Marquardt Algorithm

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Lieven Vandevelde - One of the best experts on this subject based on the ideXlab platform.

  • load frequency control for multi area power systems a new type 2 fuzzy approach based on levenberg Marquardt Algorithm
    Isa Transactions, 2021
    Co-Authors: Ali Dokht Shakibjoo, Mohammad Moradzadeh, Seyed Zeinolabedin Moussavi, Ardashir Mohammadzadeh, Lieven Vandevelde
    Abstract:

    In this study, a new fuzzy approach is proposed for load frequency control (LFC) of a multi-area power system. The main control system is constructed by use of interval type-2 fuzzy inference systems (IT2FIS) and fractional-order calculus. In designing the controller, there is no need for the system dynamics, therefore the system Jacobian is obtained by a multilayer perceptron neural network (MLP-NN). Uncertainties are modeled by IT2FIS, and for training fuzzy parameters, Levenberg-Marquardt Algorithm (LMA) is used, which is faster and more robust than gradient descent Algorithm (GDA). The system stability is studied by Matignon's stability method under time-varying disturbances. A comparison between the proposed controller with type-1 fuzzy controller on the New England 39-bus test system is also carried out. The simulations demonstrate the superiority of the designed controller.

Mohammad Moradzadeh - One of the best experts on this subject based on the ideXlab platform.

  • load frequency control for multi area power systems a new type 2 fuzzy approach based on levenberg Marquardt Algorithm
    Isa Transactions, 2021
    Co-Authors: Ali Dokht Shakibjoo, Mohammad Moradzadeh, Seyed Zeinolabedin Moussavi, Ardashir Mohammadzadeh, Lieven Vandevelde
    Abstract:

    In this study, a new fuzzy approach is proposed for load frequency control (LFC) of a multi-area power system. The main control system is constructed by use of interval type-2 fuzzy inference systems (IT2FIS) and fractional-order calculus. In designing the controller, there is no need for the system dynamics, therefore the system Jacobian is obtained by a multilayer perceptron neural network (MLP-NN). Uncertainties are modeled by IT2FIS, and for training fuzzy parameters, Levenberg-Marquardt Algorithm (LMA) is used, which is faster and more robust than gradient descent Algorithm (GDA). The system stability is studied by Matignon's stability method under time-varying disturbances. A comparison between the proposed controller with type-1 fuzzy controller on the New England 39-bus test system is also carried out. The simulations demonstrate the superiority of the designed controller.

Okyay Kaynak - One of the best experts on this subject based on the ideXlab platform.

  • levenberg Marquardt Algorithm for the training of type 2 fuzzy neuro systems with a novel type 2 fuzzy membership function
    2011 IEEE Symposium on Advances in Type-2 Fuzzy Logic Systems (T2FUZZ), 2011
    Co-Authors: Mojtaba Ahmadieh Khanesar, Erdal Kayacan, Mohammad Teshnehlab, Okyay Kaynak
    Abstract:

    A new training approach based on the Levenberg-Marquardt Algorithm is proposed for type-2 fuzzy neural networks. While conventional gradient descent Algorithms use only the first order derivative, the proposed Algorithm used in this paper benefits from the first and the second order derivatives which makes the training procedure faster. Besides, this approach is more robust than the other techniques that use the second order derivatives, e.g. Gauss-Newton's method. The training Algorithm proposed is tested on the training of a type-2 fuzzy neural network used for the prediction of a chaotic Mackey-Glass time series. The results show that the learning Algorithm proposed not only results in faster training but also in a better forecasting accuracy.

  • a novel optimization procedure for training of fuzzy inference systems by combining variable structure systems technique and levenberg Marquardt Algorithm
    Fuzzy Sets and Systems, 2001
    Co-Authors: Okyay Kaynak
    Abstract:

    Abstract This paper presents a novel training Algorithm for fuzzy inference systems. The Algorithm combines the LevenbergMarquardt Algorithm with variable structure systems approach. The combination is performed by expressing the parameter update rule in continuous time and application of sliding mode control method to the gradient-based training procedure. The proposed combination therefore exhibits a degree of robustness to the unmodeled multivariable internal dynamics of LevenbergMarquardt technique. With conventional training procedures, the excitation of this dynamics during a training cycle can lead to instability, which may be difficult to alleviate due to the multidimensionality of the solution space and the ambiguities concerning the environmental conditions. This paper proves that a fuzzy inference mechanism can be trained such that the adjustable parameter values are forced to settle down (parameter stabilization) while minimizing an appropriate cost function (cost optimization). In the application example, control of a two degrees of freedom direct drive SCARA robotic manipulator is considered. As the controller, a standard fuzzy system architecture is used and the parameter tuning is performed by the proposed Algorithm.

  • training of fuzzy inference systems by combining variable structure systems technique and levenberg Marquardt Algorithm
    Conference of the Industrial Electronics Society, 1999
    Co-Authors: Okyay Kaynak, Bogdan M Wilamowski
    Abstract:

    This paper presents a novel training Algorithm for fuzzy inference systems. The Algorithm combines the Levenberg-Marquardt Algorithm with variable structure systems approach. The combination is performed by expressing the parameter update rule in continuous time and application of sliding control method to the gradient based training procedure. In this paper, a fuzzy inference mechanism that can be trained such that the adjustable parameter values are forced to settle down (parameter stabilization) while minimizing an appropriate cost function (cost optimization), is discussed. In the application example, control of a two degrees of freedom direct drive SCARA robotic manipulator is considered. As the controller, a standard fuzzy system architecture is used and the parameter tuning is performed by the proposed Algorithm.

Ali Dokht Shakibjoo - One of the best experts on this subject based on the ideXlab platform.

  • load frequency control for multi area power systems a new type 2 fuzzy approach based on levenberg Marquardt Algorithm
    Isa Transactions, 2021
    Co-Authors: Ali Dokht Shakibjoo, Mohammad Moradzadeh, Seyed Zeinolabedin Moussavi, Ardashir Mohammadzadeh, Lieven Vandevelde
    Abstract:

    In this study, a new fuzzy approach is proposed for load frequency control (LFC) of a multi-area power system. The main control system is constructed by use of interval type-2 fuzzy inference systems (IT2FIS) and fractional-order calculus. In designing the controller, there is no need for the system dynamics, therefore the system Jacobian is obtained by a multilayer perceptron neural network (MLP-NN). Uncertainties are modeled by IT2FIS, and for training fuzzy parameters, Levenberg-Marquardt Algorithm (LMA) is used, which is faster and more robust than gradient descent Algorithm (GDA). The system stability is studied by Matignon's stability method under time-varying disturbances. A comparison between the proposed controller with type-1 fuzzy controller on the New England 39-bus test system is also carried out. The simulations demonstrate the superiority of the designed controller.

Jose Jesus De Rubio - One of the best experts on this subject based on the ideXlab platform.

  • Stability Analysis of the Modified Levenberg-Marquardt Algorithm for the Artificial Neural Network Training.
    IEEE transactions on neural networks and learning systems, 2020
    Co-Authors: Jose Jesus De Rubio
    Abstract:

    The Levenberg-Marquardt and Newton are two Algorithms that use the Hessian for the artificial neural network learning. In this article, we propose a modified Levenberg-Marquardt Algorithm for the artificial neural network learning containing the training and testing stages. The modified Levenberg-Marquardt Algorithm is based on the Levenberg-Marquardt and Newton Algorithms but with the following two differences to assure the error stability and weights boundedness: 1) there is a singularity point in the learning rates of the Levenberg-Marquardt and Newton Algorithms, while there is not a singularity point in the learning rate of the modified Levenberg-Marquardt Algorithm and 2) the Levenberg-Marquardt and Newton Algorithms have three different learning rates, while the modified Levenberg-Marquardt Algorithm only has one learning rate. The error stability and weights boundedness of the modified Levenberg-Marquardt Algorithm are assured based on the Lyapunov technique. We compare the artificial neural network learning with the modified Levenberg-Marquardt, Levenberg-Marquardt, Newton, and stable gradient Algorithms for the learning of the electric and brain signals data set.