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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]