Cut-set Theory Research Articles

Reliability Assessment of Power Systems in High-Load Areas with High Proportion of Gas-Fired Units Considering Natural Gas Loss

The “dual-carbon” policy underscores the crucial importance of a secure and stable natural gas supply to ensure the reliable operation of power systems. In high-load areas with a high proportion of gas-fired units and no alternative energy supply, urgent attention needs to be paid to the impact of natural gas loss on power system reliability. Given this background, a method to evaluate power system reliability that considers natural gas supply fluctuations is proposed. In this method, a reliability model of the natural gas supply chain based on the minimal cut set theory is constructed and the influence of policy regulations and economic market factors on system components is quantified. Then, a reliability-evaluation model for a power system that considers gas loss is constructed, and a non-sequential Monte Carlo simulation is used to solve it. Afterward, a reliability-evaluation method considering the power system reserve capacity is proposed. Finally, case studies on a natural gas system with a 14-node power system of a certain area are performed to verify the effectiveness of the proposed method, and the simulation results demonstrate that the reliability of the energy supply directly affects the reliability of the power system.

Reliability analysis of mechanisms with mixed uncertainties using polynomial chaos expansion

AbstractIn order to quantify the effect of mixed uncertainties on the reliability of mechanisms, this paper proposes a method for analyzing the reliability of mechanisms with mixed uncertainties using polynomial chaos expansion. Based on the performance margin theory, a mechanism reliability model considering mixed uncertainties is developed, and the Sobol indices can be easily calculated by an arbitrarily polynomial chaos expansion (aPCE) of the reliability function to quantify the independent contribution of each parameter to the global sensitivity and the effect of parameter coupling. Additionally, this paper also introduces a mixed uncertainties propagation method based on PCE, which treats cognitive uncertainties as fuzzy variables, converts the fuzzy variable into an interval variable using cut set theory, and transforms the PCE containing interval uncertainties into a Bernstein polynomial to calculate the membership function of the output quantity and the non‐probabilistic reliability index by area method. The final case study of a simplified automaton motion mechanism illustrates that the proposed method is effective and convincing, and the mechanism reliability decreases with increasing mixed uncertainties. The mechanism reliability index considering mixed uncertainties will give a more conservative reliability estimation.

A New Cutset-type Kernelled Possibilistic C-means Clustering Segmentation Algorithm Based on SLIC Super-pixels

: The kernelled possibilistic C-means clustering algorithm (KPCM) can effectively cluster hyper-sphere data with noise and outliers by introducing the kernelled method to the possibilistic C-means clustering (PCM) algorithm. However, the KPCM still suffers from the same coincident clustering problem as the PCM algorithm due to the lack of between-class relationships. Therefore, this paper introduces the cut-set theory into the KPCM and modifies the possibilistic memberships in the iterative process. Then a cutset-type kernelled possibilistic C-means clustering (CKPCM) algorithm is proposed to overcome the coincident clustering problem of the KPCM. Simultaneously a adaptive method of estimating the cut-set threshold is also given by averaging inter-class distances. Additionally, a cutset-type kernelled possibilistic C-means clustering segmentation algorithm based on the SLIC super-pixels (SS-C-KPCM) is also proposed to improve the segmentation quality and efficiency of the color images. Several experimental results on artificial data sets and image segmentation simulation results prove the excellent performance of the proposed algorithms in this paper.

An efficiency-based interval type-2 fuzzy multi-criteria group decision making for makeshift hospital selection

Since makeshift hospitals have strong ability in blocking the spread of the virus, how to design some methods to select the reasonable sites of makeshift hospitals is vitally important for containing COVID-19. This paper investigates an efficiency-based multi-criteria group decision making (MCGDM) method by combining the best-worst method (BWM) and data envelopment analysis (DEA) in trapezoidal interval type-2 fuzzy (TrIT2F) environment. This MCGDM method is called TrIT2F-BWM-DEA, where the TrIT2F-BWM is used to determine the weights of criteria and decision-makers, and the TrIT2F-DEA is employed to rank alternatives by measuring their overall efficiencies. Based on cut set theory, the expectation and average expectation (AE) of TrIT2FSs are successively defined. To solve three key issues in the development of the TrIT2F-BWM, this paper proposes a flexible ranking relation of TrIT2FSs to transform the TrIT2F constraints, initiates an efficient theorem to normalize the TrIT2F weights, and designs an input-based consistency ratio to check the reliability of the determined weights. A fully TrIT2F-DEA model is originally built to measure the TrIT2F efficiencies of alternatives. The alternatives are finally ranked according to the AEs of alternatives’ TrIT2F efficiencies. A site selection case of Fangcang hospitals and some comparative analyses are provided to confirm the validity and merits of the proposed TrIT2F-BWM-DEA.

On the Periodicity of a Max-type Fuzzy Difference Equations

Our aim in this paper is to discuss the periodicity and boundedness of a max-type fuzzy difference equation. When studying the periodicity of the solution to the max-fuzzy difference equation, the equation is first converted into a difference system composed of two related difference equations through the cut set theory of the fuzzy number, then the periodicity of each solution sequence in the system is obtained by means of inequality technique, mathematical induction and other theoretical methods, thus the periodicity of the solution is proved. As researching the boundedness of the solution for the fuzzy difference equation, the difference system is also obtained through the cut set theory of the fuzzy number, then analyze the boundedness to each solution sequence according to the periodicity with the solution sequence, through examining the value of the finite subsequence in each solution sequence, the boundedness with these subsequences can be obtained, and then the boundedness for each solution sequence made up of complete subsequences can be known, thus the boundedness of the solution is proved. Finally, the results obtained in this paper are simulated by using the software package MATLAB 2016, the numerical results not only show the dynamic behavior of the solutions to the fuzzy difference systems, but also verify the effectiveness of the theoretical results.

Sensor Fault Diagnosis Based on Fuzzy Neural Petri Net

This study aims to improve the operating stability of the resistance strain weighing sensor and eliminate fuzzy factors in fault diagnosis. Based on fuzzy techniques for fault diagnosis, the proposed fuzzy Petri net model uses the fault logical relationship between a sensor and an improved Petri net model. A formula for confidence-based reasoning is proposed using an algorithm, which combines neural network regulation algorithm with a transition-enabled ignition judgment matrix. This formula can yield an accurate assessment of the operating state of the sensor. Backward inference and the minimum cut set theory are also combined to obtain the priority of faults, which helps avoid blind and ambiguous maintenance. The sensor model was analyzed, and its accuracy and validity were verified through statistical analysis and comparison with other methods of fault diagnosis.

Power Tracing Monitoring incorporating Optimal Reactive Power Dispatch

General power flow studies do not manage to trace the contributors by generators on power losses in the whole power transmission system. Thus, power tracing approach is utilized to address this issue. Power tracing is a termed used to describe the contributors for the power losses dissipated on the transmission line. The traditional technique made use the knowledge of circuit analysis such as cut set theory. However, there was no element of optimization which can help to achieve the optimal solution. This paper presents the power tracing monitoring during voltage stability improvement process, implemented by optimal reactive power dispatch. In this study, the impact of power tracing on voltage stability variation was investigated. Evolutionary Programming (EP) was developed and utilized to incorporate power tracing, along with voltage stability improvement. A pre-developed scalar voltage stability index was incorporated to indicate the voltage stability condition. On the other hand, the voltage stability initiative was conducted via the optimal reactive power dispatch. The power tracing was monitored for both; the pre-optimization and post-optimization scenarios. Small system model was tested to realize the power tracing phenomenon, which is rather rare study in power system community. Results on power tracing obtained during the pre- and post-optimal reactive power dispatch revealed that not all generators will involve in the contribution on the total transmission loss in the system. This can be beneficial to power system operators for allocating the cost without discrimination in the long run.

Achievable Degrees of Freedom of Cellular Multiuser Two-Way Relay Networks

In this paper, we study a network information flow problem for cellular multiuser two-way relay networks (MU-TWRNs) where uplink and downlink messages are exchanged through a multiantenna relay node using two-way relaying. Both single- and two-cell scenarios are investigated. In particular, for the two-cell scenario, we consider two schemes with and without base station (BS) cooperation, respectively. By comparing the degrees-of-freedom (DOF) upper bounds obtained via cut-set theory, we derive the feasibility conditions to achieve the optimal DOF for all the schemes. These DOF bounds are shown to be achieved by suitably applying some physical-layer signaling techniques, such as physical-layer network coding, signal alignment, block diagonalization, and the newly proposed successive interference nulling. By comparing one-way relaying in terms of the normalized DOF, we observe that the proposed two-way-relaying-based scheme can double the performance with symmetric antenna configurations; however, the gain is reduced under unbalanced antenna configurations.

A reliability model of blade to avoid resonance considering multiple fuzziness

The reliability of aero-engine blade to avoid resonance has a great impact on the safety of airplane. The resonance problem of blade is complex and includes not only randomness but also a lot of fuzziness. By describing the fuzziness of “blade resonance will not occur” through normal bathtub membership function and the inherent frequency through trapezoidal membership function, a Posfust reliability model of blade to avoid resonance, which considers the multiple fuzziness of state and inherent frequency, was proposed based on the probability theory and fuzzy cut-set theory in this article. Meanwhile, three limit forms of the model were analyzed and it was indicated that the Posbist model, Profust model and conventional random model were special cases of the Posfust reliability model in this article. Afterward, analyzing the deficiency of the previous cut-set distributions, a new cut-set distribution named modified truncated normal distribution was proposed to ensure the model has a good convergence in the three special cases. Furthermore, a numerical method was given to solve the Posfust reliability model, and the coefficient of variation of the numerical solution was calculated subsequently. Finally, the model and the numerical method were applied to evaluate the reliability of some blades. Simulations were carried out to explain how one can utilize the model and its numerical method obtained, verify the theoretical analysis results and study the influence of fuzzy degree on the reliability.

A Fuzzy Reliability Model of Blades to Avoid Resonance and Its Convergence Analysis

The inherent frequencies of blades, especially with friction structure of shroud, are related to many uncertain factors, which include not only random factors but also fuzzy or other uncertain factors. In this paper, the fuzzy reliability model of blades to avoid resonance is investigated. By regarding the inherent frequency as a fuzzy random variable with trapezoidal or flat-normal membership function, a fuzzy reliability model of blades to avoid resonance is proposed based on the fuzzy cut-set theory, and the corresponding numerical solution is given. Further, a theorem is proposed and proved to indicate the deficiency of the previous cut-set distributions on convergence, and, then, a new cut-set distribution is given to cover this shortage and ensure that the model is of good convergence. Finally, the proposed model is applied to evaluate the reliability of one certain blade. Some simulations are carried out to compare the new cut-set distribution with the previous ones and study the influence of fuzzy degree on the reliability.

Railway Container Center Door Lane Analysis based on α-cut Theory

Number of lanes of the door of the domestic railway container center station design is imperfect. Decision-making methods and the door to the number of lanes through the in-depth study Container Center Station to learn from foreign advanced experience in the container station building fuzzy queuing theory into the door to the calculation of the number of lanes, the α- cut set theory fuzzy queuing system M/F/1 model converted into classic M/G/1 model using average captain, service costs, service time queuing performance optimization calculation, to draw new door to the number of lanes formula.The new decision-making formula is superior to the traditional empirical formula of the construction costs and the cost of the door to the number of lanes.

A Two-Echelon Supply Chain of a Buyback Policy with Fuzzy Demand

In this study, the buyback policy for two-echelon supply chain in fuzzy demand environment is studied. The models of centralized decision and buyback policy are built by the method of fuzzy cut sets theory and their optimal policies are also proposed. Finally, an example is given to illustrate and validate the models and conclusions. It is shown that the optimal order quantity of the retailer fluctuates at the center of the fuzzy demand and decreases with the raise of the customer return rate. The optimal fuzzy expected profits for the manufacturer and retailer in supply chain decrease with increasing of the customer return rate.

Fuzzy Dynamic Fault Tree Analysis for the Solar Array Drive Assembly

Solar array drive assembly, as an important part of the spacecraft, the research on its reliability is very important for fault occurs frequently. The fault tree of the solar array drive assembly is established based on the structure and principle of solar array drive assembly. Taking into account the both failure phenomenon of solar array drive assembly and many uncertainties exist in the fault status and fault reasons, fuzzy sets theory is introduced into dynamic fault tree. The failure parameters of bottom events for solar array drive assembly are modeled by triangular fuzzy numbers. Furthermore, the fuzzy dynamic fault tree analysis method for solar array drive assembly based on combination cut set theory and interval arithmetic is proposed. The system weak parts and key components can be found easily according to the fuzzy probability importance which is comes from the fuzzy probability of system top event and fuzzy probability importance of bottom events. The results show that the bearings and harmonic drive are key components for the solar array drive assembly.

Supply Chain Contracts with Multiple Retailers in a Fuzzy Demand Environment

This study investigates supply chain contracts with a supplier and multiple competing retailers in a fuzzy demand environment. The market demand is considered as a positive triangular fuzzy number. The models of centralized decision, return contract, and revenue-sharing contract are built by the method of fuzzy cut sets theory, and their optimal policies are also proposed. Finally, an example is given to illustrate and validate the models and conclusions. It is shown that the optimal total order quantity of the retailers fluctuates at the center of the fuzzy demand. With the rise of the number of retailers, the optimal order quantity and the fuzzy expected profit for each retailer will decrease, and the fuzzy expected profit for supplier will increase.

Assembly Unit Partition Based on Theory of Cut-Set

In the manufacture process of many large-scaled and complex products assembly, due to large number of parts or components, assemblies are often divided into several small assembly units in order to organize production and increase assembly efficiency. To obtain fine-grained rapid assembly unit partition, this paper presents a method of assembly unit partition based on cut-set theory with consideration of the assembly constraints and assembly complexity. The paper also discusses the method of establishing the assembly relationship graph of a product as the basis of unit partition. The relationship graph is extracted from the CAD model of the product and is used to describe the relationship of its component assembly. Using the proposed unit partition method, assembly constraints such as precedence relationship can be considered so that invalid assembly unit partition will be avoided. Furthermore, by defining assembly complexity, optimal selection of assembly unit partition can be achieved. The procedures of assembly unit partition including establishing of assembly relationship from CAD model, approach to cut-set, optimal selection and validation are addressed with an assembly example and a flow chart.

Assembly Model Based on Dynamic Transition Graph for Satellite General Assembly Process Planning

Beginning with the disassembly of the semi-finished modules, the general assembly process of satellites is quite different from that of other mechanical products. This kind of disassembly-reassembly process cannot be solved by the widely used cut-set theory that only deals with linear problems, thus an approach called Dynamic Transition Graph (DTG) is proposed to solve this nonlinear assembly sequence planning problem. By analyzing and verifying possible assembly statuses hierarchically through matrix operations, a DTG is produced on the basis of Liaison Graph, where the DTG includes all the geometric feasible assembly sequences for the general assembly of satellite. Finally, the effectiveness of this method is verified by an example.

A Dynamic Assembly Modeling Method for Satellite Final Assembly Sequence Planning

To study the effect of assembly process information combining disassemble and assemble on satellite assembly sequence, this paper presents an object-oriented and assembly information integrated model, which is composed of static model and dynamic model. The feasibility determination based on Cut-set theory is presented and the construction algorithm of dynamic model is established by static model, the dynamic assembly model tree is obtained by analyzing in layers and verifying possible states using this algorithm, where the assembly model tree includes all the geometric feasible assembly sequences of satellite. Finally, this modeling method is verified by a satellite product.

Avaliação da confiabilidade em sistemas de ditribuição considerando falhas de geração e transmissão

Este artigo apresenta uma nova metodologia para a análise da confiabilidade de sistemas de distribuição, onde se considera os impactos das falhas provenientes dos sistemas de geração e transmissão. Portanto, é viabilizada uma avaliação integrada, incluindo geração, transmissão (G&T) e distribuição, de modo a produzir uma informação mais detalhada sobre a causa das interrupções experimentadas pelos consumidores. O sistema G&T é representado por uma rede equivalente fictícia, cujos parâmetros são obtidos através de simulação Monte Carlo não-seqüencial. Esta rede equivalente G&T é conectada ao sistema de distribuição, que é então analisado utilizando a teoria dos conjuntos mínimos de corte. Índices de distribuição tradicionais (e.g. FEC, DEC, etc.) bem como a LOLC (Loss of Load Cost - Custo Esperado da Perda de Carga), são desagregados com o intuito de quantificar a contribuição dos sistemas G&T e distribuição em relação ao sistema total. O método proposto é testado em um sistema constituído pelo sistema de geração e transmissão IEEE-RTS, conectado ao sistema de distribuição IEEE-RBTS. Os resultados e suas potenciais aplicações para o novo cenário competitivo dos sistemas elétricos são discutidos.

Integrated reliability evaluation of generation, transmission and distribution systems

A new methodology evaluates the reliability of distribution systems considering the impact of failures from the generation and transmission (G&T) systems is presented. An integrated adequacy evaluation, including generation, transmission and distribution, is performed to provide detailed information on the interruptions experienced by consumers. G&T systems are represented by a fictitious equivalent network whose parameters are obtained by Monte Carlo nonsequential simulation. The equivalent G&T network is then connected with the distribution network and analysed using minimal cut-set theory. Traditional distribution indices (e.g. SAIFI, SAIDI, etc.) as well as the loss-of-load cost indices are disaggregated to measure the contribution of G&T and distribution systems on the overall system indices. The method is applied to a hybrid system created from two standard test systems. The results and their potential applications in the new power system competitive environment are discussed.

Automatic identification techniques of reliability bottlenecks in process systems under uncertainty

In design and operation of complex processing systems, two categories of uncertainty play an important role: • uncertainty with respect to the realization of continuous parameters • uncertainty with respect to discrete states Novel analytical tools (stochastic flexibility index, expected stochastic flexibility index) to simultaneously account for both type of uncertainties in process design and evaluation have recently appeared in the literature. However, discrete-state uncertainty introduces new operating states, the number of which grows exponentially. This computationally prohibits the direct evaluation of stochastic measures for the simultaneous quantification of flexibility and reliability, especially for large systems. This work focuses on developing automatic procedures for reducing the number of operating states which must be evaluated in complex process systems. First, based on structural flowsheet information and by the use of minimal cut sets theory, the relative reliability importance of the different units and subsystems is assessed, resulting in the construction of a reduced fault event tree. Rules are devised with which reliability bottlenecks are properly identified. An efficient numerical procedure has been implemented for the estimation of bounds for the expected stochastic flexibility index.