The main goal of this research is to develop and demonstrate a general, efficient, mathematically and theoretically based methodology to model nonlinear forced vibrating mechanical systems from time series measurements. A system identification modeling methodology for forced dynamical systems is presented based on dynamic system theory and nonlinear time series analysis that employs phase space reconstruction (delay vector embedding) for modeling of dynamical systems from time series data using time-delay neural networks (TDNN). The first part of this work details the modeling methodology including background on dynamic systems, phase space reconstruction, and neural networks. 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 an example of a linear system predicting lumped mass displacement using a displacement forcing. function The work discusses the application to 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 an 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.

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