Reliability analysis of TLP tethers under impulsive loading

In the present study, reliability assessment of Tension Leg Platform (TLP) tethers against maximum tension (i.e. tension exceeding yield) has been carried out under combined action of extreme wave and impulsive forces. For this purpose, a nonlinear dynamic analysis of TLP has been carried out in time domain. A limit state function for maximum tension (i.e. tension exceeding yield) has been derived employing Von-Mises theory of failure. Using this derived limit state function and responses obtained after dynamic analysis under sinusoidal, half-triangular and triangular impulsive forces, reliability assessment of the TLP tethers has been carried out. Design point, important for probabilistic design of tethers, has been located on the failure surface after solving a constrained optimization problem. To study the influence of various random variables on tether reliability, sensitivity analysis has been carried out. Effects of angle of impact; effect of variable submergence; and effect of material yield strength on tether reliability have also been studied on parametric basis. Effect of uncertainty on overall tether reliability has also been discussed to show the importance of quality control in the various design parameters.     

Reliability assessment of tension leg platform tethers under nonlinearly coupled loading

This paper deals with the design of TLP tethers under wind and wave induced loading using reliability analysis. Two modes of tether failure are considered, namely (1) the maximum life time tension exceeding yield stress and (2) the minimum life time tension less than zero. A dynamic response analysis is carried out considering nonlinearities due to drag, variable submergence, variable tether tension, wind induced loading and large displacements. Various degrees of freedom are considered to be coupled. Reliability assessment is carried out by Monte Carlo failure analysis using simulation techniques. A methodology is developed for finding the expected life of the platform based on the results of reliability study. Finally, a design approach is established involving the determination of optimum yield stress in tethers.     

Reliability analysis of standby systems with multi‐state elements subject to constant transition rates

Standby redundancy has been extensively applied to critical engineering systems to enhance system reliability. Researches on reliability evaluation for standby systems focus more on systems with binary‐state elements. However, multi‐state elements with different performances have played a significant role in engineering systems. This paper presents an approach for reliability analysis of standby systems composed of multi‐state elements with constant state transition rates and absorbing failure states. The approach allows modelling different standby systems beyond cold, warm and hot ones by taking into account differences in possible maintenance of elements in standby and operation modes and dependence of elements' operational behavior on their initial state at the time of activation. An iterative algorithm for reliability evaluation based on element state probabilities is suggested. Illustrating examples of evaluating reliability of different types of homogeneous and heterogeneous standby systems are demonstrated.     

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.     

Reliability analysis of pipelines carrying H2S for risk based inspection of heavy water plants

Reliability analysis of pipelines containing corrosion defects due to H₂S is presented. The pipeline carrying H₂S is more susceptible to the internal corrosion thereby reducing the pipeline's load carrying capacity. The objective of this study is to obtain the pipelines' failure probabilities that are required in establishing a Risk Based Inspection (RBI) programme for heavy water plants. The reliability assessment of pipelines involves the estimation of failure pressure and evaluating the limit state function. Several failure pressure models were studied for this purpose and it was found that the modified B31G failure pressure model is most suitable for the pipeline failure pressure modeling. Due to the presence of non-linearity in the limit state function and non-normal variables, the first order reliability method has been employed for carrying out the reliability analysis. The uncertainty of the random variables on which the limit state function depends is modeled using normal and non-normal probabilistic distributions. The failure probabilities and the categories of the pipelines connected to the first pair of first stage of exchange towers are presented. In addition, a sensitivity analysis was carried out on random variables involved in the problem. The results of sensitivity analysis are also presented.     

不完整结构系统同时考虑强度和刚度的可靠性分析

基于结构强度可靠性分析理论的基础之上,提出了不完整结构(结构系统中有部分元件已失效,但结构未变成机构仍具有一定的承载能力)强度、刚度可靠性的分析方法。该方法考虑了元件因强度失效对不完整结构系统强度、刚度可靠性的影响,同时导出了等效安全余量的形式,进而计算结构系统在失效各阶段的总体失效概率。并结合算例对结构系统在失效各阶段进行了强度、刚度的可靠性分析。算例表明,这样分析符合结构在使用各阶段可靠性的真实情况,从而为结构的合理利用起指导性作用。     

Reliability and risk models based on independent trials

An analysis has been made of the mathematical relationship between two alternative models for reliability and risk estimation under the assumption of mutual independence. In cases where the reliability formulation is expressible as a compound union event, the resultant reliability expressions are analogous to the Bernoulli and Poisson trials processes. Nonparametric inequality relationships aredeveloped that demonstrate that a Bayesian-Bernoulli model always predicts event probabilities that are less than Bernoulli probabilities, which are always less than or equal to probabilities predicted by the finer grained Poisson trials model. An analysis of the maximum relative prediction error indicates when the individual probabilities are less than 0.1, the relative error between the Bernoulli and Poisson models is always less than 5 percent. The results are demonstrated to have utility in system reliability, engineered design lifetime risk analysis, and simulation applications in which the model is based on independent trials.     

Set theoretic formulation of performance reliability of multiple response time‐variant systems due to degradations in system components

This paper presents a design stage method for assessing performance reliability of systems with multiple time‐variant responses due to component degradation. Herein the system component degradation profiles over time are assumed to be known and the degradation of the system is related to component degradation using mechanistic models. Selected performance measures (e.g. responses) are related to their critical levels by time‐dependent limit‐state functions. System failure is defined as the non‐conformance of any response and unions of the multiple failure regions are required. For discrete time, set theory establishes the minimum union size needed to identify a true incremental failure region. A cumulative failure distribution function is built by summing incremental failure probabilities. A practical implementation of the theory can be manifest by approximating the probability of the unions by second‐order bounds. Further, for numerical efficiency probabilities are evaluated by first‐order reliability methods (FORM). The presented method is quite different from Monte Carlo sampling methods. The proposed method can be used to assess mean and tolerance design through simultaneous evaluation of quality and performance reliability. The work herein sets the foundation for an optimization method to control both quality and performance reliability and thus, for example, estimate warranty costs and product recall. An example from power engineering shows the details of the proposed method and the potential of the approach. Copyright © 2006 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.     

水中悬浮隧道锚索在波流场中的涡激动力响应

建立了水中悬浮隧道的锚索在波流场中顺流向涡激振动的数学模型,并考虑了波浪作用下,悬浮隧道的运动引起的强迫激励和参数激励对锚索顺流向涡激振动的影响。应用Galerkin方法和数值积分法,计算分析外激励频率对锚索顺流向涡激振动的影响。计算结果表明,外激励作用下锚索顺流向涡激振动的振幅明显增大,且当外激励频率接近锚索一阶自振频率时,振幅达到最大值。     

基于动态可靠度和经济优化相结合的服役桥梁维修加固风险决策

服役桥梁的维修加固需要综合考虑安全和经济的问题,基于服役桥梁的动态可靠度,以后续服役期内收益期望值最大或损失期望值最小为目标函数,对服役桥梁的维修加固决策进行了探讨,利用实际检测数据修正抗力模型,对一座服役期为35年的钢筋混凝土梁桥动态可靠度进行了计算,同时,比较分析了汽车荷载等级的提高和采用不同维护加固措施对后续服役期内动态可靠度的影响。该方法结合工程实际,把失效损失与失效风险相结合,对桥梁结构的维修加固决策有一定的指导作用。     

Influence of probability distribution of loads on optimum reliability

Since the Hyogoken-Nambu earthquake, people have begun to pay attention not only to a building's ultimate limit state, but also to its various limit states before collapse through its lifetime. One method to determine optimum reliability has been proposed on the basis of the minimum total cost concept. Load effects are often discussed regarding modeling for probabilistic analyses. Parameters for the probabilistic model, such as the coefficient of variation, the upper bound limit and the characteristics of tail probability, are thought to be important for probabilistic analyses. The purpose of this study is to clarify the effect of these factors on the optimum reliability index, the life-cycle cost and the design point. Numerical investigations have revealed that these factors sometimes significantly affect the optimum reliability, but not the life-cycle cost or the design point for both single and multiple limit states. The minimum total cost concept provides a stable design point with optimum reliability for different load probability models.     

A study of a storage reliability estimation problem

Storage reliability, which describes the failure or deterioration of items in a dormant state, is considered in this paper. The study presented here is focused on the estimation of the storage reliability after a certain amount of storage time. We start with simple non-parametric estimation of the current reliability and then study the problem of parametric estimation based on a simple Weibull distribution assumption. Both maximum likelihood estimation and graphical techniques are considered in this case. The study is useful for planning a storage environment and making a decision about the maximum length of storage. Furthermore, the information can be used in the design and improvement of products for which the storage is an important part of the product's life cycle. A numerical example is provided to enlighten the idea.     

2D C/SiC复合材料的可靠性评价

采用概率论和数理统计方法, 以研究分析2D C/SiC复合材料的弯曲强度分布规律为切入点, 比较了失效概率预测值与实验值, 用可靠度、 风险函数和可靠强度评价了该材料可靠性。通过线性回归分析和拟合优度检验得到正态、 对数正态和三参数Weibull分布模型均可表征其弯曲强度分布规律; 确定了该材料弯曲强度失效概率、 可靠度函数、 风险函数和可靠强度的数学模型中的参数, 可以预测给定强度条件和许用可靠度条件下的多种可靠性指标; 材料弯曲强度均值的三种模型预测值与实测值最大相对误差仅0.07%, 计算得到的失效概率曲线与实验弯曲强度的失效分布均符合很好。      

Computing Transition Probability in Markov Chain for Early Prediction of Software Reliability

Early prediction of software reliability provides basis for evaluating potential reliability during early stages of a project. It also assists in evaluating the feasibility of proposed reliability requirements and provides a rational basis for design and allocation decisions. Many researchers have proposed different approaches to predict the software reliability based on a Markov model. The transition probabilities in between the states of the Markov model are input parameters to predict the software reliability. In the existing approaches, these probabilities are either assumed on some knowledge or computed using analytical method, and hence, it does not give accurate predicted reliability figure. Some authors compute them using operational profile data, but that is possible only after the deployment of the software, and this is not early prediction. The work in this paper is devoted to demonstrate the computation of transition probability in the Markov reliability model taking a case study. The proposed approach has been validated on 47 sets of real data. Copyright © 2015 John Wiley & Sons, Ltd.     

基于响应面法和Morgenstern-Price法土坡可靠度计算方法

基于响应面法,建立了一种高效的边坡可靠度指标和失效概率近似计算方法。该法在构造响应面函数时,抽样点计算采用Morgenstern-Price法取代传统费时的有限单元法,大大降低了计算工作量。利用Monte-Carlo随机抽样原理,提出了一种能同时确定边坡最危险非圆弧滑动面和最小可靠度指标的随机搜索新算法。该文给出的两个算例验证了方法的实用性和可靠性,其计算结果同时表明:当分别以最小可靠度指标和最小中值安全系数为目标函数时,搜索到的边坡最危险滑动面相差较大。最后,探讨了土性指标(c,φ)的分布概型及相关性对边坡可靠度计算结果的影响。     

Modeling the Tensile Strength of Carbon Fiber − Reinforced Ceramic − Matrix Composites Under Multiple Fatigue Loading

An analytical method has been developed to investigate the effect of interface wear on the tensile strength of carbon fiber ? reinforced ceramic ? matrix composites (CMCs) under multiple fatigue loading. The Budiansky ? Hutchinson ? Evans shear ? lag model was used to describe the micro stress field of the damaged composite considering fibers failure and the difference existed in the new and original interface debonded region. The statistical matrix multicracking model and fracture mechanics interface debonding criterion were used to determine the matrix crack spacing and interface debonded length. The interface shear stress degradation model and fibers strength degradation model have been adopted to analyze the interface wear effect on the tensile strength of the composite subjected to multiple fatigue loading. Under tensile loading, the fibers failure probabilities were determined by combining the interface wear model and fibers failure model based on the assumption that the fiber strength is subjected to two ? parameter Weibull distribution and the loads carried by broken and intact fibers satisfy the Global Load Sharing criterion. The composite can no longer support the applied load when the total loads supported by broken and intact fibers approach its maximum value. The conditions of a single matrix crack and matrix multicrackings for tensile strength corresponding to multiple fatigue peak stress levels and different cycle number have been analyzed.     

Relative equilibria of tethered satellite systems and their stability for very stiff tethers

We study the existence and stability of the relative equilibria of systems of two satellites joined by a tether. Since tethers used in practice are very stiff we consider a stiff tether as a perturbation of an inextensible tether. We show that the equations for relative equilibria and the stability conditions are continuous as stiffness approaches infinity and limit on the equations and conditions relevant to an inextensible tether. We obtain a numerical bifurcation diagram for a class of relative equilibria in the case of an inextensible tether.     

Reliability modeling of multi‐state degraded repairable systems and its applications to automotive systems

In this paper, we presented a continuous‐time Markov process‐based model for evaluating time‐dependent reliability indices of multi‐state degraded systems, particularly for some automotive subsystems and components subject to minimal repairs and negative repair effects. The minimal repair policy, which restores the system back to an “as bad as old” functioning state just before failure, is widely used for automotive systems repair because of its low cost of maintenance. The current study distinguishes with others that the negative repair effects, such as unpredictable human error during repair work and negative effects caused by propagated failures, are considered in the model. The negative repair effects may transfer the system to a degraded operational state that is worse than before due to an imperfect repair. Additionally, a special condition that a system under repair may be directly transferred to a complete failure state is also considered. Using the continuous‐time Markov process approach, we obtained the general solutions to the time‐dependent probabilities of each system state. Moreover, we also provided the expressions for several reliability measures include availability, unavailability, reliability, mean life time, and mean time to first failure. An illustrative numerical example of reliability assessment of an electric car battery system is provided. Finally, we use the proposed multi‐state system model to model a vehicle sub‐frame fatigue degradation process. The proposed model can be applied for many practical systems, especially for the systems that are designed with finite service life.     

Non-invariant failure probabilities with invariant reliability index

This paper presents a critical examination of some basic limit state functions that led to development of the invariant code format for reliability analysis. Proper methods of evaluating failure probabilities from these limit state functions are used to check failure probabilities estimated by reliability index methods, and the results show that failure probability for a limit state function that may assume different but seemingly equivalent forms is not always invariant as the invariant format would indicate.