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

This paper presents a new technique for signal and representation based on a continuous recurrent dynamic neural network (RDNN). The internal structur e of the RDNN consists of output neurons feedback and feedforward arrays of integrators, linear gains, and bipolar sigmoid functions. The neural netwo rk parameters include synaptic weights calculated as inner products of thes e vectors with the measured signal. The RDNN was applied to representing mo tor vibration data using functions basis. Training the RDNN consisted of pr ocessing the first two cycles of a vibration record of eight cycles with th e purpose of giving as outputs the appropriate expansion coefficients. The trained RDNN was then used to predict succeeding vibration cycles considere d as testing data. Results were very satisfactory, especially in the presen ce of noise, where the RDNN showed little sensitivity and considerable robu stness. The effect of varying the RDNN parameters was investigated, and if was found that for a certain set of optimal parameters, the RDNN performanc e was more satisfactory than the algebraic pseudo-inverse method. A scaling factor was introduced in the expression of the RDNN parameters and had a p ositive effect on reducing the approximation error between original and rec onstructed waveforms, especially in the presence of noise. The RDNN was ext ended through the Newton-Raphson algorithm in order to handle dependent non linearities. These technique turned out useful especially in case of ill-po sed signal problems. The various simulations presented in this paper have s hown that the proposed recurrent dynamic neural network offers an alternati ve to traditional methods when dealing with noise corrupted data, and ill-c onditioned and uncertain of linear and nonlinear equations.