Search results for: Takagi-Sugeno (TS) fuzzy control algorithm

Authors: Michael A. Folcik, Bijan Karimi

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A robot simulator was developed to measure and investigate the performance of a robot navigation system based on the relative position of the robot with respect to random obstacles in any two dimensional environment. The presented simulator focuses on investigating the ability of a fuzzy-neural system for object avoidance. A navigation algorithm is proposed and used to allow random navigation of a robot among obstacles when the robot faces an obstacle in the environment. The main features of this simulator can be used for evaluating the performance of any system that can provide the position of the robot with respect to obstacles in the environment. This allows a robot developer to investigate and analyze the performance of a robot without implementing the physical robot.

Keywords: Applications of Fuzzy Logic and Neural Networksin Robotics, Artificial Intelligence, Embedded Systems, MobileRobots, Robot Navigation, Robotics.

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Authors: Mehdi Karbalaye Zadeh, Ehsan M. Siavashi

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The controllable electrical loss which consists of the copper loss and iron loss can be minimized by the optimal control of the armature current vector. The control algorithm of current vector minimizing the electrical loss is proposed and the optimal current vector can be decided according to the operating speed and the load conditions. The proposed control algorithm is applied to the experimental PM motor drive system and this paper presents a modern approach of speed control for permanent magnet synchronous motor (PMSM) applied for Electric Vehicle using a nonlinear control. The regulation algorithms are based on the feedback linearization technique. The direct component of the current is controlled to be zero which insures the maximum torque operation. The near unity power factor operation is also achieved. More over, among EV-s motor electric propulsion features, the energy efficiency is a basic characteristic that is influenced by vehicle dynamics and system architecture. For this reason, the EV dynamics are taken into account.

Keywords: PMSM, Electric Vehicle, Optimal control, Traction.

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Authors: Kamalpreet Kaur, Harjit Pal Singh, Vikas Khullar

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In Wireless Sensor Network (WSN), the main limitation is generally inimitable energy consumption during processing of the sensor nodes. Cluster head (CH) election is one of the main issues that can reduce the energy consumption. Therefore, discovering energy saving routing protocol is the focused area for research. In this paper, fuzzy-based energy aware routing protocol is presented, which enhances the stability and network lifetime of the network. Fuzzy logic ensures the well-organized selection of CH by taking four linguistic variables that are concentration, energy, centrality, and distance to base station (BS). The results show that the proposed protocol shows better results in requisites of stability and throughput of the network.

Keywords: ERA, fuzzy logic, network model, WSN.

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Authors: Shikha Maheshwari, Amit Srivastava

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In medical investigations, uncertainty is a major challenging problem in making decision for doctors/experts to identify the diseases with a common set of symptoms and also has been extensively increasing in medical diagnosis problems. The theory of cross entropy for intuitionistic fuzzy sets (IFS) is an effective approach in coping uncertainty in decision making for medical diagnosis problem. The main focus of this paper is to propose a new intuitionistic fuzzy cross entropy measure (IFCEM), which aid in reducing the uncertainty and doctors/experts will take their decision easily in context of patient’s disease. It is shown that the proposed measure has some elegant properties, which demonstrates its potency. Further, it is also exemplified in detail the efficiency and utility of the proposed measure by using a real life case study of diagnosis the disease in medical science.

Keywords: Intuitionistic fuzzy cross entropy (IFCEM), intuitionistic fuzzy set (IFS), medical diagnosis, uncertainty.

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Authors: Ashish Saini, A.K. Saxena

Abstract:

The genetic algorithm (GA) based solution techniques are found suitable for optimization because of their ability of simultaneous multidimensional search. Many GA-variants have been tried in the past to solve optimal power flow (OPF), one of the nonlinear problems of electric power system. The issues like convergence speed and accuracy of the optimal solution obtained after number of generations using GA techniques and handling system constraints in OPF are subjects of discussion. The results obtained for GA-Fuzzy OPF on various power systems have shown faster convergence and lesser generation costs as compared to other approaches. This paper presents an enhanced GA-Fuzzy OPF (EGAOPF) using penalty factors to handle line flow constraints and load bus voltage limits for both normal network and contingency case with congestion. In addition to crossover and mutation rate adaptation scheme that adapts crossover and mutation probabilities for each generation based on fitness values of previous generations, a block swap operator is also incorporated in proposed EGA-OPF. The line flow limits and load bus voltage magnitude limits are handled by incorporating line overflow and load voltage penalty factors respectively in each chromosome fitness function. The effects of different penalty factors settings are also analyzed under contingent state.

Keywords: Contingent operation state, Fuzzy rule base, Genetic Algorithms, Optimal Power Flow.

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Authors: Tanuj Kumar, Rakesh Kumar Bajaj

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In the present paper, we analyze the vague reliability of k-out-of-n : G system (particularly, series and parallel system) with independent and non-identically distributed components, where the reliability of the components are unknown. The reliability of each component has been estimated using statistical confidence interval approach. Then we converted these statistical confidence interval into triangular intuitionistic fuzzy numbers. Based on these triangular intuitionistic fuzzy numbers, the reliability of the k-out-of-n : G system has been calculated. Further, in order to implement the proposed methodology and to analyze the results of k-out-of-n : G system, a numerical example has been provided.

Keywords: Vague set, vague reliability, triangular intuitionistic fuzzy number, k-out-of-n : G system, series and parallel system.

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Authors: A. M. Pashayev, D. D. Askerov, C. Ardil, R. A. Sadiqov, P. S. Abdullayev

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Researches show that probability-statistical methods application, especially at the early stage of the aviation Gas Turbine Engine (GTE) technical condition diagnosing, when the flight information has property of the fuzzy, limitation and uncertainty is unfounded. Hence the efficiency of application of new technology Soft Computing at these diagnosing stages with the using of the Fuzzy Logic and Neural Networks methods is considered. According to the purpose of this problem training with high accuracy of fuzzy multiple linear and non-linear models (fuzzy regression equations) which received on the statistical fuzzy data basis is made. For GTE technical condition more adequate model making dynamics of skewness and kurtosis coefficients- changes are analysed. Researches of skewness and kurtosis coefficients values- changes show that, distributions of GTE workand output parameters of the multiple linear and non-linear generalised models at presence of noise measured (the new recursive Least Squares Method (LSM)). The developed GTE condition monitoring system provides stage-by-stage estimation of engine technical conditions. As application of the given technique the estimation of the new operating aviation engine technical condition was made.

Keywords: aviation gas turbine engine, technical condition, fuzzy logic, neural networks, fuzzy statistics

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Authors: Krishnamoorthi Makkithaya, N. V. Subba Reddy, U. Dinesh Acharya

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As the number of networked computers grows, intrusion detection is an essential component in keeping networks secure. Various approaches for intrusion detection are currently being in use with each one has its own merits and demerits. This paper presents our work to test and improve the performance of a new class of decision tree c-fuzzy decision tree to detect intrusion. The work also includes identifying best candidate feature sub set to build the efficient c-fuzzy decision tree based Intrusion Detection System (IDS). We investigated the usefulness of c-fuzzy decision tree for developing IDS with a data partition based on horizontal fragmentation. Empirical results indicate the usefulness of our approach in developing the efficient IDS.

Keywords: Data mining, Decision tree, Feature selection, Fuzzyc- means clustering, Intrusion detection.

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Authors: Le Thanh Ha, Hye-Soo Kim, Chun-Su Park, Seung-Won Jung, Sung-Jea Ko

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Flexible macroblock ordering (FMO), adopted in the H.264 standard, allows to partition all macroblocks (MBs) in a frame into separate groups of MBs called Slice Groups (SGs). FMO can not only support error-resilience, but also control the size of video packets for different network types. However, it is well-known that the number of bits required for encoding the frame is increased by adopting FMO. In this paper, we propose a novel algorithm that can reduce the bitrate overhead caused by utilizing FMO. In the proposed algorithm, all MBs are grouped in SGs based on the similarity of the transform coefficients. Experimental results show that our algorithm can reduce the bitrate as compared with conventional FMO.

Keywords: Data Partition, Entropy Coding, Greedy Algorithm, H.264/AVC, Slice Group.

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Authors: Mansoureh Naderipour, Susan Bastani, Mohammad Fazel Zarandi

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Predicting links that may occur in the future and missing links in social networks is an attractive problem in social network analysis. Granular computing can help us to model the relationships between human-based system and social sciences in this field. In this paper, we present a model based on granular computing approach and Type-2 fuzzy logic to predict links regarding nodes’ activity and the relationship between two nodes. Our model is tested on collaboration networks. It is found that the accuracy of prediction is significantly higher than the Type-1 fuzzy and crisp approach.

Keywords: Social Network, link prediction, granular computing, Type-2 fuzzy sets.

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Authors: Sanjay K.Srivastava, Bhanu Gupta

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In this paper some results on strict stability heve beeb extended for fuzzy differential equations with impulse effect using Lyapunov functions and Razumikhin technique.

Keywords: Fuzzy differential equations, Impulsive differential equations, Strict stability, Lyapunov function, Razumikhin technique.

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Authors: Mansoor Ahsan, Suhail Akhtar, Adnan Ali, Farrukh Mazhar, Muddssar Khalid

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In the present era of aviation technology, autonomous navigation and control have emerged as a prime area of active research. Owing to the tremendous developments in the field, autonomous controls have led today’s engineers to claim that future of aerospace vehicle is unmanned. Development of guidance and navigation algorithms for an unmanned aerial vehicle (UAV) is an extremely challenging task, which requires efforts to meet strict, and at times, conflicting goals of guidance and control. In this paper, aircraft altitude and heading controllers and an efficient algorithm for self-governing navigation using MATLAB® mapping toolbox is presented which also enables loitering of a fixed wing UAV over a specified area. For this purpose, a nonlinear mathematical model of a UAV is used. The nonlinear model is linearized around a stable trim point and decoupled for controller design. The linear controllers are tested on the nonlinear aircraft model and navigation algorithm is subsequently developed for for autonomous flight of the UAV. The results are presented for trajectory controllers and waypoint based navigation. Our investigation reveals that MATLAB® mapping toolbox can be exploited to successfully deliver an efficient algorithm for autonomous aerial navigation for a UAV.

Keywords: Navigation, trajectory-control, unmanned aerial vehicle, PID-control, MATLAB® mapping toolbox.

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Authors: Hamed Rafiei, Masoud Rabbani

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This paper addresses one of the most important issues have been considered in hybrid MTS/MTO production environments. To cope with the problem, a mathematical programming model is applied from a tactical point of view. The model is converted to a fuzzy goal programming model, because a degree of uncertainty is involved in hybrid MTS/MTO context. Finally, application of the proposed model in an industrial center is reported and the results prove the validity of the model.

Keywords: Fuzzy sets theory, Hybrid MTS/MTO, Order penetration point, Quadratic programming.

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Authors: Zhan Haiyang, Zhang Lei, Ning Juan

Abstract:

This paper presents a configuration software solution in Linux, which is used for the control of space environment simulator. After introducing the structure and basic principle, it is said that the developing of QT software frame and the dynamic data exchanging between PLC and computer. The OPC driver in Linux is also developed. This driver realizes many-to-many communication between hardware devices and SCADA software. Moreover, an algorithm named “Scan PRI” is put forward. This algorithm is much more optimizable and efficient compared with "Scan in sequence" in Windows. This software has been used in practical project. It has a good control effect and can achieve the expected goal.

Keywords: Linux OS, configuration software, OPC server driver, MYSQL database.

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Authors: Mahamed G.H. Omran, Andries P Engelbrecht, Ayed Salman

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An end-member selection method for spectral unmixing that is based on Particle Swarm Optimization (PSO) is developed in this paper. The algorithm uses the K-means clustering algorithm and a method of dynamic selection of end-members subsets to find the appropriate set of end-members for a given set of multispectral images. The proposed algorithm has been successfully applied to test image sets from various platforms such as LANDSAT 5 MSS and NOAA's AVHRR. The experimental results of the proposed algorithm are encouraging. The influence of different values of the algorithm control parameters on performance is studied. Furthermore, the performance of different versions of PSO is also investigated.

Keywords: End-members selection, multispectral satellite imagery, particle swarm optimization, spectral unmixing.

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Authors: Panpan Xu, Shulin Sui

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The crossover probability and mutation probability are the two important factors in genetic algorithm. The adaptive genetic algorithm can improve the convergence performance of genetic algorithm, in which the crossover probability and mutation probability are adaptively designed with the changes of fitness value. We apply adaptive genetic algorithm into a function optimization problem. The numerical experiment represents that adaptive genetic algorithm improves the convergence speed and avoids local convergence.

Keywords: Genetic algorithm, Adaptive genetic algorithm, Function optimization.

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Authors: Mike Sewell, Jagath Samarabandu, Ranga Rodrigo, Kenneth McIsaac

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A novel method of individual level adaptive mutation rate control called the rank-scaled mutation rate for genetic algorithms is introduced. The rank-scaled mutation rate controlled genetic algorithm varies the mutation parameters based on the rank of each individual within the population. Thereby the distribution of the fitness of the papulation is taken into consideration in forming the new mutation rates. The best fit mutate at the lowest rate and the least fit mutate at the highest rate. The complexity of the algorithm is of the order of an individual adaptation scheme and is lower than that of a self-adaptation scheme. The proposed algorithm is tested on two common problems, namely, numerical optimization of a function and the traveling salesman problem. The results show that the proposed algorithm outperforms both the fixed and deterministic mutation rate schemes. It is best suited for problems with several local optimum solutions without a high demand for excessive mutation rates.

Keywords: Genetic algorithms, mutation rate control, adaptive mutation.

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Authors: Zhu Jiaming, Yu Mengna

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In this article, models based on quantitative analysis, physical geometry and regression analysis are established, by using analytic hierarchy process analysis, fuzzy cluster analysis, fuzzy photographic and data fitting. The reasons of various leaf shapes among different species and the differences between the leaf shapes on same tree have been solved by using software, such as Eviews, VB and Matlab. We also successfully estimate the leaf mass of a tree and the correlation with the tree profile.

Keywords: Leaf shape; Mass; Fuzzy cluster; Regression analysis; Eviews; Matlab

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Authors: Amit Kohli, Aashim Wadhwa, Tapan Virmani, Ujjwal Jain

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The objective of present work is to stimulate the machining of material by electrical discharge machining (EDM) to give effect of input parameters like discharge current (Ip), pulse on time (Ton), pulse off time (Toff) which can bring about changes in the output parameter, i.e. material removal rate. Experimental data was gathered from die sinking EDM process using copper electrode and Medium Carbon Steel (AISI 1040) as work-piece. The rules of membership function (MF) and the degree of closeness to the optimum value of the MMR are within the upper and lower range of the process parameters. It was found that proposed fuzzy model is in close agreement with the experimental results. By Intelligent, model based design and control of EDM process parameters in this study will help to enable dramatically decreased product and process development cycle times.

Keywords: Electrical discharge Machining (EDM), Fuzzy Logic, Material removal rate (MRR), Membership functions (MF).

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Authors: H. Mansor, S. B. Mohd Noor

Abstract:

This paper presents a design method of self-tuning Quantitative Feedback Theory (QFT) by using improved deadbeat control algorithm. QFT is a technique to achieve robust control with pre-defined specifications whereas deadbeat is an algorithm that could bring the output to steady state with minimum step size. Nevertheless, usually there are large peaks in the deadbeat response. By integrating QFT specifications into deadbeat algorithm, the large peaks could be tolerated. On the other hand, emerging QFT with adaptive element will produce a robust controller with wider coverage of uncertainty. By combining QFT-based deadbeat algorithm and adaptive element, superior controller that is called selftuning QFT-based deadbeat controller could be achieved. The output response that is fast, robust and adaptive is expected. Using a grain dryer plant model as a pilot case-study, the performance of the proposed method has been evaluated and analyzed. Grain drying process is very complex with highly nonlinear behaviour, long delay, affected by environmental changes and affected by disturbances. Performance comparisons have been performed between the proposed self-tuning QFT-based deadbeat, standard QFT and standard dead-beat controllers. The efficiency of the self-tuning QFTbased dead-beat controller has been proven from the tests results in terms of controller’s parameters are updated online, less percentage of overshoot and settling time especially when there are variations in the plant.

Keywords: Deadbeat control, quantitative feedback theory (QFT), robust control, self-tuning control.

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Authors: P. Selvam, S. Senthil Kumar

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Maximum Power Point Tracking (MPPT) has played a vital role to enhance the efficiency of solar photovoltaic (PV) power generation under varying atmospheric temperature and solar irradiation. However, it is hard to track the maximum power point using conventional linear controllers due to the natural inheritance of nonlinear I-V and P-V characteristics of solar PV systems. Fuzzy Logic Controller (FLC) is suitable for nonlinear system control applications and eliminating oscillations, circuit complexities present in the conventional perturb and observation and incremental conductance methods respectively. Hence, in this paper, FLC is proposed for tracking exact MPPT of solar PV power generation system under varying solar irradiation conditions. The effectiveness of the proposed FLC-based MPPT controller is validated through simulation and analysis using MATLAB/Simulink.

Keywords: Fuzzy logic controller, maximum power point tracking, photovoltaic.

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Authors: Mandana Kariminejad, Ali Ghaffari

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Today, the treatment of cancer, in a relatively short period, with minimum adverse effects is a great concern for oncologists. In this paper, based on a recently used mathematical model for cancer, a guideline has been proposed for the amount and duration of drug doses for cancer treatment by immunotherapy. Dynamically speaking, the mathematical ordinary differential equation (ODE) model of cancer has different equilibrium points; one of them is unstable, which is called the no tumor equilibrium point. In this paper, based on the number of tumor cells an intelligent soft computing controller (a combination of fuzzy logic controller and genetic algorithm), decides regarding the amount and duration of drug doses, to eliminate the tumor cells and stabilize the unstable point in a relatively short time. Two different immunotherapy approaches; active and adoptive, have been studied and presented. It is shown that the rate of decay of tumor cells is faster and the doses of drug are lower in comparison with the result of some other literatures. It is also shown that the period of treatment and the doses of drug in adoptive immunotherapy are significantly less than the active method. A recommendation to oncologists has also been presented.

Keywords: Tumor, immunotherapy, fuzzy controller, Genetic algorithm, mathematical model.

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Authors: M. Salehi, R. Tavakkoli-Moghaddam

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Selection of a project among a set of possible alternatives is a difficult task that the decision maker (DM) has to face. In this paper, by using a fuzzy TOPSIS technique we propose a new method for a project selection problem. After reviewing four common methods of comparing investment alternatives (net present value, rate of return, benefit cost analysis and payback period) we use them as criteria in a TOPSIS technique. First we calculate the weight of each criterion by a pairwise comparison and then we utilize the improved TOPSIS assessment for the project selection.

Keywords: Fuzzy Theory, Pairwise Comparison, ProjectSelection, TOPSIS Technique.

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Authors: Mir Hadi Seyedafsari, Iraj Hasanzadeh

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Like other external sorting algorithms, the presented algorithm is a two step algorithm including internal and external steps. The first part of the algorithm is like the other similar algorithms but second part of that is including a new easy implementing method which has reduced the vast number of inputoutput operations saliently. As decreasing processor operating time does not have any effect on main algorithm speed, any improvement in it should be done through decreasing the number of input-output operations. This paper propose an easy algorithm for choose the correct record location of the final list. This decreases the time complexity and makes the algorithm faster.

Keywords: External sorting algorithm, internal sortingalgorithm, fast sorting, robust algorithm.

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Authors: Hadi Gholizadeh, Ali Tajdin

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To have effective production planning, it is necessary to control the quality of processes. This paper aims at improving the performance of the disposable essentials process using statistical quality control and goal programming in a vague environment. That is expressed uncertainty because there is always a measurement error in the real world. Therefore, in this study, the conditions are examined in a vague environment that is a distance-based environment. The disposable essentials process in Kach Company was studied. Statistical control tools were used to characterize the existing process for four factor responses including the average of disposable glasses’ weights, heights, crater diameters, and volumes. Goal programming was then utilized to find the combination of optimal factors setting in a vague environment which is measured to apply uncertainty of the initial information when some of the parameters of the models are vague; also, the fuzzy regression model is used to predict the responses of the four described factors. Optimization results show that the process capability index values for disposable glasses’ average of weights, heights, crater diameters and volumes were improved. Such increasing the quality of the products and reducing the waste, which will reduce the cost of the finished product, and ultimately will bring customer satisfaction, and this satisfaction, will mean increased sales.

Keywords: Goal programming, quality control, vague environment, disposable glasses’ optimization, fuzzy regression.

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Authors: Ali Ghaffari, Mansour Nikkhah Bahrami, Hesam Parsa

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In this paper a comprehensive model of a fossil fueled power plant (FFPP) is developed in order to evaluate the performance of a newly designed turbine follower controller. Considering the drawbacks of previous works, an overall model is developed to minimize the error between each subsystem model output and the experimental data obtained at the actual power plant. The developed model is organized in two main subsystems namely; Boiler and Turbine. Considering each FFPP subsystem characteristics, different modeling approaches are developed. For economizer, evaporator, superheater and reheater, first order models are determined based on principles of mass and energy conservation. Simulations verify the accuracy of the developed models. Due to the nonlinear characteristics of attemperator, a new model, based on a genetic-fuzzy systems utilizing Pittsburgh approach is developed showing a promising performance vis-à-vis those derived with other methods like ANFIS. The optimization constraints are handled utilizing penalty functions. The effect of increasing the number of rules and membership functions on the performance of the proposed model is also studied and evaluated. The turbine model is developed based on the equation of adiabatic expansion. Parameters of all evaluated models are tuned by means of evolutionary algorithms. Based on the developed model a fuzzy PI controller is developed. It is then successfully implemented in the turbine follower control strategy of the plant. In this control strategy instead of keeping control parameters constant, they are adjusted on-line with regard to the error and the error rate. It is shown that the response of the system improves significantly. It is also shown that fuel consumption decreases considerably.

Keywords: Attemperator, Evolutionary algorithms, Fossil fuelled power plant (FFPP), Fuzzy set theory, Gain scheduling

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Authors: T. Wanyama, B. Far

Abstract:

Automatic irrigation systems usually conveniently protect landscape investment. While conventional irrigation systems are known to be inefficient, automated ones have the potential to optimize water usage. In fact, there is a new generation of irrigation systems that are smart in the sense that they monitor the weather, soil conditions, evaporation and plant water use, and automatically adjust the irrigation schedule. In this paper, we present an agent based smart irrigation system. The agents are built using a mix of commercial off the shelf software, including MATLAB, Microsoft Excel and KEPServer Ex5 OPC server, and custom written code. The Irrigation Scheduler Agent uses fuzzy logic to integrate the information that affect the irrigation schedule. In addition, the Multi-Agent system uses Open Platform Connectivity (OPC) technology to share data. OPC technology enables the Irrigation Scheduler Agent to communicate over the Internet, making the system scalable to a municipal or regional agent based water monitoring, management, and optimization system. Finally, this paper presents simulation and pilot installation test result that show the operational effectiveness of our system.

Keywords: Community water usage, fuzzy logic, irrigation, multi-agent system.

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Authors: Rohit Gupta, Ruchika

Abstract:

In this paper, a PSO based fractional order PID (FOPID) controller is proposed for concentration control of an isothermal Continuous Stirred Tank Reactor (CSTR) problem. CSTR is used to carry out chemical reactions in industries, which possesses complex nonlinear dynamic characteristics. Particle Swarm Optimization algorithm technique, which is an evolutionary optimization technique based on the movement and intelligence of swarm is proposed for tuning of the controller for this system. Comparisons of proposed controller with conventional and fuzzy based controller illustrate the superiority of proposed PSO-FOPID controller.

Keywords: CSTR, Fractional Order PID Controller, Partical Swarm Optimization.

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Authors: Emrah Bulut, Okan Duru, Shigeru Yoshida

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In this study, a fuzzy integrated logical forecasting method (FILF) is extended for multi-variate systems by using a vector autoregressive model. Fuzzy time series forecasting (FTSF) method was recently introduced by Song and Chissom [1]-[2] after that Chen improved the FTSF method. Rather than the existing literature, the proposed model is not only compared with the previous FTS models, but also with the conventional time series methods such as the classical vector autoregressive model. The cluster optimization is based on the C-means clustering method. An empirical study is performed for the prediction of the chartering rates of a group of dry bulk cargo ships. The root mean squared error (RMSE) metric is used for the comparing of results of methods and the proposed method has superiority than both traditional FTS methods and also the classical time series methods.

Keywords: C-means clustering, Fuzzy time series, Multi-variate design

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Authors: N. Samarinas, C. Evangelides, C. Vrekos

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The aim of this paper is the comparison of three different methods, in order to produce fuzzy tolerance relations for rainfall data classification. More specifically, the three methods are correlation coefficient, cosine amplitude and max-min method. The data were obtained from seven rainfall stations in the region of central Greece and refers to 20-year time series of monthly rainfall height average. Three methods were used to express these data as a fuzzy relation. This specific fuzzy tolerance relation is reformed into an equivalence relation with max-min composition for all three methods. From the equivalence relation, the rainfall stations were categorized and classified according to the degree of confidence. The classification shows the similarities among the rainfall stations. Stations with high similarity can be utilized in water resource management scenarios interchangeably or to augment data from one to another. Due to the complexity of calculations, it is important to find out which of the methods is computationally simpler and needs fewer compositions in order to give reliable results.

Keywords: Classification, fuzzy logic, tolerance relations, rainfall data.

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