A neuro-fuzzy network modeling method for uncovering the dynamic properties of time-varying systems

Abstract

Nonstationary signals are commonly encountered in various fields and applications. Modeling nonstationary signals with time-varying systems is of vital importance in understanding the underlying information and revealing the dynamic properties. In this paper, a neuro-fuzzy network-based method is proposed for the time-varying autoregressive (TVAR) system with multiple degrees of freedom. By expressing the time-varying parameters as a set of local linear models and validity functions, the TVAR system is transformed into an equivalent neural fuzzy network. The model structure and the time-varying parameters of the TVAR system correspond to the architecture and the weights of the equivalent neural network, respectively, and can be determined by training the equivalent neural network. Fundamentally, the new architecture is generated via growing and pruning the tree branches/neurons in a decision tree algorithm. Followed by a weights training process with Least Square optimization, the neural networks are finally evaluated with the target nonstationary signals. The optimal architecture and weights lie in the one with the least disparity. Several nonstationary signals, including the electroencephalogram and the radar wave that are qualitatively different in the time–frequency characteristics, are utilized to verify the effectiveness of the proposed method. Furthermore, we show that the proposed method is applicable not only to time-varying systems with complete measurements but also to incomplete measurable cases. Applying this method to the vibration signals output from a time-varying origami-tube structure under external excitations, the high time–frequency resolution of the proposed method is demonstrated via the time–frequency spectrum, from which the inherent mechanical properties and the underlying dynamic characteristics of the time-varying origami-tube structure are revealed.