Fuzzy Random Theory Research Articles

Multi-objective random-fuzzy optimal power flow of transmission-distribution interaction considering security region constraints

In order to deal with the static voltage stability region problem of the power system caused by the penetration of distributed energy resources, this paper presents an interactive random-fuzzy optimal power flow method for transmission-distribution network considering security region constraints. Firstly, based on the random-fuzzy theory, the output of wind power and multi-energy coupling energy hub connected to transmission-distribution network are obtained. On this basis, the security region model of transmission-distribution network is established. As the interaction and cooperation between multiple distribution networks and transmission network throughout the system are described, the global random-fuzzy model of transmission-distribution interaction is established. Then, the security domain opportunity constraints are incorporated into the multi-objective optimization model of transmission-distribution network. Finally, based on the improved IEEE30 bus transmission system and IEEE33 bus distribution system, the power flow of transmission-distribution interactive network under the proposed model is calculated. The simulation results validate the effectiveness of the proposed model and algorithm. The safe operation distance of the power grid system can be improved and the active power network loss and power generation cost can be reduced.

Economic dispatch of industrial park considering uncertainty of renewable energy based on a deep reinforcement learning approach

The proportions of renewable generations (RGs) and flexible loads (FLs) are rapidly increasing in the industrial park. However, the randomness of RGs and FLs challenges the economics and complexity of the industrial park dispatch. To take this challenge, this paper proposes an optimal dispatch strategy for the industrial park based on a deep reinforcement learning (DRL) approach. Firstly, RGs are modeled based on random fuzzy theory. Dynamic line rating (DLR) is introduced to improve the power flow capacity of RGs model in transmission lines. Secondly, in dispatch process is modeled as a Markov decision process (MDP) to avoid complicated linearization processes. Thirdly, we propose a variant of the distributed proximal policy optimization (DPPO) algorithm. The distributed agents in the algorithm are simultaneously trained to explore optimal strategies in different environments. The trained agents can complete the dispatch based on the current state of the industrial park. The effectiveness of the proposed method is verified by numerous simulations. Compared with PPO, DDPG, and TD3 algorithms, the training time of the proposed approach is reduced by 64.06%, 47.31% and 46.99%, respectively. In different scenes, the operating cost with the proposed method is reduced by 47.19%, 46.23%, 43.41% and 41.71%.

Multi‐objective economic dispatch of power system with wind farm considering flexible load response

The uncertainty of wind farm power and load both have a certain impact on the economic dispatch of the power system. First, this study deals with the fuzzy processing of power prediction error and load forecasting error of wind farms based on fuzzy random theory. On this basis, a multi-objective fuzzy stochastic dispatch model of a power system with flexible load is established under the carbon trading mechanism. And, the nonlinear cost of flexible load response and the cost of carbon emission compensation is introduced to the multi-objective function of the model. In addition, the fuzzy chance constraint of the spinning reserve is added to the constraint conditions. By introducing the variable, the fuzzy random dispatch model is transformed into a clear equivalent model. Finally, the discrete bacterial colony chemotaxis algorithm is used to process the model, and the optimal solution to the multi-objective function is obtained by a compromise strategy based on a small degree of satisfaction. In the simulation, a classic IEEE10 system and a wind farm are taken as examples. The results show that compared with the other three traditional dispatch models, the total power generation cost is reduced by US$13 670, US$5610 and US$86 010, respectively using the model proposed in this article.

Distribution Network Reconfiguration for Loss Reduction and Voltage Stability With Random Fuzzy Uncertainties of Renewable Energy Generation and Load

This paper presents a distribution reconfiguration framework to adapt to the distribution network considering the twofold random and fuzzy uncertainties of the wind, photovoltaic power generation, and load demand and considering the power loss reduction and voltage stability. First, the random fuzzy power output models of distributed generation and load are built based on the random fuzzy theory. Second, the corresponding objective functions are established, which are the random fuzzy expected value of active power loss and maximum probability of voltage limit. Third, the modified particle swarm optimization (MPSO) algorithm based on Kruskal algorithm is introduced for the first time to determine the optimal network topology. The Kruskal algorithm is employed to generate a radial network topology directly without checking the loops and islands. Lastly, the proposed method is applied to the IEEE33, PG&E 69-bus distribution systems, 25-bus unbalanced distribution system, as well as a real 109-bus distribution system. The results show that the proposed method has a good performance to solve distribution network reconfiguration problem.

On soft computing with random fuzzy sets in econometrics and machine learning

Several typical econometric analyses, namely fuzzy coalitional games, regression for causal inference, statistical quality control, and prediction in machine learning, are examined in this paper to point out that soft computing components such as fuzzy theory and random set theory have a major role to play. The examination of these statistical analyses suggests an extended use of random fuzzy sets, based upon theory of random fuzzy sets, to improve empirical research.

A new quadratic deviation of fuzzy random variable and its application to portfolio optimization

The aim of this paper is to propose a convex risk measure in the framework of fuzzy random theory and verify its advantage over the conventional variance approach. For this purpose, this paper defines the quadratic deviation (QD) of fuzzy random variable as the mathematical expectation of QDs of fuzzy variables. As a result, the new risk criterion essentially describes the variation of a fuzzy random variable around its expected value. For triangular and trapezoidal fuzzy random variables as well as their linear combinations, we establish the analytical expressions of their QDs, and obtain the desirable convexity about the analytical expressions with respect to critical parameters. To explore the practical value of the proposed QD, we apply it to a portfolio selection problem to quantify the investment risk, and develop three mean-QD models to find the optimal allocation of the fund in different risky securities. Due to the convexity of our QD, the original three mean-QD models can be turned into their equivalent convex parametric quadratic programming problems, which can be solved by conventional optimization methods. The computational results clearly demonstrate that our new QD significantly reduces the computational complexity that cannot be avoided when variance is used as a risk criterion. Finally, the numerical comparison between the proposed mean-QD model and mean-variance model is conducted to show the consistency between the optimal results in both techniques. Meanwhile, the comparison between the proposed QD, variance, spread, and second moment is made to summarize the similarities and differences between them, distinguish these four risk criteria and determine their respective application scopes in decision systems.

A hybrid optimization approach for unequal-sized dynamic facility layout problems under fuzzy random demands

Dynamic facility layout problems involve devising the optimal layout for each different production period. This article studies unequal-area dynamic facility layout problems under fuzzy random environment to minimize the sum of the material handling costs and rearrangement costs. For a more general situation, a novel model of unequal-area dynamic facility layout problems is proposed on the basis of fuzzy random theory, in which uncertain demands are characterized by fuzzy random variables. Unequal-area dynamic facility layout problems are one of the non-deterministic polynomial-time hard problems. Therefore, a hybrid particle swarm optimization and simulated annealing algorithm is innovated to solve the proposed unequal-area dynamic facility layout problems model under fuzzy random environment, in which the shapes and areas of facilities are changed dynamically. Two facility-swapping methods and two local search methods help hybrid algorithm escape from local optima, allowing a more reliable solution. Moreover, a new shifting method is developed to prevent the spatial overlapping between adjacent facilities and save material handling costs. The performance of the hybrid algorithm is confirmed by some test problems available. Finally, the proposed method is extended to a facility layout planning of a new aircraft assembly shop floor. Computational results show that the efficiency and effectiveness of the proposed method, in sharp comparison with other approaches.

Multi-Objective Economic Dispatch of Cogeneration Unit with Heat Storage Based on Fuzzy Chance Constraint

With the increasing expansion of wind power, its impact on economic dispatch of power systems cannot be ignored. Adding a heat storage device to a traditional cogeneration unit can break the thermoelectric coupling constraint of the cogeneration unit and meet the economic and stable operation of a power system. In this paper, an economy-environment coordinated scheduling model with the lowest economic cost and the lowest pollutant emissions is constructed. Economic costs include the cost of conventional thermal power generating units, the operating cost of cogeneration units, and the operating cost of wind power. At the same time, green certificate costs are introduced into the economic costs to improve the absorption of wind power. Pollutant emissions include SO2 and NOx emissions from conventional thermal power units and cogeneration units. The randomness and uncertainty of wind power output are fully considered, and the prediction error of wind power is fuzzy treated according to the fuzzy random theory, and the electric power balance and spinning reserve fuzzy opportunity conditions are established, which are converted into the explicit equivalent. The improved multi-objective particle swarm optimization (MOPSO) was used to solve the model. With this method, the validity of the model is verified by taking a system with 10 machines as an example.

Random fuzzy power flow of distribution network with uncertain wind turbine, PV generation, and load based on random fuzzy theory

No study in the literature considers both randomness and fuzziness simultaneously, which actually coexist as the penetration of renewable energy in power system increases. In order to handle these two kinds of uncertain features simultaneously, a novel random fuzzy power flow (RFPF) calculation method for a distribution network based on random fuzzy theory is presented here. Firstly, the random fuzzy models of wind and photovoltaic (PV) generation, and loads are set up for the first time according to their features of randomness and fuzziness. Then, a two-fold random fuzzy simulation is conducted to obtain the results of the RFPF calculations; the random simulation stage is based on the 2m + 1 scheme of the point estimate method. Finally, the proposed method is applied to two test systems. The results show that the proposed method is feasible and effective in identifying important areas in the power system affected by distribution generation and loads with these two uncertainties.

A Random Fuzzy Accelerated Degradation Model and Statistical Analysis

By elevating stress levels, accelerated degradation testing (ADT) can obtain sufficient degradation data within limited time to predict the reliability and lifetime for highly reliable and long life products. In general, the degradation data collected in ADT have three kinds of characteristics: the time-stress-dependent structure, the random uncertainties caused by random effects in time dimension, and unit-to-unit variations, and the epistemic uncertainty caused by the small sample problem. However, existing acceleration degradation models based on Brownian motion with drift can successfully consider the time-stress-dependent structure and the random uncertainty, while failing to take the epistemic uncertainty into account. In this paper, based on the random fuzzy theory, a new random fuzzy accelerated degradation model and its corresponding statistical analysis method are proposed. The proposed model can take the above three kinds of characteristics into consideration simultaneously. The application case indicates that the proposed methodology is applicable for modeling the ADT data under small sample size. The simulation results show that the proposed methodology is more stable and slightly more conservative than the ADT model considering unit-to-unit variations. In addition, under small sample size (from 3 to 10), the proposed methodology is more stable and more accurate than the ADT model considering unit-to-unit variations.

Random Fuzzy Repairable Coherent Systems with Independent Components

Nondeterministic variables of certain distributions are employed to represent uncertain lifetimes and repair times in repairable systems, which are usually treated as stochastic variables and the probability distributions of the stochastic variables have crisp parameters. However, in practice, the parameters may not be precisely represented due to a lack of sufficient data. The main purpose of this paper is to apply the random fuzzy theory to the establishment of repairable coherent system models. Then the expressions of limiting availability and steady state failure frequency of the random fuzzy coherent systems are proposed, respectively. Finally, some numerical examples are given for illustration.

Residual Life Assessment of Power Transformer Based on Random Fuzzy Theory

Both the cost-effective operation of power systems and reliable operation are inextricably linked with the transformer life assessment. This paper analyzes the composition of the transformer life, life assessment factors and existing assessment methods. Based on factors of the current life assessment and problems of assessment methods, the paper analyzed the importance significance of uncertainty in the transformer life assessment and proposed the transformer remaining life assessment model, and methods based the random fuzzy theory. Assessment results can provide the basis for the transformer maintenance and help safe and economic operation of power systems.

Applications of Decision Making with Uncertain Information

In the process of decision making, a variety of unpredictable factors can result in imprecise information, which can be classified into randomness, fuzziness and uncertainty within mathematical frameworks. Accordingly, probability theory, fuzzy set theory and uncertainty theory, respectively, have been used to describe and handle these types of uncertainties. Moreover, as multi-fold uncertainties can often occur simultaneously in a complicated system, fuzzy random theory and uncertain random theory have been also developed to handle mixed models of uncertainty. Typically, all these approaches can provide efficient methodologies to handle real-world uncertain information. This special issue aims to cover all aspects of employing uncertain technologies to find optimal solutions and assist in making the best possible decisions. It also intends to provide the readership with the recent and significant research on the theoretical results in the framework of uncertain technologies and their applications to a variety of real-world problems, including transportation, management, information systems, economics, supply chain, finance, among others. After the call for papers was announced in late January, 2013, this special issue has been attracted tremendous attentions from a lot of researchers. Totally, we had received 15 manuscripts before the submission deadline. After a rigorous review process, only five papers are finally accepted for publication in this special issue. The first paper by Lixing Yang et al. proposed an integer programming model for train scheduling on a single-track railway line by using space-time network representation. In their research, the velocity choice is considered to decrease the expected energy consumption and interactions between different trains, where link energy consumption is deduced by Davis formula. The second paper by Meiyi Wei et al. proposed a chance-constrained programming model for the hazardous materials transportation within the framework of credibility theory, which aims to obtain the tradeoff between the transportation risk and cost. The third paper by Yuhan Liu et al. formulated an uncertain currency model by considering the foreign exchange rate as an uncertain processes described by uncertain differential equations driven by Liu process. Furthermore, European and American currency option pricing formulas were derived for the proposed uncertain currency model. The fourth paper by Jinwu Gao and Kai Yao proposed an uncertain random process as a generalization of both stochastic process and uncertain process, and some special types of uncertain random processes such as stationary increment process and renewal process were also discussed. The fifth paper by Hua Ke et al. considered a project scheduling problem in the environment with uncertainty and randomness, and a hybrid intelligent algorithm was proposed to search the quasi-optimal schedules. Finally, we in particular thank Editor-in-Chief and all the reviewers for their kind supports in the process of organization and review for this special issue.

The Minimum Weight Dominating Set Problem under Hybrid Uncertain Environments

The minimum weight dominating set problem (MWDSP) has been a popular research topic in recent years. The weights of vertexes may be considered as cost, time, or opponent’s payoff, which are uncertain in most cases. This paper discusses MWDSP under hybrid uncertain environments where the weights of vertexes are random fuzzy variables. First, random fuzzy theory is introduced to describe these hybrid uncertain variables. Then we propose three decision models based on three different decision criteria to solve MWDSP under hybrid uncertain environments. To solve the proposed models, we present a hybrid intelligent algorithm where random fuzzy simulation and genetic algorithm are embedded. Numerical experiments are performed in the last to show the robustness and effectiveness of the presented hybrid intelligent algorithm.

A cloud theory-based particle swarm optimization for multiple decision maker vehicle routing problems with fuzzy random time windows

This article puts forward a cloud theory-based particle swarm optimization (CTPSO) algorithm for solving a variant of the vehicle routing problem, namely a multiple decision maker vehicle routing problem with fuzzy random time windows (MDVRPFRTW). A new mathematical model is developed for the proposed problem in which fuzzy random theory is used to describe the time windows and bi-level programming is applied to describe the relationship between the multiple decision makers. To solve the problem, a cloud theory-based particle swarm optimization (CTPSO) is proposed. More specifically, this approach makes improvements in initialization, inertia weight and particle updates to overcome the shortcomings of the basic particle swarm optimization (PSO). Parameter tests and results analysis are presented to highlight the performance of the optimization method, and comparison of the algorithm with the basic PSO and the genetic algorithm demonstrates its efficiency.

Modeling project time–cost trade-off in fuzzy random environment

In real projects, the trade-off between the project cost and the project completion time, and the environmental uncertainty are aspects of considerable importance for managers. For complex environment with more than one type of uncertainty, this paper presents three types of time–cost trade-off models, in which the project environment is described via introducing the fuzzy random theory. The expected value and the chance measure of fuzzy random variable are introduced for modeling the problem under different decision-making criteria. After that, this paper is devoted to designing a searching method integrating the technique of fuzzy random simulations and genetic algorithm for searching the quasi-optimal schedules. Finally, some numerical examples are given to demonstrate the effectiveness of the designed method for solving the proposed models.

The Economic Life Assessment of Transformer Based on Random Fuzzy Theory

According to the Life Cycle Cost theory, the paper sets up the Life Cycle Cost model of the transformer that covers initial investment cost, operation cost, failure cost and retirement cost, and puts forward a new concept of economic life, determining the economic life of transformer through comparing the annual net profit of the old transformer with the largest annual net profit of the new transformer. As the transformer serves for a long time and the running environment is complicated, parameters, which are required for in evaluation, are both random and fuzzy. Then, introduce random and fuzzy theory that can handle the uncertainties at the same time to assess the economic life of the transformer. This model not only can get the expectancy of economic life of the transformer, but also can get the economic life interval under different confidence level and the economic life interval whose chance measure is the biggest under the same economic life span. Finally, take the assessed transformer as a example to verify the rationality and validity of the model.

On the Application of Digital Video Watermarking Technology

Digital watermarkingtechnology as an emerging interdisciplinary application of technology is animportant branch of information hiding science . It combines differenttheoretical and technical disciplines , such as information theory,communication theory , signal processing, random probability theory , codingtheory , optimization theory , fuzzy theory, detection theory , matrixanalysis, pattern recognition , cryptography , computer science and networktechnology, algorithm design , etc., but also including legal and other issues. Digital watermarking of multimedia information security field as the currenthot technology , has received international academic community and the businesscommunity 's attention [ 1 ] [ 2 ]

Blackwell’s theorem for fuzzy variables

Recently, Zhao et al. (Euro J Oper Res 169:189---201, 2006) discussed a random fuzzy renewal process based on the random fuzzy theory and established Blackwell's theorem in random fuzzy sense. They obtained Blackwell's theorem for fuzzy variables by degenerating the process. However, this result is invalid. We provide some counterexamples and offer a corrected version of fuzzy Blackwell's theorem.

Fuzzy Reliability Optimization Design Method of Flange Based on the Tightness of Bolted Flanged Connections

Based on the time-correlated leakage model and fuzzy random probability theory, a formula for calculating fuzzy random reliability of sealing performance of bolted flanged connections was derived. The optimization variables were defined according to the sensitivity analysis of design parameters on fuzzy reliability of sealing performance. A fuzzy reliability optimization design method of flange was investigated, in which both the tightness of bolted flanged connections and the strength of flange were taken into consideration. As an example, an integral welding necked pipe flange was designed according to the optimization design method proposed in this paper. The designed flange not only satisfies the requirements of flange strength and sealing reliability of connections, but also its weight is reduced by 16% compared with that prescribed in the standard.