The Experts below are selected from a list of 297 Experts worldwide ranked by ideXlab platform
Jerry M. Mendel - One of the best experts on this subject based on the ideXlab platform.
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Maclaurin Series expansion complexity-reduced center of sets type-reduction + defuzzification for interval type-2 fuzzy systems
2016 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), 2016Co-Authors: Mojtaba Ahmadieh Khanesar, Jerry M. MendelAbstract:This paper provides a mathematical analysis that shows how the crisp output of an IT2 FLS that is obtained by using the Begian-Melek-Mendel (BMM) formula compares to the one obtained by using center-of-sets type-reduction followed by defuzzification (COS TR + D). This is made possible by reformulating the structural solutions of the two optimization problems that are associated with COS TR, and then expanding each of them using a Maclaurin Series expansion. As a result of doing this, we show that BMM is the zero-order approximation to COS TR + D. Additionally, by retaining the zero-order and first-order terms from the Maclaurin Series expansions, we provide a new Enhanced BMM, one that is non-iterative, has a closed form and is much faster than using the EKM algorithms for COS TR. Although the Enhanced BMM formula is slower than BMM, we demonstrate, by means of extensive simulations, that it is from 5% to 50% more accurate than is BMM for achieving the same numerical solution that is obtained from COS TR + D; and, it is at least 94% faster than when EKM is used for COS TR +D, which makes the Extended BMM a very strong candidate for use in real time applications of IT2 FLSs.
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Maclaurin Series expansion complexity reduced center of sets type reduction defuzzification for interval type 2 fuzzy systems
IEEE International Conference on Fuzzy Systems, 2016Co-Authors: Mojtaba Ahmadieh Khanesar, Jerry M. MendelAbstract:This paper provides a mathematical analysis that shows how the crisp output of an IT2 FLS that is obtained by using the Begian-Melek-Mendel (BMM) formula compares to the one obtained by using center-of-sets type-reduction followed by defuzzification (COS TR + D). This is made possible by reformulating the structural solutions of the two optimization problems that are associated with COS TR, and then expanding each of them using a Maclaurin Series expansion. As a result of doing this, we show that BMM is the zero-order approximation to COS TR + D. Additionally, by retaining the zero-order and first-order terms from the Maclaurin Series expansions, we provide a new Enhanced BMM, one that is non-iterative, has a closed form and is much faster than using the EKM algorithms for COS TR. Although the Enhanced BMM formula is slower than BMM, we demonstrate, by means of extensive simulations, that it is from 5% to 50% more accurate than is BMM for achieving the same numerical solution that is obtained from COS TR + D; and, it is at least 94% faster than when EKM is used for COS TR +D, which makes the Extended BMM a very strong candidate for use in real time applications of IT2 FLSs.
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FUZZ-IEEE - Maclaurin Series expansion complexity-reduced center of sets type-reduction + defuzzification for interval type-2 fuzzy systems
2016 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), 2016Co-Authors: Mojtaba Ahmadieh Khanesar, Jerry M. MendelAbstract:This paper provides a mathematical analysis that shows how the crisp output of an IT2 FLS that is obtained by using the Begian-Melek-Mendel (BMM) formula compares to the one obtained by using center-of-sets type-reduction followed by defuzzification (COS TR + D). This is made possible by reformulating the structural solutions of the two optimization problems that are associated with COS TR, and then expanding each of them using a Maclaurin Series expansion. As a result of doing this, we show that BMM is the zero-order approximation to COS TR + D. Additionally, by retaining the zero-order and first-order terms from the Maclaurin Series expansions, we provide a new Enhanced BMM, one that is non-iterative, has a closed form and is much faster than using the EKM algorithms for COS TR. Although the Enhanced BMM formula is slower than BMM, we demonstrate, by means of extensive simulations, that it is from 5% to 50% more accurate than is BMM for achieving the same numerical solution that is obtained from COS TR + D; and, it is at least 94% faster than when EKM is used for COS TR +D, which makes the Extended BMM a very strong candidate for use in real time applications of IT2 FLSs.
Mojtaba Ahmadieh Khanesar - One of the best experts on this subject based on the ideXlab platform.
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Maclaurin Series expansion complexity-reduced center of sets type-reduction + defuzzification for interval type-2 fuzzy systems
2016 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), 2016Co-Authors: Mojtaba Ahmadieh Khanesar, Jerry M. MendelAbstract:This paper provides a mathematical analysis that shows how the crisp output of an IT2 FLS that is obtained by using the Begian-Melek-Mendel (BMM) formula compares to the one obtained by using center-of-sets type-reduction followed by defuzzification (COS TR + D). This is made possible by reformulating the structural solutions of the two optimization problems that are associated with COS TR, and then expanding each of them using a Maclaurin Series expansion. As a result of doing this, we show that BMM is the zero-order approximation to COS TR + D. Additionally, by retaining the zero-order and first-order terms from the Maclaurin Series expansions, we provide a new Enhanced BMM, one that is non-iterative, has a closed form and is much faster than using the EKM algorithms for COS TR. Although the Enhanced BMM formula is slower than BMM, we demonstrate, by means of extensive simulations, that it is from 5% to 50% more accurate than is BMM for achieving the same numerical solution that is obtained from COS TR + D; and, it is at least 94% faster than when EKM is used for COS TR +D, which makes the Extended BMM a very strong candidate for use in real time applications of IT2 FLSs.
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Maclaurin Series expansion complexity reduced center of sets type reduction defuzzification for interval type 2 fuzzy systems
IEEE International Conference on Fuzzy Systems, 2016Co-Authors: Mojtaba Ahmadieh Khanesar, Jerry M. MendelAbstract:This paper provides a mathematical analysis that shows how the crisp output of an IT2 FLS that is obtained by using the Begian-Melek-Mendel (BMM) formula compares to the one obtained by using center-of-sets type-reduction followed by defuzzification (COS TR + D). This is made possible by reformulating the structural solutions of the two optimization problems that are associated with COS TR, and then expanding each of them using a Maclaurin Series expansion. As a result of doing this, we show that BMM is the zero-order approximation to COS TR + D. Additionally, by retaining the zero-order and first-order terms from the Maclaurin Series expansions, we provide a new Enhanced BMM, one that is non-iterative, has a closed form and is much faster than using the EKM algorithms for COS TR. Although the Enhanced BMM formula is slower than BMM, we demonstrate, by means of extensive simulations, that it is from 5% to 50% more accurate than is BMM for achieving the same numerical solution that is obtained from COS TR + D; and, it is at least 94% faster than when EKM is used for COS TR +D, which makes the Extended BMM a very strong candidate for use in real time applications of IT2 FLSs.
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FUZZ-IEEE - Maclaurin Series expansion complexity-reduced center of sets type-reduction + defuzzification for interval type-2 fuzzy systems
2016 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), 2016Co-Authors: Mojtaba Ahmadieh Khanesar, Jerry M. MendelAbstract:This paper provides a mathematical analysis that shows how the crisp output of an IT2 FLS that is obtained by using the Begian-Melek-Mendel (BMM) formula compares to the one obtained by using center-of-sets type-reduction followed by defuzzification (COS TR + D). This is made possible by reformulating the structural solutions of the two optimization problems that are associated with COS TR, and then expanding each of them using a Maclaurin Series expansion. As a result of doing this, we show that BMM is the zero-order approximation to COS TR + D. Additionally, by retaining the zero-order and first-order terms from the Maclaurin Series expansions, we provide a new Enhanced BMM, one that is non-iterative, has a closed form and is much faster than using the EKM algorithms for COS TR. Although the Enhanced BMM formula is slower than BMM, we demonstrate, by means of extensive simulations, that it is from 5% to 50% more accurate than is BMM for achieving the same numerical solution that is obtained from COS TR + D; and, it is at least 94% faster than when EKM is used for COS TR +D, which makes the Extended BMM a very strong candidate for use in real time applications of IT2 FLSs.
Sishaj P Simon - One of the best experts on this subject based on the ideXlab platform.
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emission constrained economic dispatch with valve point effect using Maclaurin Series based lagrangian method
International Journal of Power and Energy Conversion, 2012Co-Authors: S Hemamalini, Sishaj P SimonAbstract:This paper presents Lagrangian-based technique to solve economic emission load dispatch (EELD) of valve-point loaded generating units considering emission constraint. The EELD problem has gained recent attention due to the deregulation of power industry and environmental regulations. In this paper, two conflicting functions (fuel cost and emission) are considered and formulated as a single objective optimisation problem by the weighted sum method. Based on the literature survey, it is found that cost function is taken as a quadratic function and solved for emission economic dispatch. Here, in cost function, a sine term is added to model the valve-point effect and an exponential term is used to model the emission function. Using Maclaurin Series, the sine and exponential terms are expanded and solved with Lagrangian multiplier method. The objective function is highly non-linear and the feasibility of the proposed method is validated with IEEE 30-bus system and ten-unit system. Results obtained with the proposed approach are compared with genetic algorithm.
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dynamic economic dispatch using Maclaurin Series based lagrangian method
Energy Conversion and Management, 2010Co-Authors: S Hemamalini, Sishaj P SimonAbstract:Abstract Dynamic economic dispatch (DED) is one of the important optimization problems in power system operation. This paper proposes Maclaurin Series based Lagrangian method (MSL) to solve the DED problem for generating units with valve-point effect, considering the ramp-rate limits and spinning reserve constraint. Using Maclaurin Series, the sine term used to model the valve-point effect is expanded and solved with Lagrangian method. The feasibility of the proposed method is validated with five unit test system for 24 h. Minute-by-minute dispatch for a large system with 40-units is also carried out in this work. Test results obtained with the proposed approach are compared with other techniques in the literature. The results obtained substantiate the applicability of the proposed method for solving dynamic economic dispatch problems with non-smooth cost functions.
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dynamic economic dispatch with valve point effect using Maclaurin Series based lagrangian method
International Journal of Computer Applications, 2010Co-Authors: S Hemamalini, Sishaj P SimonAbstract:Dynamic Economic Dispatch (DED) plays a vital role in power generation, operation and control. It is a complicated, non-linear constrained problem. In this paper, Maclaurin Series based Lagrangian method (MSL) is used to solve the DED problem for generating units with valve-point effect, considering the ramp rate limits. Using Maclaurin Series, the sine term used to model the valve-point effect is expanded and solved with Lagrangian method. The feasibility of the proposed method is validated for static economic dispatch problem for forty unit system and DED problem for five unit test system for 24 hour time interval. Results obtained with the proposed approach are compared with other techniques in the literature. The results obtained substantiate the applicability of the proposed method for solving static and dynamic economic dispatch problems with non-smooth cost functions.
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Maclaurin Series-based lagrangian method for economic dispatch with valve-point effect
IET Generation Transmission & Distribution, 2009Co-Authors: S Hemamalini, Sishaj P SimonAbstract:Power utilities in general use Lagrangian method to solve economic dispatch (ED) problem for ease of implementation. This is possible only if the cost function of generating units is convex. Owing to valve-point effect exhibited by multi-valve steam turbines, the cost function is non-convex. The Maclaurin Series-based Lagrangian method is proposed to solve complicated, non-convex and non-linear ED problems. In this method, the rectified sinusoid function is represented by Maclaurin sine Series expansion and is solved using the Lagrangian method. The problem is solved iteratively using lambda iteration method. The proposed methodology is validated using IEEE 30-bus test system. In addition, the effectiveness of the new algorithm is demonstrated with 3, 13 and 40 generator test systems available in the literature. The results obtained substantiate the applicability of the proposed method for solving ED problems with non-smooth cost functions at par with stochastic search techniques generally used.
S Hemamalini - One of the best experts on this subject based on the ideXlab platform.
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emission constrained economic dispatch with valve point effect using Maclaurin Series based lagrangian method
International Journal of Power and Energy Conversion, 2012Co-Authors: S Hemamalini, Sishaj P SimonAbstract:This paper presents Lagrangian-based technique to solve economic emission load dispatch (EELD) of valve-point loaded generating units considering emission constraint. The EELD problem has gained recent attention due to the deregulation of power industry and environmental regulations. In this paper, two conflicting functions (fuel cost and emission) are considered and formulated as a single objective optimisation problem by the weighted sum method. Based on the literature survey, it is found that cost function is taken as a quadratic function and solved for emission economic dispatch. Here, in cost function, a sine term is added to model the valve-point effect and an exponential term is used to model the emission function. Using Maclaurin Series, the sine and exponential terms are expanded and solved with Lagrangian multiplier method. The objective function is highly non-linear and the feasibility of the proposed method is validated with IEEE 30-bus system and ten-unit system. Results obtained with the proposed approach are compared with genetic algorithm.
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dynamic economic dispatch using Maclaurin Series based lagrangian method
Energy Conversion and Management, 2010Co-Authors: S Hemamalini, Sishaj P SimonAbstract:Abstract Dynamic economic dispatch (DED) is one of the important optimization problems in power system operation. This paper proposes Maclaurin Series based Lagrangian method (MSL) to solve the DED problem for generating units with valve-point effect, considering the ramp-rate limits and spinning reserve constraint. Using Maclaurin Series, the sine term used to model the valve-point effect is expanded and solved with Lagrangian method. The feasibility of the proposed method is validated with five unit test system for 24 h. Minute-by-minute dispatch for a large system with 40-units is also carried out in this work. Test results obtained with the proposed approach are compared with other techniques in the literature. The results obtained substantiate the applicability of the proposed method for solving dynamic economic dispatch problems with non-smooth cost functions.
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dynamic economic dispatch with valve point effect using Maclaurin Series based lagrangian method
International Journal of Computer Applications, 2010Co-Authors: S Hemamalini, Sishaj P SimonAbstract:Dynamic Economic Dispatch (DED) plays a vital role in power generation, operation and control. It is a complicated, non-linear constrained problem. In this paper, Maclaurin Series based Lagrangian method (MSL) is used to solve the DED problem for generating units with valve-point effect, considering the ramp rate limits. Using Maclaurin Series, the sine term used to model the valve-point effect is expanded and solved with Lagrangian method. The feasibility of the proposed method is validated for static economic dispatch problem for forty unit system and DED problem for five unit test system for 24 hour time interval. Results obtained with the proposed approach are compared with other techniques in the literature. The results obtained substantiate the applicability of the proposed method for solving static and dynamic economic dispatch problems with non-smooth cost functions.
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Maclaurin Series-based lagrangian method for economic dispatch with valve-point effect
IET Generation Transmission & Distribution, 2009Co-Authors: S Hemamalini, Sishaj P SimonAbstract:Power utilities in general use Lagrangian method to solve economic dispatch (ED) problem for ease of implementation. This is possible only if the cost function of generating units is convex. Owing to valve-point effect exhibited by multi-valve steam turbines, the cost function is non-convex. The Maclaurin Series-based Lagrangian method is proposed to solve complicated, non-convex and non-linear ED problems. In this method, the rectified sinusoid function is represented by Maclaurin sine Series expansion and is solved using the Lagrangian method. The problem is solved iteratively using lambda iteration method. The proposed methodology is validated using IEEE 30-bus test system. In addition, the effectiveness of the new algorithm is demonstrated with 3, 13 and 40 generator test systems available in the literature. The results obtained substantiate the applicability of the proposed method for solving ED problems with non-smooth cost functions at par with stochastic search techniques generally used.
Weibo Gong - One of the best experts on this subject based on the ideXlab platform.
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The mean waiting time of a GI/G/1 queue in light traffic via random thinning
Journal of Applied Probability, 1995Co-Authors: S. Nananukul, Weibo GongAbstract:In this paper, we derive the Maclaurin Series of the mean waiting time in light traffic for a GI/G/1 queue. The light traffic is defined by random thinning of the arrival process. The Maclaurin Series is derived with respect to the admission probability, and we prove that it has a positive radius of convergence. In the numerical examples, we use the Maclaurin Series to approximate the mean waiting time beyond light traffic by means of Padé approximation.
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THE MEAN WAITING TIME OF A GI/G/1 QUEUE IN LIGHT TRAFFIC VIA RANDOM THINNING
Journal of Applied Probability, 1995Co-Authors: S. Nananukul, Weibo GongAbstract:In this paper, we derive the Maclaurin Series f the mean waiting time in light traffic for a GI/G/1 queue. The light traffic is defined by random thinning of the arrival process. The Maclaurin Series is derived with respect to the admission probability, and we prove that it has a positive radius of convergence. In the numerical examples, we use the Maclaurin Series to approximate the mean waiting time beyond light traffic by means of Pade approximation
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On the Maclaurin Series in light traffic for a single server queue
Proceedings of 32nd IEEE Conference on Decision and Control, 1993Co-Authors: S. Nananukul, Weibo GongAbstract:In this paper, we consider 2 definitions of light traffic: 1) rescaling the interarrival times, and 2) thinning the arrival process. We derive the Maclaurin Series of the mean waiting time E[W] in light traffic for a GI/G/1 queue using each definition. Also, we show that the Maclaurin Series have a positive radius of convergence.
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THE Maclaurin Series FOR THE GI/G/1 QUEUE
Journal of Applied Probability, 1992Co-Authors: Weibo Gong, Jian-qiang HuAbstract:We derive the Maclaurin Series for the moments of the system time and the delay with respect to the parameters in the service time or interarrival time distributions in the GI/G /1 queue. The coefficients in these Series are expressed in terms of the derivatives of the interarrival time density function evaluated at zero and the moments of the service time distribution, which can be easily calculated through a simple recursive procedure. The light traffic derivatives can be obtained from these Series. For the M/G /1 queue, we are able to recover the formulas for the moments of the system time and the delay, including the Pollaczek–Khinchin mean-value formula.
