Development and assessment of uncertainty quantification methods for ship hydrodynamics

An overview is provided of stochastic uncertainty quantification (UQ) and validation methods for application to realistic problems in ship hydrodynamics. The paper summarizes the research activities conducted by the hydrodynamics team within the NATO Task Group AVT-191 "Application of Sensitivity Analysis and Uncertainty Quantification to Military Vehicle Design." UQ methods assess the expected value (EV), standard deviation (SD) and cumulative distribution function or probability density function (CDF/PDF) of the hydrodynamic performance of interest. The hydrodynamic solvers include unsteady Reynolds-averaged Navier-Stokes and potential flow. Three UQ problems are presented. The first is a unit study, addressing the effects of stochastic Reynolds number on the lift and drag of a NACA 0012 2D hydrofoil at constant angle of attack. The second and the third are industrial problems of a high-speed catamaran, advancing in calm water and waves respectively, with stochastic operating conditions and geometry. Numerical validation benchmarks include the deterministic V&V for selected conditions, along with converged (quasi) Monte Carlo (MC) samples. Non-intrusive UQ methods are applied and discussed. MC simulations with direct CFD simulations and with metamodels are shown. Metamodels include linear and Hermite-cubic interpolation, inverse distance weighting, quadratic and cubic response surface, Hermite and Legendre polynomial expansions, least-square support vector machine, thin plate spline, radial basis functions network with multiquadric kernels, polyharmonic splines, Kriging using linear and exponential covariance functions, dynamic radial basis functions and dynamic Kriging. Polynomial chaos method and quadrature formulas (trapezoidal, Simpson's rule, Gaussian quadrature) are also assessed and compared to metamodel-based methods. Convergence criteria for UQ methods include deterministic and stochastic convergence criteria for MC simulation, along with convergence criteria for MC with metamodels, and quadrature formulas. UQ methods have shown their maturity for application to realistic stochastic design optimization problems. MC with dynamic metamodels is found the most promising method overall, due to its function-adaptation capability and high computational efficiency, which make the method also recommended for stochastic optimization.