Efficient optimization procedure in non-linear fluid-structure interaction problem: Application to mainsail trimming in upwind conditions

Abstract 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.

[1]  Donald R. Jones,et al.  Efficient Global Optimization of Expensive Black-Box Functions , 1998, J. Glob. Optim..

[2]  Zhonghua Han,et al.  Efficient aerodynamic shape optimization of transonic wings using a parallel infilling strategy and surrogate models , 2016, Structural and Multidisciplinary Optimization.

[3]  Régis Duvigneau,et al.  Kriging‐based optimization applied to flow control , 2012 .

[4]  R. Ghanem,et al.  Stochastic Finite Elements: A Spectral Approach , 1990 .

[5]  Kazuomi Yamamoto,et al.  Efficient Optimization Design Method Using Kriging Model , 2005 .

[6]  Christine A. Shoemaker,et al.  Corrigendum to “Comparison of optimization algorithms for parameter estimation of multi-phase flow models with application to geological carbon sequestration” [Adv. Water Resour. 54 (2013) 133–148] , 2013 .

[7]  V. Saul'ev,et al.  Approximation methods for the unconstrained optimization of functions of several variables , 1975 .

[8]  Youssef M. Marzouk,et al.  Adaptive Smolyak Pseudospectral Approximations , 2012, SIAM J. Sci. Comput..

[9]  Roger Woodard,et al.  Interpolation of Spatial Data: Some Theory for Kriging , 1999, Technometrics.

[10]  M. Natori,et al.  Efficient Modification Scheme of Stress-Strain Tensor for Wrinkled Membranes , 2005 .

[11]  P. Van Oossanen,et al.  Predicting the speed of sailing yachts. Discussion. Author's closure , 1993 .

[12]  Vladimir N. Vapnik,et al.  The Nature of Statistical Learning Theory , 2000, Statistics for Engineering and Information Science.

[13]  N. Zheng,et al.  Global Optimization of Stochastic Black-Box Systems via Sequential Kriging Meta-Models , 2006, J. Glob. Optim..

[14]  Nikolaus Hansen,et al.  The CMA Evolution Strategy: A Comparing Review , 2006, Towards a New Evolutionary Computation.

[15]  Stephen Barnett,et al.  Matrix Methods for Engineers and Scientists , 1982 .

[16]  Michel Visonneau,et al.  FSI investigation on stability of downwind sails with an automatic dynamic trimming , 2013 .

[17]  Timothy W. Simpson,et al.  Metamodels for Computer-based Engineering Design: Survey and recommendations , 2001, Engineering with Computers.

[18]  Richard Von Mises,et al.  Mathematical Theory of Probability and Statistics , 1966 .

[19]  Michael S. Eldred,et al.  Sparse Pseudospectral Approximation Method , 2011, 1109.2936.

[20]  Carl E. Rasmussen,et al.  Gaussian processes for machine learning , 2005, Adaptive computation and machine learning.

[21]  Michael Schäfer,et al.  Efficient shape optimization for fluid–structure interaction problems , 2015 .

[22]  Richard G. J. Flay,et al.  A twisted flow wind tunnel for testing yacht sails , 1996 .

[23]  Ignazio Maria Viola,et al.  Upwind sail aerodynamics: A RANS numerical investigation validated with wind tunnel pressure measurements , 2013 .

[24]  Stefano Tarantola,et al.  Sensitivity Analysis in Practice: A Guide to Assessing Scientific Models , 2004 .

[25]  Jack P. C. Kleijnen,et al.  Kriging Metamodeling in Simulation: A Review , 2007, Eur. J. Oper. Res..

[26]  G. Iaccarino,et al.  Near-wall behavior of RANS turbulence models and implications for wall functions , 2005 .

[27]  Tom Dhaene,et al.  Inverse modelling of an aneurysm’s stiffness using surrogate-based optimization and fluid-structure interaction simulations , 2012 .

[28]  R. V. Mises,et al.  Mathematical Theory of Probability and Statistics , 1966 .

[29]  P. Sagaut,et al.  Building Efficient Response Surfaces of Aerodynamic Functions with Kriging and Cokriging , 2008 .

[30]  Richard J. Beckman,et al.  A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output From a Computer Code , 2000, Technometrics.

[31]  Olivier P. Le Maître,et al.  Polynomial chaos expansion for sensitivity analysis , 2009, Reliab. Eng. Syst. Saf..

[32]  Donald R. Jones,et al.  A Taxonomy of Global Optimization Methods Based on Response Surfaces , 2001, J. Glob. Optim..

[33]  D. Ginsbourger,et al.  A benchmark of kriging-based infill criteria for noisy optimization , 2013, Structural and Multidisciplinary Optimization.

[34]  Vincent Chapin,et al.  Design optimization of interacting sails through viscous cfd , 2008 .

[35]  Benoit Augier,et al.  Études expérimentales de l'interaction fluide-structure sur surface souple : application aux voiles de bateaux , 2012 .

[36]  Mathieu Durand Interaction fluide-structure souple et legere, application aux voiliers , 2012 .

[37]  Richard P. Dwight,et al.  Uncertainty quantification for a sailing yacht hull, using multi-fidelity kriging , 2015 .

[38]  M. Boroomand,et al.  Turbulence , Heat and Mass Transfer 7 2 . Turbulence Model , 2015 .

[39]  Thomas Bäck,et al.  An Overview of Evolutionary Algorithms for Parameter Optimization , 1993, Evolutionary Computation.

[40]  Nikolaus Hansen,et al.  Completely Derandomized Self-Adaptation in Evolution Strategies , 2001, Evolutionary Computation.

[41]  Régis Duvigneau,et al.  Study of some strategies for global optimization using Gaussian process models with application to aerodynamic design , 2009 .

[42]  M. J. Rose,et al.  Classification of a set of elements , 1964, Comput. J..

[43]  Robert Ranzenbach,et al.  Mainsail Planform Optimization for IRC 52 Using Fluid Structure Interaction , 2013 .

[44]  Frédéric Hauville,et al.  Inviscid approach for upwind sails aerodynamics. How far can we go , 2016 .

[45]  Li Liu,et al.  Helicopter vibration reduction throughout the entire flight envelope using surrogate-based optimization , 2007 .

[46]  Daniele Trimarchi,et al.  Analysis of downwind sail structures using non-linear shell finite elements: wrinkle development and fluid interaction effects , 2012 .

[47]  Lionel Huetz,et al.  Database building and statistical methods to predict sailing yacht hydrodynamics , 2014 .

[48]  Michel Visonneau,et al.  Strongly coupled VPP and CFD RANSE code for sailing yacht performance prediction , 2008 .

[49]  J. Katz,et al.  Low-Speed Aerodynamics , 1991 .

[50]  Mathieu Durand,et al.  Experimental validation of unsteady models for fluid structure interaction: Application to yacht sails and rigs , 2012 .

[51]  van,et al.  PREDICTING THE SPEED OF SAILING YACHTS , 1993 .

[52]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[53]  D. Ginsbourger,et al.  Kriging is well-suited to parallelize optimization , 2010 .

[54]  Bruno Sudret,et al.  Global sensitivity analysis using polynomial chaos expansions , 2008, Reliab. Eng. Syst. Saf..

[55]  Omar M. Knio,et al.  Sparse Pseudo Spectral Projection Methods with Directional Adaptation for Uncertainty Quantification , 2016, J. Sci. Comput..

[56]  Luigi Berardi,et al.  Efficient multi-objective optimal design of water distribution networks on a budget of simulations using hybrid algorithms , 2009, Environ. Model. Softw..