Survivability of series–parallel systems with multilevel protection

In this paper, we consider vulnerable systems which can have different states corresponding to different combinations of available elements composing the system. Each state can be characterized by a performance rate, which is the quantitative measure of a system's ability to perform its task. Both the impact of external factors (attack) and internal causes (failures) affect system survivability, which is determined as the probability of meeting a given demand.In order to increase the system's survivability a multilevel protection can be applied to its subsystems. In such systems, the protected subsystems are destroyed by external impacts only if all of the levels of their protection are destroyed.The paper describes an algorithm for evaluating the survivability of series–parallel systems with arbitrary configuration of multilevel protection. The algorithm is based on a composition of Boolean and the Universal Generating Function techniques. The adaptation of the algorithm for numerical implementation is suggested.Illustrative examples are presented.     

Protection Survivability Importance in Systems with Multilevel Protection

This paper considers systems that can have different states corresponding to different combinations of available elements constituting the system. Each state can be characterized by a performance rate, which is the quantitative measure of a system's ability to perform its task. Both the impact of external factors (attack) and internal causes (failures) affect system survivability, which is determined as the probability of meeting a given demand. In order to increase the system's survivability a multilevel protection is applied to its subsystems. This means that a subsystem and its inner level of protection are in turn protected by the protection of an outer level. This double‐protected subsystem has its outer protection and so forth. In such systems, the protected subsystems can be destroyed only if all of the levels of their protection are destroyed. Each level of protection can be destroyed only if all of the outer levels of protection are destroyed. In such systems, different protections play different roles in providing for the system's survivability. The evaluation of the relative influence of the protections' survivability on the survivability of the entire system provides useful information about the importance of these protections. The protection survivability importance index is introduced in order to evaluate this influence and an algorithm for evaluating the index is presented. The relevancy of protection is also considered. Illustrative examples are presented. Copyright © 2004 John Wiley & Sons, Ltd.     

Optimal multilevel protection in series–parallel systems

This paper considers vulnerable systems that can have different states corresponding to different combinations of available elements composing the system. Each state can be characterized by a performance rate, which is the quantitative measure of a system's ability to perform its task. Both the impact of external factors (attack) and internal causes (failures) affect system survivability, which is determined as the probability of meeting a given demand.In order to increase the system's survivability a multilevel protection is applied to its subsystems. This means that a subsystem and its inner level of protection are in their turn protected by the protection of an outer level. This double-protected subsystem has its outer protection and so forth. In such systems, the protected subsystems can be destroyed only if all of the levels of their protection are destroyed. Each level of protection can be destroyed only if all of the outer levels of protection are destroyed.In such systems, different protections play different roles in providing for the system's survivability. Subject to budget limitations a question arises which protections should be applied to obtain the desired survivability. An algorithm for solving the protection cost minimization problem subject to survivability constraint is presented in the paper. The algorithm is based on a universal generating function technique used for system survivability evaluation and on a genetic algorithm used as an optimization engine.Illustrative example is presented.     

Optimizing survivability of multi-state systems with multi-level protection by multi-processor genetic algorithm

In this paper we consider vulnerable systems which can have different states corresponding to different combinations of available elements composing the system. Each state can be characterized by a performance rate, which is the quantitative measure of a system's ability to perform its task. Both the impact of external factors (stress) and internal causes (failures) affect system survivability, which is determined as probability of meeting a given demand.In order to increase the survivability of the system, a multi-level protection is applied to its subsystems. This means that a subsystem and its inner level of protection are in their turn protected by the protection of an outer level. This double-protected subsystem has its outer protection and so forth. In such systems, the protected subsystems can be destroyed only if all of the levels of their protection are destroyed. Each level of protection can be destroyed only if all of the outer levels of protection are destroyed.We formulate the problem of finding the structure of series–parallel multi-state system (including choice of system elements, choice of structure of multi-level protection and choice of protection methods) in order to achieve a desired level of system survivability by the minimal cost. An algorithm based on the universal generating function method is used for determination of the system survivability. A multi-processor version of genetic algorithm is used as optimization tool in order to solve the structure optimization problem. An application example is presented to illustrate the procedure presented in this paper.     

Optimal separation of elements in vulnerable multi-state systems

In this paper we consider vulnerable systems, which can have different states corresponding to different combinations of available elements composing the system. Each state can be characterized by a system performance rate, which is the quantitative measure of a system’s ability to perform its task. Both the impact of external factors (attack) and internal causes (failures) affect system survivability, which is determined as probability of meeting a given demand.One of the ways to enhance system survivability is to separate elements with the same functionality (parallel elements). Since system elements can have different performance rates and different availability, the way in which they are separated strongly affects system survivability. In this paper we formulate the problem of how to separate the elements of series-parallel system in order to achieve a maximal possible level of system survivability by the limited cost.An algorithm based on the universal moment generating function method is suggested for determination of the vulnerable series-parallel multi-state system survivability. A genetic algorithm is used as optimization tool in order to solve the structure optimization problem.     

Optimizing survivability of vulnerable series–parallel multi-state systems

In this paper we consider vulnerable systems which can have different states corresponding to different combinations of available elements composing the system. Each state can be characterized by a system performance rate, which is the quantitative measure of a system's ability to perform its task. Both the impact of external factors (attack) and internal causes (failures) affect system survivability which is determined as probability of meeting a given demand.We formulate the problem of finding structure of series–parallel multi-state system (including choice of system elements, their separation and protection) in order to achieve a desired level of system survivability by the minimal cost.An algorithm based on the universal generating function method is suggested for determination of the vulnerable series–parallel multi-state system survivability. A genetic algorithm is used as optimization tool in order to solve the structure optimization problem.     

Minmax defense strategy for complex multi-state systems

This paper presents a general optimization methodology that merges game theory and multi-state system survivability theory. The defender has multiple alternatives of defense strategy that presumes separation and protection of system elements. The attacker also has multiple alternatives of its attack strategy based on a combination of different possible attack actions against different groups of system elements. The defender minimizes, and the attacker maximizes, the expected damage caused by the attack (taking into account the unreliability of system elements and the multi-state nature of complex series-parallel systems). The problem is defined as a two-period minmax non-cooperative game between the defender who moves first and the attacker who moves second. An exhaustive minmax optimization algorithm is presented based on a double-loop genetic algorithm for determining the solution. A universal generating function technique is applied for evaluating the losses caused by system performance reduction. Illustrative examples with solutions are presented.     

Block diagram method for analyzing multi-state systems with uncovered failures

The paper suggests a modification of the generalized reliability block diagram (RBD) method for evaluating reliability and performance indices of multi-state systems with uncovered failures. Such systems (or their subsystems) can fail to perform their task in the case of undetected failure of any one of their elements. Examples of this effect can be found in computing systems, electrical power distribution networks, pipe lines carrying dangerous materials etc. The suggested method based on a universal generating function technique allows performance distribution of complex multi-state series-parallel system with uncovered failures to be obtained using a straightforward recursive procedure. Illustrative examples are presented.     

Reliability analysis of complex systems using symbolic logic

System reliability is an important parameter in the operation of modern utility systems, spacecraft and manufacturing facilities. Over the last several decades researchers have used many different methods to determine complex system reliability. This paper uses new and novel techniques which are based on artificial intelligence and expert systems to determine system reliability. This work is based on heuristic search and a symbolic logic system which provides symbolic representation for overall system reliability when there is a single input and single output. Pivotal decomposition is used on a recursive basis to repeatedly reduce complex systems/subsystems to simpler systems. Eventually, these simpler systems are further reduced into easily resolved series-parallel arrangements. This symbolic logic system uses a heuristic based ‘hill climbing’ search algorithm. The algorithm identifies the pivotal or complex component. Once this pivotal component is selected, additional procedures are used to symbolically recognize other components within the resulting subgraphs which are made superfluous by the selection of the pivot component. These superfluous components are removed, and the simplification process is allowed to continue on a recursive basis. Once further recursive analysis is not needed, additional rules are employed to reduce the result to a system recognizable form in terms of series-parallel components. Finally, a ‘symbolic processor’ is used to convert this recognized form into a symbolic sum of products equation representing the overall system.     

Multi-state systems with selective propagated failures and imperfect individual and group protections

The paper presents an algorithm for evaluating performance distribution of complex series-parallel multi-state systems with propagated failures and imperfect protections. The failure propagation can have a selective effect, which means that the failures originated from different system elements can cause failures of different subsets of elements. Individual elements or some disjoint groups of elements can be protected from propagation of failures originated outside the group. The protections can fail with given probabilities. The suggested algorithm is based on the universal generating function approach and a generalized reliability block diagram method. The performance distribution evaluation procedure is repeated for each combination of propagated failures and protection failures. Both an analytical example and a numerical example are provided to illustrate the suggested algorithm.     

Reliability optimization of series-parallel systems with a choice of redundancy strategies using a genetic algorithm

This paper proposes a genetic algorithm (GA) for a redundancy allocation problem for the series-parallel system when the redundancy strategy can be chosen for individual subsystems. Majority of the solution methods for the general redundancy allocation problems assume that the redundancy strategy for each subsystem is predetermined and fixed. In general, active redundancy has received more attention in the past. However, in practice both active and cold-standby redundancies may be used within a particular system design and the choice of the redundancy strategy becomes an additional decision variable. Thus, the problem is to select the best redundancy strategy, component, and redundancy level for each subsystem in order to maximize the system reliability under system-level constraints. This belongs to the NP-hard class of problems. Due to its complexity, it is so difficult to optimally solve such a problem by using traditional optimization tools. It is demonstrated in this paper that GA is an efficient method for solving this type of problems. Finally, computational results for a typical scenario are presented and the robustness of the proposed algorithm is discussed.     

Importance of protections against intentional attacks

The paper presents a generalized model of damage caused to a complex multi-state series-parallel system by intentional attack. The model takes into account the separation and protection of system elements. Protection importance indices are suggested that can be used for tracing bottlenecks in defense strategy and in identifying the most important protections. An algorithm for evaluating these indices is presented that uses a universal generating function technique for obtaining the system performance distribution. Illustrative example is presented.     

Characterizing secondary debris impact ejecta

All spacecraft in low earth orbit are subject to high-speed impacts by meteoroids and orbital debris particles. These impacts can damage flight-critical systems, which can in turn lead to catastrophic failure of the spacecraft. In addition to threatening the operation of the spacecraft itself, on-orbit impacts also generate a significant amount of damaging ricochet ejecta particles. These high-speed particles can destroy critical external spacecraft subsystems, which also poses a threat to the spacecraft and its inhabitants. Since the majority of on-orbit debris impacts are expected to occur at oblique angles, the characterization of ricochet debris created in an orbital debris particle impact is an issue that must be addressed. This paper presents the results of a study performed to develop an empirical model that characterizes the secondary ejecta created by a high speed impact on a typical aerospace structural surface. Specifically, the model predicts the spread and trajectory of ricochet debris particles created in a hypervelocity impact as well as the size an velocity of the most damage particle in the ricochet debris cloud. Results obtained using the model are compared with experimental results and predictions obtained in a previous study.     

Allocation of test times in multi-state systems for reliability growth testing

This paper generalizes a reliability growth test allocation problem to series-parallel multi-state systems. An algorithm, which determines the testing time for each system element in order to maximize the entire system reliability when total testing resources are limited, is suggested. The algorithm can handle both repairable and non-repairable multi-state systems. The Crow/AMSAA reliability growth model is used to evaluate the influence of testing time on the reliability of the elements composing the system. System reliability is defined as the ability of the system to satisfy variable demand represented by a cumulative demand curve. To evaluate multi-state system reliability, a universal generating function technique is applied. A Genetic Algorithm (GA) is used as an optimization technique. The basic GA procedures adapted to the given problem are presented. Examples of the determination of reliability growth test plans are demonstrated.     

Determination of Pareto frontier in multi-objective maintenance optimization

The objective of a maintenance policy generally is the global maintenance cost minimization that involves not only the direct costs for both the maintenance actions and the spare parts, but also those ones due to the system stop for preventive maintenance and the downtime for failure. For some operating systems, the failure event can be dangerous so that they are asked to operate assuring a very high reliability level between two consecutive fixed stops. The present paper attempts to individuate the set of elements on which performing maintenance actions so that the system can assure the required reliability level until the next fixed stop for maintenance, minimizing both the global maintenance cost and the total maintenance time. In order to solve the previous constrained multi-objective optimization problem, an effective approach is proposed to obtain the best solutions (that is the Pareto optimal frontier) among which the decision maker will choose the more suitable one. As well known, describing the whole Pareto optimal frontier generally is a troublesome task. The paper proposes an algorithm able to rapidly overcome this problem and its effectiveness is shown by an application to a case study regarding a complex series-parallel system.     

Auxiliary subsystems of a General-Purpose IGBT Stack for high-performance laboratory power converters

A PWM converter is the prime component in many power electronic applications such as static UPS, electric motor drives, power quality conditioners and renewable-energy-based power generation systems. While there are a number of computer simulation tools available today for studying power electronic systems, the value added by the experience of building a power converter and controlling it to function as desired is unparalleled. A student, in the process, not only understands power electronic concepts better, but also gains insights into other essential engineering aspects of auxiliary subsystems such as start-up, sensing, protection, circuit layout design, mechanical arrangement and system integration. Higher levels of protection features are critical for the converters used in a laboratory environment, as advanced protection schemes could prevent unanticipated failures occurring during the course of research. This paper presents a laboratory-built General-Purpose IGBT Stack (GPIS), which facilitates students to practically realize different power converter topologies. Essential subsystems for a complete power converter system is presented covering details of semiconductor device driving, sensing circuit, protection mechanism, system start-up, relaying and critical PCB layout design, followed by a brief comparison to commercially available IGBT stacks. The results show the high performance that can be obtained by the GPIS converter.     

中小跨径梁桥地震易损性研究

为对桥梁系统地震易损性进行准确评估,结合Copula函数技术,提出基于串-并联组合体系的桥梁系统易损性分析方法。桥墩是桥梁抗震中的控制构件且较难修复,采用串联体系将多个桥墩进行组合,对于修复难度较低的桥台及支座构件,采用并联体系进行模拟。在此基础上,将桥墩、桥台及支座三类构件体系进行串联,构成桥梁系统的串-并联组合体系。以三跨连续箱梁桥为例,阐明了基于串-并联体系的桥梁系统易损性分析方法,并将分析结果与基于串联体系的桥梁系统易损性进行对比。结果表明:对于中小跨径的连续梁桥,基于单一串联体系会明显高估桥梁系统的易损性,相对于串-并联体系,在轻微、中等、严重及完全四种破坏状态下,其中位值偏差在纵桥向分别为22.2%、20.7%、20.5%及24.6%;在横桥向分别为30.0%、16.1%、9.8%及11.3%,基于串-并联组合体系建立桥梁系统地震易损性更切实合理。     

Optimal load distribution in series-parallel systems

This paper presents an algorithm for determining an optimal loading of elements in series-parallel systems. The optimal loading is aimed at achieving the greatest possible expected system performance subject to repair resource constraint. The model takes into account the dependence of elements’ failure rates on their load. The optimization algorithm uses a universal generating function technique for evaluating the expected system performance, and a genetic algorithm for determining the optimal load distribution. An illustrative example of load distribution optimization is presented.     

A joint reliability-redundancy optimization approach for multi-state series-parallel systems

In this paper, we present a practical approach for the joint reliability-redundancy optimization of multi-state series-parallel systems. In addition to determining the optimal redundancy level for each parallel subsystem, this approach also aims at finding the optimal values for the variables that affect the component state distributions in each subsystem. The key point is that technical and organizational actions can affect the state transition rates of a multi-state component, and thus affect the state distribution of the component and the availability of the system. Taking this into consideration, we present an approach for determining the optimal versions and numbers of components and the optimal set of technical and organizational actions for each subsystem of a multi-state series-parallel system, so as to minimize the system cost while satisfying the system availability constraint. The approach might be considered to be the multi-state version of the joint system reliability-redundancy optimization methods.