Global sensitivity analysis using sparse high dimensional model representations generated by the group method of data handling

• The group method of data handling (GMDH) is used to construct the high dimensional model representation (HDMR) to calculate Sobol’s first and second order global sensitivity analysis indices.
• This methodology uses the parameter selection features of GMDH to construct a sparse HDMR expansion for high dimensional problems from a limited number of function evaluations.
• By design, the method also allows for the optimal (i.e. balancing accuracy and complexity) polynomial order selection in the HDMR expansion.

In this paper, the parameter selection capabilities of the group method of data handling (GMDH) as an inductive self-organizing modelling method are used to construct sparse random sampling high dimensional model representations (RS-HDMR), from which the Sobol’s first and second order global sensitivity indices can be derived. The proposed method is capable of dealing with high-dimensional problems without the prior use of a screening technique and can perform with a relatively limited number of function evaluations, even in the case of under-determined modelling problems. Four classical benchmark test functions are used for the evaluation of the proposed technique.