Identification of response surface models using genetic programming

There is a move in modem research in Structural Dynamics towards analysing the inherent uncertainty in a given problem. This may be quantifying or fusing uncertainty models, or can be propagation of uncertainty through a system or calculation. If the system of interest is represented by e.g. a large Finite Element (FE) model the large number of computations involved can rule out many approaches due to the expense of carrying out many runs. One way of circumnavigating this problem is to replace the true system by an approximate surrogate model, which is fast-running compared to the original. In traditional approaches using response surfaces a simple least-squares multinomial model is often adopted. The object of this paper is to extend the class of possible models considerably by carrying out a general symbolic regression using a Genetic Programming approach. The approach is demonstrated on both univariate and multivariate problems with both computational and experimental data.