Minimal Path Sets Research Articles

Mining Similar Aspects for Gene Similarity Explanation Based on Gene Information Network.

Analysis of gene similarity not only can provide information on the understanding of the biological roles and functions of a gene, but may also reveal the relationships among various genes. In this paper, we introduce a novel idea of mining similar aspects from a gene information network, i.e., for a given gene pair, we want to know in which aspects (meta paths) they are most similar from the perspective of the gene information network. We defined a similarity metric based on the set of meta paths connecting the query genes in the gene information network and used the rank of similarity of a gene pair in a meta path set to measure the similarity significance in that aspect. A minimal set of gene meta paths where the query gene pair ranks the highest is a similar aspect, and the similar aspect of a query gene pair is far from trivial. We proposed a novel method, SCENARIO, to investigate minimal similar aspects. Our empirical study on the gene information network, constructed from six public gene-related databases, verified that our proposed method is effective, efficient, and useful.

Minimal path set importance in complex systems

To find the best mode for system design in reliability optimization, risk engineers around the world use the importance measure as a basic tool. This paper introduces a new importance measure taking into account minimal path sets of the system. It helps to optimize the system designs that occur in many situations. For instance, this importance measure can be used (a) in identifying important components of any complex system and (b) solving constrained redundancy optimization problems. This is illustrated by providing two heuristic algorithms. In the first algorithm, this measure is used to find important components of any complex system ensuring improved system reliability. The second algorithm is used to solve a constrained redundancy optimization problem for any general coherent system giving (near) optimal solutions in 1-neighborhood. The results show that the new importance measure is easily applicable, unlike the classical ones. Hence, it serves as a very useful tool in measuring the important component(s) and solving constrained redundancy optimization problems of complex systems. Thus, it can be considered as a good alternative to the existing importance measures.

An optimal delay routing algorithm considering delay variation in the LEO satellite communication network

In the LEO satellite communication network, delay is not fixed but varying in a regular manner. Moreover, traditional routing planning algorithms lose sight of delay variation and need intensive computation. These have led to incomprehensive performance assessment of the satellite network and large resource occupancy. Effective routing scheme with uncertain delay information is the novel problem that we solve in this paper. An optimal delay routing algorithm called delay queuing graphical evaluation and review technique minimal path set is proposed. First, based on the delay queuing graphical evaluation and review technique (DQ-GERT) and the minimum path set, the satellite network is characterized and all valid candidate paths are selected. Second, the delay evaluation index that includes delay and its variation to evaluate possible routes is derived. Simulation results show the superiority of the proposed algorithm by comparing with existing algorithms.

Reliability analysis for electric power systems of more-electric aircraft based on the minimal path set

With the raise of aircraft performance and the increasing electrical applications, the more-electrical or all-electric aircraft will become the main aircraft model in future. The reliability assessment of aircraft electric power system is critical to guarantee the reliable operation of the aircraft . A reliability assessment method for complex power system of large aircraft such as Boeing 787 has been described in this paper. First the aircraft power distribution system is abstracted as a topology diagram based on the graph theory. Then the minimal path sets are searching from the source node to the load nodes by the depth-first search. These path sets can represent the normal power supply path of the electric power system. Finally, using the raw reliability data of components, the reliability function of various important buses is established and the reliability index of large aircraft power distribution system is calculated. This assessment method can be used to analyze and assess the reliability of power supply and distribution system of different models and to provide a reference for the design and analysis of complex electric power system of civil aircraft.

Comparisons of coherent systems under the time-transformed exponential model

The coherent systems are basic concepts in reliability theory and survival analysis. They contain as particular cases the popular series, parallel and k-out-of-n systems (order statistics). Many results have been obtained for them by assuming that the component lifetimes are independent. In many practical cases, this assumption is unrealistic. In this paper, we study them by assuming a time-transformed exponential model for the joint distribution of the component lifetimes. This model is equivalent to the frailty model which assumes that they are conditionally independent given a common risk parameter (which represents the common environment risk). Under this model, we obtain explicit expressions for the system reliability function and comparison results for the main stochastic orders. We obtain both expressions from minimal path sets and those from minimal survival signatures. Some aging classes and the system residual lifetime (under different assumptions) are studied as well.

Expanding a complex networked system for enhancing its reliability evaluated by a new efficient approach

The economic development and social well-being of a society are highly dependent on many complex networked systems, such as power transmission and distribution, telecommunications, transportation and so forth, which calls for the enhancement of their reliable functioning. To fulfil this purpose, the first essential step is to effectively evaluate their reliability, which is intractable since they usually contain a large amount of components organized via complex structures. To deal with this computational complexity, this research proposes a new network reliability evaluation approach by identifying minimal path sets that may have edges in common, but consist of only parallel and series structures when considered together. Our proposed approach can efficiently approximate network reliability more precisely than the existing edge-packing methods. We then propose a multi-objective optimization approach to solve the problem of expanding a complex networked system to enhance its reliability. The solutions obtained by our proposed approach can help in well understanding the trade-off between the reliability and cost of network expansion solutions. Finally, an application of the proposed method to the high-speed railway network of China is implemented.

Reliability calculation of AC/DC hybrid distribution network with a solid‐state transformer

With extensive access of distributed energy resources and DC loads, the traditional 10 kV AC distribution network has greatly increased the number of converters and reduced the reliability of power supply. A solid-state transformer (SST) containing AC and DC terminals to build AC/DC hybrid distribution networks has become the focus of the current research. This study presents an AC/DC hybrid distribution network structure with 10 kV AC, 10 kV DC, ±375 V DC, and 380 V AC four voltage levels. In this network, the load is data centre, which needs high security for power supply reliability. According to the characteristics of this network, this study takes the reliability evaluation by using the minimum path set method and the state enumeration method, and the reliability of this new structure with SST is calculated. Through the study of a numerical example, the results show that after adding the multi-terminal SST, the reliability of the AC/DC hybrid distribution network is suitable for data centre load, and the quantity of the converters can decrease.

An efficient searching method for minimal path vectors in multi-state networks

Searching for minimal path vectors (MPVs) is an important topic in solving network related problems, especially for the evaluation of network reliability. One of the popular approaches, namely the three-stage method (TSM), is influenced deeply on the efficiency of searching for minimal path vectors in multi-state networks (MSN). TSM consists of three stages, i.e., searching for all minimal path sets, searching for all MPVs, and calculating union probability on MPVs. After reviewing previous works in the literaure, this paper proposes a more efficient method based on cyclic check on the candidates of MPVs, which can do an efficient searching for MPVs in MSNs and even reduce the three-step approach to two-step approach. Benchmarking with the well-known algorithms are made in this paper, and more complicated networks are also examined for verification of the proposed method.

Design and Reliability Evaluation of Gamma-Minus Interconnection Network

Gamma Interconnection Network (GIN) is characterized as Redundant Multistage Interconnection Network (MIN) which is considered as a potential candidate for use in broadband communications. Several advancements have been made to improve Reliability indices such as Terminal Reliability (TR), Broadcast Reliability (BR) and Network Reliability (NR) of these networks. But inspite of these advancements, there are certain issues which are yet to be explored such as Complexity, Cost, Number of disjoint paths on presumption that source/destination are failure free. Most of the work done in the literature addresses TR only and less work has been done on analysis of BR and NR. In literature networks, [Formula: see text] size has been explored and no attention has been paid to bigger network sizes although reliability of bigger size network is important for parallel processing systems. In this paper, existing class of Gamma Networks has been studied extensively and modifications have been proposed in existing Gamma Network which minimizes or resolves most of the limitations mentioned above. The proposed Gamma-Minus Network has more redundant paths than other networks. Proposed Network has been compared with some recently introduced members of this class. The results show that newly proposed Gamma-Minus Network has better reliability with lowest cost and path length and provides disjoint minimal-path set for [Formula: see text] to [Formula: see text] network size. The routing used in this paper eliminates the backtracking overhead which minimizes transmission delay.

On computing the reliability of opportunistic multihop networks with Mobile relays

AbstractOpportunistic multihop networks with mobile relays recently have drawn much attention from researchers across the globe due to their wide applications in various challenging environments. However, because of their peculiar intrinsic features like lack of continuous connectivity, network partitioning, highly dynamic behavior, and long delays, it is very arduous to model and effectively capture the temporal variations of such networks with the help of classical graph models. In this work, we utilize an evolving graph to model the dynamic network and propose a matrix‐based algorithm to generate all minimal path sets between every node pair of such network. We show that these time‐stamped‐minimal‐path sets (TS‐MPS) between each given source‐destination node pair can be used, by utilizing the well‐known Sum‐of‐Disjoint Products technique, to generate various reliability metrics of dynamic networks, ie, two‐terminal reliability of dynamic network and its related metrics, ie, two‐terminal reliabilities of the foremost, shortest, and fastest TS‐MPS, and Expected Hop Count. We also introduce and compute a new network performance metric−Expected Slot Count. We use two illustrative examples of dynamic networks, one of four nodes, and the other of five nodes, to show the salient features of our technique to generate TS‐MPS and reliability metrics.

Fault tree analysis of large-scale blackout accidents

Fault tree analysis method is used to analyze the large-scale blackout accidents. Minimum cut sets and minimum path sets of large-scale blackout accidents are calculated, and the structural importance degree of the accidents is analyzed according to the minimum path sets. Direct factors that cause large-scale blackout accidents are determined. Effective measures are put forward to prevent large-scale blackouts, and the theoretical basis is put forward to prevent large-scale blackouts.

An Efficient Algorithm for Enumerating all Minimal Paths of a Graph

The enumeration of all minimal paths between a terminal pair of a given graph is widely used in a lot of applications such as network reliability assessment. In this paper, we present a new and efficient algorithm to generate all minimal paths in a graph G(V, E). The algorithm proposed builds the set of minimal paths gradually, starting from the source nodes. We present two versions of our algorithm; the first version determines all feasible paths between a pair of terminals in a directed graph without cycle, and this version runs in linear time O(|V| + |E|). The second version determines all minimal paths in a general graph (directed and undirected graph). In order to show the process and the effectiveness of our method, an illustrative example is presented for each case.

Approximate Method to Evaluate Reliability of Complex Networks

This paper deals with the issue of reliability evaluation in complex networks, in which both link and node failures are considered, and proposes an approximate method based on the minimal paths between two specified nodes. The method requires an algorithm for transforming the set of minimal paths into a sum of disjoint products (SDP). To reduce the computation burden, in the first stage, only the links of the network are considered. Then, in the second stage, each term of the set of disjoint link-products is separately processed, taking into consideration the reliability values for both links and adjacent nodes. In this way, a reliability expression with a one-to-one correspondence to the set of disjoint products is obtained. This approximate method provides a very good accuracy and greatly reduces the computation for complex networks.

Investigation of extremely severe traffic crashes using fault tree analysis

ABSTRACTThis study aimed to use the fault tree analysis (FTA) to investigate the casual relationship among the event and causes contributing to extremely severe crash that leads to more than 10 deaths. The characteristics of extremely severe traffic crashes were compared with those of normal crashes in terms of gender, driving experience, road technical level, road alignment, time, and weather conditions. A fault tree was developed to provide an overview of the basic causes and their causal relationship. The minimal cut sets were derived to reveal the causal relationships among events and causes contributing to extremely severe crashes. Then, quantitative assessment was conducted to evaluate the importance of various events. The results can help to prioritize actions and resources for crash prevention. Finally, the minimal path set analysis was conducted to identify the minimal sets of basic events needed to be prevented so that extremely severe crash will not occur.

Sand casting safety assessment for foundry enterprises: fault tree analysis, Heinrich accident triangle, HAZOP-LOPA, bow tie model.

Sand casting operations, though commonplace, pose a significant threat of explosion accidents. This paper presents a novel sand casting safety assessment technique based on fault tree analysis, Heinrich accident triangle, hazard and operability–layer of protection analysis (HAZOP–LOPA) and bow tie model components. Minimal cut sets and minimal path sets are first determined based on fault tree analysis, then the frequency of sand casting explosion accidents is calculated based on the Heinrich accident triangle. Third, the risk level of venting quality can be reduced by adopting HAZOP–LOPA; the residual risk level of venting quality remains excessive even after adopting two independent protective layers. The bow tie model is then adopted to determine the causes and consequences of venting quality. Five preventative measures are imposed to enhance the venting quality of foundry sand accompanied by 16 mitigative safety measures. Our results indicate that the risk attributable to low foundry sand venting quality can be minimized via bow tie analysis.

Path Sets Combination Method for Reliability Analysis of Phased-Mission Systems Based on Cumulative Exposure Model

The modeling of phased-mission systems is difficult and the solving process is complex because of the relevance of the phase tasks and the sharing of components existing in different phases or between phases. To solve the problem, based on the cumulative exposure model, the path sets combination method of phased-mission systems is proposed. Aiming at the problem of the cross-stage correlation of components and its different failure rate in each phase, the cumulative exposure model considering the historical damage of components is used to solve by obtaining the cumulative damage distribution of each component in each phase. Firstly, a phased-mission systems reliability model is build by mapping phased-mission system fault trees into a Bayesian network. By traversing the Bayesian network, the minimal path sets of each phase are obtained. Secondly, the disjoint formulas introduced by variable elimination method are used to do the disjoint operation of the minimal path sets of each phase and the conditional probability relations of the common components are used to reduce the minimal path sets scale. Finally, the minimum disjoint path sets of each phase are combined and summed according to the component conditional probability relation. The path sets combination method of phased-mission systems avoids the large conditional probability table, large storage and large computation problems caused by the excessive discrete states in the traditional Bayesian method and the problem that the PMS-BDD method has strict requirements for variable ordering and is difficult to solve the system reliability with multiple failure distribution types of components. In the end, a phased-mission systems reliability modeling and solving is carried out for a geosynchronous orbit satellite, and compared with the PMS-BDD method, which verifies the correctness of the method.

ACTIVE REDUNDANCY ALLOCATION FOR COHERENT SYSTEMS WITH INDEPENDENT AND HETEROGENEOUS COMPONENTS

This paper studies the allocation of active redundancies to coherent systems on the context that the base and redundancy components have mutual independent lifetimes. For systems with two symmetric components and systems with one component's minimal cut sets (minimal path sets) covering those of another, we derive sufficient conditions to compare the resultant system lifetimes. Some numerical examples are also presented to illustrate the theoretical results.

Mine safety assessment based on basic event importance: grey relational analysis and bow tie model.

Safety assessments are a crucial first step in preventing coal and gas outburst accidents. The main purpose of this study was to create a new accident prevention technique using a novel safety assessment method based on fault tree basic event importance, grey relational analysis and the bow tie model. The innovation of the proposed method lies in generating the composite importance of a basic event from the fundamental importance via grey relational analysis; bow tie analysis serves to reveal the most critical basic event. First, the minimal cut sets and minimal path sets of a coal and gas outburst accident are determined by fault tree analysis. The role of minimal cut and path sets is determined and the coal and gas outburst occurrence frequency is calculated accordingly. Second, the structure, probability, critical and Fussell–Vesely importance ranked basic events differently due to different aspects of the basic events as investigated. We establish a composite importance to represent single basic events and achieved new ranking results by grey relational analysis. Third, the critical basic event low permeability coefficient is analysed via bow tie model and safety measures are defined which prevent the dangerous consequences of a low permeability coefficient. An actual coal and gas outburst accident is used as a case study to test the feasibility and effectiveness of the proposed method.

Reliability evaluation of circular k-out-of-n: G balanced systems through minimal path sets

This paper studies a circular k-out-of-n: G balanced systems with identical and independent spatially distributed units. The system consists of an even number of units n which have constant survival probability r and failure probability 1 – r. The system is operating if at least k units are operating and it is balanced. A new balance definition is proposed for this system and the system reliability is calculated when the existing and the proposed system balance conditions are considered. The minimal path sets of the system are considered in the evaluation of the system reliability. The difference between the system reliability values reinforces the need to carefully select the system balance definition, depending on the system.

Risk analysis of dairy safety incidents in China

In order to improve the condition of food safety management and prevent the dairy safety incidents effectively, supply chain and fault tree analysis (FTA) can be integrated to analyze the cause of such issues comprehensively. As a result, the main cause of the dairy incident can be found. Based on the analysis and identification of hazards in dairy foods across the entire supply chain from raw material sources to end-customers, the basic events which can lead to dairy incidents are given, and the accident tree of dairy foods is constructed. After a qualitative and quantitative analysis on the tree on the tree, the minimum cut sets and path sets are calculated. Then, the accidents mode and the accidents control mode are obtained, respectively. The Sanlu milk powder incident and the Fuyang milk powder affair are selected as the cases to prove the feasibility of FTA. We have analyzed 34 basic events quantitatively. Then 114 minimum cut sets and 78 minimum path sets are obtained. From the analysis of structure importance degree of the basic events, the most critical factors are production enterprises lack feedback mechanism (X1), Food and Drug Administration failed to sample (X33), Ministry of Health and other government departments overlook or don't have a good supervision (X34), supermarkets and other distributors make a wrong judgement and sell unsafe dairy (X32), the industrial and commercial department failed to sample (X31), personal preference (X2), family members need dairy (X3), supermarkets and other dealers promote unsafe dairy (X4), and their structural importance coefficients are 1, 1, 1, 0.567, 0.5, 0.25, 0.25, and 0.25, respectively. The corresponding dairy safety strategies are discussed qualitatively, which include: dairy enterprise establishes a feedback mechanism and strengthens industry self-regulation; regulatory authorities strengthen supervision; supermarket and other dealers enhance self-construction; consumers learn how to differentiate between unhealthy and healthy dairy foods; the government makes related food safety laws.