Search results for: radial basis function neural networks

Authors: Hazem M. El-Bakry, Qiangfu Zhao

Abstract:

In recent years, fast neural networks for object/face detection have been introduced based on cross correlation in the frequency domain between the input matrix and the hidden weights of neural networks. In our previous papers [3,4], fast neural networks for certain code detection was introduced. It was proved in [10] that for fast neural networks to give the same correct results as conventional neural networks, both the weights of neural networks and the input matrix must be symmetric. This condition made those fast neural networks slower than conventional neural networks. Another symmetric form for the input matrix was introduced in [1-9] to speed up the operation of these fast neural networks. Here, corrections for the cross correlation equations (given in [13,15,16]) to compensate for the symmetry condition are presented. After these corrections, it is proved mathematically that the number of computation steps required for fast neural networks is less than that needed by classical neural networks. Furthermore, there is no need for converting the input data into symmetric form. Moreover, such new idea is applied to increase the speed of neural networks in case of processing complex values. Simulation results after these corrections using MATLAB confirm the theoretical computations.

Keywords: Fast Code/Data Detection, Neural Networks, Cross Correlation, real/complex values.

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Authors: Abdulbaset Saad, Adel Younis, Zuomin Dong

Abstract:

For design optimization with high-dimensional expensive problems, an effective and efficient optimization methodology is desired. This work proposes a series of modification to the Differential Evolution (DE) algorithm for solving computation Intensive Black-Box Problems. The proposed methodology is called Radial Basis Meta-Model Algorithm Assisted Differential Evolutionary (RBF-DE), which is a global optimization algorithm based on the meta-modeling techniques. A meta-modeling assisted DE is proposed to solve computationally expensive optimization problems. The Radial Basis Function (RBF) model is used as a surrogate model to approximate the expensive objective function, while DE employs a mechanism to dynamically select the best performing combination of parameters such as differential rate, cross over probability, and population size. The proposed algorithm is tested on benchmark functions and real life practical applications and problems. The test results demonstrate that the proposed algorithm is promising and performs well compared to other optimization algorithms. The proposed algorithm is capable of converging to acceptable and good solutions in terms of accuracy, number of evaluations, and time needed to converge.

Keywords: Differential evolution, engineering design, expensive computations, meta-modeling, radial basis function, optimization.

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Authors: Naiqin Feng, Fang Wang, Yuhui Qiu

Abstract:

A new approach to promote the generalization ability of neural networks is presented. It is based on the point of view of fuzzy theory. This approach is implemented through shrinking or magnifying the input vector, thereby reducing the difference between training set and testing set. It is called “shrinking-magnifying approach" (SMA). At the same time, a new algorithm; α-algorithm is presented to find out the appropriate shrinking-magnifying-factor (SMF) α and obtain better generalization ability of neural networks. Quite a few simulation experiments serve to study the effect of SMA and α-algorithm. The experiment results are discussed in detail, and the function principle of SMA is analyzed in theory. The results of experiments and analyses show that the new approach is not only simpler and easier, but also is very effective to many neural networks and many classification problems. In our experiments, the proportions promoting the generalization ability of neural networks have even reached 90%.

Keywords: Fuzzy theory, generalization, misclassification rate, neural network.

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Authors: Aziah Khamis, H. Shareef

Abstract:

The purpose of planned islanding is to construct a power island during system disturbances which are commonly formed for maintenance purpose. However, in most of the cases island mode operation is not allowed. Therefore distributed generators (DGs) must sense the unplanned disconnection from the main grid. Passive technique is the most commonly used method for this purpose. However, it needs improvement in order to identify the islanding condition. In this paper an effective method for identification of islanding condition based on phase space and neural network techniques has been developed. The captured voltage waveforms at the coupling points of DGs are processed to extract the required features. For this purposed a method known as the phase space techniques is used. Based on extracted features, two neural network configuration namely radial basis function and probabilistic neural networks are trained to recognize the waveform class. According to the test result, the investigated technique can provide satisfactory identification of the islanding condition in the distribution system.

Keywords: Classification, Islanding detection, Neural network, Phase space.

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Authors: Miaomiao Yang, Shouming Zhong

Abstract:

This paper studies the problem of stability criteria for neural networks with two additive time-varying delays.A new Lyapunov-Krasovskii function is constructed and some new delay dependent stability criterias are derived in the terms of linear matrix inequalities(LMI), zero equalities and reciprocally convex approach.The several stability criterion proposed in this paper is simpler and effective. Finally,numerical examples are provided to demonstrate the feasibility and effectiveness of our results.

Keywords: Stability, Neural networks, Linear Matrix Inequalities (LMI) , Lyapunov function, Time-varying delays

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Authors: Ernst D. Schmitter

Abstract:

Monitoring lightning electromagnetic pulses (sferics) and other terrestrial as well as extraterrestrial transient radiation signals is of considerable interest for practical and theoretical purposes in astro- and geophysics as well as meteorology. Managing a continuous flow of data, automation of the analysis and classification process is important. Features based on a combination of wavelet and statistical methods proved efficient for this task and serve as input into a radial basis function network that is trained to discriminate transient shapes from pulse like to wave like. We concentrate on signals in the Very Low Frequency (VLF, 3 -30 kHz) range in this paper, but the developed methods are independent of this specific choice.

Keywords: Transient signals, statistics, wavelets, neural networks

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Authors: Miaomiao Yang, Shouming Zhong

Abstract:

This paper studies the problem of asymptotically stability for neural networks with time-varying delays.By establishing a suitable Lyapunov-Krasovskii function and several novel sufficient conditions are obtained to guarantee the asymptotically stability of the considered system. Finally,two numerical examples are given to illustrate the effectiveness of the proposed main results.

Keywords: Neural networks, Lyapunov-Krasovskii, Time-varying delays, Linear matrix inequality.

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Authors: A. Johannet, B. Vayssade, D. Bertin

Abstract:

Neural networks are well known for their ability to model non linear functions, but as statistical methods usually does, they use a no parametric approach thus, a priori knowledge is not obvious to be taken into account no more than the a posteriori knowledge. In order to deal with these problematics, an original way to encode the knowledge inside the architecture is proposed. This method is applied to the problem of the evapotranspiration inside karstic aquifer which is a problem of huge utility in order to deal with water resource.

Keywords: Neural-Networks, Hydrology, Evapotranpiration, Hidden Function Modeling.

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Authors: Rajoo Pandey

Abstract:

Most of the commonly used blind equalization algorithms are based on the minimization of a nonconvex and nonlinear cost function and a neural network gives smaller residual error as compared to a linear structure. The efficacy of complex valued feedforward neural networks for blind equalization of linear and nonlinear communication channels has been confirmed by many studies. In this paper we present two neural network models for blind equalization of time-varying channels, for M-ary QAM and PSK signals. The complex valued activation functions, suitable for these signal constellations in time-varying environment, are introduced and the learning algorithms based on the CMA cost function are derived. The improved performance of the proposed models is confirmed through computer simulations.

Keywords: Blind Equalization, Neural Networks, Constant Modulus Algorithm, Time-varying channels.

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Authors: Guang Zhou, Shouming Zhong

Abstract:

In this paper, we investigate the problem of the existence, uniqueness and global asymptotic stability of the equilibrium point for a class of neural networks, the neutral system has mixed time delays and parameter uncertainties. Under the assumption that the activation functions are globally Lipschitz continuous, we drive a new criterion for the robust stability of a class of neural networks with time delays by utilizing the Lyapunov stability theorems and the Homomorphic mapping theorem. Numerical examples are given to illustrate the effectiveness and the advantage of the proposed main results.

Keywords: Neural networks, Delayed systems, Lyapunov function, Stability analysis.

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Authors: A. Mirzaaghazadeh, H. Motameni, M. Karshenas, H. Nematzadeh

Abstract:

Learning the gradient of neuron's activity function like the weight of links causes a new specification which is flexibility. In flexible neural networks because of supervising and controlling the operation of neurons, all the burden of the learning is not dedicated to the weight of links, therefore in each period of learning of each neuron, in fact the gradient of their activity function, cooperate in order to achieve the goal of learning thus the number of learning will be decreased considerably. Furthermore, learning neurons parameters immunes them against changing in their inputs and factors which cause such changing. Likewise initial selecting of weights, type of activity function, selecting the initial gradient of activity function and selecting a fixed amount which is multiplied by gradient of error to calculate the weight changes and gradient of activity function, has a direct affect in convergence of network for learning.

Keywords: Back propagation, Flexible, Gradient, Learning, Neural network, Pattern recognition.

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Authors: Hazem M. El-Bakry, Qiangfu Zhao

Abstract:

Here, a new idea to speed up the operation of complex valued time delay neural networks is presented. The whole data are collected together in a long vector and then tested as a one input pattern. The proposed fast complex valued time delay neural networks uses cross correlation in the frequency domain between the tested data and the input weights of neural networks. It is proved mathematically that the number of computation steps required for the presented fast complex valued time delay neural networks is less than that needed by classical time delay neural networks. Simulation results using MATLAB confirm the theoretical computations.

Keywords: Fast Complex Valued Time Delay Neural Networks, Cross Correlation, Frequency Domain

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Authors: Miaomiao Yang, Shouming Zhong

Abstract:

This paper studies the problem of exponential stability analysis for uncertain neural networks with discrete and distributed time-varying delays. Together with a suitable augmented Lyapunov Krasovskii function, zero equalities, reciprocally convex approach and a novel sufficient condition to guarantee the exponential stability of the considered system. The several exponential stability criterion proposed in this paper is simpler and effective. Finally,numerical examples are provided to demonstrate the feasibility and effectiveness of our results.

Keywords: Exponential stability, Uncertain Neural networks, LMI approach, Lyapunov-Krasovskii function, Time-varying.

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Authors: S. Deswal, M. Pal

Abstract:

Presently various computational techniques are used in modeling and analyzing environmental engineering data. In the present study, an intra-comparison of polynomial and radial basis kernel functions based on Support Vector Regression and, in turn, an inter-comparison with Multi Linear Regression has been attempted in modeling mass transfer capacity of vertical (θ = 90O) and inclined (θ multiple plunging jets (varying from 1 to 16 numbers). The data set used in this study consists of four input parameters with a total of eighty eight cases, forty four each for vertical and inclined multiple plunging jets. For testing, tenfold cross validation was used. Correlation coefficient values of 0.971 and 0.981 along with corresponding root mean square error values of 0.0025 and 0.0020 were achieved by using polynomial and radial basis kernel functions based Support Vector Regression respectively. An intra-comparison suggests improved performance by radial basis function in comparison to polynomial kernel based Support Vector Regression. Further, an inter-comparison with Multi Linear Regression (correlation coefficient = 0.973 and root mean square error = 0.0024) reveals that radial basis kernel functions based Support Vector Regression performs better in modeling and estimating mass transfer by multiple plunging jets.

Keywords: Mass transfer, multiple plunging jets, polynomial and radial basis kernel functions, Support Vector Regression.

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Authors: Zixin Liu, Huawei Yang, Fangwei Chen

Abstract:

This paper studies the mean square exponential synchronization problem of a class of stochastic neutral type chaotic neural networks with mixed delay. On the Basis of Lyapunov stability theory, some sufficient conditions ensuring the mean square exponential synchronization of two identical chaotic neural networks are obtained by using stochastic analysis and inequality technique. These conditions are expressed in the form of linear matrix inequalities (LMIs), whose feasibility can be easily checked by using Matlab LMI Toolbox. The feedback controller used in this paper is more general than those used in previous literatures. One simulation example is presented to demonstrate the effectiveness of the derived results.

Keywords: Exponential synchronization, stochastic analysis, chaotic neural networks, neutral type system.

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Authors: H. B. Mehta, Vipul M. Patel, Jyotirmay Banerjee

Abstract:

The present paper discusses the prediction of gas-liquid two-phase frictional pressure drop in a 2.12 mm horizontal circular minichannel using Artificial Neural Network (ANN). The experimental results are obtained with air as gas phase and water as liquid phase. The superficial gas velocity is kept in the range of 0.0236 m/s to 0.4722 m/s while the values of 0.0944 m/s, 0.1416 m/s and 0.1889 m/s are considered for superficial liquid velocity. The experimental results are predicted using different Artificial Neural Network (ANN) models. Networks used for prediction are radial basis, generalised regression, linear layer, cascade forward back propagation, feed forward back propagation, feed forward distributed time delay, layer recurrent, and Elman back propagation. Transfer functions used for networks are Linear (PURELIN), Logistic sigmoid (LOGSIG), tangent sigmoid (TANSIG) and Gaussian RBF. Combination of networks and transfer functions give different possible neural network models. These models are compared for Mean Absolute Relative Deviation (MARD) and Mean Relative Deviation (MRD) to identify the best predictive model of ANN.

Keywords: Minichannel, Two-Phase Flow, Frictional Pressure Drop, ANN, MARD, MRD.

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Authors: Anita S. Gangal, P. K. Kalra, D. S. Chauhan

Abstract:

The backpropagation algorithm in general employs quadratic error function. In fact, most of the problems that involve minimization employ the Quadratic error function. With alternative error functions the performance of the optimization scheme can be improved. The new error functions help in suppressing the ill-effects of the outliers and have shown good performance to noise. In this paper we have tried to evaluate and compare the relative performance of complex valued neural network using different error functions. During first simulation for complex XOR gate it is observed that some error functions like Absolute error, Cauchy error function can replace Quadratic error function. In the second simulation it is observed that for some error functions the performance of the complex valued neural network depends on the architecture of the network whereas with few other error functions convergence speed of the network is independent of architecture of the neural network.

Keywords: Complex backpropagation algorithm, complex errorfunctions, complex valued neural network, split activation function.

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Authors: Fengxia Zheng, Shouming Zhong

Abstract:

ANNARIMA that combines both autoregressive integrated moving average (ARIMA) model and artificial neural network (ANN) model is a valuable tool for modeling and forecasting nonlinear time series, yet the over-fitting problem is more likely to occur in neural network models. This paper provides a hybrid methodology that combines both radial basis function (RBF) neural network and auto regression (AR) model based on binomial smoothing (BS) technique which is efficient in data processing, which is called BSRBFAR. This method is examined by using the data of Canadian Lynx data. Empirical results indicate that the over-fitting problem can be eased using RBF neural network based on binomial smoothing which is called BS-RBF, and the hybrid model–BS-RBFAR can be an effective way to improve forecasting accuracy achieved by BSRBF used separately.

Keywords: Binomial smoothing (BS), hybrid, Canadian Lynx data, forecasting accuracy.

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Authors: S. Mousavian, D. Ashouri, F. Mousavian, V. Nikkhah Rashidabad, N. Ghazinia

Abstract:

PH, temperature and time of extraction of each stage,  agitation speed and delay time between stages effect on efficiency of  zinc extraction from concentrate. In this research, efficiency of zinc  extraction was predicted as a function of mentioned variable by  artificial neural networks (ANN). ANN with different layer was  employed and the result show that the networks with 8 neurons in  hidden layer has good agreement with experimental data.

 

Keywords: Zinc extraction, Efficiency, Neural networks, Operating condition.

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Authors: Marina Velikova, Hennie Daniels, Ad Feelders

Abstract:

In many applications, it is a priori known that the target function should satisfy certain constraints imposed by, for example, economic theory or a human-decision maker. Here we consider partially monotone problems, where the target variable depends monotonically on some of the predictor variables but not all. We propose an approach to build partially monotone models based on the convolution of monotone neural networks and kernel functions. The results from simulations and a real case study on house pricing show that our approach has significantly better performance than partially monotone linear models. Furthermore, the incorporation of partial monotonicity constraints not only leads to models that are in accordance with the decision maker's expertise, but also reduces considerably the model variance in comparison to standard neural networks with weight decay.

Keywords: Mixture models, monotone neural networks, partially monotone models, partially monotone problems.

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Authors: P. Latha, L. Ganesan, N. Ramaraj, P. V. Hari Venkatesh

Abstract:

Motion detection is a basic operation in the selection of significant segments of the video signals. For an effective Human Computer Intelligent Interaction, the computer needs to recognize the motion and track the moving object. Here an efficient neural network system is proposed for motion detection from the static background. This method mainly consists of four parts like Frame Separation, Rough Motion Detection, Network Formation and Training, Object Tracking. This paper can be used to verify real time detections in such a way that it can be used in defense applications, bio-medical applications and robotics. This can also be used for obtaining detection information related to the size, location and direction of motion of moving objects for assessment purposes. The time taken for video tracking by this Neural Network is only few seconds.

Keywords: Frame separation, Correlation Network, Neural network training, Radial Basis Function, object tracking, Motion Detection.

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Authors: Yunquan Ke, Chunfang Miao

Abstract:

In this paper, the exponential stability of periodic solutions in inertial neural networks with unbounded delay are investigated. First, using variable substitution the system is transformed to first order differential equation. Second, by the fixed-point theorem and constructing suitable Lyapunov function, some sufficient conditions guaranteeing the existence and exponential stability of periodic solutions of the system are obtained. Finally, two examples are given to illustrate the effectiveness of the results.

Keywords: Inertial neural networks, unbounded delay, fixed-point theorem, Lyapunov function, periodic solutions, exponential stability.

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Authors: Qianhong Zhang, Lihui Yang, Daixi Liao

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In this paper, by employing a new Lyapunov functional and an elementary inequality analysis technique, some sufficient conditions are derived to ensure the existence and uniqueness of periodic oscillatory solution for fuzzy bi-directional memory (BAM) neural networks with time-varying delays, and all other solutions of the fuzzy BAM neural networks converge the uniqueness periodic solution. These criteria are presented in terms of system parameters and have important leading significance in the design and applications of neural networks. Moreover an example is given to illustrate the effectiveness and feasible of results obtained.

Keywords: Fuzzy BAM neural networks, Periodic solution, Global exponential stability, Time-varying delays

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Authors: Farhad Asadi, S. Hossein Sadati

Abstract:

This paper presents a prediction performance of feedforward Multilayer Perceptron (MLP) and Echo State Networks (ESN) trained with extended Kalman filter. Feedforward neural networks and ESN are powerful neural networks which can track and predict nonlinear signals. However, their tracking performance depends on the specific signals or data sets, having the risk of instability accompanied by large error. In this study we explore this process by applying different network size and leaking rate for prediction of nonlinear or chaotic signals in MLP neural networks. Major problems of ESN training such as the problem of initialization of the network and improvement in the prediction performance are tackled. The influence of coefficient of activation function in the hidden layer and other key parameters are investigated by simulation results. Extended Kalman filter is employed in order to improve the sequential and regulation learning rate of the feedforward neural networks. This training approach has vital features in the training of the network when signals have chaotic or non-stationary sequential pattern. Minimization of the variance in each step of the computation and hence smoothing of tracking were obtained by examining the results, indicating satisfactory tracking characteristics for certain conditions. In addition, simulation results confirmed satisfactory performance of both of the two neural networks with modified parameterization in tracking of the nonlinear signals.

Keywords: Feedforward neural networks, nonlinear signal prediction, echo state neural networks approach, leaking rates, capacity of neural networks.

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Authors: Hazem M. El-Bakry, Qiangfu Zhao

Abstract:

Recently, neural networks have shown good results for detection of a certain pattern in a given image. In our previous papers [1-5], a fast algorithm for pattern detection using neural networks was presented. Such algorithm was designed based on cross correlation in the frequency domain between the input image and the weights of neural networks. Image conversion into symmetric shape was established so that fast neural networks can give the same results as conventional neural networks. Another configuration of symmetry was suggested in [3,4] to improve the speed up ratio. In this paper, our previous algorithm for fast neural networks is developed. The frequency domain cross correlation is modified in order to compensate for the symmetric condition which is required by the input image. Two new ideas are introduced to modify the cross correlation algorithm. Both methods accelerate the speed of the fast neural networks as there is no need for converting the input image into symmetric one as previous. Theoretical and practical results show that both approaches provide faster speed up ratio than the previous algorithm.

Keywords: Fast Pattern Detection, Neural Networks, Modified Cross Correlation

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Authors: Hazem M. El-Bakry, Qiangfu Zhao

Abstract:

Recently, fast neural networks for object/face detection were presented in [1-3]. The speed up factor of these networks relies on performing cross correlation in the frequency domain between the input image and the weights of the hidden layer. But, these equations given in [1-3] for conventional and fast neural networks are not valid for many reasons presented here. In this paper, correct equations for cross correlation in the spatial and frequency domains are presented. Furthermore, correct formulas for the number of computation steps required by conventional and fast neural networks given in [1-3] are introduced. A new formula for the speed up ratio is established. Also, corrections for the equations of fast multi scale object/face detection are given. Moreover, commutative cross correlation is achieved. Simulation results show that sub-image detection based on cross correlation in the frequency domain is faster than classical neural networks.

Keywords: Conventional Neural Networks, Fast Neural Networks, Cross Correlation in the Frequency Domain.

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Authors: Truong Quang Dang Khoa, Masahiro Nakagawa

Abstract:

Chaos and fractals are novel fields of physics and mathematics showing up a new way of universe viewpoint and creating many ideas to solve several present problems. In this paper, a novel algorithm based on the chaotic sequence generator with the highest ability to adapt and reach the global optima is proposed. The adaptive ability of proposal algorithm is flexible in 2 steps. The first one is a breadth-first search and the second one is a depth-first search. The proposal algorithm is examined by 2 functions, the Camel function and the Schaffer function. Furthermore, the proposal algorithm is applied to optimize training Multilayer Neural Networks.

Keywords: learning and evolutionary computing, Chaos Optimization Algorithm, Artificial Neural Networks, nonlinear optimization, intelligent computational technologies.

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Authors: Somayeh Komeylian

Abstract:

The direction of arrival (DoA) estimation is the crucial aspect of the radar technologies for detecting and dividing several signal sources. In this scenario, the antenna array output modeling involves numerous parameters including noise samples, signal waveform, signal directions, signal number, and signal to noise ratio (SNR), and thereby the methods of the DoA estimation rely heavily on the generalization characteristic for establishing a large number of the training data sets. Hence, we have analogously represented the two different optimization models of the DoA estimation; (1) the implementation of the decision directed acyclic graph (DDAG) for the multiclass least-squares support vector machine (LS-SVM), and (2) the optimization method of the deep neural network (DNN) radial basis function (RBF). We have rigorously verified that the LS-SVM DDAG algorithm is capable of accurately classifying DoAs for the three classes. However, the accuracy and robustness of the DoA estimation are still highly sensitive to technological imperfections of the antenna arrays such as non-ideal array design and manufacture, array implementation, mutual coupling effect, and background radiation and thereby the method may fail in representing high precision for the DoA estimation. Therefore, this work has a further contribution on developing the DNN-RBF model for the DoA estimation for overcoming the limitations of the non-parametric and data-driven methods in terms of array imperfection and generalization. The numerical results of implementing the DNN-RBF model have confirmed the better performance of the DoA estimation compared with the LS-SVM algorithm. Consequently, we have analogously evaluated the performance of utilizing the two aforementioned optimization methods for the DoA estimation using the concept of the mean squared error (MSE).

Keywords: DoA estimation, adaptive antenna array, Deep Neural Network, LS-SVM optimization model, radial basis function, MSE.

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Authors: Zixin Liu, Shu Lü, Shouming Zhong, Mao Ye

Abstract:

The problem of exponential stability and periodicity for a class of cellular neural networks (DCNNs) with time-varying delays is investigated. By dividing the network state variables into subgroups according to the characters of the neural networks, some sufficient conditions for exponential stability and periodicity are derived via the methods of variation parameters and inequality techniques. These conditions are represented by some blocks of the interconnection matrices. Compared with some previous methods, the method used in this paper does not resort to any Lyapunov function, and the results derived in this paper improve and generalize some earlier criteria established in the literature cited therein. Two examples are discussed to illustrate the main results.

Keywords: Cellular neural networks, exponential stability, time varying delays, partitioned matrices, periodic solution.

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Authors: A. Chaouachi, R. M. Kamel, K. Nagasaka

Abstract:

This paper presents a novel methodology for Maximum Power Point Tracking (MPPT) of a grid-connected 20 kW Photovoltaic (PV) system using neuro-fuzzy network. The proposed method predicts the reference PV voltage guarantying optimal power transfer between the PV generator and the main utility grid. The neuro-fuzzy network is composed of a fuzzy rule-based classifier and three Radial Basis Function Neural Networks (RBFNN). Inputs of the network (irradiance and temperature) are classified before they are fed into the appropriated RBFNN for either training or estimation process while the output is the reference voltage. The main advantage of the proposed methodology, comparing to a conventional single neural network-based approach, is the distinct generalization ability regarding to the nonlinear and dynamic behavior of a PV generator. In fact, the neuro-fuzzy network is a neural network based multi-model machine learning that defines a set of local models emulating the complex and non-linear behavior of a PV generator under a wide range of operating conditions. Simulation results under several rapid irradiance variations proved that the proposed MPPT method fulfilled the highest efficiency comparing to a conventional single neural network.

Keywords: MPPT, neuro-fuzzy, RBFN, grid-connected, photovoltaic.

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