Advertisement

Structural and Multidisciplinary Optimization

, Volume 59, Issue 2, pp 595–611 | Cite as

Knowledge discovery in databases for determining formulation in topology optimization

  • Shintaro YamasakiEmail author
  • Kentaro Yaji
  • Kikuo Fujita
Research Paper
  • 229 Downloads

Abstract

Whereas topology optimization has achieved immense success, it involves an intrinsic difficulty. That is, optimized structures obtained by topology optimization strongly depend on the settings of the objective and constraint functions, i.e., the formulation. Nevertheless, the appropriate formulation is not usually obvious when considering structural design problems. Although trial-and-error to determine appropriate formulations are implicitly performed in several studies on topology optimization, it is important to explicitly support the process of trial-and-error. Therefore, in this study, we propose a new framework for topology optimization to determine appropriate formulations. The basic idea of this framework is incorporating knowledge discovery in databases (KDD) and topology optimization. Thus, we construct a database by collecting various and numerous material distributions that are obtained by solving various structural design problems with topology optimization, and find useful knowledge with respect to appropriate formulations from the database on the basis of KDD. An issue must be resolved when realizing the above idea, namely the material distribution in the design domain of a data record must be converted to conform to the design domain of the target design problem wherein an appropriate formulation should be determined. For this purpose, we also propose a material distribution-converting method termed as design domain mapping (DDM). Several numerical examples are used to demonstrate that the proposed framework including DDM successfully and explicitly supports the process of trial-and-error to determine the appropriate formulation.

Keywords

Topology optimization Knowledge Discovery in Databases (KDD) Formulation support system Design Domain Mapping (DDM) 

Notes

References

  1. Adhikari A, Adhikari J (2015) Advances in knowledge discovery in databases. Springer.  https://doi.org/10.1007/978-3-319-13212-9
  2. Allaire G, Jouve F (2008) Minimum stress optimal design with the level set method. Eng Anal Bound Elem 32(11):909–918.  https://doi.org/10.1016/j.enganabound.2007.05.007 CrossRefzbMATHGoogle Scholar
  3. Allaire G, Jouve F, Toader AM (2004) Structural optimization using sensitivity analysis and a level-set method. J Comput Phys 194(1):363–393.  https://doi.org/10.1016/j.jcp.2003.09.032 MathSciNetCrossRefzbMATHGoogle Scholar
  4. Amstutz S, Novotny AA (2010) Topological optimization of structures subject to Von Mises stress constraints. Struct Multidiscip Optim 41(3):407–420.  https://doi.org/10.1007/s00158-009-0425-x MathSciNetCrossRefzbMATHGoogle Scholar
  5. Antonie ML, Zaïane OR, Coman A (2001) Application of data mining techniques for medical image classification. In: Proceedings of the second international conference on multimedia data mining. San Francisco, pp 94–101Google Scholar
  6. Arthur D, Vassilvitskii S (2007) K-means++: the advantages of careful seeding. In: Proceedings of the eighteenth annual ACM-SIAM symposium on discrete algorithms, society for industrial and applied mathematics, pp 1027–1035Google Scholar
  7. Bendsøe MP (1989) Optimal shape design as a material distribution problem. Struct Optim 1(4):193–202CrossRefGoogle Scholar
  8. Bendsøe MP, Kikuchi N (1988) Generating optimal topologies in structural design using a homogenization method. Comput Methods Appl Mech Eng 71(2):197–224MathSciNetCrossRefzbMATHGoogle Scholar
  9. Bendsøe MP, Sigmund O (2003) Topology optimization: theory methods and applications, 2nd edn. Springer, BerlinzbMATHGoogle Scholar
  10. Borrvall T, Petersson J (2003) Topology optimization of fluids in stokes flow. Int J Numer Methods Fluids 41(1):77–107.  https://doi.org/10.1002/fld.426 MathSciNetCrossRefzbMATHGoogle Scholar
  11. Diaz AR, Kikuchi N (1992) Solutions to shape and topology eigenvalue optimization using a homogenization method. Int J Numer Methods Eng 35(7):1487–1502MathSciNetCrossRefzbMATHGoogle Scholar
  12. Diaz AR, Sigmund O (2010) A topology optimization method for design of negative permeability metamaterials. Struct Multidiscip Optim 41(2):163–177.  https://doi.org/10.1007/s00158-009-0416-y MathSciNetCrossRefzbMATHGoogle Scholar
  13. Duysinx P, Bendsøe MP (1998) Topology optimization of continuum structures with local stress constraints. Int J Numer Methods Eng 43(8):1453–1478.  https://doi.org/10.1002/(SICI)1097-0207(19981230)43:8<1453::AID-NME480>3.0.CO;2-2 MathSciNetCrossRefzbMATHGoogle Scholar
  14. Fayyad U, Piatetsky-Shapiro G, Smyth P (1996) From data mining to knowledge discovery in databases. AI Mag 17:37–54Google Scholar
  15. Gersborg-Hansen A, Sigmund O, Haber RB (2005) Topology optimization of channel flow problems. Struct Multidiscip Optim 30(3):181–192.  https://doi.org/10.1007/s00158-004-0508-7 MathSciNetCrossRefzbMATHGoogle Scholar
  16. Gersborg-Hansen A, Bendsøe MP, Sigmund O (2006) Topology optimization of heat conduction problems using the finite volume method. Struct Multidiscip Optim 31(4):251–259.  https://doi.org/10.1007/s00158-005-0584-3 MathSciNetCrossRefzbMATHGoogle Scholar
  17. Guest JK (2009) Topology optimization with multiple phase projection. Comput Methods Appl Mech Eng 199(1–4):123–135.  https://doi.org/10.1016/j.cma.2009.09.023 MathSciNetCrossRefzbMATHGoogle Scholar
  18. Guest JK, Prėvost JH, Belytschko T (2004) Achieving minimum length scale in topology optimization using nodal design variables and projection functions. Int J Numer Methods Eng 61(2):238–254.  https://doi.org/10.1002/nme.1064 MathSciNetCrossRefzbMATHGoogle Scholar
  19. Ha SH, Cho S (2005) Topological shape optimization of heat conduction problems using level set approach. Numer Heat Transfer Part B 48(1):67–88.  https://doi.org/10.1080/10407790590935966 CrossRefGoogle Scholar
  20. Haslinger J, Hillebrand A, Kärkkäinen T, Miettinen M (2002) Optimization of conducting structures by using the homogenization method. Struct Multidiscip Optim 24(2):125–140.  https://doi.org/10.1007/s00158-002-0223-1 CrossRefGoogle Scholar
  21. Holmberg E, Torstenfelt B, Klarbring A (2013) Stress constrained topology optimization. Struct Multidiscip Optim 48(1):33–47.  https://doi.org/10.1007/s00158-012-0880-7 MathSciNetCrossRefzbMATHGoogle Scholar
  22. Hsu W, Lee ML, Zhang J (2002) Image mining: trends and developments. J Intell Inf Syst 19(1):7–23.  https://doi.org/10.1023/A:1015508302797 CrossRefGoogle Scholar
  23. Ignizio JP (1990) A brief introduction to expert systems. Comput Oper Res 17(6):523–533.  https://doi.org/10.1016/0305-0548(90)90058-F CrossRefGoogle Scholar
  24. Jain MB, Srinivas MB, Jain A (2008) A novel web based expert system architecture for on-line and off-line fault diagnosis and control (FDC) of transformers. In: Proceedings of 2008 IEEE region 10 conference, pp 1–5.  https://doi.org/10.1109/TENCON.2008.4766606
  25. Kawamoto A, Matsumori T, Yamasaki S, Nomura T, Kondoh T, Nishiwaki S (2011) Heaviside projection based topology optimization by a PDE-filtered scalar function. Struct Multidiscip Optim 44(1):19–24.  https://doi.org/10.1007/s00158-010-0562-2 CrossRefzbMATHGoogle Scholar
  26. Lazarov BS, Sigmund O (2011) Filters in topology optimization based on Helmholtz-type differential equations. Int J Numer Methods Eng 86(6):765–781.  https://doi.org/10.1002/nme.3072 MathSciNetCrossRefzbMATHGoogle Scholar
  27. Ma ZD, Kikuchi N, Cheng HC (1995) Topological design for vibrating structures. Comput Methods Appl Mech Eng 121(1–4):259–280MathSciNetCrossRefzbMATHGoogle Scholar
  28. Nomura T, Sato K, Taguchi K, Kashiwa T, Nishiwaki S (2007) Structural topology optimization for the design of broadband dielectric resonator antennas using the finite difference time domain technique. Int J Numer Methods Eng 71(11):1261–1296.  https://doi.org/10.1002/nme.1974 CrossRefzbMATHGoogle Scholar
  29. Olesen LH, Okkels F, Bruus H (2006) A high-level programming-language implementation of topology optimization applied to steady-state Navier-Stokes flow. Int J Numer Methods Eng 65(7):975–1001MathSciNetCrossRefzbMATHGoogle Scholar
  30. Osher SJ, Santosa F (2001) Level-set methods for optimization problems involving geometry and constraints: Frequencies of a two-density inhomogeneous drum. J Comput Phys 171(1):272–288MathSciNetCrossRefzbMATHGoogle Scholar
  31. Papalambros PY, Wilde DJ (2017) Principles of optimal design: modeling and computation, 3rd edn. Cambridge University Press, CambridgeCrossRefzbMATHGoogle Scholar
  32. Ravindran A, Ragsdell KM, Reklaitis GV (2007) Engineering optimization: methods and applications, 2nd edn. Wiley, HobokenGoogle Scholar
  33. Sethian JA, Wiegmann A (2000) Structural boundary design via level-set and immersed interface methods. J Comput Phys 163(2):489–528MathSciNetCrossRefzbMATHGoogle Scholar
  34. Siddall JN (1982) Optimal engineering design: principles and applications. Marcel Dekker Inc., New YorkGoogle Scholar
  35. Srivastava J, Cooley R, Deshpande M, Tan PN (2000) Web usage mining: discovery and applications of usage patterns from web data. SIGKDD Explor Newslett 1(2):12–23.  https://doi.org/10.1145/846183.846188 CrossRefGoogle Scholar
  36. Tsai CW, Lai CF, Chiang MC, Yang LT (2014) Data mining for internet of things: a survey. IEEE Commun Surv Tutor 16(1):77–97.  https://doi.org/10.1109/SURV.2013.103013.00206 CrossRefGoogle Scholar
  37. Wang MY, Wang X, Guo D (2003) A level set method for structural topology optimization. Comput Methods Appl Mech Eng 192(1–2):227–246MathSciNetCrossRefzbMATHGoogle Scholar
  38. Yamasaki S, Nomura T, Kawamoto A, Sato K, Izui K, Nishiwaki S (2010) A level set based topology optimization method using the discretized signed distance function as the design variables. Struct Multidiscip Optim 41(5):685–698.  https://doi.org/10.1007/s00158-009-0453-6 MathSciNetCrossRefzbMATHGoogle Scholar
  39. Yamasaki S, Nomura T, Kawamoto A, Sato K, Nishiwaki S (2011) A level set-based topology optimization method targeting metallic waveguide design problems. Int J Numer Methods Eng 87(9):844–868.  https://doi.org/10.1002/nme.3135 MathSciNetCrossRefzbMATHGoogle Scholar
  40. Yamasaki S, Kawamoto A, Nomura T (2012a) Compliant mechanism design based on the level set and arbitrary Lagrangian Eulerian methods. Struct Multidiscip Optim 46(3):343–354.  https://doi.org/10.1007/s00158-011-0738-4 MathSciNetCrossRefzbMATHGoogle Scholar
  41. Yamasaki S, Nomura T, Sato K, Michishita N, Yamada Y, Kawamoto A (2012b) Level set-based topology optimization targeting dielectric resonator-based composite right- and left-handed transmission lines. Int J Numer Methods Eng 89(10):1272–1295.  https://doi.org/10.1002/nme.3287 CrossRefzbMATHGoogle Scholar
  42. Yamasaki S, Yamada T, Matsumoto T (2013) An immersed boundary element method for level-set based topology optimization. Int J Numer Methods Eng 93(9):960–988.  https://doi.org/10.1002/nme.4417 MathSciNetCrossRefzbMATHGoogle Scholar
  43. Yamasaki S, Kawamoto A, Nomura T, Fujita K (2015) A consistent grayscale-free topology optimization method using the level-set method and zero-level boundary tracking mesh. Int J Numer Methods Eng 101(10):744–773.  https://doi.org/10.1002/nme.4826 MathSciNetCrossRefzbMATHGoogle Scholar
  44. Yamasaki S, Kawamoto A, Saito A, Kuroishi M, Fujita K (2017a) Grayscale-free topology optimization for electromagnetic design problem of in-vehicle reactor. Struct Multidiscip Optim 55(3):1079–1090.  https://doi.org/10.1007/s00158-016-1557-4 MathSciNetCrossRefGoogle Scholar
  45. Yamasaki S, Yamanaka S, Fujita K (2017b) Three-dimensional grayscale-free topology optimization using a level-set based r-refinement method. Int J Numer Methods Eng 112(10):1402–1438.  https://doi.org/10.1002/nme.5562 MathSciNetCrossRefGoogle Scholar
  46. Yoon GH, Sigmund O (2008) A monolithic approach for topology optimization of electrostatically actuated devices. Comput Methods Appl Mech Eng 197(45–48):4062–4075.  https://doi.org/10.1016/j.cma.2008.04.004 MathSciNetCrossRefzbMATHGoogle Scholar
  47. Zahradnikova B, Duchovicova S, Schreiber P (2015) Image mining: review and new challenges. Int J Adv Comput Sci Appl 6(7).  https://doi.org/10.14569/IJACSA.2015.060732

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringOsaka UniversitySuitaJapan

Personalised recommendations