Application of Time Series Analysis and Neural Networks to the Modeling and Analysis of Forced Vibrating Mechanical Systems

Abstract

A theoretical and mathematical based methodogy is discussed that utilizes time series analysis techniques and neural networks to model forced vibrating mechanical systems using measured input-output data. A technique in nonlinear time series analysis known as phase space reconstruction may be used to extend our understanding of the active dynamics recorded in a single time series measurement. Using a recorded output (response) measurement phase space reconstruction parameters are calculated; the embedding dimension is estimated using the method of false nearest neighbor, and the time delay is estimated from the first minimum of the mutual information. The phase space reconstruction characteristics are then used to fully shape the architecture of a time delayed neural network model for the dynamical system. The modeling methodology is applied to several forced vibrating systems common to many fields of engineering. The neural models are then used to analyze new input, demonstrating the usefulness and importance of the methodology.