A New Robust Surrogate Model: Reliability Based Hybrid Functions

Abstract

The determination of complex underlying relationships between system parameters from simulated and/or recorded data requires advanced interpolating functions, also known as surrogates. The development of surrogates for such complex relationships often requires the modeling of high dimensional and non-smooth functions using limited information. To this end, the hybrid surrogate modeling paradigm, where different surrogate models are aggregated, offers a robust solution. In this paper, we develop a new high fidelity surrogate modeling technique that we call the Reliability Based Hybrid Functions (RBHF). The RBHF formulates a reliable Crowding Distance-Based Trust Region (CD-TR), and adaptively combines the favorable characteristics of different surrogate models. The weight of each contributing surrogate model is determined based on the local reliability measure for that surrogate model in the pertinent trust region. Such an approach is intended to exploit the advantages of each component surrogate. This approach seeks to simultaneously capture the global trend of the function and the local deviations. In this paper, the RBHF integrates four component surrogate models: (i) the Quadratic Response Surface Model (QRSM), (ii) the Radial Basis Functions (RBF), (iii) the Extended Radial Basis Functions (E-RBF), and (iv) the Kriging model. The RBHF is applied to standard test problems. Subsequent evaluations of the Root Mean Squared Error (RMSE) and the Maximum Absolute Error (MAE), illustrate the promising potential of this hybrid surrogate modeling approach.