Comparing multi-index stochastic collocation and multi-fidelity stochastic radial basis functions for forward uncertainty quantification of ship resistance

• Published in: Engineering with computers Vol. 39; no. 3; pp. 2209 - 2237
• Main Authors: Piazzola, Chiara, Tamellini, Lorenzo, Pellegrini, Riccardo, Broglia, Riccardo, Serani, Andrea, Diez, Matteo
• Format: Journal Article
• Language: English
• Published: London Springer London 01.06.2023; Springer Nature B.V
• Subjects: Accuracy; Approximation; Budgets; CAE) and Design; Calculus of Variations and Optimal Control; Optimization; Classical Mechanics; Collocation; Computational fluid dynamics; Computer Science; Computer-Aided Engineering (CAD; Control; Design of experiments; Engineering; Expected values; Ferries; Fluid dynamics; Kurtosis; Math. Applications in Chemistry; Mathematical and Computational Engineering; Multigrid methods; Naval engineering; Optimization; Original Article; Probability density functions; Radial basis function; Reynolds averaged Navier-Stokes method; Robustness (mathematics); Skewness; Solvers; Statistical analysis; Systems Theory; Uncertainty; Uncertainty quantification; Multi-index stochastic collocation; Reynolds-averaged Navier–Stokes equations; Finite volumes; Computational fluid dynamics; Multi-fidelity stochastic radial basis functions
• ISSN: 0177-0667; 1435-5663
• DOI: 10.1007/s00366-021-01588-0

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 passenger ferry advancing in calm water and subject to two operational uncertainties (ship speed and payload). The first four statistical moments (mean, variance, skewness, and 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) and an adaptive multi-fidelity Stochastic Radial Basis Functions (SRBF). 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 χ 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 implementation of both methods, MISC could be preferred whenever a limited computational budget is available, whereas for a larger computational budget SRBF seems to be preferable, thanks to its robustness to the numerical noise in the evaluations of the QoI.