Tools for Modelling and Identiﬁcation with Bond Graphs and Genetic Programming
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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.