Identification of Nonlinear Vibration System by a Neural Network. The Prediction of Chaos by Learning of Periodic Response.

Abstract

This paper describes a convenient method of identification of a nonlinear vibration system by a neural network using time series data. A neural network using a suitable system of inputs and outputs is applicable for system identification of nonlinear vibration by learning periodic response. By learning only time serie data of periodic response in coexisting regions of chaos and periodic response, it is possible to predict both forced vibration chaos response and periodic response on predicting conditions near learning data by the neural network. The effectiveness of the method presented is demonstrated by numerical simulations for the Duffing system.