The effects of explosive blast load variability on safety hazard and damage risks for monolithic window glazing

Although the modelling of built infrastructure subject to blast loading has been well developed, considerable uncertainty remains with respect to explosive loading parameters and structural response. This paper focuses on facade glazing – as this poses significant safety hazards when affected by explosive blast loads. A structural reliability analysis is used to calculate probabilities of glazing damage and safety hazards conditional on given threat scenarios. The analysis considers the variability of explosive blast loading; in particular, from variations in explosive weight, explosion effects in terms of pressure, stand-off distance, inherent blast load variability and model error. Uncertainties in structural response (including the variability in glazing stress limits, situational geometry, fragment drag coefficients and modelling error) are then considered in the analysis. This allows the prediction of likelihood and extent of damage and casualties. It was found that damage and safety hazard risks are very sensitive to the accuracy of the blast loading prediction model and the inherent variability of blast loading.     

Reliability assessment of structures based upon probabilistic fracture mechanics

The stochastic fatigue crack growth model (termed the Tsurui-Ishikawa model) based upon the Markov approximation method introducing the notion of death point has been proposed, and a great deal of its practical usefulness in the reliability assessment of structures has been demonstrated for those cases where the fatigue crack propagation process plays a crucial role toward their failure. By performing the reliability analysis, based upon the model, in consideration of uncertainties of both initial crack length and their number, the effect of such uncertainties has been clarified on the reliability degradation of a structural component. This result is of much interest from a practical viewpoint because it gives a guideline to determine the safe life (design life or inspection interval) to assure the prescribed level of reliability for random loadings with a variety of correlation times. Further, studies have been made on which parameter is the most significant according to the problem through parameter sensitivity study. With the aid of the proposed model, reliability assurance or reliability-based design can be performed properly against fatigue failure of structures subjected to random loading.     

不确定视角下产品结构性能优化设计综述与展望

目的 复杂产品在工程装备、航空航天等我国优先发展的战略领域中扮演着不可替代的重要角色,在其结构设计过程中普遍存在着各种不确定性,导致产品结构性能很难实现最优,甚至出现重大故障。方法 针对复杂产品设计过程中的多粒度模糊不确定、随机不确定、不完备区间不确定和高维混合不确定等特点,将不确定性理论与产品结构设计过程相结合,系统地构建了不确定视角下产品结构性能优化设计理论体系,提出了多粒度模糊不确定下产品质量特性精准提取、随机不确定下产品功能结构模块化求解、不完备区间不确定下产品结构方案多属性决策、高维混合不确定下产品关键结构可靠性优化等关键技术,并指出了产品结构性能优化设计的未来发展方向。结论 此设计理论能够充分适应和利用产品设计过程的多种不确定信息,为在结构设计环节切实提升产品性能提供了有力参考。     

Accident probabilities and seat belt usage: A psychological perspective

Motorists' reluctance to wear seat belts is examined in light of research showing (a) that protective behavior is influenced more by the probability of a hazard than by the magnitude of its consequences and (b) that people are not inclined to protect themselves voluntarily against very low probability threats. It is argued that the probability of death or injury on any single auto trip may be too low to incite a motorist's concern. Maintenance of a “single trip” perspective makes it unlikely that seat belts will be used. Change of perspective, towards consideration of the risks faced during a lifetime of driving, may increase the perceived probabilities of injury and death and, therefore, induce more people to wear seat belts.     

Fuzzy logic based approach to FRP retrofit of columns

Current design approaches for seismic retrofit use deterministic variables to describe the geometry, material properties and the applied loads on the bridge column. Using a mechanistic model that considers nonlinear material behavior, these deterministic input variables can be directly mapped to the design parameters. However the results often give a false sense of reliability due to neglecting uncertainties related to the input variables of the analysis (data uncertainty), unpredictable fluctuations of loads and natural variability of material properties, and/or the uncertainty in the analytical model itself (model uncertainty). While methods of reliability analysis can provide a means for designing so as not to exceed specific levels of “acceptable” risk, they do not consider the uncertainty in the assumption of distribution functions for each of the input variables and are built on the basic assumption that the models used perfectly describe reality. This, however, still results in significant unknowns and often design models that are not truly validated across their response space. This paper describes the application of a fuzzy probabilistic approach to capture the inherent uncertainty in such applications. The application of the approach is demonstrated through an example and results are compared to those obtained from conventional deterministic analytical models. It is noted that the confidence in the achieved safety of the retrofit system that is based on the use of the fuzzy probabilistic approach is much higher than that achieved using the deterministic approach. This is due to the consideration of uncertainty in the material parameters as well as the consideration of uncertainty in the assumed crack angle during the design process.     

Development of environmental consequence index (ECI) using fuzzy composite programming

Estimation of environmental consequences of hazardous substances in chemical industries is a very difficult task owing to (i) diversity in the types of hazards and their effects, (ii) location, and (ii) uncertainty in input information. Several indices have been developed over the years to estimate the environmental consequences. In this paper, a critical literature review was done on the existing environmental indices to identify their applications and limitations. The existing indices lack in consideration of all environmental consequence factors such as material hazard factors, dispersion factors, environmental effects, and their uncertainty. A new methodology is proposed for the development of environmental consequence index (ECI), which can overcome the stated limitations. Moreover, the recently developed fuzzy composite programming (FCP) is used to take care of the uncertainty in estimation. ECI is applied to benzene extraction unit (BEU) of a petrochemical industry situated in eastern part of India. The ECI for all the eight sections of BEU are estimated and ranked. The results are compared with well-established indices such as Dow fire and explosion index, safety weight hazard index (SWeHI), and environmental accident index (EAI). The proposed ECI may outperform other indices based on its detailed consideration of the factors and performed equally to Dow F&E index, and EAI in most of the cases for the present application.     

Reliability-oriented optimal design of intentional mistuning for a bladed disk with random and interval uncertainties

When interblade coupling is weak, the dynamic response of a bladed disk is very sensitive to the presence of uncertainties. Excessive response variation can be very harmful. Previous studies have indicated that introducing blade-to-blade difference in nominal design, known as intentional mistuning, could reduce the level of response variation. In this research, an efficient computational framework that yields the optimal design of intentional mistuning is developed to maximize the bladed disk reliability. Both the random uncertainty of blades and the interval uncertainty of disk connections are considered. The Metropolis–Hastings algorithm is applied to find the worst case response under interval uncertainty, and Monte Carlo simulation is employed to account for the random mistuning effect. A gradient-based approach is then established to find the minimum design modification needed to achieve a designated reliability level. Case studies are carried out to illustrate the effectiveness of the proposed method.     

Effectiveness of mitigation measures against natural hazards

We describe a general procedure to assess the effectiveness of mitigation measures against the following natural hazards: snow avalanches, rockfall, landslides, debris flows and floods. First the basic principles necessary for considering mitigation measures related to hazard maps are defined. These principles ensure that a minimal level of quality, safety and sustainability is met and that mitigation measures are tested not only with respect to regular design events but also to extreme events. Once the basic standards are met, the effectiveness of a mitigation measure is analyzed in more detail. This approach is subdivided into three main steps. In the first step, the question of whether the mitigation measures may be relevant in any way to the hazard assessment or not is investigated. In the second step, the mitigation measures are assessed technically by determining their reliability, defined in terms of structural safety, serviceability and durability. The third step involves the quantification of the effectiveness, taking into account the mitigation measures with respect to their reliability. Finally, the adaptation of hazard zones can be elaborated based on this information.     

General principles of the use of safety factors in design and assessment

Any structure or component can be made to fail if it is subjected to loadings in excess of its strength. Structural integrity is achieved by ensuring that there is an adequate safety margin or reserve factor between strength and loading effects. The basic principles of ‘allowable stress’ and ‘limit state’ design methods to avoid failure in structural and pressure vessel components are summarised. The use of risk as a means of defining adequate safety is introduced where risk is defined as the product of probability of failure multiplied by consequences of failure. The concept of acceptable ‘target’ levels of risk is discussed. The use of structural reliability theory to determine estimates of probability of failure and the use of the reliability index β are described. The need to consider the effects of uncertainties in loading information, calculation of stresses, input data and material properties is emphasised. The way in which the effect of different levels of uncertainty can be dealt with by use of partial safety factors in limit state design is explained. The need to consider all potential modes of failure, including the unexpected, is emphasised and an outline given of safety factor treatments for crack tip dependent and time dependent modes. The relationship between safety factors appropriate for the design stage and for assessment of structural integrity at a later stage is considered. The effects of redundancy and system behaviour on appropriate levels of safety factors are discussed.     

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.     

Bayesian calculation of optimal burn‐in time using the joint criteria of cost and delivered reliability

Burn‐in is a quality control process used to minimize the warranty cost of a product by screening out defective products through prior operation for a period of time before sale. Two decision criteria used to determine the optimal burn‐in time are the maximization of the reliability of the delivered product and the minimization of the total cost, which are composed of the cost of burn‐in process and the cost of warranty claims. Because of uncertainty regarding the underlying lifetime distribution of the product, both the product reliability and the total cost are random variables. In this paper, the uncertainty in reliability and cost is quantified by use of Bayesian analysis. The joint distribution of reliability and cost is inferred from the uncertainty distribution of the parameters of the product lifetime distribution. To incorporate the uncertainty in reliability and cost as well as the tradeoff between them into the selection of optimal burn‐in time, the joint utility function of reliability and cost is constructed using the joint distribution of reliability and cost. The optimal burn‐in time is selected as the time that maximizes the joint utility function. Copyright © 2010 John Wiley & Sons, Ltd.     

基于贝叶斯理论的非线性结构模型修正及其动力可靠度分析EI北大核心CSCD

提出一种基于贝叶斯推理的非线性结构模型修正方法,同时考虑激励的随机性,建立了复合随机振动系统的动力可靠度分析方法。利用实测结构动力响应主分量的瞬时特征参数作为非线性指标构建似然函数,结合拒绝延缓自适应(Delayed Rejection and Adaptive Metropolis,DRAM)算法和高斯过程替代模型实现了非线性结构模型修正及其参数的不确定性量化。根据首次超越破坏准则,利用广义概率密度演化方法,分别对仅考虑激励随机性的确定性模型和同时考虑结构参数与激励不确定性的复合随机振动模型进行动力可靠度分析,并利用蒙特卡洛随机抽样方法验证了计算结果的准确性。研究结果表明:基于振动响应瞬时特征参数的贝叶斯推理方法能够快速、准确地实现结构的非线性模型修正及其参数的不确定性量化。与具有初始设计参数名义值的确定性模型相比,考虑参数不确定性的复合随机模型的动力可靠度总体偏低,因此,在结构安全评估中应考虑非线性模型参数不确定性的影响,使评估结果更加安全、可靠。     

Analysis of Confidence Lower Limits of Reliability and Hazard Rate for Electronic Stability Control Systems

This article describes an evaluation method for reliability and hazard rate of lifetime distribution confidence lower limits for electronic stability control (ESC) system using test data from multistage and subsystems. This method provides estimation that can potentially and significantly reduce the amount of testing, without sacrificing the one‐sided confidence level of reliability. This also allows quicker design verification and validation for ESC systems. The method is derived under the assumption that the reliability parameter is a random variable with a given distribution function, and the product's reliability increases monotonously during the development process. This new method is applied to the analysis of reliability of an ESC system. Copyright © 2012 John Wiley & Sons, Ltd.     

A new reliability measure based on specified minimum distances before the locations of random variables in a finite interval

A new reliability measure is proposed and equations are derived which determine the probability of existence of a specified set of minimum gaps between random variables following a homogeneous Poisson process in a finite interval. Using the derived equations, a method is proposed for specifying the upper bound of the random variables' number density which guarantees that the probability of clustering of two or more random variables in a finite interval remains below a maximum acceptable level. It is demonstrated that even for moderate number densities the probability of clustering is substantial and should not be neglected in reliability calculations.In the important special case where the random variables are failure times, models have been proposed for determining the upper bound of the hazard rate which guarantees a set of minimum failure-free operating intervals before the random failures, with a specified probability. A model has also been proposed for determining the upper bound of the hazard rate which guarantees a minimum availability target. Using the models proposed, a new strategy, models and reliability tools have been developed for setting quantitative reliability requirements which consist of determining the intersection of the hazard rate envelopes (hazard rate upper bounds) which deliver a minimum failure-free operating period before random failures, a risk of premature failure below a maximum acceptable level and a minimum required availability. It is demonstrated that setting reliability requirements solely based on an availability target does not necessarily mean a low risk of premature failure. Even at a high availability level, the probability of premature failure can be substantial. For industries characterised by a high cost of failure, the reliability requirements should involve a hazard rate envelope limiting the risk of failure below a maximum acceptable level.     

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...     

短缺量拖后率与价格折扣相关变质品VMI模型

考虑短缺量拖后率与订货商给予顾客的价格折扣正线性相关,提出一种需求指数时变的变质物品供应商管理库存模型,研究了供应链最优库存策略。数值仿真和主要参数灵敏度分析表明,订货商在缺货期间向顾客提供价格折扣有利于降低丢单损失和系统库存总成本;当需求增长因子变化时,VMI系统应保持库存控制策略不变;当变质系数和拖后率上限变大时,VMI系统则应保持订货商补货次数和价格折扣不变,同时适当降低订货商服务水平。     

Setting reliability requirements based on minimum failure‐free operating periods

A new reliability methodology and tools have been created for setting reliability requirements. At the heart of the new methodology are reliability requirements based on specified minimum failure‐free operating (MFFOP) intervals and a maximum acceptable level of the probability of premature failure. These types of requirements are suitable to industries where the consequences of failure and the cost of intervention for maintenance are very high (e.g. deepwater offshore oil and gas industries). The methodology proposed includes models and tools for: (i) setting reliability requirements to limit the risk of premature failure below an acceptable level; (ii) setting reliability requirements to minimize the total losses; and (iii) setting reliability requirements to guarantee a set of MFFOP intervals. An advantage of the MFFOP approach is that it directly links the reliability requirements with health, safety, environmental and business risks. Another advantage is that the MFFOP requirements are suitable for non‐constant hazard rates where the mean time to failure (MTTF) reliability measure is often misleading. A solution to the important problem of determining the maximum hazard rate that guarantees with a required probability the existence of a specified set of MFFOP intervals has also been found. The reliability tools proposed also permit the extraction of useful information from data sets containing a given number of random failures, in cases where the failure times are unknown. Copyright © 2003 John Wiley & Sons, Ltd.     

Uncertainty propagation in inverse reliability-based design of composite structures

An approach for the analysis of uncertainty propagation in reliability-based design optimization of composite laminate structures is presented. Using the Uniform Design Method (UDM), a set of design points is generated over a domain centered on the mean reference values of the random variables. A methodology based on inverse optimal design of composite structures to achieve a specified reliability level is proposed, and the corresponding maximum load is outlined as a function of ply angle. Using the generated UDM design points as input/output patterns, an Artificial Neural Network (ANN) is developed based on an evolutionary learning process. Then, a Monte Carlo simulation using ANN development is performed to simulate the behavior of the critical Tsai number, structural reliability index, and their relative sensitivities as a function of the ply angle of laminates. The results are generated for uniformly distributed random variables on a domain centered on mean values. The statistical analysis of the results enables the study of the variability of the reliability index and its sensitivity relative to the ply angle. Numerical examples showing the utility of the approach for robust design of angle-ply laminates are presented.     

Uncertainty analysis and reliability improvement of planetary roller screw mechanism using active learning Kriging model

The uncertainties in the geometry, material and operation conditions may cause structural failure of the planetary roller screw mechanism (PRSM). The uncertainty analysis model is the key to the reliability assessment of the PRSM, however, the relevant studies have been rarely reported in the past. This paper focuses on establishing a preliminary mathematical model of the PRSM considering uncertain factors. The quasi-Monte Carlo (QMC) method is introduced to improve the solving efficiency of the multidimensional and nonlinear implicit limit state function (LSF). Then, the parameter sensitivities of the uncertain factors to the load distribution and contact characteristics are comprehensively ranked by the design of experiment (DoE). The computational cost for constructing the active learning Kriging (ALK) model of PRSM is decreased by only selecting the most sensitive variables. Moreover, the ALK model and QMC method (ALK-QMC) are combined to explore how the main factors affect the structural reliability of PRSM, which further guides the implementation of multi-objective optimization to improve the reliability by the developed NSGA-II-Downhill algorithm. Finally, the theoretical model and optimization results are verified by the finite element method.     

基于概率的高层建筑地震需求模型与风险评估EI北大核心CSCD

提出了基于贝叶斯理论的地震风险评估方法,综合考虑了地震危险性模型、输入地震动记录、结构参数和需求模型的不确定性,并以云南大理地区1970年-2017年间的地震数据为研究基础进行了详细讨论。在传统基于概率地震危险性分析方法的基础上,提出了基于贝叶斯理论的地震危险性分析方法,通过贝叶斯更新准则,确定了地震概率模型中未知参数的后验概率分布;通过贝叶斯理论建立了基于概率的地震需求模型,并在易损性中考虑了需求模型认知不确定性的影响;以42层钢框架-RC核心筒建筑为例,开展了地震作用下的风险评估。研究表明:基于贝叶斯理论的地震危险性分析方法,能够获得更为合理的危险性模型;忽略需求模型中参数不确定性的影响,将错误估计结构的地震易损性;不同加载工况将对高层建筑的地震风险产生显著影响。提出的概率风险评估方法,提供了可以考虑固有不确定性和认知不确定性的有效途径,有助于推动高性能结构地震韧性评价和设计理论的发展。