A Simple Method to Derive Minimal Cut Sets for a Non-coherent Fault Tree

Minimal cut sets （or prime implicants： minimal combinations of basic event conditions leading to system failure） are important information for reliability/safety analysis and design. To obtain minimal cut sets for general non-coherent fault trees, including negative basic events or multi-valued basic events, a special procedure such as the consensus rule must be applied to the results obtained by logical operations for coherent fault trees, which will require more steps and time. This paper proposes a simple method for a non-coherent fault tree, whose top event is represented as an AND combination of monotonic sub-trees. A ＂monotonic＂ sub-tree means that it does not have both positive and negative representations for each basic event. It is proven that minimal cut sets can be obtained by a conventional method for coherent fault trees. An illustrative example of a simple event tree analysis shows the detail and characteristics of the proposed method.

Concurrent Two-Scale Topology Optimization of Thermoelastic Structures Using a M-VCUT Level Set Based Model of Microstructures

By analyzing the results of compliance minimization of thermoelastic structures,we observed that microstructures play an important role in this optimization problem.Then,we propose to use a multiple variable cutting(M-VCUT)level set-based model of microstructures to solve the concurrent two-scale topology optimization of thermoelastic structures.A microstructure is obtained by combining multiple virtual microstructures that are derived respectively from multiple microstructure prototypes,thus giving more diversity of microstructure and more flexibility in design optimization.The effective mechanical properties of microstructures are computed in an off-line phase by using the homogenization method,and then a mapping relationship between the design variables and the effective properties is established,which gives a data-driven model of microstructure.In the online phase,the data-driven model is used in the finite element analysis to improve the computational efficiency.The compliance minimization problem is considered,and the results of numerical examples prove that the proposed method is effective.

STUDY ON MODULAR FAULT TREE ANALYSIS TECHNIQUE WITH CUT SETS MATRIX METHOD

A new fault tree analysis (FTA) computation method is put forth by using modularization technique in FTA with cut sets matrix, and can reduce NP (Nondeterministic polynomial) difficulty effectively. This software can run in IBM PC and DOS 3.0 and up. The method provides theoretical basis and computation tool for application of FTA technique in the common engineering system

Analysis of traffic safety in airport aircraft activity areas based on bayesian networks and fault trees

To assess road traffic safety risk in civil aviation airports and develop effective accident prevention measures,this study proposed a risk assessment method based on accident tree and Bayesian network for airport aircraft activity areas.It identified influencing factors in the aircraft activity area from the perspectives of person-vehicle-road-environment-management and analyzed their relationships.The Bayesian network was utilized to determine initial probabilities for each influencing factor.Findings indicated a relatively high overall safety level in the airport's road traffic system.Accident trees were employed to qualitatively and quantitatively analyze common human-vehicle accident patterns.The initial probabilities obtained from the Bayesian network served as basic event probabilities in the accident tree to determine the occurrence probability of the top event.Taking a 4F airport in China as an example,accident cause analysis identified five important risk sources in human-vehicle accidents,including blind spots for special vehicles,illegal driving by drivers,pedestrians violating regulations,passengers entering restricted areas,and blind spots at intersections.Corresponding safety management measures were formulated.The study concluded that the integration of Bayesian networks and accident trees effectively determines accident probabilities and offers specific solutions,thus playing a crucial role in enhancing road traffic safety management within aviation airports.

DATA TRANSFORMATION OF FAULT TREE BY USING MATRIX OPERATION

On the base of study of the correlation of fault tree's main data-minimum cutsets, minimum path sets, non-intersect minimum cut sets and non-intersect minimum path sets,transformation method among main data are found, i.e. the transformation can be realized by theoperation of cut sets matrixes. This method provides anew way to reduce 'NP' difficulty and simplifyFTA.

A SIMULATED ANNEALING METHOD FOR FAULT TREE ANALYSIS

This paper presents an approximate algorithm based on simulated annealing to achieve the maximum probability of the minimal cut sets for a fault tree. Near optimal minimal cut sets and important sequence of the basic events are also solved by the method. Computer simulations show that the algorithm performs very well.

Cayley Picture Fuzzy Graphs and Interconnected Networks

Theory of the Cayley graphs is directly linked with the group theory.However,if there are uncertainties on the vertices or edges or both then fuzzy graphs have an extraordinary importance.In this perspective,numbers of generalηizations of fuzzy graphs have been explored in the literature.Among the others,picture fuzzy graph(PFG)has its own importance.A picture fuzzy graph(PFG)is a pair G=(C,D)defined on a H^(*)=(A,B),where C=(ηC,θ_(C),■_(C))is a picture fuzzy set on A and D=(ηD,θ_(D),■_(D))is a picture fuzzy set over the set B∈A×A such that for any edge mn∈ B with ηD(m,n)≤min(ηC(m),ηC(n)),θD(m,n)≤min(θC(m),θC(n))and ■_(D)(m,n)≥max(■_(C)(m),■_(C)(n)).In this manuscript,we introduce the notion of the Cayley picture fuzzy graphs on groups which is the generalization of the picture fuzzy graphs.Firstly,we discuss few important characteristics of the Cayley picture fuzzy graphs.We show that Cayley picture fuzzy graphs are vertex transitive and hence regular.Then,we investigate different types of Cayley graphs induced by the Cayley picture fuzzy graphs by using different types of cuts.We extensively discuss the term connectivity of the Cayley picture fuzzy graphs.Vertex connectivity and edge connectivity of the Cayley picture fuzzy graphs are also addressed.We also investigate the linkage between these two.Throughout,we provide the extensions of some characηteristics of both the PFGs and Cayley fuzzy graphs in the setting of Cayley picture fuzzy graphs.Finally,we provide the model of interconnected networks based on the Cayley picture fuzzy graphs.

Application of causality diagram in system safety analysis

Causality Diagram (CD) is a new graphical knowledge representation based on probability theory. The application of this methodology in the safety analysis of the gas explosion in collieries was discussed in this paper, and the Minimal Cut Set, the Minimal Path Set and the Importance were introduced to develop the methodology. These concepts are employed to analyze the influence each event has on the top event ? the gas explosion, so as to find out about the defects of the system and accordingly help to work out the emphasis of the precautionary work and some preventive measures as well. The results of the safety analysis are in accordance with the practical requirements; therefore the preventive measures are certain to work effectively. In brief, according to the research CD is so effective in the safety analysis and the safety assessment that it can be a qualitative and quantitative method to predict the accident as well as offer some effective measures for the investigation, the prevention and the control of the accident.

Fault Tree Analysis of a Launching with Binary Decision Diagram Method and Fuzzy Theory

Fault tree analysis(FTA),as a structurally simple,visualized and scientific method,is widely used in various fields.To complete the FTA of the launching device,the binary decision diagram(BDD)method is used to obtain the non-intersect cut sets,the minimum cut sets and the probability importance of components.Then,the expert evaluation method is applied to solving fuzzy probability rate of bottom event with zero failure data.In this paper,the BDD and expert evaluation method are applied into FTA to analyze a launch device.

The waiting spectra of the sets described by the quantitative waiting time indicators

The waiting spectra of the sets consisting of pairs of sequences with prescribed quantitative waiting time indicators are determined. More precisely,let R(x,y) and R(x,y) be the lower and upper quantitative waiting time indicators of y by x respectively in the symbolic space Σm(integer m 2) and define the level sets Sα,β={(x,y)∈Σ2m:R(x,y)=α,R(x,y)=β},where 0αβ∞,it is shown that the sets Sα,βare all of Hausdorff dimension 2.Besides,some further extensions of this result are also made.

Exact Reliability Formulas for Linear Consecutive-k-out-of-n: F Systems

A consecutive k out of n: F System, with n linearly arranged i. i. d. components, is examined. This paper gives an exact formula for computing the system's reliability directly. Complexity of this algorithm is an O(n k). Further more, the system's reliability can be computed more quickly and more effectively from this formula than those previously given.

A Study on the Degree of Barrier Coverage in Wireless Sensor Networks

Recently, the barrier coverage was proposed and received much attention in wireless sensor network (WSN), and the degree of the barrier coverage, one of the critical parameters of WSN, must be re-studied due to the difference between the barrier coverage and blanket coverage. In this paper, we propose two algorithms, namely, local tree based no-way and back (LTNWB) algorithm and sensor minimum cut sets (SMCS) algorithm, for the opened and closed belt regions to determine the degree of the barrier coverage of WSN. Our main objective is to minimize the complexity of these algorithms. For the opened belt region, both algorithms work well, and for the closed belt region, they will still come into existence while some restricted conditions are taken into consideration. Finally, the simulation results demonstrate the feasibility of the proposed algorithms.

Analysis of Low Frequency Oscillation and Source Location in Power Systems

The major problem in current online diagnosis and analysis for power system oscillation is mainly concerned with finding the oscillation source in a fast and correct way using the data collected by the Wide Area Measurement System(WAMS).This paper for the first time proposes a scheme of cut set energy based on WAMS.Independent of accurate parameters,the scheme can make full use of WAMS data based on cut set energy construction and fast calculation to locate the source during oscillation.Afterwards,a scheme of torque decomposition is proposed,based on which the controller’s torque can be divided into damping torque and synchronous torque by calculation through WAMS data,and this paper puts forward the abnormal response and simulation models calibration of influential controllers.Analysis of an oscillation case shows how the cut set energy scheme and the torque decomposition scheme are applied in a real-world power system,and the schemes are proven to be reliable and practical in identifying and locating oscillation sources.

Numerical Simulation to Reliability Analysis of Fault-Tolerant Repairable System

In the traditional method for the reliability analysis of fault-tolerant system,the system structure is described by means of binary decision diagram (BDD) and Markov process,and then the reliability indexes are calculated.However,as the size of system augments,the size of state space will increase exponentially.Additionally,Markov approach requires that the failure and repair time of the components obey an exponential distribution.In this study,by combining dynamic fault tree (DFT) and numerical simulation based on the minimal sequence cut set (MSCS),a new method to evaluate reliability of fault-tolerant system with repairable components is proposed.The method presented does not depend on Markov model,so that it can effectively solve the problem of the state-space combination explosion.Moreover,it is suitable for systems whose failure and repair time obey an arbitrary distribution.Therefore,our method is more flexible than the traditional method.At last,an example is given to verify the method.