An artificial neural network residual kriging based surrogate model for curvilinearly stiffened panel optimization

  • Sunny, Mohammed R. ;
  • Mulani, Sameer B. ;
  • Sanyal, Subrata ;
  • Kapania, Rakesh K.
  • Received : 2016.01.01
  • Accepted : 2016.06.07
  • Published : 2016.07.25


We have performed a design optimization of a stiffened panel with curvilinear stiffeners using an artificial neural network (ANN) residual kriging based surrogate modeling approach. The ANN residual kriging based surrogate modeling involves two steps. In the first step, we approximate the objective function using ANN. In the next step we use kriging to model the residue. We optimize the panel in an iterative way. Each iteration involves two steps-shape optimization and size optimization. For both shape and size optimization, we use ANN residual kriging based surrogate model. At each optimization step, we do an initial sampling and fit an ANN residual kriging model for the objective function. Then we keep updating this surrogate model using an adaptive sampling algorithm until the minimum value of the objective function converges. The comparison of the design obtained using our optimization scheme with that obtained using a traditional genetic algorithm (GA) based optimization scheme shows satisfactory agreement. However, with this surrogate model based approach we reach optimum design with less computation effort as compared to the GA based approach which does not use any surrogate model.


surrogate model;optimization;artificial neural network;kriging;stiffened panel


  1. Ahmed, M.Y.M. and Qin, N. (2009), "Surrogate-based aerodynamic design optimization: Use of Surrogates in Aerodynamic Design Optimization", 13th International Conference on Aerspace Sciences & Aviation Technology, ASAT-13-AE-14, 1-26.
  2. Balabanov, V.O., Giunta, A.A., Golovidov, O., Grossman, B., Mason, W.H., Watson, L.T. and Haftka, R.T. (1999), "Reasonable design space approach to response surface approximation", J. Aircraft, 36(1), 308-315.
  3. Booker, A.J., Dennis, J.E., Frank, P.D., Serafini, D. and Torczon, V. (1998), "Optimization using surrogate objectives on a helicopter test example", Comput. Meth. Optim. Des. Control, Boston: Birkhauser, 49-58.
  4. Box, G.E.P. and Wilson, K.B. (1951), "On the experimental attainment of optimum conditions", J. Roy. Statist. Soc., Series B, 13(1), 1-35.
  5. Daberkow, D.D. and Mavris, D.N. (1998), "New approaches to conceptual and preliminary aircraft design: a comparative assessment of a neural network formulation and a response surface methodology", 1998 World Aviation Conference, Anaheim, CA.
  6. Demyanov, V., Kanevsky, M., Chernov, S., Savelieva, E. and Timonin, V. (1998), "Neural network residual kriging application for climatic data", J. Geographic Inform. Decision Anal., 2(2), 215-232.
  7. Efron, B. (1983), "Estimating the error rate of a prediction rule: improvement on cross-validation", J. Am. Statist. Assoc., 78(382), 316-331.
  8. Forrester, A.I.J. and Keane, A.J. (2009), "Recent advances in surrogate based optimization", Prog. Aero. Sci., 45(1), 50-79.
  9. Giunta, A.A. (1997), "Aircraft multidisciplinary design optimization using design of experiments theory and response surface modeling methods", Ph.D. Dissertation, Faculty of Virginia Polytechnic Inst. And State Univ., Blacksburg, VA.
  10. Hagan, M.T., Demuth, H.B. and Beale, M. (1996), Neural network design, PWS Publishing Company.
  11. Hebb, D.O. (2002), Organization of behavior: a neuropsychological theory, L. Erlbaum Associates.
  12. Hedayat, A., Sloane, N. and Stufken, J. (1999), Orthogonal arrays: theory and applications, Springer, Series in Statistics, Berlin.
  13. Jones, D.R. (2001), "A taxonomy of global optimization methods based on response surface", J. Global Optimiz., 21(4), 345-383.
  14. Jones, D. and Schonlau, M. (1998), "Expensive global optimization of expensive black-box functions", J. Global Optimiz., 13, 455-492.
  15. Keane, A.J. (2004), "Design search and optimization using radial basis functions with regression capabilities", ParmeeIC Berlin, 39-49.
  16. Kim, Y.Y. and Kapania, R.K. (2003), "Neural networks for inverse problems in damage identification and optical imaging", AIAA J., 41(4), 732-740.
  17. Kiranyaz, S., Ince, T., Yildirim, A. and Gabbouj, M. (2009), "Evolutionary artificial neural networks by multi dimensional particle swarm optimization", Neural Networks, 22(10), 1448-1462.
  18. Leary, S., Bhaskar, A. and Keane, A. (2003), "Optimal orthogonal array based latin hypercubes", J. Appl. Statist., 30(5), 585-598.
  19. Matheron, G. (1963), "Principles of geostatics", Economic Geol., 58(8), 1246-1266.
  20. McKay, M., Conover, W. and Beckman, R. (1979), "A comparison of three methods for selecting values of input variables in the analysis of output from a computer code", Technometrics, 42(1), 239-245.
  21. Michler, A. and Heinrich, R. (2012), "Surrogate-enhanced simulation of aircraft in trimmed state", Comput. Meth. Appl. Mech. Eng., 217-220, 96-110.
  22. Mulani, S.B., Slemp, W.C.H. and Kapania, R.K. (2010), "Curvilinear stiffened panel optimization framework for multiple load cases", 13th AIAA/ISSMO Multidisciplinary Analysis Optimization Conference, Fort Worth, Texas.
  23. Mulani, S.B., Slemp, W.C.H. and Kapania, R.K. (2012), "EBF3PanelOpt: An overview and recent developments of an optimization framework for stiffened panel using curvilinear stiffeners", AeroMat 2012 Conference and Exposition, Charlotte, NC.
  24. Mulani, S.B., Slemp, W.C.H. and Kapania, R.K. (2013), "EBF3PanelOpt: An optimization framework for curvilinear blade-stiffened panels", Thin-Wall. Struct., 63, 13-26.
  25. Myers, R.H. and Montgomery, D.C. (1995), Response surface methodology-process and product optimization using designed experiment, New York: Wiley.
  26. Niu, M.C.Y. (2005), Airframe stress analysis and sizing, Technical Book Company.
  27. Palmer, K. and Tsui, K. (2001), "A minimum bias latin hypercube design", IIE Trans, 33(9), 793-808.
  28. Queipo, N.V., Haftka, R.T., Shyy, W., Goel, T., Vidyanathan, R. and Tucker, P.K. (2005), "Surrogate based analysis and optimization", Prog. Aero. Sci., 41(1), 1-28.
  29. Rossenbrock, H.H. (1960), "An automatic method for finding the greatest or least value of a function", Comput. J., 3(3), 173-184.
  30. Sacks, J., Schiller, S. and Welch, W. (1989), "Designs for computer experiments", Technometrics, 31(1), 41-47.
  31. Sacks, J., Welch W., Mitchell T. and Wynn H. (1993), "Design and analysis of computer experiments", Statistic. Sci., 4, 409-423.
  32. Shen, Z.Q., Shi, J.B., Wang, K., Kong, F.S. and Bailey, J.S. (2004), "Neural network ensemble residual kriging application for spatial variability of soil properties", Podesphere, 14(3), 289-296.
  33. Sunny, M.R. and Kapania, R.K. (2013), "Damage detection in a prestressed membrane using a waveletbased neurofuzzy system", AIAA J., 51(11), 2558-2569.
  34. Toal, D.J. and Keane, A.J. (2011), "Efficient multipoint aerodynamic design optimization via cokriging", J. Aircraft, 48(5), 1685-1695.
  35. Vavalle, A. and Qin, N. (2007), "Iterative response surface based optimization scheme for transonic airfoil design", J. Aircraft, 44(2), 365-376.
  36. Venter, G., Haftka, R.T. and Starnes, J.H. (1998), "Construction of response surface approximations for design optimization", AIAA J., 36(12), 2242-2249.
  37. Wang, H., Li, E., Li, G.Y. and Zhong, Z.H. (2008), "Development of metamodeling based optimization system for high nonlinear engineering problems", Adv. Eng. Softw., 39(8), 629-645.
  38. Welch, S.M., Roe, J.L. and Dong, Z. (2003), "A genetic neural network model of flowering time control in arabidopsis thaliana", Agronomy J., 95(1), 71-81.
  39. Ye, K. (1998), "Orthogonal column latin hypercubes and their application in computer experiments", J. Am. Statist. Assoc., 93(444), 1430-1439.
  40. Zaabab, A.H., Zhang, Q-L. and Nakhla, M. (1995), "A neural modeling approach to circuit optimization and statistical design", IEEE Transactions on Microwave Theory and Techniques, 43, 1349-1358.

Cited by

  1. Accurate modelling of lossy SIW resonators using a neural network residual kriging approach vol.14, pp.6, 2017,