Comparing Multi-Index Stochastic Collocation and Multi-Fidelity Stochastic Radial Basis Functions for Forward Uncertainty Quantification of Ship Resistance

TL;DR

This paper compares the effectiveness of Multi-Index Stochastic Collocation and multi-fidelity Stochastic Radial Basis Functions in quantifying uncertainty in ship resistance, highlighting their performance differences based on computational budget and robustness to noise.

Contribution

It provides a comparative analysis of MISC and SRBF methods for forward uncertainty quantification in naval engineering using CFD simulations.

Findings

MISC is preferable with limited computational resources.

SRBF is more robust and better for larger computational budgets.

Both methods effectively compute statistical moments and PDFs of ship resistance.

Abstract

This paper presents a comparison of two multi-fidelity methods for the forward uncertainty quantification of a naval engineering problem. Specifically, we consider the problem of quantifying the uncertainty of the hydrodynamic resistance of a roll-on/roll-off passengers ferry advancing in calm water and subject to two operational uncertainties (ship speed and payload). The first four statistical moments (mean, variance, skewness, kurtosis), and the probability density function for such quantity of interest (QoI) are computed with two multi-fidelity methods, i.e., the Multi-Index Stochastic Collocation (MISC) method and an adaptive multi-fidelity Stochastic Radial Basis Functions (SRBF) algorithm. The QoI is evaluated via computational fluid dynamics simulations, which are performed with the in-house unsteady Reynolds-Averaged Navier-Stokes (RANS) multi-grid solver $\chi$navis. The different fidelities employed by both methods are obtained by stopping the RANS solver at different grid levels of the multi-grid cycle. The performance of both methods are presented and discussed: in a nutshell, the findings suggest that, at least for the current implementations of both algorithms, MISC could be preferred whenever a limited computational budget is available, whereas for a larger computational budget SRBFs seem to be preferable, thanks to its robustness to the numerical noise in the evaluations of the QoI.