Abstract
We have recently presented an initial study of evolutionary algorithms used to design vertical-axis wind turbines (VAWTs) wherein candidate prototypes are evaluated under fan generated wind conditions after being physically instantiated by a 3D printer. That is, unlike other approaches such as computational fluid dynamics simulations, no mathematical formulations are used and no model assumptions are made. However, the representation used significantly restricted the range of morphologies explored. In this paper, we present initial explorations into the use of a simple generative encoding, known as Gielis superformula, that produces a highly flexible 3D shape representation to design VAWT. First, the target-based evolution of 3D artefacts is investigated and subsequently initial design experiments are performed wherein each VAWT candidate is physically instantiated and evaluated under fan generated wind conditions. It is shown possible to produce very closely matching designs of a number of 3D objects through the evolution of supershapes produced by Gielis superformula. Moreover, it is shown possible to use artificial physical evolution to identify novel and increasingly efficient supershape VAWT designs.
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Notes
A supershape visualisation tool and its source code produced by Martin Schneider, licensed under Creative Commons Attribution Share Alike 3.0 and GNU GPL license, can be found at http://openprocessing.org/visuals/?visualID=2638.
Antenna Company http://www.antennacompany.com.
MeshLab is an open source, portable, and extensible system for the processing and editing of unstructured 3D triangular meshes. http://meshlab.sourceforge.net.
References
Anderson JD (1995) Computational fluid dynamics: the basics with applications. McGraw Hill, New York
Barr AH (1981) Superquadrics and angle-preserving transformations. IEEE Comput Graph Appl 1(1):11–23
Barr AH (1984) Global and local deformations of solid primitives. In: Proceedings of the 11th annual conference on computer graphics and interactive techniques, SIGGRAPH ’84, pp 21–30
Barthelmie RJ, Larsen GC, Frandsen ST, Folkerts L, Rados K, Pryor SC, Lange B, Schepers G (2006) Comparison of wake model simulations with offshore wind turbine wake profiles measured by sodar. Atmos Ocean Technol 23:888–901
Bentley PJ (1996) Generic evolutionary design of solid objects using a genetic algorithm. PhD thesis, School of Engineering, University of Huddersfield, Huddersfield, UK
Bia P, Caratelli D, Mescia L, Gielis J (2013) Electromagnetic characterization of supershaped lens antennas for high-frequency applications. In: Proceedings of the 2013 European Microwave Conference, EuMC ’13, IEEE, pp 1679–1682
Blanc C, Schlick C (1996) Ratioquadrics: an alternative model for superquadrics. Vis Comput 12(8):420–428
Bokhabrine Y, Fougerolle YD, Foufou S, Truchetet F (2007) Genetic algorithms for Gielis surface recovery from 3D data sets. IEEE Int Conf Image Process 2:549–552
Boria F, Stanford B, Bowman S, Ifju P (2009) Evolutionary optimization of a morphing wing with wind-tunnel hardware in the loop. AIAA J 47(2):399–409
Carrigan TJ, Dennis BH, Han ZX, Wang BP (2012) Aerodynamic shape optimization of a vertical-axis wind turbine using differential evolution. ISRN Renewable Energy, article ID: 528418
Charwat AF (1978) Performance of counter—and corotating arrays of savonius turbines. J Energy 2:61–63
Clune J, Lipson H (2011) Evolving three-dimensional objects with a generative encoding inspired by developmental biology. In: Lenaerts T, Giacobini M, Bersini H, Bourgine P, Dorigo M, Doursat R (eds) Advances in artificial life, ECAL 2011. MIT Press, Cambridge, pp 141–148
Clune J, Chen A, Lipson H (2013) Upload any object and evolve it: Injecting complex geometric patterns into CPPNs for further evolution. In: Proceedings of the IEEE Congress on evolutionary computation, CEC 2013, p 3395–3402
Cohen DL, Lipton JI, Bonassar LJ, Lipson H (2010) Additive manufacturing for in situ repair of osteochondral defects. Biofabrication 2(3):035004
Dabiri JO (2011) Potential order-of-magnitude enhancement of wind farm power density via counter-rotating vertical-axis wind turbine arrays. J Renew Sustain Energy 3(4):043104
Darrieus GJM (1931) Turbine having its rotating shaft transverse to the flow of the current. US Patent 1 835 018, Dec 8
Dunham B, Fridshal R, North JH (1963) Design by natural selection. Synthese 15(2):254–259
Eggenberger P (1997) Evolving morphologies of simulated 3D organisms based on differential gene expression. In: Husbands P, Harvey I (eds) Proceedings of the fourth European conference on artificial life, MIT Press, pp 205–213
Eriksson S, Bernhoff H, Leijon M (2008) Evaluation of different turbine concepts for wind power. Renew Sustain Energy Rev 12:1419–1434
Fougerolle YD, Gribok A, Foufou S, Truchetet F, Abidi MA (2006) Supershape recovery from 3D data sets. In: IEEE international conference on image processing, pp 2193–2196
Funes P, Pollack J (1998) Evolutionary body building: adaptive physical designs for robots. Artif Life 4(4):337–357
Gielis J (2003) A generic geometric transformation that unifies a wide range of natural and abstract shapes. Am J Bot 90(3):333–338
Gräning L, Jin Y, Sendhoff B (2007) Individual-based management of meta-models for evolutionary optimization with application to three-dimensional blade optimization. In: Yang S, Ong YS, Jin Y (eds) Evolutionary computation in dynamic and uncertain environments, studies in computational intelligence, vol 51. Springer, Berlin, pp 225–250
Gupta A, Bajcsy R (1993) Volumetric segmentation of range images of 3D objects using superquadric models. Comput Vis Graph Image Process Image Underst 58(3):302–326
Hacioglu A, Ozkol I (2003) Transonic airfoil design and optimization by using vibrational genetic algorithm. Aircr Eng Aerosp Technol 75(4):350–357
Hajela P, Lee J (1995) Genetic algorithms in multidisciplinary rotor blade design. In: Proceedings of the 36th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics and material conference, New Orleans, Louisiana, USA, pp 2187–2197
Hampsey M (2002) Multiobjective evolutionary optimisation of small wind turbine blades. PhD thesis, Department of Mechanical Engineering, University of Newcastle, Callaghan, NSW, Australia
Hanson AJ (1988) Hyperquadrics: smoothly deformable shapes with convex polyhedral bounds. Comput Vis Graph Image Process 44(2):191–210
Hao L, Seaman O, Mellor S, Henderson J, Sewell N, Sloan M (2009) Extrusion behavior of chocolate for additive layer manufacturing. In: da Silva Bartolo PJ, Jorge MA, da Conceicao Batista F, Almeida HA, Matias JM, Vasco JC, Gaspar JB, Correia MA, Andre NC, Alves NF, Novo PP, Martinho PG, Carvalho RA (eds) Innovative developments in design and manufacturing—advanced research in virtual and rapid prototyping. CRC Press, Boca Raton, pp 245–250. ISBN:9781439859216
Harding SL, Miller JF (2004) Evolution in materio: initial experiments with liquid crystal. In: Proceedings of the NASA/DoD workshop on evolvable hardware, IEEE, pp 289–299
Hasager CB, Rasmussen L, Peña A, Jensen LE, Réthoré PE (2013) Wind farm wake: the Horns Rev photo case. Energies 6:696–716
Hasenjäger M, Sendhoff B, Sonoda T, Arima T (2005) Three dimensional evolutionary aerodynamic design optimization with CMA-ES. In: Proceedings of the 7th annual conference on genetic and evolutionary computation, GECCO ’05, pp 2173–2180
Herdy M (1996) Evolution strategies with subjective selection. In: Ebeling W, Rechenberg I, Schwefel HP, Voigt HM (eds) Parallel problem solving from nature: PPSN IV, vol 1141., Lecture notes in computer scienceSpringer, Berlin, pp 22–26
Holland JH (1975) Adaptation in natural and artificial systems. University of Michigan Press, Ann Arbor
Hornby GS, Pollack JB (2001) The advantages of generative grammatical encodings for physical design. In: Proceedings of the IEEE congress on evolutionary computation, CEC 2001, vol 1, pp 600–607
Hornby GS, Lohn JD, Linden DS (2011) Computer-automated evolution of an X-band antenna for NASA’s space technology 5 mission. Evol Comput 19(1):1–23
Howey DA, Bansal A, Holmes AS (2011) Design and performance of a centimetre-scale shrouded wind turbine for energy harvesting. Smart Mater Struct 20(8):085021
Husbands P, Mill F (1991) Simulated coevolution as the mechanism for emergent planning and scheduling. In: Belew RK, Booker LB (eds) Proceedings of the fourth international conference on genetic algorithms. Morgan Kaufmann, pp 264–270
Husbands P, Jermy G, McIlhagga M, Ives R (1996) Two applications of genetic algorithms to component design. In: Fogarty TC (ed) Evolutionary computing, vol 1143., Lecture notes in computer scienceSpringer, Berlin, pp 50–61
Jacob CJ, Hushlak G (2007) Evolutionary and swarm design in science, art, and music. The art of artificial evolution, natural computing series. Springer, Berlin, pp 145–166
Jacob CJ, Nazir A (2002) Polyhedron evolver—evolution of 3D shapes with evolvica. In: Proceedings of the 6th world multiconference on systemics, cybernetics and informatics, SCI 2002, International Institute of Informatics and Systemics, vol VII
Jakab K, Norotte C, Damon B, Marga F, Neagu A, Besch-Williford CL, Kachurin A, Church KH, Park H, Mironov V, Markwald R, Vunjak-Novakovic G, Forgacs G (2008) Tissue engineering by self-assembly of cells printed into topologically defined structures. Tissue Eng Part A 14(3):413–421
Jakobi N, Husbands P, Harvey I (1995) Noise and the reality gap: the use of simulation in evolutionary robotics. In: Morán F, Moreno A, Merelo JJ, Chacón P (eds) Advances in artificial life lecture notes in computer science, vol 929. Springer, Berlin, pp 704–720
Ladd C, So JH, Muth J, Dickey MD (2013) 3D printing of free standing liquid metal microstructures. Adv Mater 25(36):5081–5085
Leigh SJ, Bradley RJ, Purssell CP, Billson DR, Hutchins DA (2012) A simple, low-cost conductive composite material for 3D printing of electronic sensors. PLoS One 7(11):e49365
Lipson H, Pollack J (2000) Automatic design and manufacture of robotic lifeforms. Nature 406(6799):974–978
Lipton JI, Arnold D, Nigl F, Lopez N, Cohen DL, Noren N, Lipson H (2010) Multi-material food printing with complex internal structure suitable for conventional post-processing. In: 21st solid freeform fabrication symposium, SFF ’10. The University of Texas at Austin, Texas, USA, pp 809–815
McGuire F (1993) The origins of sculpture: evolutionary 3D design. IEEE Comput Graph Appl 13(1):9–11
Menzel S, Sendhoff B (2008) Representing the change-free form deformation for evolutionary design optimization evolutionary computation in practice. In: Yu T, Davis L, Baydar C, Roy R (eds) Studies in computational intelligence, vol 88, Springer, Berlin, pp 63–86
Miller JF, Downing K (2002) Evolution in materio: looking beyond the silicon box. In: Proceedings of the NASA/DoD workshop on evolvable hardware, IEEE, pp 167–176
Miller JS, Stevens KR, Yang MT, Baker BM, Nguyen DHT, Cohen DM, Toro E, Chen AA, Galie PA, Yu X, Chaturvedi R, Bhatia SN, Chen CS (2012) Rapid casting of patterned vascular networks for perfusable engineered three-dimensional tissues. Nat Mater 11:768–774
Morales AK, Bobadilla EA (2008) Clustering with an N-dimensional extension of Gielis superformula. In: Proceedings of the 7th WSEAS international conference on artificial intelligence, knowledge engineering and databases, World Scientific and Engineering Academy and Society, pp 343–350
Mosetti G, Poloni C, Diviacco B (1994) Optimization of wind turbine positioning in large wind farms by means of a genetic algorithm. J Wind Eng Ind Aerodyn 51(1):105–116
Nolfi S (1992) Evolving non-trivial behaviours on real-robots: a garbage collecting robot. Robot Auton Syst 22:187–198
Ong YS, Keane AJ (2004) Meta-Lamarckian learning in memetic algorithms. IEEE Trans Evol Comput 8(2):99–110
Oyama A, Obayashi S, Nakamura T (2001) Real-coded adaptive range genetic algorithm applied to transonic wing optimization. Appl Soft Comput 1(3):179–187
Park JW, Jung HJ, Jo H, Spencer BF Jr (2012) Feasibility study of micro-wind turbines for powering wireless sensors on a cable-stayed bridge. Energies 5:3450–3464
Preen RJ, Bull L (2013) Towards the evolution of novel vertical-axis wind turbines. In: Proceedings of the 13th annual UK workshop on computational intelligence, UKCI 2013, IEEE, pp 74–81
Preen RJ, Bull L (2014) Towards the coevolution of novel vertical-axis wind turbines. IEEE Trans Evol Comput. doi:10.1109/TEVC.2014.2316199
Press WH, Teukolsky SA, Vetterling WT, Flannery BP (1992) Numerical recipes in C: the art of scientific computing, 2nd edn. Cambridge University Press, Cambridge
Prusinkiewicz PW, Lindenmayer A (1990) The algorithmic beauty of plants. Springer, Berlin
Quagliarella D, Cioppa AD (1995) Genetic algorithms applied to the aerodynamic design of transonic airfoils. J Aircr 32(4):889–891
Rechenberg I (1971) Evolutionsstrategie—optimierung technischer systeme nach prinzipien der biologischen evolution. PhD thesis, Technical University of Berlin, Berlin, Germany
REN21 (2013) Renewables 2013 global status report. Renewable Energy Policy Network for the 21st Century
Rieffel J, Sayles D (2010) EvoFAB: a fully embodied evolutionary fabricator. In: Tempesti G, Tyrrell AM, Miller JF (eds) Evolvable systems: from biology to hardware—9th international conference. Springer, Berlin, pp 372–380
Salcedo-Sanz S, Saavedra-Moreno B, Paniagua-Tineo A, Portilla-Figueras A (2011) A review of recent evolutionary computation-based techniques in wind turbines layout optimization problems. Cent Eur J Comput Sci 1(1):101–107
Savonius SJ (1930) Wind rotor. US Patent 1 766 765, June 24
Schoenauer M (1996) Shape representations and evolution schemes. In: Fogel LJ, Angeline PJ, Back T (eds) Proceedings of the 5th annual conference on evolutionary programming. MIT Press, pp 121–129
Sederberg TW, Parry SR (1986) Free-form deformation of solid geometric models. In: Proceedings of the 13th annual conference on computer graphics and interactive techniques, SIGGRAPH ’86, pp 151–160
Simeoni M, Cicchetti R, Yarovoy A, Caratelli D (2009) Supershaped dielectric resonator antennas. In: Proceedings of the IEEE antennas and propagation society international symposium, APSURSI ’09, pp 1–4
Simeoni M, Cicchetti R, Yarovoy A, Caratelli D (2011) Plastic-based supershaped dielectric resonator antennas for wide-band applications. IEEE Trans Antennas Propag 59(12):4820–4825
Sims K (1994) Evolving 3D morphology and behavior by competition. Artif Life 1(4):353–372
Song W (2002) Shape optimization of turbine blade firtrees. PhD thesis, School of Engineering Sciences, University of Southampton, Southampton, UK
Stanley KO (2007) Compositional pattern producing networks: a novel abstraction of development. Genet Program Evolv Mach 8(2):131–162
Symes MD, Kitson PJ, Yan J, Richmond CJ, Cooper GJT, Bowman RW, Vilbrandt T, Cronin L (2012) Integrated 3D-printed reactionware for chemical synthesis and analysis. Nat Chem 4:349–354
Theis M, Gazzola G, Forlin M, Poli I, Hanczyc M, Bedau M (2006) Optimal formulation of complex chemical systems with a genetic algorithm. In: Jost J, Reed-Tsochas F, Schuster P (eds) Proceedings of the European conference on complex systems, ECCS ’06 Saïd Business School. University of Oxford, Oxford, UK, p 50
Thompson A (1998) Hardware evolution: automatic design of electronic circuits in reconfigurable hardware by artificial evolution. Distinguished dissertations. Springer, Berlin
Toja-Silva F, Colmenar-Santos A, Castro-Gil M (2013) Urban wind energy exploitation systems: behaviour under multidirectional flow conditions–opportunities and challenges. Renew Sustain Energy Rev 24:364–378
Voisin S, Abidi MA, Foufou S, Truchetet F (2009) Genetic algorithms for 3D reconstruction with supershapes. In: Proceedings of the 16th IEEE international conference on image processing, ICIP 2009, pp 529–532
Watabe H, Okino N (1993) A study on genetic shape design. In: Proceedings of the 5th international conference on genetic algorithms, ICGA 93, Morgan Kaufmann, pp 445–451
Xu T, Binder KW, Albanna MZ, Dice D, Zhoa W, Yoo JJ, Atala A (2013) Hybrid printing of mechanically and biologically improved constructs for cartilage tissue engineering applications. Biofabrication 5(1):015001
Zhou L, Kambhamettu C (1999) Extending superquadrics with exponent functions: modeling and reconstruction. In: Proceedings of the IEEE computer society conference on computer vision and pattern Recognition, vol 2, pp 73–78
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This work was supported by the UK Leverhulme Trust under Grant RPG-2013-344.
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Preen, R.J., Bull, L. Towards the evolution of vertical-axis wind turbines using supershapes. Evol. Intel. 7, 155–167 (2014). https://doi.org/10.1007/s12065-014-0116-4
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DOI: https://doi.org/10.1007/s12065-014-0116-4