Efficient global optimization (EGO) has become a standard approach for the global optimization of complex systems with high computational costs. EGO uses a training set of objective function values computed at selected input points to construct a statistical surrogate model, with low evaluation cost, on which the optimization procedure is applied. The training set is sequentially enriched, selecting new points, according to a prescribed infilling strategy, in order to converge to the optimum of the original costly model. Multifidelity approaches combining evaluations of the quantity of interest at different fidelity levels have been recently introduced to reduce the computational cost of building a global surrogate model. However, the use of multifidelity approaches in the context of EGO is still a research topic. In this work, we propose a new effective infilling strategy for multifidelity EGO. Our infilling strategy has the particularity of relying on non-nested training sets, a characteristic that comes with several computational benefits. For the enrichment of the multifidelity training set, the strategy selects the next input point together with the fidelity level of the objective function evaluation. This characteristic is in contrast with previous nested approaches, which require estimation of all lower fidelity levels and are more demanding to update the surrogate. The resulting EGO procedure achieves a significantly reduced computational cost, avoiding computations at useless fidelity levels whenever possible, but it is also more robust to low correlations between levels and noisy estimations. Analytical problems are used to test and illustrate the efficiency of the method. It is finally applied to the optimization of a fully nonlinear fluid-structure interaction system to demonstrate its feasibility on real large-scale problems, with fidelity levels mixing physical approximations in the constitutive models and discretization refinements.

Gaussian-Process based optimization methods have become very popular in recent years for the global optimization of complex systems with high computational costs. These methods rely on the sequential construction of a statistical surrogate model, using a training set of computed objective function values, which is refined according to a prescribed infilling strategy. However, this sequential optimization procedure can stop prematurely if the objective function cannot be computed at a proposed point. Such a situation can occur when the search space encompasses design points corresponding to an unphysical configuration, an ill-posed problem, or a non-computable problem due to the limitation of numerical solvers. To avoid such a premature stop in the optimization procedure, we propose to use a classification model to learn non-computable areas and to adapt the infilling strategy accordingly. Specifically, the proposed method splits the training set into two subsets composed of computable and non-computable points. A surrogate model for the objective function is built using the training set of computable points, only, whereas a probabilistic classification model is built using the union of the computable and non-computable training sets. The classifier is then incorporated in the surrogate-based optimization procedure to avoid proposing new points in the non-computable domain while improving the classification uncertainty if needed. The method has the advantage to automatically adapt both the surrogate of the objective function and the classifier during the iterative optimization process. Therefore, non-computable areas do not need to be a priori known. The proposed method is applied to several analytical problems presenting different types of difficulty, and to the optimization of a fully nonlinear fluid-structure interaction system. The latter problem concerns the drag minimization of a flexible hydrofoil with cavitation constraints. The efficiency of the proposed method compared favorably to a reference evolutionary algorithm, except for situations where the feasible domain is a small portion of the design space.

This paper investigates the use of Gaussian processes to solve sail trimming optimization problems. The Gaussian process, used to model the dependence of the performance with the trimming parameters, is constructed from a limited number of performance estimations at carefully selected trimming points, potentially enabling the optimization of complex sail systems with multiple trimming parameters. The proposed approach is tested on a two-parameter trimming for a scaled IMOCA mainsail in upwind sailing conditions. We focus on the robustness of the proposed approach and study especially the sensitivity of the results to noise and model error in the point estimations of the performance. In particular, we contrast the optimization performed on a real physical model set in a wind tunnel with a fully non-linear numerical fluid-structure interaction model of the same experiments. For this problem with a limited number of trimming parameters, the numerical optimization was affordable and found to require a comparable amount of performance estimation as for the experimental case. The results reveal a satisfactory agreement for the numerical and experimental optimal trimming parameters, considering the inherent sources of errors and uncertainties in both numerical and experimental approaches. Sensitivity analyses have been eventually performed in the numerical optimization problem to determine the dominant source of uncertainties and characterize the robustness of the optima.

This paper investigates the use of constrained surrogate models to solve the multi-design optimization problem of a flexible hydrofoil. The surrogate-based optimization (EGO) substitutes the complex objective function of the problem by an easily evaluable model, constructed from a limited number of computations at carefully selected design points. Associated with ad-hoc statistical strategies to propose optimum candidates within the estimated feasible domain, EGO enables the resolution of complex optimization problems. In this work, we rely on Gaussian processes (GP) to model the objective function and adopt a probabilistic classification method to treat non-explicit inequality constraints and non-explicit representation of the feasible domain. This procedure is applied to the design of the shape and the elastic characteristics of a hydrofoil equipped with deformable elements providing flexibility to the trailing edge. The optimization concerns the minimization of the hydrofoil drag while ensuring a non-cavitating flow, at selected sailing conditions (boat speed and lifting force). The drag value and cavitation criterion are determined by solving a two-dimensional nonlinear fluid-structure interaction problem, based on a static vortex lattice method with viscous boundary layer equations, for the flow, and a nonlinear elasticity solver for the deformations of the elastic components of the foil. We compare the optimized flexible hydrofoil with a rigid foil geometrically optimized for the same sailing conditions. This comparison highlights the hydrodynamical advantages brought by the flexibility: a reduction of the drag over a large range of boat speeds, less susceptibility to cavitation and a smaller angle of attack tuning range.

The precise control of geometric models plays an important role in many domains such as computer-aided geometric design and numerical simulation. For shape optimization in computational fluid dynamics (CFD), the choice of control parameters and the way to deform a shape are critical. In this article, we describe a skeleton-based representation of shapes adapted for CFD simulation and automatic shape optimization. Instead of using the control points of a classic B-spline representation, we control the geometry in terms of architectural parameters. We assure valid shapes with a strong shape consistency control. Deformations of the geometry are performed by solving optimization problems on the skeleton. Finally, a surface reconstruction method is proposed to evaluate the shape's performances with CFD solvers. We illustrate the approach on two problems: the foil of an AC45 racing sail boat and the bulbous bow of a fishing trawler. For each case, we obtained a set of shape deformations and then we evaluated and analyzed the performances of the different shapes with CFD computations.

This paper investigates the use of meta-models for optimizing sails trimming. A Gaussian process is used to robustly approximate the dependence of the performance with the trimming parameters to be optimized. The Gaussian process construction uses a limited number of performance observations at carefully selected trimming points, potentially enabling the optimization of complex sail systems with multiple trimming parameters. We test the optimization procedure on the (two parameters) trimming of a scaled IMOCA mainsail in upwind conditions. To assess the robustness of the Gaussian process approach, in particular its sensitivity to error and noise in the performance estimation, we contrast the direct optimization of the physical system with the optimization of its numerical model. For the physical system, the optimization procedure was fed with wind tunnel measurements, while the numerical modeling relied on a fully nonlinear Fluid-Structure Interaction solver. The results show a correct agreement of the optimized trimming parameters for the physical and numerical models, despite the inherent errors in the numerical model and the measurement uncertainties. In addition, the number of performance estimations was found to be affordable and comparable in the two cases, demonstrating the effectiveness of the approach

We present a new algorithm based on a quasi-monolithic approach to solve strongly coupled fluid-structure interaction problems. This approach is an implicit coupling adapted to a partitioned solver while conserving the property of convergence and stability of the monolithic approach. The coupling is done between a finite element program ARA developed by K-Epsilon and the Reynolds-averaged Navier-Stokes code, ISIS-CFD, part of the commercial software FINE/Marine. The fluid mesh is deformed using a fast, robust and parallelized method which propagates the deformation state. The mesh deformation is taken into account through the ALE method. Validation of the coupling was performed against the experimental results of a flapping membrane. Application of the coupling is made to compare the unsteady flying stability of two downwind sails using an automatic trimming algorithm. Future application to a respiring tube is discussed.

A numerical investigation of the dynamic fluid structure interaction (FSI) of a yacht sail plan submitted to harmonic pitching is presented to analyse the system׳s dynamic behaviour and the effects of motion simplifications and rigging adjustments on aerodynamic forces. It is shown that the dynamic behaviour of a sail plan subject to yacht motion clearly deviates from the quasi-steady theory. The aerodynamic forces presented as a function of the instantaneous apparent wind angle show hysteresis loops. It is shown that the hysteresis phenomenon dissipates some energy and that the dissipated energy increases strongly with the pitching reduced frequency and amplitude. The effect of reducing the real pitching motion to a simpler surge motion is investigated. Results show significant discrepancies with underestimated aerodynamic forces and no more hysteresis when a surge motion is considered. However, the superposition assumption consisting in a decomposition of the surge into two translations normal and collinear to the apparent wind is verified. Then, simulations with different dock tunes and backstay loads highlight the importance of rig adjustments on the aerodynamic forces and the dynamic behaviour of a sail plan. The energy dissipated by the hysteresis is higher for looser shrouds and a tighter backstay.

Gennakers are lightweight and flexible sails, used for downwind sailing configurations. Qualities sought for this kind of sail are propulsive force and dynamic stability. To simulate accurately the flow surrounding a sail, several problems need to be solved. Firstly, the structural code has to take into account cloth behavior, orientation and reinforcements. Moreover, wrinkles need to be taken into account through modeling or fine enough discretization. Secondly, the fluid solver needs to reproduce the atmospheric boundary layer as an input boundary condition, and be able to simulate separation. Thirdly, the fluid-structure interaction (FSI) is strongly coupled due to the lightness and the flexibility of the structure. The added mass is three orders of magnitude greater than the mass of the sail, and large structural displacement occur, which makes the coupling between the two solvers difficult to achieve. Finally, the problem is unsteady, and dynamic trimming is important to the simulation of gennakers (Graf and Renzsch, 2006). As the FSI procedure is detailed in Durand (2012), the present work is rather focused on its application to downwind sail stability.The main objective of this paper is to use numerical simulations to model gennakers, in order to predict both propulsive force and sail dynamic stability. Recent developments from Durand (2012) are used to solve these problems mentioned earlier, using a finite element structural analysis program dedicated to sails and rig simulations coupled with an unsteady Reynolds averaged Navier-Stokes equations (URANSE) solver. The FSI coupling is done through a partitioned approach with quasi-monolithic properties. An arbitrary Lagrangian Eulerian (ALE) formulation is used, hence the fluid mesh follows the structural deformation while keeping the same topology. The fluid mesh deformation is carried out with a fast, robust and parallelized method based on the propagation of the deformation state of the sail boundary fluid faces (Durand et al., 2010).Tests were realized on a complete production chain: a sail designer from Incidences-Sails has designed two different shapes of an IMOCA60 gennaker with the SailPack software. An automatic procedure was developed to transfer data from Sailpack to a structure input file taking into account the orientation of sailcloth and reinforcements. The same automatic procedure is used for both gennakers, in order to compare dynamic stability and propulsion forces. A new method is then developed to quantify the practical stability of a downwind sail. (C) 2014 Elsevier Ltd. All rights reserved.

A numerical investigation of the dynamic Fluid-Structure Interaction (FSI) of a yacht sail plan submitted to harmonic pitching is presented to address both issues of aerodynamic unsteadiness and structural deformation. The FSI model - Vortex Lattice Method fluid model and Finite Element structure model - have been validated with full-scale measurements. It is shown that the dynamic behaviour of a sail plan subject to yacht motion clearly deviates from the quasi-steady theory. The aerodynamic forces presented as a function of the instantaneous apparent wind angle show hysteresis loops, suggesting that some energy is exchanged by the system. The area included in the hysteresis loop increases with the motion reduced frequency and amplitude. Comparison of rigid versus soft structures shows that FSI increases the energy exchanged by the system and that the oscillations of aerodynamic forces are underestimated when the structure deformation is not considered. Dynamic loads in the fore and aft rigging wires are dominated by structural and inertial effects. This FSI model and the obtained results may be useful firstly for yacht design, and also in the field of auxiliary wind assisted ship propulsion, or to investigate other marine soft structures. (c) 2013 Elsevier Ltd. All rights reserved.

The authors are grateful to Prof. Fossati of Politecnico di Milano for valuable discussions and to the K-Epsilon company for continuous collaboration. This work was supported by the French Naval Academy.

In this paper, a dynamic computation of the Groupama 3 foil is performed. Foils are thin profiles, placed under the hull of a ship, allowing it to provide a lifting force. This study is placed in the context of the 2013 America’s Cup, which will see the appearance of a new kind of high performance multihull. At high speeds, the foils are subject to intense hydrodynamic forces and to movement due to the sea state. The deformations are then sizable and there is a risk of ventilation, cavitation or vibration which could lead to a large modification of the hydrodynamic forces or to the destruction of the foil. The foil being light compared to the added mass effect, the interaction is a strongly coupled problem. In this paper, the problem is solved using a segregated approach. The main problems resulting of such a method are the numerical stability and remeshing. These problems are detailed and some results presented. As a first test case, the simulation of a vortex excited elastic plate proposed by Hubner is presented. This case is very demanding in terms of coupling stability and mesh deformation. Then, the foil of Groupama 3 is modelled in a simplified form without hull and free surface, and then in a more realistic conditions with free surface and waves.

This work presents a full scale experimental study on the aero-elastic wind/sails/rig interaction in real navigation conditions with the aim to give an experimental validation of unsteady fluid structure interaction (FSI) models applied to yacht sails. An inboard instrumentation system has been developed on a J80 yacht to simultaneously and dynamically measure the navigation parameters, yacht's motion, and sails flying shape and loads in the standing and running rigging. The first results recorded while sailing upwind in head waves are shown. Variations of the measured parameters are characterized and related to the yacht motion (trim mainly). Correlations between the different parameters are examined. In the system's response to the dynamic forcing (pitching motion) we attempt to distinguish between the aerodynamic effect of varying apparent wind induced by the motion and the structural effect of varying stresses and strains due to the motion and inertia. The dynamic full scale measurements presented underline the necessity of considering the unsteadiness of phenomena to correctly simulate a yacht's behavior in actual sailing conditions. The simulation results from the FSI model compare very well with the experimental data for steady sailing conditions. For the unsteady conditions obtained in head waves, the first results show a good agreement between measurements and simulation.

Modelling the wind, sail and rig interactions on a sailing yacht is a complex subject, because the quality of simulation depends on the accuracy of both structural and fluid simulations which strongly interact. Moreover, the sails are submitted to highly unsteady sollicitations due to waves, wind variations, course changes or trimming for example, but sometimes also due to the unsteadiness of the flow itself (vortex shedding,…). The problem for downwind sails is even more complex because the flow is often detached from the sails, and the sails are subject to large shape changes. A specific dynamic coupling has been developed between a RANSE code from Ecole Centrale de Nantes for the aerodynamics (ISIS-CFD) and a FEM code from K-Epsilon for the structure (ARA) specialized to simulate the aero-elastic problem of yacht sails and rig. In this paper, the particular issues of coupling, remeshing and transfer of forces from one code to the other are detailed. An experimental comparison is made on a well controlled test case with an original experiment developed by IRENav Ecole Navale, consisting in a square of spinnaker fabric mounted on two carbon battens which are moved in a forced oscillation. The good agreement of numerical results with experimentals results permits to be confident to go ahead and investigate a full example of application on a racing yacht spinnaker.

ABSTRACT This study adds to the development of a non linear aeroelastic model which is destined to predict the behaviour of a thin flexible surface in contact with a flow under the hypothesis of an inviscid fluid. This fluid structure interaction model integrates a structure calculation, based on a membrane model, with a fluid calculation, based on a singularity method associated with a vortex method. The results on a J80 rig are compared to the experiments in situ.

Les outils de simulation numerique permettant de predire le comportement d'un voi-lier en navigation reel sont de plus en plus utilises par les architectes navals. Nous presentons et comparons dans cet article deux modeles de structure (reseaux de fils et membrane CST) utilises dans le calcul aeroelastique d'une structure tridimensionnelle idealement flexible avec un ecoulement instationnaire. L'ecoulement aerodynamique est modelise par une methode de surface portante associee a une methode particulaire. Apres validation du comportement meca-nique des tissus utilises pour la fabrication des voiles, nous presentons les resultats d'un calcul aeroelastique d'une voile sur son etai avec ses differents reglages.