Blind identification of quadratic nonlinear models using neural networks with higher order cumulants

Abstract

A novel approach to blindly estimate kernels of any discrete- and finite-extent quadratic models in higher order cumulants domain based on artificial neural networks is proposed in this paper. The input signal is assumed an unobservable independently identically, distributed random sequence which is viable for engineering practice. Because of the properties of the third-order cumulant functions, identifiability of the nonlinear model holds, even when the model output measurement is corrupted by a Gaussian random disturbance. The proposed approach enables a nonlinear relationship between model kernels and model output cumulants to be established by means of neural networks. The approximation ability of the neural network with the weights-decoupled extended Kalman filter training algorithm is then used to estimate the model parameters. Theoretical statements and simulation examples together with practical application to the train vibration signals modeling corroborate that the developed methodology is capable of providing a very promising way to identify truncated Volterra models blindly.