Marc Karam

A recurrent dynamic neural network for noisy signal representation

Abstract This paper presents a new recurrent dynamic neural network approach to solve noisy signal representation and processing problems. Essentially, the neural network solves, in a systematic way, for the sets of representation coefficients required to model a given signal in terms of basis elementary signals. The network converges by seeking the minimum energy states. The perceived advantages over traditional approaches are in robustness of computation and ability to handle time-varying noisy signals.

Robust optimal control using recurrent dynamic neural network

A modular recurrent dynamic neural network (RDNN) based on the Hopfield model is applied to the linear quadratic regulator (LQR) optimal control of a nonlinear slider inverted pendulum (SIP). The main advantage of using neural networks is their robustness and flexibility when dealing with uncertain and ill-conditioned problems. The combination of the RDNN with LQR control is done in two ways. In the first technique, the LQR control gains are calculated by solving the algebraic Riccati equation (ARE) using the RDNN. Robustness of the control is further improved by appropriately tuning the LQR gains. In the second technique, the RDNN is trained to learn the connections between the controllers inputs and outputs. The efficacy of the training is confirmed as the neural controller performs successfully when tested on-line. Neural control results in more robustness, especially when noise is added to the system. The overall positive results of this study show that the proposed LQR/RDNN control offers an efficient alternative to traditional LQR control when dealing with noise corrupted data, and confirm the feasibility of using neural networks in the design of robust optimal controllers.

Augmentation of optimal control with recurrent neural network and wavelet signals

A modular dynamic neural network which has been used in preceding research to solve uncertain algebraic problems and to represent and compress signals, is applied to the representation of an adjustment control in the optimal control of simple nonlinear systems. The optimal control method implemented is based on the loop transfer recovery (LTR) technique, and the basis for signal representation is composed of Daubechies wavelets. Averaging the optimal controllers obtained at three representative equilibrium states followed by using the adjustment control signal leads to a single structure capable of controlling the system over a wider range of operation. A simple inverted pendulum example is presented, and an averaging optimal controller is designed. The neural network is used to represent an adjustment control signal by a linear combination of six wavelets. The resulting signal is incorporated with the averaging LTR controller in order to enhance its performance. Simulation results are presented and discussed.

Increasing Additive Noise Removal in Speech Processing Using Spectral Subtraction

In this research, we present a technique to increase noise removal from noisy speech signals using spectral subtraction. The noise removal algorithm includes storing the noisy speech data into Hanning time-widowed half-overlapped data buffers, computing the corresponding spectrums using the FFT, removing the noise from the noisy speech, and reconstructing the speech back into the time domain using the inverse fast Fourier transform (IFFT). Performance of the algorithm was evaluated by calculating the speech to noise ratio (SNR). The improvement technique involved varying the lengths of the Hanning time windows, as well as the degrees of data buffers overlapping. Further improvement was sought by using frames averaging technique, which consists in averaging various spectrum frames before removing the noise. Results showed that using one-fourth overlapped data buffers with 256 points Hanning windows and no frames averaging lead to the best performance in removing noise from the noisy speech.

Particle Swarm Optimization for the Minimization of Power Losses in Distribution Networks

This research utilizes particle swarm optimization (PSO) to minimize the total active power losses in an IEEE 6-bus transmission system. The complexity of the problem lies in integrating Newton-Raphson load flow algorithm, which is used in computing power losses, with PSO algorithm, which is used to minimize these losses. The considered PSO control variables are: the reactive power output of generators, the tap ratios of transformers, and the reactive power output of shunt compensators. PSO was chosen as optimization method due to its popularity as a successful algorithm in solving non-smooth global optimization problems. The proposed PSO algorithm gave very satisfactory simulation results. Power losses were reduced by 13.9% for an initial set of PSO parameters. These parameters were thereafter varied in order to improve PSO performance by further minimizing the power losses. Effectively, we were able to obtain a set of parameters that resulted in a 19.31% reduction in power losses. These successful simulation results confirm the effectiveness of PSO in minimizing distribution networks power losses.

System identification using a Fourier/Hopfield neural network

We use a Fourier/Hopfield network for the identification of a periodic system based on input-output data. The network automatically optimizes the model parameters and adapts by adding more neurons until the modeling error drops below a specified level. We show that, for periodic systems, Fourier basis functions are the best choice for system identification.

Computational results on recurrent dynamic neural network for signal analysis

This paper presents a new recurrent dynamic neural network to solve signal analysis and processing problems. The neural network is essentially composed of feedback-type connections and arrays of integrators, linear gains, and nonlinear activation functions. By seeking a minimum global energy state, the network solves for the best set of representation coefficients required to model a given signal in terms of suitable elementary basis signals. An analytical model of the recurrent neural network is obtained through discretization of the integrator blocks and linearization of the activation function. Continuity of the algorithm when segment boundaries are crossed is accomplished by varying the slope of the linearized activation function. The proposed approach results in a closed analytical form of the recurrent neural network solution. The perceived advantages of using the network are estimation of robustness, prediction of convergence by examining the eigenvalues of the analytical state matrix, and increase of computational speed. Moreover, unlike traditional numerical methods, the new approach offers the possibility of handling time-varying signals with uncertainties.

PID Speed Control of a DC Motor Using Particle Swarm Optimization

This research is based on applying Particle Swarm Optimization (PSO) to the Proportional-Integral-Derivative (PID) speed control of a permanent magnet DC motor. The integration of PID control and PSO optimization technique starts by designing the initial PID control gains so that the DC motor angular speed exhibits a given overshoot (OS) and settling time (t s ). Based on these gains, we designed an initial set of particles that were subsequently modified using PSO algorithm with the goal of reducing OS and t s . Simulation results led to the desired swarming since the PID gains converged, causing the OS and t s to get below the desired threshold. Thus, our proposed PID-PSO algorithm was very successful in achieving the optimization goal of reducing OS and t s by means of PSO-optimized PID control.

Performance enhancement of a Fourier/Hopfield neural network for nonlinear periodic systems representation

Nonlinear periodic systems arise in many important practical applications including systems with multirate sampling. System identification in such applications is possible by representing the system in terms of basis functions of our choice. Fourier basis functions are the natural choice when identifying periodic systems. In this paper, we examine the performance of a three-layer Fourier/Hopfield network designed for system identification. We study the effect of network parameters such as absolute and relative error tolerances, discretization step size, and the saturation level of the activation function on the performance of the network and propose a new approach for their selection. We demonstrate our approach through a numerical example.

Uncertain nonlinear algebraic solutions and their implementation using neural networks

In this article, we propose a dynamic recurrent approach to solve uncertain nonlinear algebraic equations. The approach is justified on the basis of net construction that recursively produces minimum neuron state energy which corresponds to the desired solution. Linearization via the Newton-Raphson method is employed in order to make the net converge to an appropriate region in the solution space. Some preliminary experimentation on non-trivial nonlinear examples are included and discussed. Approaches for hardware implementation of the recurrent dynamic neural network are presented. Comparison between a totally digital chip design and a hybrid analog/digital implementation utilizing MOSIS facilities is made. Evaluation and simulations on system, logic, and circuit levels are emphasized.