Designing and Implementation of Stable Sinusoidal Rough-Neural Identifier

A rough neuron is defined as a pair of conventional neurons that are called the upper and lower bound neurons. In this paper, the sinusoidal rough-neural networks (SR-NNs) are used to identify the discrete dynamic nonlinear systems (DDNSs) with or without noise in series-parallel configuration. In the identification of periodic nonlinear systems, sinusoidal activation functions provide more efficient neural networks than the sigmoidal activation functions. Based on the Lyapunov stability theory, an online learning algorithm is developed to train the SR-NNs. The asymptotically convergence of the identification error to zero and the boundedness of parameters as well as predictions are proved. SR-NNs are used to identify some DDNSs and the cement rotary kiln (CRK). CRK is a complex nonlinear system in the cement factory, which produces the cement clinker. The experiments show that the SR-NNs in the identification of nonlinear systems have better performances than multilayer perceptrons (MLPs), sinusoidal neural networks, and rough MLPs, particularly in the presence of noise.