Computers and Concrete

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Nonlinear structural modeling using multivariate adaptive regression splines

  • Zhang, Wengang (School of Civil & Environmental Engineering, Nanyang Technological University) ;
  • Goh, A.T.C. (School of Civil & Environmental Engineering, Nanyang Technological University)
  • Received : 2012.11.26
  • Accepted : 2015.10.22
  • Published : 2015.10.25
⟨ Previous Next ⟩

Abstract

Various computational tools are available for modeling highly nonlinear structural engineering problems that lack a precise analytical theory or understanding of the phenomena involved. This paper adopts a fairly simple nonparametric adaptive regression algorithm known as multivariate adaptive regression splines (MARS) to model the nonlinear interactions between variables. The MARS method makes no specific assumptions about the underlying functional relationship between the input variables and the response. Details of MARS methodology and its associated procedures are introduced first, followed by a number of examples including three practical structural engineering problems. These examples indicate that accuracy of the MARS prediction approach. Additionally, MARS is able to assess the relative importance of the designed variables. As MARS explicitly defines the intervals for the input variables, the model enables engineers to have an insight and understanding of where significant changes in the data may occur. An example is also presented to demonstrate how the MARS developed model can be used to carry out structural reliability analysis.

Keywords

References

  1. Alacali, S.N., Akbas, B. and Doran, B. (2011), "Prediction of lateral confinement coefficient in reinforced concrete columns using neural network simulation", Appl. Soft Comput., 11(2), 2645-2655. https://doi.org/10.1016/j.asoc.2010.10.013
  2. Alavi, A.H. and Gandomi, A.H. (2011), "Prediction of principal ground-motion parameters using a hybrid method coupling artificial neural networks and simulated annealing", Comput. Struct., 89(23-24), 2176-2194. https://doi.org/10.1016/j.compstruc.2011.08.019
  3. Arafa, M., Alqedra, M. and Najjar, H.A. (2011), "Neural network models for predicting shear strength of reinforced normal and high-strength concrete deep beams", J. Appl. Sci., 11(2), 266-274. https://doi.org/10.3923/jas.2011.266.274
  4. Attoh Okine, N.O., Cooger, K. and Mensah, S. (2009), "Multivariate Adaptive Regression (MARS) and Hinged Hyperplanes (HHP) for Doweled Pavement Performance Modeling", Constr. Build. Mater., 23, 3020-3023. https://doi.org/10.1016/j.conbuildmat.2009.04.010
  5. Caglar, N. (2009), "Neural network based approach for determining the shear strength of circular reinforced concrete columns", Constr. Build. Mater., 23(10), 3225-3232. https://doi.org/10.1016/j.conbuildmat.2009.06.002
  6. Chua, C.G. (2001), "Prediction of the behavior of braced excavation systems using Bayesian neural networks", Master Thesis, Nanyang Technological University, Singapore.
  7. Chua, C.G. and Goh, A.T.C. (2003), "A hybrid Bayesian back-propagation neural network approach to multivariate modeling", Int. J. Numer. Anal. Meter., 27, 651-667. https://doi.org/10.1002/nag.291
  8. Chuang, P.H., Goh, A.T.C. and Wu, X. (1998), "Modeling the capacity of pin-ended slender reinforced concrete columns using neural networks", J. Struct. Eng., 124(7), 830-838. https://doi.org/10.1061/(ASCE)0733-9445(1998)124:7(830)
  9. Friedman, J.H. (1991), "Multivariate adaptive regression splines", Ann. Stat., 19, 1-141. https://doi.org/10.1214/aos/1176347963
  10. Gandomi, A.H., Alavi, A.H., Kazemi, S., Alinia, M.M. (2009). "Behavior appraisal of steel semi-rigid joints using linear genetic programming", J. Constr. Steel Res., 65, 1738-1750. https://doi.org/10.1016/j.jcsr.2009.04.010
  11. Gandomi, A.H., Yang, X.S., Talatahari, S., Alavi, A.H., (2013), Metaheuristic Applications in Structures and Infrastructures, Elsevier, Waltham, MA, USA.
  12. Goh, A.T.C. (1995), "Neural networks to predict shear strength of deep beams", ACI Struct. J., 92(1), 28-32.
  13. Goh, A.T.C. and Chua, C.G. (2004), "Nonlinear modeling with confidence estimation using Bayesian neural networks", Elect. J. Struct. Eng., 1, 108-118.
  14. Goh, A.T.C. and Zhang, W.G. (2014), "An improvement to MLR model for predicting liquefaction-induced lateral spread using multivariate adaptive regression splines", Eng. Geol., 170, 1-10. https://doi.org/10.1016/j.enggeo.2013.12.003
  15. Gulec, C.K. (2009), "Performance-based assessment and design of squat reinforced concrete shear walls", Ph.D. Thesis, the State University of New York at Buffalo.
  16. Hastie, T., Tibshirani, R. and Friedman, J. (2009), The Elements of Statistical Learning: Data Mining, Inference and Prediction, 2nd Edition, Springer.
  17. Jekabsons, G. (2011), ARESLab: Adaptive Regression Splines toolbox for Matlab / Octave, Available at http://www.cs.rtu.lv/jekabsons/
  18. Jenkins, W.M. (2006), "Neural network weight training by mutation", Comput. Struct., 84(31-32), 2107-2112. https://doi.org/10.1016/j.compstruc.2006.08.066
  19. Lashkari, A. (2012), "Prediction of the shaft resistance of nondisplacement piles in sand", Int. J. Numer. Anal. Meter. 37, 904-931.
  20. Mackay, D.J.C. (1991), "Bayesian methods for adaptive models", Ph.D. Thesis, California Institute of Technology.
  21. Mirzahosseini, M., Aghaeifar, A., Alavi, A., Gandomi, A. and Seyednour, R. (2011), "Permanent deformation analysis of asphalt mixtures using soft computing techniques", Expert Syst. Appl., 38(5), 6081-6100. https://doi.org/10.1016/j.eswa.2010.11.002
  22. Neal, R.M. (1992), "Bayesian training of back-propagation networks by the hybrid Monte Carlo method", Technical report CRG-TG-92-1, Department of Computer Science, University of Toronto, Canada.
  23. Oreta, A.W.C. and Kawashima, K. (2003), "Neural network modeling of confined compressive strength and strain of circular concrete columns", J. Struct. Eng., 129(4), 554-561. https://doi.org/10.1061/(ASCE)0733-9445(2003)129:4(554)
  24. Rumelhart, D.E., Hinton, G.E. and Williams, R.J. (1986), "Learning internal representations by error propagation", Parallel Distributed Processing, Eds. D.E. Rumelhart & J.L. McClelland, MIT Press, Cambridge, MA.
  25. Samui, P. (2011), "Determination of ultimate capacity of driven piles in cohesionless soil: a multivariate adaptive regression spline approach", Int. J. Numer. Anal. Meter., 36, 1434-1439.
  26. Samui, P. and Karup, P. (2011), "Multivariate adaptive regression spline and least square support vector machine for prediction of undrained shear strength of clay", IJAMC, 3(2), 33-42.
  27. Samui, P., Das, S. and Kim, D. (2011), "Uplift capacity of suction caisson in clay using multivariate adaptive regression spline", Ocean Eng., 38, 2123-2127. https://doi.org/10.1016/j.oceaneng.2011.09.036
  28. Sanad, A. and Saka, M.P. (2001), "Prediction of ultimate shear strength of reinforced-concrete deep beams using neural networks", J. Struct. Eng., 127(7), 818-828. https://doi.org/10.1061/(ASCE)0733-9445(2001)127:7(818)
  29. Tsai, H.C. (2010), "Hybrid high order neural networks", Appl. Soft Comput., 9, 874-881.
  30. Tsai, H.C. (2011), "Using weighted genetic programming to program squat wall strengths and tune associated formulas", Eng. Appl. Artif. Intel., 24, 526-533. https://doi.org/10.1016/j.engappai.2010.08.010
  31. Yang, K.H., Ashour, A.F., Song, J.K. and Lee, E.T. (2008), "Neural network modeling of RC deep beam shear strength", Struct. Build., 161(1), 29-39. https://doi.org/10.1680/stbu.2008.161.1.29
  32. Zarnani, S., El-Emam, M. and Bathurst, R.J. (2011), "Comparison of numerical and analytical solutions for reinforced soil wall shaking table tests", Geomech. Eng., 3(4), 291-321. https://doi.org/10.12989/gae.2011.3.4.291
  33. Zhang, W. G. and Goh, A. T. C. (2013), "Multivariate adaptive regression splines for analysis of geotechnical engineering systems", Comput. Geotech., 48, 82-95. https://doi.org/10.1016/j.compgeo.2012.09.016
  34. Zhang, W.G. and Goh, A.T.C. (2014), "Multivariate adaptive regression splines model for reliability assessment of serviceability limit state of twin caverns", Geomech. Eng., 7(4), 431-458. https://doi.org/10.12989/gae.2014.7.4.431
  35. Zhang, W.G., Goh, A.T.C., Zhang, Y.M., Chen, Y.M. and Xiao, Y. (2015), "Assessment of soil liquefaction based on capacity energy concept and multivariate adaptive regression splines", Eng. Geol., 188, 29-37. https://doi.org/10.1016/j.enggeo.2015.01.009

Cited by

  1. MARS inverse analysis of soil and wall properties for braced excavations in clays vol.16, pp.6, 2015, https://doi.org/10.12989/gae.2018.16.6.577
  2. GS-MARS method for predicting the ultimate load-carrying capacity of rectangular CFST columns under eccentric loading vol.25, pp.1, 2015, https://doi.org/10.12989/cac.2020.25.1.001