Optimization approaches to some problems of building design

Jiří Vala; Petra Jarošová

Applications of Mathematics (2018)

  • Volume: 63, Issue: 3, page 305-331
  • ISSN: 0862-7940

Abstract

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Advanced building design is a rather new interdisciplinary research branch, combining knowledge from physics, engineering, art and social science; its support from both theoretical and computational mathematics is needed. This paper shows an example of such collaboration, introducing a model problem of optimal heating in a low-energy house. Since all particular function values, needed for optimization are obtained as numerical solutions of an initial and boundary value problem for a sparse system of parabolic partial differential equations of evolution with at least two types of physically motivated nonlinearities, the usual gradient-based methods must be replaced by the downhill simplex Nelder-Mead approach or its quasi-gradient modifications. One example of the real low-energy house in Moravian Karst is demonstrated with references to other practical applications.

How to cite

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Vala, Jiří, and Jarošová, Petra. "Optimization approaches to some problems of building design." Applications of Mathematics 63.3 (2018): 305-331. <http://eudml.org/doc/294796>.

@article{Vala2018,
abstract = {Advanced building design is a rather new interdisciplinary research branch, combining knowledge from physics, engineering, art and social science; its support from both theoretical and computational mathematics is needed. This paper shows an example of such collaboration, introducing a model problem of optimal heating in a low-energy house. Since all particular function values, needed for optimization are obtained as numerical solutions of an initial and boundary value problem for a sparse system of parabolic partial differential equations of evolution with at least two types of physically motivated nonlinearities, the usual gradient-based methods must be replaced by the downhill simplex Nelder-Mead approach or its quasi-gradient modifications. One example of the real low-energy house in Moravian Karst is demonstrated with references to other practical applications.},
author = {Vala, Jiří, Jarošová, Petra},
journal = {Applications of Mathematics},
keywords = {building design; heat transfer; inverse and optimization problems; Nelder-Mead algorithm},
language = {eng},
number = {3},
pages = {305-331},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Optimization approaches to some problems of building design},
url = {http://eudml.org/doc/294796},
volume = {63},
year = {2018},
}

TY - JOUR
AU - Vala, Jiří
AU - Jarošová, Petra
TI - Optimization approaches to some problems of building design
JO - Applications of Mathematics
PY - 2018
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 63
IS - 3
SP - 305
EP - 331
AB - Advanced building design is a rather new interdisciplinary research branch, combining knowledge from physics, engineering, art and social science; its support from both theoretical and computational mathematics is needed. This paper shows an example of such collaboration, introducing a model problem of optimal heating in a low-energy house. Since all particular function values, needed for optimization are obtained as numerical solutions of an initial and boundary value problem for a sparse system of parabolic partial differential equations of evolution with at least two types of physically motivated nonlinearities, the usual gradient-based methods must be replaced by the downhill simplex Nelder-Mead approach or its quasi-gradient modifications. One example of the real low-energy house in Moravian Karst is demonstrated with references to other practical applications.
LA - eng
KW - building design; heat transfer; inverse and optimization problems; Nelder-Mead algorithm
UR - http://eudml.org/doc/294796
ER -

References

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  1. Abdelhalim, A., Nakata, K., El-Alem, M., Eltawil, A., 10.1080/0305215X.2017.1340945, Eng. Optim. 50 (2018), 568-583. (2018) MR3766656DOI10.1080/0305215X.2017.1340945
  2. Castro, A. Bermúdez de, 10.1007/3-7643-7383-0, Progress in Mathematical Physics 43, Birkhäuser, Basel (2005). (2005) Zbl1070.74001MR2145925DOI10.1007/3-7643-7383-0
  3. Bomberg, M., 10.1016/j.foar.2012.10.003, Frontiers of Architectural Research 1 (2012), 421-423. (2012) DOI10.1016/j.foar.2012.10.003
  4. Brandts, J., Korotov, S., Křížek, M., Šolc, J., 10.1137/060669073, SIAM Rev. 51 (2009), 317-335. (2009) Zbl1172.51012MR2505583DOI10.1137/060669073
  5. Chen, S., Wang, X., 10.4236/ajcm.2013.31003, American Journal of Computational Mathematics 3 (2013), 16-26. (2013) DOI10.4236/ajcm.2013.31003
  6. Colaço, M. J., Orlande, H. R. B., Dulikravich, G. S., 10.1590/S1678-58782006000100001, J. Braz. Soc. Mech. Sci. & Eng. 28 (2006), 1-24. (2006) DOI10.1590/S1678-58782006000100001
  7. Coope, I. D., Price, C. J., 10.1023/A:1026429319405, J. Optim. Theory Appl. 107 (2000), 261-274. (2000) Zbl0983.90074MR1800945DOI10.1023/A:1026429319405
  8. 10.3000/17252555.L_2010.153.eng, Official Journal of the European Union L 153/13 (2010). (2010) DOI10.3000/17252555.L_2010.153.eng
  9. Feist, W., Gestaltungsgrundlagen Passivhäuser, Das Beispiel, Darmstadt (2000), German. (2000) 
  10. Fiedler, M., Special Matrices and Their Applications in Numerical Mathematics, Dover Publications, Mineola (1981). (1981) Zbl1170.65018MR2517585
  11. Gao, F., Han, L., 10.1007/s10589-010-9329-3, Comput. Optim. Appl. 51 (2012), 259-277. (2012) Zbl1245.90121MR2872499DOI10.1007/s10589-010-9329-3
  12. Gavin, H. P., The Nelder-Mead algorithm in two dimensions, CEE 201L Uncertainty, Design, and Optimization Lecture Notes, Duke University, Durham (2016). (2016) 
  13. Hicken, J. E., Alonso, J. J., Multidisciplinary Design Optimization, Lecture Notes, Stanford University, Stanford (2012). (2012) 
  14. Hudec, M., Johanisová, B., Mansbart, T., Pasivní domy z přírodních materiálů, Grada, Praha (2012), Czech. (2012) 
  15. Jarošová, P., Optimalizace vybraných parametrů pro návrh objektů s nízkou energetickou náročností, Dissertation thesis, Brno University of Technology, Brno (2017), Avai-lable at https://www.vutbr.cz/wwwbase/zavpracesouborverejne.php?fileid=156981Czech. (2017) 
  16. Jarošová, P., Vala, J., 10.4028/www.scientific.net/AMR.1126.59, Advanced Materials Research 1126 (2015), 59-66. (2015) DOI10.4028/www.scientific.net/AMR.1126.59
  17. Kelley, C. T., 10.1137/S1052623497315203, SIAM J. Optim. 10 (1999), 43-55. (1999) Zbl0962.65048MR1722147DOI10.1137/S1052623497315203
  18. Klaus, V., Blue Planet in Green Shackles: What Is Endangered: Climate or Freedom?, Competitive Enterprise Institute, Washington (2008). (2008) 
  19. Korjenic, A., Steuer, R., Šťastník, S., Vala, J., Bednar, T., 10.1002/bapi.200910045, Bauphysik 31 (2009), 343-353 German. (2009) DOI10.1002/bapi.200910045
  20. Lagarias, J. C., Poonen, B., Wright, M. H., 10.1137/110830150, SIAM J. Optim. 22 (2012), 501-532. (2012) Zbl1246.49029MR2968864DOI10.1137/110830150
  21. Lagarias, J. C., Reeds, J. A., Wright, M. H., Wright, P. E., 10.1137/S1052623496303470, SIAM J. Optim. 9 (1998), 112-147. (1998) Zbl1005.90056MR1662563DOI10.1137/S1052623496303470
  22. Luersen, M. A., Riche, R. Le, Guyon, F., 10.1007/s00158-003-0320-9, Struct. Multidiscip. Optim. 27 (2004), 43-54. (2004) DOI10.1007/s00158-003-0320-9
  23. Lukšan, L., Numerické Optimalizační metody, Technical report 930, Institute of Informatics AS CR, Praha (2005), Czech. (2005) 
  24. McKinnon, K. I. M., 10.1137/S1052623496303482, SIAM J. Optim. 9 (1998), 148-158. (1998) Zbl0962.65049MR1662567DOI10.1137/S1052623496303482
  25. Meir, I. A., Pearlmutter, D., 10.1179/147842209X12476568584548, Corrosion Engineering Science and Technology 45 (2010), 70-75. (2010) DOI10.1179/147842209X12476568584548
  26. Nawaz, A., Malik, T. H., Saleem, N., Mustafa, E., Globalized Nelder Mead trained artificial neural networks for short term load forecasting, J. of Basic and Applied Scientific Research 5 (2015), 1-13. (2015) 
  27. Nelder, J. A., Mead, R., 10.1093/comjnl/7.4.308, Computer J. 7 (1965), 308-313. (1965) Zbl0229.65053MR3363409DOI10.1093/comjnl/7.4.308
  28. Pacheco-Vega, A., 10.1007/978-3-642-22176-7_1, Soft Computing in Green and Renewable Energy Systems K. Gopalakrishnan, S. K. Khaitan, S. Kalogirou Studies in Fuzziness and Soft Computing 269, Springer, Berlin (2011), 1-35. (2011) DOI10.1007/978-3-642-22176-7_1
  29. Pham, N., Wilamowski, B. M., Improved Nelder-Mead's simplex method and applications, J. Computing 3 (2011), 55-63. (2011) 
  30. Price, C. J., Coope, I. D., Byatt, D., 10.1023/A:1014849028575, J. Optim. Theory Appl. 113 (2002), 5-19. (2002) Zbl1172.90508MR1896704DOI10.1023/A:1014849028575
  31. Rode, C., 10.1177/1744259112462107, J. Building Phys. 36 (2013), 337-352. (2013) DOI10.1177/1744259112462107
  32. Roubíček, T., 10.1007/978-3-0348-0513-1, International Series of Numerical Mathematics 153, Birkhäuser, Basel (2005). (2005) Zbl1087.35002MR2176645DOI10.1007/978-3-0348-0513-1
  33. Šťastník, S., Vala, J., On the thermal stability in dwelling structures, Building Research J. 52 (2004), 31-55. (2004) 
  34. Vala, J., Computational approaches to some inverse problems from engineering practice, Programs and Algorithms of Numerical Mathematics. Proc. of the 17th Seminar J. Chleboun et al. Academy of Sciences of the Czech Republic, Institute of Mathematics, Praha (2015), 215-230. (2015) Zbl1374.80001
  35. Vala, J., Computational design optimization of low-energy buildings, Proc. 14th Equadiff in Bratislava Spektrum STU, Bratislava (2017), 265-274. (2017) 
  36. Vala, J., On some non-gradient approaches to inverse and optimization problems of thermal transfer, Proc. 23rd Thermophysics in Smolenice American Institute of Physics, Melville (2018), 5. Submitted. (2018) 
  37. Vala, J., Jarošová, P., Computational optimization of energy consumption in the design of buildings, Proc. 15th International Conference on Numerical Analysis and Applied Mathematics (ICNAAM) American Institute of Physics, Melville (2018), 4. In print. (2018) 
  38. Wright, M. H., Nelder, Mead, and the other simplex method, Doc. Math. (Bielefeld) Extra Vol., Optimization Stories (2012), 271-276. (2012) Zbl1262.49003MR2991490

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