Application of Machine Learning Principles to Modeling of Nonlinear Dynamic Systems

A method for the development of mathematical models for dynamic systems with arbitrary nonlinearities from measured data is described. The method involves the use of neural networks as embedded processors in dynamic system simulation models. The technique is demonstrated through generation of models for anharmonic oscillators described by the Duffing Equation and the Van der Pol Equation from measured input/output data. It is shown that high quality models of these systems can be developed using this technique which are efficient in terms of model size. Using neural networks as embedded processors, accurate models of the Duffing Oscillator and the Van der Pol Oscillator were generated which contained eighteen parameters in each case. The architecture used requires that the neural networks perform only function fitting, a task to which they are well suited while integrators handle the modeling of energy storage by the system. This allows model parameter count to remain low, averting the undesirable high parameter counts sometimes associated with neural network based models. Model architecture, test problem specification, model optimization techniques used, quality of the models produced, practical applications and future work are discussed