Non-Linear Identification in Modal Space Using a Genetic Algorithm Approach for Model Selection

The Non-Linear Resonant Decay Method is an approach for the identification of non-linear
systems with large numbers of degrees of freedom. The identified non-linear model is
expressed in linear modal space and comprises the modal model of the underlying linear
system with additional terms representing the non-linear behaviour. Potentially, a large
number of these non-linear terms will exist but not all of them will be significant. The
problem of deciding which and how many terms are required for an accurate identification has
previously been addressed using the Forward Selection and Backward Elimination techniques.
In this paper, a Genetic Algorithm optimisation is proposed as an alternative to those methods.
A simulated lumped parameter non-linear dynamic system is used to demonstrate the
proposed optimisation. The use of separate data sets for the identification and validation of the
modal model is also investigated. It is found that the Genetic Algorithm approach yields
significantly better results than the Backward Elimination and Forward Selection algorithms
in many cases.