Skip to main content
SpringerLink
Log in

Dealing with limited data in ballistic impact scenarios: an empirical comparison of different neural network approaches

  • Published:
Applied Intelligence Aims and scope Submit manuscript

Abstract

In the domain of high-speed impact between solids, the simulation of one trial entails the use of large resources and an elevated computational cost. The objective of this research is to find the best neural network associated with a new problem of ballistic impact, maximizing the quantity of trials available and simplifying their architecture. To achieve this goal, this paper proposes a tuning performance process based on four stages. These stages include existing statistical techniques, a combination of proposals to improve the performance and analyze the influence of each variable. To measure the quality of the different networks, two criteria based on information theory have been incorporated to reflect the fit of the data with respect to their complexity. The results obtained show that the application of an integrated tuning process in this domain permits improvement in the performance and efficiency of a neural network in comparison with different machine learning alternatives

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. ABAQUS (2003) ABAQUS/Explicit v6.4 users manual. ABAQUS Inc., Richmond

    Google Scholar 

  2. Adeli H, Yeh C (1989) Perceptron learning in engineering design. Microcomput Civ Eng 4:247–256

    Article  Google Scholar 

  3. Akaike H (1974) A new look at the statistical model identification. IEEE Trans Automat Contr 19(6):716–723

    Article  MathSciNet  MATH  Google Scholar 

  4. Alfaro-Cortes E, Gamez-Martinez M, Garcia-Rubio N (2007) A boosting approach for corporate failure prediction. Appl Intell 27(1):29–37

    Article  Google Scholar 

  5. An G (1996) The effects of adding noise during backpropagation training on a generalization performance. Neural Comput 8(3):643–674

    Article  Google Scholar 

  6. Anderson C (1987) An overview of the theory of hydrocodes. Int J Impact Eng 5(1–4):33–59

    Article  Google Scholar 

  7. Anlauf J, Biehl M (1989) The adatron: an adaptive perceptron algorithm. Europhys Lett 10:687

    Article  Google Scholar 

  8. Awerbuch J, Bodner S (1974) Analysis of the mechanics of perforation of projectiles in metallic plates. Int J Solids Struct 10:671–684

    Article  Google Scholar 

  9. Bauer E, Kohavi R (1999) An empirical comparison of voting classification algorithms: bagging boosting, and variants. Mach Learn 36(1–2):105–139

    Article  Google Scholar 

  10. Bisagni C, Lanzi L, Ricci S (2002) Optimization of helicopter subfloor components under crashworthiness requirements using neural networks. J Aircr 39(2):296–304

    Article  Google Scholar 

  11. Bishop C (1995) Training with noise is equivalent to Tikhonov regularization. Neural Comput 7:108

    Article  Google Scholar 

  12. Bishop C (1996) Neural networks for pattern recognition. Oxford University Press, Oxford. Diferencias entre RBF and MLP

    MATH  Google Scholar 

  13. Boonyanunta N, Zeephongsekul P (2004) Predicting the relationship between the size of training sample and the predictive power of classifiers. Knowl-Based Intell Inf Eng Syst 3215:529–535

    Article  Google Scholar 

  14. Borvik T, Langseth M, Hopperstad O, Malo K (1999) Ballistic penetration of steel plates—analysis and experiment. Int J Impact Eng 22(9–10):855–886

    Article  Google Scholar 

  15. Breiman L (1996) Bagging predictors. Mach Learn 26(2):123

    Google Scholar 

  16. Breiman L, Spector P (1992) Submodel selection and evaluation in regression. The x-random case. Int Stat Rev 60:291–319

    Article  Google Scholar 

  17. Burger M, Neubauer A (2003) Analysis of Tikhonov regularization for function approximation by neural networks. Neural Netw 16(1):79–90

    Article  Google Scholar 

  18. Choi B, Hendtlass T, Bluff K (2004) A comparison of neural network input vector selection techniques. In: IEA/AIE’2004: Proceedings of the 17th international conference on innovations in applied artificial intelligence. Springer, Berlin, pp 1–10

    Google Scholar 

  19. Cover T (1965) Geometrical and statistical properties of systems of linear inequalities with applications in pattern recognition. IEEE Trans Electron Comput EC-14(3):326–334

    Article  Google Scholar 

  20. Cybenko G (1989) Approximation by superpositions of a sigmoidal function. Math Control Signals Syst 2:303–314

    Article  MathSciNet  MATH  Google Scholar 

  21. Devijver P, Kittler J (1982) Pattern recognition: a statistical approach. Prentice Hall, New York

    MATH  Google Scholar 

  22. Du H, Zhang N (2008) Time series prediction using evolving radial basis function networks with new encoding scheme. Neurocomput. 71(7–9):1388–1400

    Article  Google Scholar 

  23. Efron B (1979) Bootstrap methods: another look at the jackknife. Ann Stat 7(1):1–26

    Article  MathSciNet  MATH  Google Scholar 

  24. Efron B (1983) Estimating the error rate of a prediction rule: improvement on cross-validation. J Am Stat Assoc 78(382):316–331

    Article  MathSciNet  MATH  Google Scholar 

  25. Efron B, Tibshirani RJ (1994) An introduction to the bootstrap. Chapman & Hall/CRC, London. Hardcover

    Google Scholar 

  26. Fogel D (1990) An information criterion for optimal neural network selection. Signals, systems and computers, 1990 conference record twenty-fourth Asilomar conference on, vol 2, p 998

  27. Foley D (1972) Considerations of sample and feature size. IEEE Trans Inf Theory 18(5):618–626

    Article  MATH  Google Scholar 

  28. Garcia-Crespo A, Ruiz-Mezcua B, Fernandez D, Zaera R (2006) Prediction of the response under impact of steel armours using a multilayer perceptron. Neural Comput Appl 16(2):147–154

    Google Scholar 

  29. Garcia-Crespo A, Ruiz-Mezcua B, Gonzalez-Carrasco I, Lopez-Cuadrado J (2008) Multilayer perceptron training optimization for high speed impacts classification. Springer, pp 377–388

  30. Gevrey MID, Lek S (2003) Review and comparison of methods to study the contribution of variables in artificial neural network models. Ecol Model 160(16):249–264

    Article  Google Scholar 

  31. Girosi F, Jones M, Poggio T (1995) Regularization theory and neural networks architectures. Neural Comput 7:219

    Article  Google Scholar 

  32. Goldsmith W (1960) Impact: the theory and physical behaviour of colliding solids. Edward Arnold Publishers Ltd., Sevenoaks

    MATH  Google Scholar 

  33. Goutte C (1997) Note on free lunches and cross-validation. Neural Comput 9(6):1245–1249

    Article  Google Scholar 

  34. Harpham C, Dawson C (2006) The effect of different basis functions on a radial basis function network for time series prediction: a comparative study. Neurocomputing 69(16–18):2161–2170. Brain inspired cognitive systems—selected papers from the 1st international conference on brain inspired cognitive systems (BICS 2004)

    Article  Google Scholar 

  35. He Y, Sun Y (2001) Neural network-based l1-norm optimisation approach for fault diagnosis of nonlinear circuits with tolerance. IEE Proc Circuits Devices Syst 148(4):223–228

    Article  MathSciNet  Google Scholar 

  36. Hinton G, Van-Camp D (1993) Keeping the neural networks simple by minimizing the description length of the weights. In: COLT ’93: Proceedings of the sixth annual conference on computational learning theory. ACM, New York, pp 5–13

    Chapter  Google Scholar 

  37. Holmstrom L, Koistinen P (1992) Using additive noise in back-propagation training. IEEE Trans Neural Netw 3(1):24–38

    Article  Google Scholar 

  38. Hornik K, Stinchcombe M, White H (1989) Multilayer feedforward networks are universal approximators. Neural Netw 2(5):359–366

    Article  Google Scholar 

  39. Ince R (2004) Prediction of fracture parameters of concrete by artificial neural networks. Eng Fract Mech 71(15):2143–2159

    Article  Google Scholar 

  40. Johnson G, Cook W (1983) A constitutive model and data for metals subjected to large strains, high strain rates, and temperatures. In: International symposium ballistics

  41. Karystinos G, Pados D (2000) On overfitting, generalization, and randomly expanded training sets. IEEE Trans Neural Netw 11(5):1050–1057

    Article  Google Scholar 

  42. Kohavi R (1995) A study of cross-validation and bootstrap for accuracy estimation and model selection. In: Proceedings of international joint conference on artificial intelligence. Morgan Kaufmann, San Mateo, pp 1137–1143

    Google Scholar 

  43. Koistinen P, Holmstrom L (1991) Kernel regression and backpropagation training with noise. In: Neural networks, 1991. 1991 IEEE international joint conference on, vol 1, pp 367–372

  44. Lanzi L, Bisagni C, Ricci S (2004) Neural network systems to reproduce crash behavior of structural components. Comput Struct 82(1):93

    Article  Google Scholar 

  45. Leclercq E, Druaux F, Lefebvre D, Zerkaoui S (2005) Autonomous learning algorithm for fully connected recurrent networks. Neurocomputing 63:25–44. New aspects in neurocomputing: 11th European symposium on artificial neural networks

    Article  Google Scholar 

  46. Lippmann R (1987) An introduction to computing with neural nets. ASSP Mag IEEE 4(2):4–22 [see also IEEE signal processing magazine]

    Article  Google Scholar 

  47. Liu H, Setiono R (1998) Incremental feature selection. Appl Intell 9(3):217–230

    Article  Google Scholar 

  48. Liu S, Huang J, Sung J, Lee C (2002) Detection of cracks using neural networks and computational mechanics. Comput Methods Appl Mech Eng 191(25–26):2831

    Article  MATH  Google Scholar 

  49. Majumder M, Roy P, Mazumdar A (2007) Optimization of the water use in the river Damodar in West Bengal in India: an integrated multi-reservoir system with the help of artificial neural network. Eng Comput Arch 1(2)

  50. Mandal S, Saha D, Banerjee T (2005) A neural network based prediction model for flood in a disaster management system with sensor networks. In: Intelligent sensing and information processing, 2005. Proceedings of 2005 international conference on, pp 78–82

  51. Mandic D, Chambers J (2001) Recurrent neural networks for prediction: learning algorithms, architectures and stability. Wiley, New York

    Book  Google Scholar 

  52. Masters T (1995) Advanced algorithms for neural networks: a C++ sourcebook. Wiley, New York

    Google Scholar 

  53. Matsuoka K (1992) Noise injection into inputs in back-propagation learning. IEEE Trans Syst Man Cybern 22(3):436–440

    Article  Google Scholar 

  54. Mrazova I, Wang D (2007) Improved generalization of neural classifiers with enforced internal representation. Neurocomputing 70(16–18):2940–2952

    Article  Google Scholar 

  55. Murata N, Yoshizawa S, Amari SI (1994) Network information criterion—determining the number of hidden units for an artificial neural network model. IEEE Trans Neural Netw 5:865

    Article  Google Scholar 

  56. Opitz D, Maclin R (1999) Popular ensemble methods: an empirical study. J Artif Intell Res 11:169

    MATH  Google Scholar 

  57. Park J, Sandberg I (1991) Universal approximation using radial-basis-function networks. Neural Comput 3(2):246–257

    Article  Google Scholar 

  58. Priddy K, Keller P (2005) Artificial neural networks: an introduction. SPIE Press, Bellingham

    Google Scholar 

  59. Principe J, Euliano N, Lefebvre W (1999) Neural and adaptive systems: fundamentals through simulations with CD-ROM. Wiley, New York

    Google Scholar 

  60. Ravid M, Bodner S (1983) Dynamic perforation of viscoplastic plates by rigid projectiles. Int J Eng Sci 21:577–591

    Article  Google Scholar 

  61. Rissanen J (1978) Modeling by shortest data description. Automatica 14:445–471

    Article  Google Scholar 

  62. Sietsma J, Dow R (1991) Creating artificial neural networks that generalize. Neural Netw 4(1):67–79

    Article  Google Scholar 

  63. Sokolova M, Rasras R, Skopin D (2006) The artificial neural network based approach for mortality structure analysis. Am J Appl Sci 3(2):1698–1702

    Article  Google Scholar 

  64. Songwu L, Member S, Basar T (1998) Robust nonlinear system identification using neural network models. IEEE Trans Neural Netw 9:407

    Article  Google Scholar 

  65. Swingler K (1996) Applying neural networks. A practical guide. Academic Press, New York

    Google Scholar 

  66. Tarassenko L (1998) A guide to neural computing applications. Arnold/NCAF

  67. Tibshirani R (1996) A comparison of some error estimates for neural network models. Neural Comput 8(1):152–163

    Article  Google Scholar 

  68. Ueda N (2000) Optimal linear combination of neural networks for improving classification performance. IEEE Trans Pattern Anal Mach Intell 22(2):207–215

    Article  MathSciNet  Google Scholar 

  69. Vapnik V (1995) The nature of statistical learning theory. Springer, Berlin

    MATH  Google Scholar 

  70. Vapnik V (1998) Statistical learning theory. Wiley, New York

    MATH  Google Scholar 

  71. Waszczyszyn Z, Ziemianski L (2001) Neural networks in mechanics of structures and materials—new results and prospects of applications. Comput Struct 79(16):2261–2276

    Article  Google Scholar 

  72. Wythoff B (1993) Backpropagation neural networks: a tutorial. Chemom Intell Lab Syst 18:115–155

    Article  Google Scholar 

  73. Xu S, Chen L (2008) A novel approach for determining the optimal number of hidden layer neurons for fnns and its application in data mining. In: 5th international conference on information technology and applications, pp 23–26

  74. Zhao Y, Small M (2006) Minimum description length criterion for modeling of chaotic attractors with multilayer perceptron networks. IEEE Trans Circuits Syst I: Reg Pap 53(3):722–732

    Article  Google Scholar 

  75. Zhao Z, Zhang Y, Liao H (2008) Design of ensemble neural network using the akaike information criterion. Eng Appl Artif Intell 21(8):1182–1188

    Article  Google Scholar 

  76. Zukas J (1990) High velocity impact dynamics. Wiley, New York

    Google Scholar 

  77. Zupan J (1995) Neural networks in chemistry. The first European conference on computational chemistry 330(1), 469–470

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, Universidad Carlos III, Av. Universidad 30, 28911, Leganes (Madrid), Spain

    Israel Gonzalez-Carrasco, Angel Garcia-Crespo, Belen Ruiz-Mezcua & Jose Luis Lopez-Cuadrado

Authors
  1. Israel Gonzalez-Carrasco
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Angel Garcia-Crespo
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Belen Ruiz-Mezcua
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jose Luis Lopez-Cuadrado
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Israel Gonzalez-Carrasco.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gonzalez-Carrasco, I., Garcia-Crespo, A., Ruiz-Mezcua, B. et al. Dealing with limited data in ballistic impact scenarios: an empirical comparison of different neural network approaches. Appl Intell 35, 89–109 (2011). https://doi.org/10.1007/s10489-009-0205-8

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10489-009-0205-8

Search

Navigation