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

A novel approach to blindly estimate kernels of any discrete- and finite-ex tent quadratic models in higher order cumulants domain based on artificial neural networks is proposed in this paper. The input signal is assumed an u nobservable independently identically, distributed random sequence which is viable for engineering practice. Because of the properties of the third-or der cumulant functions, identifiability of the nonlinear model holds, even when the model output measurement is corrupted by a Gaussian random disturb ance. The proposed approach enables a nonlinear relationship between model kernels and model output cumulants to be established by means of neural net works. The approximation ability of the neural network with the weights-dec oupled extended Kalman filter training algorithm is then used to estimate t he model parameters. Theoretical statements and simulation examples togethe r with practical application to the train vibration signals modeling corrob orate that the developed methodology is capable of providing a very promisi ng way to identify truncated Volterra models blindly.