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In this paper, an application of an adaptive differential evolution (DE) algorithm with multiple trial vectors for training artificial neural networks (ANNs) is presented. The proposed method is \DE-ANNT+, which is a DE-ANN Training (DE-ANNT) modified by adding a multiple trial vectors technique. \DE-ANNT+ allows one to train an ANN of arbitrary architectures, and it offers a nondifferentiable neuron activation function. In contrast to a basic DE algorithm, \DE-ANNT+ possesses two modifications. In \DE-ANNT+, adaptive selection of control parameters and a multiple trial vectors technique are introduced. Adaptive selection means that the number of required parameters of the algorithm is decreased. The multiple trial vectors technique increases the probability of generating a better solution because a greater number of temporary solutions is generated around the existing solutions. The \DE-ANNT+ algorithm, with these two modifications, is used for ANN training to classify the parity-p problem. The results from the obtained algorithm have been compared with results from the following algorithms: an evolutionary algorithm, a DE algorithm without multiple trial vectors, gradient training methods, such as error back-propagation, and the Levenberg-Marquardt method. [ABSTRACT FROM PUBLISHER]

This paper describes a new algorithm with neuron-by-neuron computation methods for the gradient vector and the Jacobian matrix. The algorithm can handle networks with arbitrarily connected neurons. The training speed is comparable with the Levenberg-Marquardt algorithm, which is currently considered by many as the fastest algorithm for neural network training. More importantly, it is shown that the computation of the Jacobian, which is required for second-order algorithms, has a similar computation complexity as the computation of the gradient for first-order learning methods. This new algorithm is implemented in the newly developed software, Neural Network Trainer, which has unique capabilities of handling arbitrarily connected networks. These networks with connections across layers can be more efficient than commonly used multilayer perceptron networks. [ABSTRACT FROM AUTHOR]

Generation of harmonics and the existence of wave-form pollution in power system networks are important problems facing the power utilities. The determination of harmonic currents injected into a power network by a nonlinear load is complicated when the supply voltage waveform to the load is distorted by other loads and not a pure sinusoid. This paper proposes a neural network solution to this problem. A recurrent neural network trained with the backpropagation through time training algorithm is used to find a way of distinguishing between the so-called load harmonics and supply harmonics, without disconnecting the load from the network. The advantage of this method is that only waveforms of voltages and currents have to be measured. This method is applicable for both single and three phase loads and could be fabricated into a commercial instrument that could be installed in substations of large customer loads, or used as a hand-held clip on instrument. This paper is particularly useful in determining whether the utility or the customer side has a higher contribution to harmonic pollution in a network. Hence, this method would be helpful in settling utility-customer disputes over who is responsible for harmonic pollution. [ABSTRACT FROM AUTHOR]

In recent years, harmonic pollution has worried the power engineers considerably due to the increased penetration of power-electronics-based devices in the utility grid. Monitoring of certain low-order harmonics in the power supply is more important than monitoring of the entire spectrum because, usually, these are the most significant ones. In this paper, a technique based on an adaptive wavelet neural network that is the most suitable for dominant low-order harmonic estimation is presented. The proposed method works with only half-cycle data point inputs, compared to the requirement of at least one-complete-cycle data for other estimation techniques. A simple, fast converging, and reliable learning algorithm based on back propagation is used for training of the network parameters. The proposed method is examined with a number of simulated and experimental signals. The test results confirm that the proposed method accurately estimates the dominant low-order harmonics in pragmatic situations of fundamental frequency deviation, presence of interharmonics, low signal-to-noise ratio, etc. [ABSTRACT FROM PUBLISHER]

The Levenberg–Marquardt (LM) algorithm is a nonlinear parameter learning algorithm that converges accurately and quickly. This paper demonstrates for the first time to our knowledge, a real-time implementation of the LM algorithm on field programmable gate arrays (FPGAs). It was used to train neural networks to solve the eXclusive Or function (XOR), and for 3D-to-2D camera calibration parameter estimation. A Xilinx Virtex-5 ML506 was used to implement the LMA as a hardware-in-the-loop system. The XOR function was approximated in only 13 iterations from zero initial conditions, usually the same function is approximated in thousands of iterations using the error backpropagation algorithm. Also, this type of training not only reduced the number of iterations but also achieved a speed up in excess of 3 \times 10^6 when compared to the software implementation. A real-time camera calibration and parameter estimation was performed successfully on FPGAs. Compared to the software implementation the FPGA implementation led to an increase in the mean squared error and standard deviation by only 17.94% and 8.04% respectively. The FPGA increased the calibration speed by a factor of 1.41 \times 10^6. There are a wide range of systems problems solved via nonlinear parameter optimization, this study demonstrated that a hardware solution for systems such as automated optical inspection systems or systems dealing with projective geometry estimation and motion compensation systems in robotic vision systems is possible in real time. [ABSTRACT FROM PUBLISHER]