Tools for Modelling and Identification with Bond Graphs and Genetic Programming

Abstract

The contributions of this work include genetic programming grammars for bond graph modelling and for direct symbolic regression of sets of differential equations; a bond graph modelling library suitable for programmatic use; a symbolic algebra library specialized to this use and capable of, among other things, breaking algebraic loops in equation sets extracted from linear bond graph models. Several non-linear multi-body mechanics examples are pre- sented, showing that the bond graph modelling library exhibits well-behaved simulation results. Symbolic equations in a reduced form are produced au- tomatically from bond graph models. The genetic programming system is tested against a static non-linear function identification problem using type- less symbolic regression. The direct symbolic regression grammar is shown to have a non-deceptive fitness landscape: perturbations of an exact pro- gram have decreasing fitness with increasing distance from the ideal. The planned integration of bond graphs with genetic programming for use as a system identification technique was not successfully completed. A catego- rized overview of other modelling and identification techniques is included as context for the choice of bond graphs and genetic programming.