Development and validation of a dynamic metamodel based on stochastic radial basis functions and uncertainty quantification

Abstract

A dynamic radial basis function (DRBF) metamodel is derived and validated, based on stochastic RBF and uncertainty quantification (UQ). A metric for assessing metamodel efficiency is developed and used. The validation includes comparisons with a dynamic implementation of Kriging (DKG) and static metamodels for both deterministic test functions (with dimensionality ranging from two to six) and industrial UQ problems with analytical and numerical benchmarks, respectively. DRBF extends standard RBF using stochastic kernel functions defined by an uncertain tuning parameter whose distribution is arbitrary and whose effects on the prediction are determined using UQ methods. Auto-tuning based on curvature, adaptive sampling based on prediction uncertainty, parallel infill, and multiple response criteria are used. Industrial problems are two UQ applications in ship hydrodynamics using high-fidelity computational fluid dynamics for the high-speed Delft catamaran with stochastic operating and environmental conditions: (1) calm water resistance, sinkage and trim with variable Froude number; and (2) mean value and root mean square of resistance and heave and pitch motions with variable regular head wave. The number of high-fidelity evaluations required to achieve prescribed error levels is considered as the efficiency metric, focusing on fitting accuracy and UQ variables. DKG is found more efficient for fitting low-dimensional test functions and one-dimensional UQ, whereas DRBF has a greater efficiency for fitting higher-dimensional test functions and two-dimensional UQ.