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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.

to be addressed. The objective of the paper is to present a formulation for the evaluation of the power spectral density of the acoustic pressure at any given point in the field in terms of the power spectral density of the transpiration velocity: this is a quantity defined in terms of the vorticity and is closely related to the equivalent source concept introduced by Lighthill 7 (the relationship between the two is addressed in Appendix B). Specifically, the formulation used allows one to obtain, in the frequency domain (Fourier transform), a matrix relationship between the transpiration velocity at a number of points on the surface of the object (those arising from the boundary‐element discretization) and the pressure at given points in the irrotational region. 1 From this, the relationship between the corresponding power spectral densities is easily obtained using the Wiener-Khintchine theorem. The approach used here is based upon a formulation introduced for aerodynamics in Ref. 11, and refined in Refs. 13 and 14. The commonality between aerodynamics and aeroacoustics is addressed in Ref. 12 (which provides a synthesis of all the preceding work), and is exploited here. Although applications to aeroacoustics implicitly imply compressibility, for the sake of clarity in the main body of the paper the formulation is presented for an incompressible flow (the formulation for compressible flows is presented in Appendix C).

The paper presents the authors’ most recent advances in the development of a reliable and eective algorithm for the inclusion of community noise consideration within a Multidisciplinary Design Optimization (MDO) framework. The attention is here focused on the possibility to include sound quality issues as an alternative to the classical sound-level-based approach. The improvement of the sound quality could be seen as an additional “degree of freedom” available to the designer to reduce the impact of the air trac on residents’ life. One of the primary objectives of the European Research Project SEFA (Sound Engineering For Aircraft) is the definition of those characteristics that make the aircraft acoustic emissions less annoying. This is done by means of an extensive campaign of psychometric tests, supported by a careful sound engineering work. One of the outcomes of this activity is the synthesis of a target sound, having all the characteristics of “pleasantness” defined. The role of the authors within the project is the development of an algorithm capable to evaluate the feasibility of the target sound matching since the conceptual phase of the design of the aircraft. To accomplish this, a method for the quantitative evaluation of the dierence between the target sound and the acoustic emissions of the aircraft is needed. A careful definition of the “distance” between two sounds is introduced and validated, in order to identify a metric useful to properly build an objective function capable to drive the optimization process toward the target-sound-matching configurations. In this work, the evaluation of the sounds distance is extended to the analysis of non-stationary sounds and applied to match the emissions of recorded sounds in the final approach procedure. Specifically, the distance is evaluated as the L p -norm of the dierence between the current spectrum and target spectrum over the frequency-time domain. In order to evaluate the current spectrum, the computation of airframe noise, fan and compressor noise, buzz-saw and jet noise is performed. Atmospheric attenuation, ground reflection and doppler eect are also taken into account. In this work, an L 2 -distance between current and target spectra is taken as the objective function of an evolutionary algorithm. The static equilibrium of the aircraft is used as a constraint, whereas the variables space used includes both design and procedural parameters. Preliminary numerical results show that the method is capable to eectively drive the optimization process towards those configurations satisfying the sound-matching criterion.

This paper deals with the acoustic field generated by rigid bodies in arbitrary motion. The Ffowcs Williams and Hawkings equation is the starting point for the derivation of a boundary integral formulation for the acoustic disturbance. It yields a unified approach for the prediction of both sound generated aerodynamically and sound scattered by arbitrarily moving, (eventually) vibrating, surfaces impinged by an acoustic signal. The advantages of the acoustic formulation presented here with respect to other approaches that are commonly used are discussed. A boundary element method is applied for its numerical solution and the resulting prediction tool is validated by analysing the problem of low-frequency and high-frequency plane waves impinging on a rigid sphere. Then, the formulation is applied to an aeronautical configuration for the determination of the scattered pressure field generated by a fuselage impinged by the incident pressure wave emitted by a propeller.

In the present work we address the problem of the dynamic response of an acoustoaeroelastic system, i.e., a fluid-filled elastic structure in motion within a compressible fluid in presence of a sound source. The analysis is accomplished by a fully integrated approach, taking into account the feedbacks between the structure, the cavity, and the exterior flow, leading to a single acoustoaeroelastic (matrix) equation. This is formulated in terms of the amplitudes of the structural models, considered in vacuo. Such an approach is developed by expressing the pressure in the cavity using its acoustic natural modes of vibration, while for the pressure in the exterior field we rely on a direct boundary integral formulation, numerically solved using BEM. Dealing with the BEM applied to the exterior problem, we address the issue of the so-called FED (Fictitious Eigenvalues Difficulty). Such difficulty involves the arising of fictitious (not physical) resonances for frequency values coincident with the eigenvalues of the associated interior problem. We present a reduction to the finite-state aerodynamics for the matrix resulting from the BEM, which seems convenient to bypass the FED. (Author)