A methodology for the modeling of forced dynamical systems from time series measurements using time-delay neural networks

The main goal of this research is to develop a general, efficient, mathematically and theoretically based methodology to model nonlinear forced vibrating mechanical systems from time series measurements. This dissertation details a novel system identification modeling methodology for dynamical systems based on dynamic system theory and nonlinear time series analysis that employs phase space reconstruction (delay vector embedding) and neural networks for modeling of dynamical systems from time series data using time-delay neural networks (TDNN). The first part of this dissertation details the development of the modeling methodology including background on dynamic systems, system identification, neural networks, and phase space reconstruction. A brief description of the modeling methodology is as follow: (1) A dynamic system is forced with a representative sampled input [x(t)] and a set of sample outputs [y(t)] is measured; (2) Output data, [y(t)], is then used to determine the phase space reconstruction parameters of embedding dimension and time lag, and an input/output delay vector for the dynamic system is defined; (3) Using the dynamic systems delay vector, the architecture of a time-delayed neural network with feedback from the output (predicted output, [ ŷ(t)]) is constructed and trained using a segment of the measured input-output data from Step 1; (4) The neural model is validated and evaluated for its ability to generalize the response of the dynamic system; and (5) The validated neural model is used to predict dynamic system response for a new input forcing.; In the second part of this work the methodology is evaluated based on its ability to model selected analytical lumped parameter forced vibrating dynamic systems including linear systems, nonlinear systems, multi degree-of-freedom systems, and multi-input systems. The methodology is further evaluated on its ability to model an analytical passenger rail vehicle predicting vertical wheel/rail force using vertical rail profile as input. Studying the neural modeling methodology using analytical systems shows the clearest observations from results which provide prospective users of this tool an understanding of the expectations and limitations of the modeling methodology.