Oh, Sahuck; Jiang, Chung-Hsiang; Jiang, Chiyu; Marcus, Philip S. Finding the optimal shape of the leading-and-trailing car of a high-speed train using design-by-morphing. (English) Zbl 1470.76091 Comput. Mech. 62, No. 1, 23-45 (2018). Summary: We present a new, general design method, called design-by-morphing for an object whose performance is determined by its shape due to hydrodynamic, aerodynamic, structural, or thermal requirements. To illustrate the method, we design a new leading-and-trailing car of a train by morphing existing, baseline leading-and-trailing cars to minimize the drag. In design-by-morphing, the morphing is done by representing the shapes with polygonal meshes and spectrally with a truncated series of spherical harmonics. The optimal design is found by computing the optimal weights of each of the baseline shapes so that the morphed shape has minimum drag. As a result of optimization, we found that with only two baseline trains that mimic current high-speed trains with low drag that the drag of the optimal train is reduced by 8.04% with respect to the baseline train with the smaller drag. When we repeat the optimization by adding a third baseline train that under-performs compared to the other baseline train, the drag of the new optimal train is reduced by 13.46%. This finding shows that bad examples of design are as useful as good examples in determining an optimal design. We show that design-by-morphing can be extended to many engineering problems in which the performance of an object depends on its shape. Cited in 1 Document MSC: 76N25 Flow control and optimization for compressible fluids and gas dynamics 76M99 Basic methods in fluid mechanics 92B20 Neural networks for/in biological studies, artificial life and related topics Keywords:optimal train head; genetic algorithm; artificial neural network; drag reduction; polygonal mesh; spherical harmonics series Software:TensorFlow; SHTns PDFBibTeX XMLCite \textit{S. Oh} et al., Comput. Mech. 62, No. 1, 23--45 (2018; Zbl 1470.76091) Full Text: DOI References: [1] Abadi M, Agarwal A, Barham P, Brevdo E, Chen Z, Citro C, Corrado GS, Davis A, Dean J, Devin M et al (2016) Tensorflow: large-scale machine learning on heterogeneous distributed systems. arXiv preprint arXiv:1603.04467 [2] Aider, JL; Beaudoin, JF; Wesfreid, JE, Drag and lift reduction of a 3d bluff-body using active vortex generators, Experiments in fluids, 48, 771-789, (2010) [3] Anjum, MF; Tasadduq, I; Al-Sultan, K, Response surface methodology: a neural network approach, Eur J Op Res, 101, 65-73, (1997) · Zbl 0928.93007 [4] Baker, C; Cheli, F; Orellano, A; Paradot, N; Proppe, C; Rocchi, D, Cross-wind effects on road and rail vehicles, Veh Syst Dyn, 47, 983-1022, (2009) [5] Inc Bambardier (2010) Aeroefficient optimised train shaping. Bambardier Inc., Montreal [6] Baş, D; Boyacı, İH, Modeling and optimization i: usability of response surface methodology, J Food Eng, 78, 836-845, (2007) [7] Boyd JP (2001) Chebyshev and fourier spectral methods. Courier Corporation, North Chelmsford · Zbl 0994.65128 [8] Brechbühler, C; Gerig, G; Kübler, O, Parametrization of closed surfaces for 3-D shape description, Comput Vis Image Underst, 61, 154-170, (1995) [9] Canuto C, Hussaini M, Quarteroni A, Zang T (2007) Spectral methods: evolution to complex geometries and applications to fluid dynamics. Scientific computation. Springer, Berlin · Zbl 1121.76001 [10] Chen, J; Shapiro, V; Suresh, K; Tsukanov, I, Shape optimization with topological changes and parametric control, Int J Numer Methods Eng, 71, 313-346, (2007) · Zbl 1194.74236 [11] Chung, MK; Worsley, KJ; Nacewicz, BM; Dalton, KM; Davidson, RJ, General multivariate linear modeling of surface shapes using surfstat, NeuroImage, 53, 491-505, (2010) [12] Cooper, R, The effect of cross-winds on trains, Journal of Fluids Engineering, 103, 170-178, (1981) [13] Cybenko, G, Approximation by superpositions of a sigmoidal function, Math Control Signals Syst (MCSS), 2, 303-314, (1989) · Zbl 0679.94019 [14] De Berg M, Van Kreveld M, Overmars M, Schwarzkopf OC (2000) Computational geometry. In: Computational geometry, Springer, Berlin pp 1-17 · Zbl 0939.68134 [15] Demeulenaere A, Ligout A, Hirsch C (2004) Application of multipoint optimization to the design of turbomachinery blades. In: ASME Turbo Expo 2004: power for land, sea, and air, american society of mechanical engineers, pp 1481-1489 [16] Demeulenaere A, Bonaccorsi JC, Gutzwiller D, Hu L, Sun H (2015) Multi-disciplinary multi-point optimization of a turbocharger compressor wheel. In: ASME Turbo Expo 2015: turbine technical conference and exposition, American society of mechanical engineers, pp V02CT45A020-V02CT45A020 [17] Desbrun M, Meyer M, Alliez P (2002) Intrinsic parameterizations of surface meshes. Computer Graphics Forum. Wiley, Hoboken, pp 209-218 [18] do Carmo MP (1976) Differential geometry of curves and surfaces. Prentice-Hall [19] DuMouchel, W; Jones, B, A simple Bayesian modification of d-optimal designs to reduce dependence on an assumed model, Technometrics, 36, 37-47, (1994) · Zbl 0800.62472 [20] Duriez T, Aider JL, Masson E, Wesfreid JE (2009) Qualitative investigation of the main flow features over a TGV. In: EUROMECH COLLOQUIUM 50, vol 509 [21] Elef, A; Mousa, M; Nassar, H, An efficient technique for morphing zero-genus 3D objects, Int J Phys Sci, 9, 302-308, (2014) [22] Feng, J; Ma, L; Peng, Q, A new free-form deformation through the control of parametric surfaces, Comput Gr, 20, 531-539, (1996) [23] Gottlieb D, Orszag SA (1977) Numerical analysis of spectral methods: theory and applications, vol 26. Siam, Philadelphia · Zbl 0412.65058 [24] Hemida HN (2006) Large-eddy simulation of the flow around simplified high-speed trains under side wind conditions. PhD thesis, Chalmers University of Technology Goteborg, Sweden [25] Hornik, K; Stinchcombe, M; White, H, Multilayer feedforward networks are universal approximators, Neural Netw, 2, 359-366, (1989) · Zbl 1383.92015 [26] Hughes, TJ; Cottrell, JA; Bazilevs, Y, Isogeometric analysis: cad, finite elements, nurbs, exact geometry and mesh refinement, Comput Methods Appl Mech Eng, 194, 4135-4195, (2005) · Zbl 1151.74419 [27] Jakubek D, Wagner C (2016) Adjoint-based, cad-free aerodynamic shape optimization of high-speed trains. In: Dillmann A, Heller G, Krämer E, Wagner C, Breitsamter C (eds) New results in numerical and experimental fluid mechanics X. Springer, Berlin, pp 409-419 [28] Jameson A (1989) Aerodynamic design via control theory. In: Chao CC, Orszag SA, Shyy W (eds) Recent advances in computational fluid dynamics. Springer, Berlin, pp 377-401 [29] Jameson A, Pierce N, Martinelli L (1998) Optimum aerodynamic design using the Navier-stokes equations. In: 35th aerospace sciences meeting and exhibit, p 101 [30] Jiaqi, L; Feng, L, Multi-objective design optimization of a transonic compressor rotor using an adjoint equation method, AIAA Paper, 2732, 2013, (2013) [31] Kang, J, Design of marine structures through morphing method and its supporting techniques, Marine Technol Soc J, 48, 81-89, (2014) [32] Khuri, AI; Mukhopadhyay, S, Response surface methodology, Wiley Interdiscip Rev Comput Stat, 2, 128-149, (2010) [33] Kleijnen, JP, Response surface methodology for constrained simulation optimization: an overview, Simul Modell Pract Theory, 16, 50-64, (2008) [34] Ku YC, Kwak MH, Park HI, Lee DH (2010) Multi-objective optimization of high-speed train nose shape using the vehicle modeling function. In: 48th AIAA aerospace sciences meeting. Orlando, USA [35] Li, R; Xu, P; Peng, Y; Ji, P, Multi-objective optimization of a high-speed train head based on the FFD method, J Wind Eng Ind Aerodyn, 152, 41-49, (2016) [36] Long, C; Marsden, A; Bazilevs, Y, Shape optimization of pulsatile ventricular assist devices using FSI to minimize thrombotic risk, Comput Mech, 54, 921-932, (2014) · Zbl 1314.74056 [37] Lyu, Z; Kenway, GK; Martins, JR, Aerodynamic shape optimization investigations of the common research model wing benchmark, AIAA J, 53, 968-985, (2014) [38] Marcus PS (1986) Description and philosophy of spectral methods. In: Winkler K-HA, NormanML (eds) Astrophysical Radiation Hydrodynamics. Springer, Berlin, pp 359-386 [39] Mocanu BC (2012) 3d mesh morphing. PhD thesis, Institut National des Télécommunications [40] Muñoz-Paniagua, J; García, J; Crespo, A, Genetically aerodynamic optimization of the nose shape of a high-speed train entering a tunnel, J Wind Eng Ind Aerodyn, 130, 48-61, (2014) [41] Munoz-Paniagua, J; García, J; Crespo, A; Laspougeas, F, Aerodynamic optimization of the nose shape of a train using the adjoint method, J Appl Fluid Mech, 8, 601-612, (2015) [42] Nemec M, Zingg DW, Pulliam TH (2004) Multipoint and multi-objective aerodynamic shape optimization. AIAA journal 42(6):1057-1065 [43] Oh S (2016) Finding the optimal shape of an object using design-by-morphing. PhD dissertation, University of California, Berkeley [44] Peters, J, Optimising aerodynamics to raise IC performance, Railw Gaz Int, 10, 78-91, (1982) [45] Pironneau, O, On optimum design in fluid mechanics, J Fluid Mech, 64, 97-110, (1974) · Zbl 0281.76020 [46] Poole J, Allen C, Rendall T (2014) Application of control point-based aerodynamic shape optimization to two-dimensional drag minimization. In: 52nd AIAA aerospace sciences meeting, National Harbor, Maryland, pp 2014-0413 [47] Praun E, Sweldens W, Schröder P (2001) Consistent mesh parameterizations. In: Proceedings of the 28th annual conference on computer graphics and interactive techniques, ACM, pp 179-184 [48] Press WH, Flannery BP, Teukolsky SA, Vetterling WT et al (1989) Numerical recipes, vol 3. Cambridge University Press, cambridge · Zbl 0698.65001 [49] Samareh J (2004) Aerodynamic shape optimization based on free-form deformation. In: 10th AIAA/ISSMO multidisciplinary analysis and optimization conference, p 4630 [50] Schaeffer, N, Efficient spherical harmonic transforms aimed at pseudospectral numerical simulations, Geochem Geophys Geosyst, 14, 751-758, (2013) [51] Shen, L; Ford, J; Makedon, F; Saykin, A, A surface-based approach for classification of 3D neuroanatomic structures, Intell Data Anal, 8, 519-542, (2004) [52] Shen, L; Farid, H; McPeek, MA, Modeling three-dimensional morphological structures using spherical harmonics, Evolution, 63, 1003-1016, (2009) [53] Shojaeefard, MH; Mirzaei, A; Babaei, A, Shape optimization of draft tubes for agnew microhydro turbines, Energy Convers Manag, 79, 681-689, (2014) [54] Shyy, W; Papila, N; Vaidyanathan, R; Tucker, K, Global design optimization for aerodynamics and rocket propulsion components, Prog Aerosp Sci, 37, 59-118, (2001) [55] Sorkine O, Alexa M (2007) As-rigid-as-possible surface modeling. In: Symposium on geometry processing, vol 4 [56] Styner, M; Oguz, I; Xu, S; Brechbühler, C; Pantazis, D; Levitt, JJ; Shenton, ME; Gerig, G, Framework for the statistical shape analysis of brain structures using spharm-pdm, Insight J, 1071, 242, (2006) [57] Sun, Z; Song, J; An, Y, Optimization of the head shape of the CRH3 high speed train, Sci China Technol Sci, 53, 3356-3364, (2010) · Zbl 1278.76039 [58] Hq, Tian, Formation mechanism of aerodynamic drag of high-speed train and some reduction measures, J Cent South Univ Technol, 16, 166-171, (2009) [59] Vanaja, K; Shobha Rani, R, Design of experiments: concept and applications of plackett burman design, Clin Res Regul Aff, 24, 1-23, (2007) [60] Vassberg J, Jameson A (2014) Influence of shape parameterization on aerodynamic shape optimization. In: Verstraete T, Periaux J (eds) Introduction to optimization and multidisciplinary design in aeronautics and turbomachinery. Von Karman Institute Sint-Genesius-Rode, pp 1-19 [61] Viana, FA; Venter, G; Balabanov, V, An algorithm for fast optimal Latin hypercube design of experiments, Int J Numer Methods Eng, 82, 135-156, (2010) · Zbl 1188.65088 [62] Wang, X; Hirsch, C; Kang, S; Lacor, C, Multi-objective optimization of turbomachinery using improved NSGA-II and approximation model, Comput Methods Appl Mech Eng, 200, 883-895, (2011) · Zbl 1225.76255 [63] Yao, S; Guo, D; Sun, Z; Yang, G, A modified multi-objective sorting particle swarm optimization and its application to the design of the nose shape of a high-speed train, Eng Appl Comput Fluid Mech, 9, 513-527, (2015) [64] Zhang, WH; Beckers, P; Fleury, C, A unified parametric design approach to structural shape optimization, Int J Numer Methods Eng, 38, 2283-2292, (1995) · Zbl 0854.73040 This reference list is based on information provided by the publisher or from digital mathematics libraries. 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