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 highfidelity 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

A Proposal of PSO Particles’ Initialization for Costly Unconstrained Optimization Problems: ORTHOinit

“…Thus, the eigenvectors of a symmetric matrix are also mutually conjugate directions with respect to that matrix. As a consequence, in order to satisfy condition (14) it suffices to compute the eigenvectors of (15), and set the vectors in (16) as proportional to the latter eigenvectors. After some computation we have for the corresponding 2n eigenvectors u…”

Ship hydrodynamic optimization by local hybridization of deterministic derivative-free global algorithms

“…The metamodel used is a first order polyharmonic spline, which is a special case of radial basis function (RBF) interpolation [9].…”

“…), the optimization process is computationally expensive and its effectiveness and efficiency remain an algorithmic and technological challenge. Although complex SBD applications are often solved by metamodels [9,10], their development and assessment require benchmark solutions, with simulations directly connected to the optimization algorithm. These solutions are achieved only if affordable and effective optimization procedures are available.…”

“…This first problem was already addressed in the early work [27], of which the present paper can be considered the natural evolution. The second problem (II) is solved using a RANS solver (CFDShip-Iowa v4.5) [24] with a first order polyharmonic spline metamodel [9]. The basis functions for the shape modification are eleven and are the result of a dimensionality reduction analysis, based on the Karhunen-Loève expansion (KLE) [25,26].…”

Uncertainty quantification for a sailing yacht hull, using multi-fidelity kriging

“…the reduction of discretisation errors) and due to a rapid increase of computer power, the focus of uncertainty analysis has been shifting from grid convergence and time discretisation errors towards stochastic uncertainty a Australian National University (j.h.s.debaar@gmail.com) b Australian National University c Delft University of Technology d Numeca, Brussels quantification (UQ) [33,6]. The main challenge, especially when considering multiple uncertain input parameters, is to decrease the number of simulations required to arrive at accurate UQ results [29,30,38]. A promising approach to this challenge are non-intrusive multi-fidelity methods, which combine a small number of expensive high-fidelity simulations with a larger number of less expensive low-fidelity simulations [36].…”