Redundancy and robustness of systems of events

The article aims to add a new impetus to rational and objective probabilistic evaluation of redundancy and robustness, based on uncertainties of systems and subsystems of events. An attempt is made to demonstrate the relevance of intuitive comprehension of redundancy and robustness of engineering systems of events. An event-oriented system analysis of a number of random observable operational and failure modes, with adverse probability distributions in a lifetime, may provide a deeper understanding of systems operational abundance and endurance. The system uncertainty analysis is based on the concept of entropy as defined in information theory and applied to probability theory. The article relates reliability, uncertainty, redundancy and robustness of systems of events and their application is illustrated in numerical examples.     

Quantitative analysis of a fault tree with priority AND gates

A method for calculating the exact top event probability of a fault tree with priority AND gates and repeated basic events is proposed when the minimal cut sets are given. A priority AND gate is an AND gate where the input events must occur in a prescribed order for the occurrence of the output event. It is known that the top event probability of such a dynamic fault tree is obtained by converting the tree into an equivalent Markov model. However, this method is not realistic for a complex system model because the number of states which should be considered in the Markov analysis increases explosively as the number of basic events increases. To overcome the shortcomings of the Markov model, we propose an alternative method to obtain the top event probability in this paper. We assume that the basic events occur independently, exponentially distributed, and the component whose failure corresponds to the occurrence of the basic event is non-repairable. First, we obtain the probability of occurrence of the output event of a single priority AND gate by Markov analysis. Then, the top event probability is given by a cut set approach and the inclusion–exclusion formula. An efficient procedure to obtain the probabilities corresponding to logical products in the inclusion–exclusion formula is proposed. The logical product which is composed of two or more priority AND gates having at least one common basic event as their inputs is transformed into the sum of disjoint events which are equivalent to a priority AND gate in the procedure. Numerical examples show that our method works well for complex systems.     

Development and evaluation of an uncertainty importance measure in fault tree analysis

In a fault tree analysis, an uncertainty importance measure is used to identify those basic events that significantly contribute to the uncertainty of the top-event probability. This paper defines an uncertainty importance measure of a basic event or of a group of basic events, and develops a two-stage procedure for experimentally evaluating the measure under the assumption that the probability of each basic event follows a lognormal distribution. The proposed method utilizes the Taguchi tolerance design technique with modifications. Then, the so-called contribution ratios which evaluate the main and/or interaction effects of the uncertainties of log-transformed basic-event probabilities on the uncertainty of the log-transformed top-event probability are calculated. The contribution ratios are used to estimate the defined uncertainty importance measure of a basic event or of a group of basic events. The proposed method consists of two stages for computational efficiency. In the first stage, the basic events with negligible effects on the uncertainty of the log-transformed top-event probability are screened out, and more detailed analyses are conducted in the second stage with a substantially smaller number of basic events. In addition, this paper presents an analysis method to quantify the percentage reduction in the uncertainty of the log-transformed top-event probability when the uncertainty of each basic-event probability is reduced.     

复杂产品的多学科鲁棒协同设计优化方法研究

为了处理好复杂产品各子系统之间的耦合关系以及各子系统的异构性问题,以协同优化(CO)算法为基础,结合系统不确定分析(SUA)方法和近似不确定传播(IUP)方法,构建了多学科鲁棒协同设计优化算法框架.在设计变量的不确定性能够被概率分布函数描述的情况下,此算法框架能够解决复杂产品的设计优化问题.通过对梳齿式微加速度计的多学科鲁棒协同优化设计算例的计算,验证了此算法在输入参数存在微小扰动的情况下能够有效提高设计解的鲁棒性.     

A hybrid reliability model for structures with truncated probability distributions

In traditional reliability analysis, the uncertain parameters are generally treated by some ideal probability distributions with infinite tails, which, however, seems inconsistent with the practical situations as nearly all the uncertain parameters in engineering structures will get their values within a limited interval. To eliminate such an inconsistence and thereby improve the precision of the reliability analysis, the truncated probability distributions are then employed to quantify the uncertainty in this paper, and a corresponding reliability analysis method is developed. Two cases of positional relations are summarized for the uncertainty domain and the failure surface according to whether their intersection set is non-empty or empty. The probability and non-probability convex model methods are employed to deal with these two cases, respectively, and based on it, a hybrid reliability model is then constructed for truncated distribution problems. An efficient approach is also provided to distinguish these two positional relations and thereby determine which one of the probability and non-probability methods should be used when computing a real hybrid reliability. Five numerical examples are investigated to demonstrate the effectiveness of the present method.     

Assessing uncertainty in extreme events: Applications to risk-based decision making in interdependent infrastructure sectors

Risk-based decision making often relies upon expert probability assessments, particularly in the consequences of disruptive events and when such events are extreme or catastrophic in nature. Naturally, such expert-elicited probability distributions can be fraught with errors, as they describe events which occur very infrequently and for which only sparse data exist. This paper presents a quantitative framework, the extreme event uncertainty sensitivity impact method (EE-USIM), for measuring the sensitivity of extreme event consequences to uncertainties in the parameters of the underlying probability distribution. The EE-USIM is demonstrated with the Inoperability input-output model (IIM), a model with which to evaluate the propagation of inoperability throughout an interdependent set of economic and infrastructure sectors. The EE-USIM also makes use of a two-sided power distribution function generated by expert elicitation of extreme event consequences.     

Knowledge-based support for event tree construction

A prototype system called EventMAP has been developed to provide knowledge-based support for event tree construction. It comprehends an event tree model of a physical system, which represents the possible event sequences following an initial incident. This model can be used to identify potentially hazardous accident or failure scenarios, to help in assessing the possible outcomes of an observed incident, and to support decisions about appropriate actions. It can also be used during modification to provide insights into the needs for specific safety features.

EventMAP incorporates explicit knowledge about safety engineering and good event tree construction practice. This assures that model building will be more systematic, and will produce more complete and correct event trees. Assumptions underlying the model are tracked explicitly, allowing ‘what-if’ exploration. Moreover, the safety-related design rationale will be preserved despite personnel changes over time. EventMAP incorporates knowledge about: plant structure in terms of subsystems, components, and interconnections; cause/effect relationships and other interactions among subsystems; and failure modes, including human errors. The role of EventMAP is to act as an ‘intelligent assistant’ for the event tree developer; it monitors the evolving model and issues suggestions and warnings to the user as appropriate.     

Computation of probabilistic stability measures for a controlled distributed parameter system

Parameter uncertainty can degrade the performance of an otherwise well-designed control system, sometimes leading to system instability. In the context of structural control, performance degradation and instability imply excessive vibration and even structural failure. The ability of a controller to maintain the stability of a system in spite of parameter uncertainty is measured by its robustness, which can be viewed as a probability measure, wherein the joint distribution is of dimension equal to the number of uncertain parameters and the failure hypersurface is defined by the onset of instability in the eigenspace. This observation has led to some recent analyses employing FORM/SORM methods and Monte Carlo simulation.The extension of these concepts to distributed parameter systems is, unfortunately, not immediate. The mere fact that these systems are infinite dimensional precludes the use of much of the machinery available for discrete systems, unless the distributed system is first discretized, which itself introduces error into the analysis, or is represented by an eigenfunction expansion, which requires truncation after some finite number of modes, also a potential source of error. In fact, the system will behave as one with an infinite number of subsystems with highly dependent failure modes in series.In Bergman and Hall, Effect of controller uncertainty on the stability of a distributed parameter system, Structural Safety and Reliability, eds. Schuëller, Shinozuka and Yao, Balkema, Rotterdam, 1993, pp. 210–220, root locus analysis was employed to assess the reliability of the system, requiring the repetitive solution of a transcendental characteristic equation over a range of the parameter under investigation. The loci then provide a mapping from the probability distribution of the random parameter to the probability distribution of the system eigenvalues. This approach was utilized over 30 years ago by Boyce, Random vibration of strings and bars, Proc. of the Fourth US National Congress of Applied Mechanics, Berkeley, 18–21 June, 1962, pp. 77–85, who examined eigenvalue distributions for undamped taut strings and Euler-Bernoulli beams, each subjected to the action of a single point actuator. He demonstrated that, for the case of uncertainty in the actuator gain alone, a simple, closed form mapping leading to the distributions of the eigenvalues of the system could be determined directly from the distribution of the actuator gain, and for uncertainty in the remaining parameters, approximate distributions could be obtained through the application of perturbation methods.In the current paper, the FORM/SORM approach is applied to the taut string problem, where the distributed nature of the system is maintained throughout the analysis. Uncertain parameters, in this case the proportional gain and time delay, are characterized by probability distributions with known mean and variance. Each is transformed to a standard normal variate via Rosenblatt transformations, and the most likely failure point in the parameter space is found using a constrained optimization procedure. The effect of distribution is shown through parameter studies, and verification is provided by Monte Carlo simulation. As expected, time delay is shown to have a pronounced effect upon system robustness.     

Reliability modeling and optimization of K/N phased mission system with backup missions and global redundancy strategy

The mission success probability (MSP) is a critical indicator for phased mission systems (PMSs). In the modern aerospace industry, redundancy techniques, including component/phase redundancy, are commonly seen to increase the MSP of the whole system. These component/phase redundancies make the reliability analysis more complex. Meanwhile, one or more components are required for normal working for different subsystems, called the K/N structure. In this article, a Markov-process method is proposed for PMS with K/N subsystems and different redundancy strategies. Then, a universal system optimization model is proposed to optimize system structure and redundancy strategies for all subsystems at the same time. Then, an improved genetic algorithm (GA) is used to resolve the optimization problem. At last, a propulsion system is used as an engineering case, showing the proposed binary decision diagram-based method.     

Analysis of complex system reliability with correlated random vectors

The analysis of reliability of complex engineering systems remains a challenge in the field of reliability. It will be even more difficult if correlated random vectors are involved, which is generally the case as practical engineering systems invariably contain parameters that are mutually correlated. A new method for transforming correlated distributions, involving the Nataf transformation, is proposed that avoids the solution of integral equations; the method is based on the Taylor series expansion of the probability density function (PDF) of a bivariate normal distribution resulting in an explicit polynomial equation of the equivalent correlation coefficient. The required numerical results can be obtained efficiently and accurately.The proposed method for transformation of correlated random vectors is useful for developing a method for system reliability including complex systems with correlated random vectors. Based on the complete system failure process (originally defined as the development process of nonlinearity) and the fourth-moment method, the analysis of system reliability for elastic-plastic material avoids the identification of the potential failure modes of the system and their mutual correlations which are required in the traditional methods. Finally, four examples are presented – two examples to illustrate the potential of the new method for transformation of correlated random vectors, and two examples to illustrate the application of the proposed more effective method for system reliability.     

Criteria for evaluating protection from single points of failure for partially expanded fault trees

Fault tree analysis (FTA) is a technique that describes the combinations of events in a system which result in an undesirable outcome. FTA is used as a tool to quantitatively assess a system's probability for an undesirable outcome. Time constraints from concept to production in modern engineering often limit the opportunity for a thorough statistical analysis of a system. Furthermore, when undesirable outcomes are considered such as hazard to human(s), it becomes difficult to identify strict statistical targets for what is acceptable. Consequently, when hazard to human(s) is concerned a common design target is to protect the system from single points of failure (SPOF) which means that no failure mode caused by a single event, concern, or error has a critical consequence on the system. Such a design target is common with “by-wire” systems. FTA can be used to verify if a system is protected from SPOF. In this paper, sufficient criteria for evaluating protection from SPOF for partially expanded fault trees are proposed along with proof. The proposed criteria consider potential interactions between the lowest drawn events of a partial fault tree expansion which otherwise easily leads to an overly optimistic analysis of protection from SPOF. The analysis is limited to fault trees that are coherent and static.     

Reliability analysis of systems with discrete event data using association rules

With the popularization of big data, an increasing number of discrete event data have been collected and recorded during system operations. These events are usually stored in the form of event logs, which contain rich information of system operations and have potential applications in fault diagnosis and failure prediction. In manufacturing processes, various levels of correlations exist among the events, which can be used to predict the occurrence of failure events. However, two challenges remain to be solved for effective reliability analysis and failure prediction: (1) how to leverage various information from the event log to predict the occurrence of failure events and (2) how to model the effects of multiple correlations on the prediction. To address these issues, this paper proposes a novel reliability model, which integrates Cox proportional hazards (PHs) regression into survival analysis and association rule mining methodology. The model is used to evaluate the probability of failure event, which occurs within a certain period of time conditional on the occurrence history of correlated events. To estimate parameters and predict occurrence of failure events in the model, an effective algorithm is proposed based on piecewise-constant time axis division, Cox PHs model, and maximum likelihood estimation. Unlike the existing literature, our model focuses on the interactions among events. The applicability of the proposed model is illustrated through a case study of a manufacturing company. Sensitivity analysis is conducted to illustrate the effectiveness of the proposed model.     

Rigorous uncertainty quantification without integral testing

We describe a rigorous approach for certifying the safe operation of complex systems that bypasses the need for integral testing. We specifically consider systems that have a modular structure. These systems are composed of subsystems, or components, that interact through unidirectional interfaces. We show that, for systems that have the structure of an acyclic graph, it is possible to obtain rigorous upper bounds on the probability of failure of the entire system from an uncertainty analysis of the individual components and their interfaces and without the need for integral testing. Certification is then achieved if the probability of failure upper bound is below an acceptable failure tolerance. We demonstrate the approach by means of an example concerned with the performance of a fractal electric circuit.     

基于模糊故障树的军用气象物资包装可靠性分析

应用模糊故障树分析方法对军用气象物资包装可靠性进行了系统分析,简要介绍了模糊故障树分析方法的基本理论,利用专家判断和模糊集理论相结合的方法,评估了故障树底事件发生的模糊失效概率。并以"TFS-1通风干湿表包装"为例,建立了包装系统的故障树,采用下行法求解了引起顶事件发生的最小割集,定量分析计算,得出模糊失效率为0.0705,同时计算了各底事件的重要度。模糊故障树分析方法对于提高军用气象物资包装防护能力,确保物资装备质量,具有非常重要的意义。     

FAILURE ANALYSIS FOR AN AIRBAG INFLATOR BY PETRI NETS

Petri nets are useful for modelling a variety of asynchronous and concurrent systems, such as automated manufacturing, computer fault tolerant systems, and communication networks. This study employs an airbag inflator system as an example to demonstrate a Petri net approach to failure analysis. This paper uses Petri nets to study minimum cut sets finding, marking transfer, and dynamic behaviour of system failure. For Petri net models incorporating sensors, fault detection and higher-level fault avoidance is dealt with. Compared with fault trees that present only static logic relations between events, Petri nets indeed offer more capabilities in the scope of failure analysis. © 1997 John Wiley & Sons, Ltd.     

用分解—集结法研究复杂转子—轴承系统的稳定性

本文探讨应用大系统稳定性理论的分解—集结法研究复杂转子—轴承系统的运动稳定性问题。与目前常采用的传统分析方法，如特征根判稳法及派生的各种稳定性判据相比，这种方法的独到之处在于其不仅能提供整个系统的稳定性信息，还能反映子系统及其复合关系对整体系统稳定性的作用及影响等信息。这是传统的整体直接处理方式较难达到的。本文举出几个实例验证了这一系统工程方法的有效性和独特性，其直接应用背景是大型汽轮发电机组轴系的稳定性问题。     

Enhancement of seismic sustainability of critical facilities through system analysis

Proper functioning of critical facilities such as acute care hospitals and fire stations are essential in the aftermath of a severe earthquake. For these facilities to remain operational, not only their building structures must remain safe for continued occupancy, but also their nonstructural components/systems must remain functional. Motivated by a previous study by the second author, this paper demonstrates a probabilistic system analysis for enhancing the sustainability of deficient critical facilities. The analysis, in principle, utilizes event and fault tree procedures to evaluate the system fragility defined by the probability that the system will not perform its intended purpose. Enhancement of sustainability is demonstrated by using a representative numerical model of an existing facility. The study shows that by selecting the most vulnerable components, utilizing the concept of annual sensitivity index, the annual probability of failure can be reduced significantly in a cost-effective way.     

2008 ASEM Conference Announcement

Abstract:

This article describes the development of a new, integrated approach to system safety engineering. The approach is illustrated in a case study involving the design of a high-pressure experimental research facility. The system safety engineering framework incorporates five main groups of activities, including system design visualization, failure modes and effects analysis, multidisciplinary teaming, benchmarking, and enterprise management. Coupling a systems engineering approach with the recognized principals of failure mode avoidance was found to significantly enhance the engineering design process.     

A systemic overview of the evolution of electrical engineering: aSouth African perspective

The paper uses the systems approach to analyse how the discipline of electrical engineering has evolved over the years and to ascertain whether the custodians of the discipline have kept pace with this evolution. Particular attention is given to the knowledge system, the societal system, the education system, the world of work and the learned societies. The paper focuses on understanding the various dynamics among the systems so that strategic attention can be given to the relationships between subsystems, rather than specific solutions     

An approximation approach for uncertainty quantification using evidence theory

Over the last two decades, uncertainty quantification (UQ) in engineering systems has been performed by the popular framework of probability theory. However, many scientific and engineering communities realize that there are limitations in using only one framework for quantifying the uncertainty experienced in engineering applications. Recently evidence theory, also called Dempster–Shafer theory, was proposed to handle limited and imprecise data situations as an alternative to the classical probability theory. Adaptation of this theory for large-scale engineering structures is a challenge due to implicit nature of simulations and excessive computational costs. In this work, an approximation approach is developed to improve the practical utility of evidence theory in UQ analysis. The techniques are demonstrated on composite material structures and airframe wing aeroelastic design problem.