Shamanskii Method for Solving Parameterized Fuzzy Nonlinear Equations

Sulaiman, Ibrahim Mohammed; Mamat, Mustafa; Ghazali, Puspa Liza

doi:10.11121/ijocta.01.2021.00843

Cited by 4 publications

(3 citation statements)

References 21 publications

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“…FLC has an advanced level of efficiency for nonlinear converters [10]. Many researchers approved FLC to become one of intelligent controller for their appliances and successfully implemented their tactics [11][12][13][14]. FLC does not require an accurate mathematical model of a circuit.…”

Section: Fuzzy Logic Controllermentioning

confidence: 99%

Fractional fuzzy PI controller using particle swarm optimization to improve power factor by boost converter

Demirtas,

Ahmad

2023

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

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The power circuit of AC voltage controller capable of operating at a leading, lagging, and unity power factor is studied by a lot of researchers in the literature. Circuits working with high switching frequency are known as power factor correctors (PFCs). The single-phase boost converter has become the most popular topology for power factor correction (PFC) in general purpose power supplies. Power factor correction circuit provides conventional benefits to electric power systems. The benefits are the reduction of power factor penalty and utility bill and power loss. Therefore, a boost converter power factor correction scheme is presented in this paper. A PI, fuzzy logic PI and fractional order PI (FOPI) controllers are used to fix an active shaping of input current of the circuit and to improve the power factor. The controller parameters (coefficients) are optimized using the Particle Swarm Optimization (PSO) algorithm. Average current mode control (ACMC) method is used in the circuit. The converter circuit consists of a single-phase bridge rectifier, boost converter, transformer and load. A mathematical model of the plant is required to design the PI controller. A model for power factor correction circuit is formed in MATLAB/Simulink toolbox and a filter is designed to reduce THD value. The proposed model is simulated using a combination of PI, fuzzy logic and FOPI controllers. The control scheme is applied to 600 Watt PFC boost converter to get 400 Volt DC output voltage and 0.99 power factor. The input voltage is 230 VRMS with 50 Hz. The combination of FOPI and PI controller has the best solution to control the power factor according to PI and fuzzy controllers.

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Section: Fuzzy Logic Controllermentioning

confidence: 99%

Fractional fuzzy PI controller using particle swarm optimization to improve power factor by boost converter

Demirtas,

Ahmad

2023

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

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“…One of the disadvantages of the method is that it requires calculating the inverse Hessian matrix for each iteration. The Shamanskii method was used in [29]. One of the disadvantages of the method is that it does not guarantee reaching a solution.…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

Optimization algorithm based on the Euler method for solving fuzzy nonlinear equations

Ibraheem

Khudhur

2022

EEJET

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In a variety of engineering, scientific challenges, mathematics, chemistry, physics, biology, machine learning, deep learning, regression classification, computer science, programming, artificial intelligence, in the military, medical and engineering industries, robotics and smart cars, fuzzy nonlinear equations play a critical role. As a result, in this paper, an Optimization Algorithm based on the Euler Method approach for solving fuzzy nonlinear equations is proposed. In mathematics and computer science, the Euler approach (sometimes called the forward Euler method) is a first-order numerical strategy for solving ordinary differential equations (ODEs) with a specified initial value. The local error is proportional to the square of the step size, while the general error is proportional to the step size, according to the Euler technique. The Euler method is frequently used to create more complicated algorithms. The Optimization Algorithm Based on the Euler Method (OBE) uses the logic of slope differences, which is computed by the Euler approach for global optimizations as a search mechanism for promising logic. Furthermore, the mechanism of the proposed work takes advantage of two active phases: exploration and exploitation to find the most important promising areas within the distinct space and the best solutions globally based on a positive movement towards it. In order to avoid the solution of local optimal and increase the rate of convergence, we use the ESQ mechanism. The optimization algorithm based on the Euler method (OBE) is very efficient in solving fuzzy nonlinear equations and approaches the global minimum and avoids the local minimum. In comparison with the GWO algorithm, we notice a clear superiority of the OBE algorithm in reaching the solution with higher accuracy. We note from the numerical results that the new algorithm is 50 % superior to the GWO algorithm in Example 1, 51 % in Example 2 and 55 % in Example 3.

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“…(1) 𝑎𝑥 3 + 𝑏𝑥 2 + 𝑐𝑥 − 𝑑 = 𝑒 (2) 𝑝𝑥 2 + 𝑞𝑐𝑜𝑠(𝑥) = 𝑟 (3) 𝑐𝑥 2 + 𝑑 = 𝑒 Where 𝑎, 𝑏, 𝑐, 𝑑, 𝑒, 𝑝, 𝑞, 𝑎𝑛𝑑 𝑟 are intuitionistic fuzzy numbers. Numerous numerical algorithms have been developed for solving fuzzy nonlinear equations to overcome this drawback (Yang et al, 2008;Abbasbandy and Asady, 2004;Kajani et al, 2005;Sulaiman et al, 2016;Mohammed et al, 2020;Umar et al, 2020a;Sulaiman et al, 2021Sulaiman et al, , 2022b. However, only a few works of literature have investigated the performance of new iterative methods for solving equations whose coefficients are intuitionistic.…”

Section: Introductionmentioning

confidence: 99%

An Efficient Hybrid Conjugate Gradient Algorithm for Solving Intuitionistic Fuzzy Nonlinear Equations

Omesa¹,

Sulaiman²,

Yusuf³

et al. 2023

BAS-SJKFU

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This paper presents an iterative algorithm for solving intuitionistic fuzzy nonlinear equations (IFNEs). The proposed method is based on the classical conjugate gradient (CG) search direction. An interesting feature of the new algorithm is that it considers problems based on the special triangular intuitionistic fuzzy number. For this purpose, intuitionistic fuzzy quantities are transformed into membership and non-membership parametric forms, and a line search procedure is employed to compute the step length. Preliminary results from numerical experiments are presented to demonstrate the performance of the method. It is observed that the proposed hybrid CG method is highly effective and promising. KEYWORDS Hybrid CG, intuitionistic fuzzy nonlinear equation, parametric form, step length, inexact line search

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Shamanskii Method for Solving Parameterized Fuzzy Nonlinear Equations

Cited by 4 publications

References 21 publications

Fractional fuzzy PI controller using particle swarm optimization to improve power factor by boost converter

Fractional fuzzy PI controller using particle swarm optimization to improve power factor by boost converter

Optimization algorithm based on the Euler method for solving fuzzy nonlinear equations

An Efficient Hybrid Conjugate Gradient Algorithm for Solving Intuitionistic Fuzzy Nonlinear Equations

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