,并通过大量算例验证...     

多源不确定性条件下气动弹性系统颤振可靠性分析方法

传统的气动弹性系统颤振分析模型大多是在确定性参数条件下建立的,当系统中存在不确定因素时,按确定性方法设计的气动弹性系统存在颤振失效风险。以概率和非概率区间模型为基础,建立了单源不确定性条件下颤振可靠性分析模型;在此基础上,针对含随机和区间多源不确定参数的气动弹性系统颤振可靠性分析问题,提出一种基于分步求解策略的新型混合可靠性分析与度量法,获取多源不确定性条件下气动弹性系统的颤振可靠度,实现了对多源不确定性条件下颤振可靠性的有效评估。数值算例表明,该方法与蒙特卡洛模拟法相吻合,且具有显著的计算效率优势。     

Integration of computation and testing for reliability estimation

This paper develops a methodology to integrate reliability testing and computational reliability analysis for product development. The presence of information uncertainty such as statistical uncertainty and modeling error is incorporated. The integration of testing and computation leads to a more cost-efficient estimation of failure probability and life distribution than the tests-only approach currently followed by the industry. A Bayesian procedure is proposed to quantify the modeling uncertainty using random parameters, including the uncertainty in mechanical and statistical model selection and the uncertainty in distribution parameters. An adaptive method is developed to determine the number of tests needed to achieve a desired confidence level in the reliability estimates, by combining prior computational prediction and test data. Two kinds of tests — failure probability estimation and life estimation — are considered. The prior distribution and confidence interval of failure probability in both cases are estimated using computational reliability methods, and are updated using the results of tests performed during the product development phase.     

基于生产管理系统可靠性因素的激励模型

假定企业生产与管理系统运作可靠性这一内部因素已经被量化,在此基础上描述了非对称信息条件下企业经营者的激励模型。通过对模型最优解的分析以及非对称信息问题的贝叶斯分析,讨论了观测力度对企业经营者努力水平、激励水平、风险成本和代理成本等的影响。研究结论表明,观测带来了自然状态方差的下降;随着委托者观测力度的增加,经营者减少了消极怠工的机会,同时得到了更高水平的激励;除去观测成本这一因素,委托人对企业经营者的观测节约了总的代理成本。     

密闭空间爆炸温度动态不确定度评估方法研究

融合了灰色模型GM(1,1)、Bootstrap方法以及不确定度评定理论,建立了密闭空间内爆炸温度动态测量不确定度的灰自助评估模型GBM(1,1),选取某次爆炸试验300s的温度数据作为分析数据,运用估计真值、估计区间和平均不确定度等参数表征其估计结果。实验结果表明,GBM(1,1)模型融合了灰色模型GM(1,1)和Bootstrap方法的优势,可以准确模拟动态测量数据的概率分布,并实时跟踪被测量瞬时值的变化趋势。相比于灰色模型GM(1,1)和Bootstrap方法,灰自助模型GBM(1,1)具有更高的真值估计准确度和区间估计可靠度,其估计误差分布区间为［-12.62, 13.58］,标准差为8.69℃,最大相对误差为1.2%,区间估计可靠度高于90%,估计区间能够较完整地包络被测量的动态波动范围。由此证明GBM(1,1)模型能够对密闭空间内爆炸温度的动态测量不确定度做出准确评估。     

Reliability analysis for multidisciplinary systems with the mixture of epistemic and aleatory uncertainties

Epistemic and aleatory uncertain variables always exist in multidisciplinary system simultaneously and can be modeled by probability and evidence theories, respectively. The propagation of uncertainty through coupled subsystem and the strong nonlinearity of the multidisciplinary system make the reliability analysis difficult and computational cost expensive. In this paper, a novel reliability analysis procedure is proposed for multidisciplinary system with epistemic and aleatory uncertain variables. First, the probability density function of the aleatory variables is assumed piecewise uniform distribution based on Bayes method, and approximate most probability point is solved by equivalent normalization method. Then, important sampling method is used to calculate failure probability and its variance and variation coefficient. The effectiveness of the procedure is demonstrated by two numerical examples. Copyright © 2013 John Wiley & Sons, Ltd.     

Weak ternary interval evaluation of fatigue life and its application to mining dump truck

A method of weak ternary interval (TI) evaluation of fatigue life is proposed in this study to reasonably evaluate the nonprobabilistic reliability considering the interval uncertainty. The conventional interval is extended into a TI by introducing an expected value, that is, a value without uncertainty, as the third parameter of the interval to deal with the deviation between the expected value and the median value of the interval. Next, the TI of fatigue life is evaluated by introducing an index of attitude in the exponential function to weaken the unimportant upper bound and deal with the overconservative lower bound. Therefore, the evaluation is reflected in the form of an equivalent fatigue life as an indicator of the nonprobabilistic reliability. Next, the TIs of the fatigue parameters are obtained with limited fatigue test data from a practical engineering application. Finally, the proposed method is applied to a mining dump truck frame to demonstrate its significance and validity.     

Trading reliability targets within a supply chain using Shapley's value

The development of complex systems involves a multi-tier supply chain, with each organisation allocated a reliability target for their sub-system or component part apportioned from system requirements. Agreements about targets are made early in the system lifecycle when considerable uncertainty exists about the design detail and potential failure modes. Hence resources required to achieve reliability are unpredictable. Some types of contracts provide incentives for organisations to negotiate targets so that system reliability requirements are met, but at minimum cost to the supply chain. This paper proposes a mechanism for deriving a fair price for trading reliability targets between suppliers using information gained about potential failure modes through development and the costs of activities required to generate such information. The approach is based upon Shapley's value and is illustrated through examples for a particular reliability growth model, and associated empirical cost model, developed for problems motivated by the aerospace industry. The paper aims to demonstrate the feasibility of the method and discuss how it could be extended to other reliability allocation models.     

Response surface method based on uniform design and weighted least squares for non-probabilistic reliability analysis

The non-probabilistic reliability theory is a promising methodology for implementing structural reliability analysis in case of scarce statistical data. One of the main obstacles to implement non-probabilistic reliability analysis is the implication of the limit state function (LSF) for complex structures. This paper aims to establish a surrogate model of the LSF with higher simulation precision, and whereby proposes a response surface method based on the combination of uniform design (UD) and weighted least squares (WLS). At first, the UD method is selected as the sampling method of interval variables to realize the uniform space-filling of the initial samples, and the sample set is updated by gradually adding the approximate optimal points to increase the sampling density of critical domain. Then, the WLS method is applied to improve the precision of the response surface by adjusting the importance of samples to the function fitting. Finally, a method of constructing sample weights is developed. Two examples are applied to validate the feasibility and efficiency of the proposed method. Results show that the proposed method is effective for non-probabilistic reliability analysis of complex structures owning to high computational precision and low computational cost in both numerical and case study.     

Application of discrete‐time Bayesian network on reliability analysis of uncertain system with common cause failure

With the increasing complexity of engineering systems, reliability analysis and evaluation of systems with traditional methods can't meet practical engineering requirements. Based on limited experimental conditions, lack of data, complex structure models, insufficient cognitive abilities, and many other issues, people have to consider many uncertain factors in system reliability research. Besides, common cause failure (CCF) has become an important factor of system failure. In this paper, a discrete‐time Bayesian network (DTBN) associated with an eight‐rotor unmanned aerial vehicle (UAV) system is presented to discuss above problems. In this approach, the system is assumed as a two‐state system. After that, interval analysis theory is employed to deal with uncertainty. We consider the four sets of auxiliary propellers in the auxiliary power group as a 3/8 voting system, and β factor model is used to process CCF in the auxiliary power group. The proposed methods prove the validity of proposing interval analysis theory to solve uncertain problems and it is necessary to consider reducing or avoiding CCFs in system.     

A single-loop optimization method for reliability analysis with second order uncertainty

Reliability analysis may involve random variables and interval variables. In addition, some of the random variables may have interval distribution parameters owing to limited information. This kind of uncertainty is called second order uncertainty. This article develops an efficient reliability method for problems involving the three aforementioned types of uncertain input variables. The analysis produces the maximum and minimum reliability and is computationally demanding because two loops are needed: a reliability analysis loop with respect to random variables and an interval analysis loop for extreme responses with respect to interval variables. The first order reliability method and nonlinear optimization are used for the two loops, respectively. For computational efficiency, the two loops are combined into a single loop by treating the Karush–Kuhn–Tucker (KKT) optimal conditions of the interval analysis as constraints. Three examples are presented to demonstrate the proposed method.