Robust recurrent dynamic neural network for solving linear and nonlinear signal representation problems

Abstract

This paper presents a new technique for signal processing and representation based on a continuous recurrent dynamic neural network (RDNN). The internal structure of the RDNN consists of output neurons feedback and feedforward arrays of integrators, linear gains, and bipolar sigmoid functions. The neural network parameters include synaptic weights calculated as mutual inner products of basis signals, and bias inputs calculated as inner products of these vectors with the measured signal. The RDNN was applied to representing motor vibration data using functions basis. Training the RDNN consisted of processing the first two cycles of a vibration record of eight cycles with the purpose of giving as outputs the appropriate expansion coefficients. The trained RDNN was then used to predict succeeding vibration cycles considered as testing data. Results were very satisfactory, especially in the presence of noise, where the RDNN showed little sensitivity and considerable robustness. The effect of varying the RDNN parameters was investigated, and it was found that for a certain set of optimal parameters, the RDNN performance was more satisfactory than the algebraic pseudo-inverse method. A scaling factor was introduced in the expression of the RDNN parameters and had a positive effect on reducing the approximation error between original and reconstructed waveforms, especially in the presence of noise. The RDNN was extended through the Newton-Raphson algorithm in order to handle dependent nonlinearities. This technique turned out useful especially in case of ill-posed signal problems. The various simulations presented in this paper have shown that the proposed recurrent dynamic neural network offers an alternative to traditional methods when dealing with noise corrupted data, and ill-conditioned and uncertain systems of linear and nonlinear equations.