Modeling Beach Rotation Using a Novel Legendre Polynomial Feedforward Neural Network Trained by Nonlinear Constrained Optimization

  • Anastasios Rigos
  • George E. Tsekouras
  • Antonios Chatzipavlis
  • Adonis F. Velegrakis
Conference paper
Part of the IFIP Advances in Information and Communication Technology book series (IFIPAICT, volume 475)


A Legendre polynomial feedforward neural network is proposed to model/predict beach rotation. The study area is the reef-fronted Ammoudara beach, located at the northern coastline of Crete Island (Greece). Specialized experimental devices were deployed to generate a set of input-output data concerning the inshore bathymetry, the wave conditions and the shoreline position. The presence of the fronting beachrock reef (parallel to the shoreline) increases complexity and imposes high non-linear effects. The use of Legendre polynomials enables the network to capture data non-linearities. However, in order to maintain specific functional requirements, the connection weights must be confined within a pre-determined domain of values; it turns out that the network’s training process constitutes a constrained nonlinear programming problem, solved by the barrier method. The performance of the network is compared to other two neural-based approaches. Simulations show that the proposed network achieves a superior performance, which could be improved if an additional wave parameter (wave direction) was to be included in the input variables.


Beach rotation Feedforward neural network Legendre polynomials Perched beach Nonlinear constrained optimization 



This research has been co-financed in 85 % by the EEA GRANTS, 2009–2014, and 15 % by the Public Investments Programme (PIP) of the Hellenic Republic. Project title: Recording of and Technical Responses to Coastal Erosion of Touristic Aegean island beaches (ERA BEACH).


  1. 1.
    Thomas, T., Phillips, M.R., Williams, A.T.: A Centurial Record of Beach Rotation. J. Coast. Res. 65, 594–599 (2013)CrossRefGoogle Scholar
  2. 2.
    Thomas, T., Rangel-Buitrago, N., Phillips, M.R., Anfuso, G., Williams, A.T.: Mesoscale morphological change, beach rotation and storm climate influences along a macrotidal embayed beach. J. Marine Sci. Eng. 3, 1006–1026 (2015)CrossRefGoogle Scholar
  3. 3.
    Ranasinghe, R., McLoughlan, R., Seasonal, A., Symonds, G.: The southern oscillation index, wave climate and beach rotation. Marine Geol. 204(3–4), 273–287 (2004)CrossRefGoogle Scholar
  4. 4.
    Klein, A.H.F., Filho, L.B., Schumacher, D.H.: Seasonal-term beach rotation processes in distinct Headland Bay systems. J. Coast. Res. 18(3), 442–458 (2002)Google Scholar
  5. 5.
    Harley, M.D., Turner, I.L., Short, A.D.: New insights into embayed beach rotation: The importance of wave exposure and cross-shore processes. J. Geophys. Res. 120(8), 16 (2015)Google Scholar
  6. 6.
    Gallop, S.L., Bosserelle, C., Eliot, I., Pattiaratchi, C.B.: The influence of lime-stone reefs on storm erosion and recovery of a perched beach. Cont. Shelf Res. 47, 16–27 (2012)CrossRefGoogle Scholar
  7. 7.
    Gallop, S.L., Bosserelle, C., Eliot, I., Pattiaratchi, C.B.: The influence of coastal reefs on spatial variability in seasonal sand fluxes. Marine Geol. 344, 132–143 (2013)CrossRefGoogle Scholar
  8. 8.
    Velegrakis, A.F., Trygonis, V., Chatzipavlis, A.E., Karambas, Th., Vousdoukas, M.I., Ghionis, G., Monioudi, I.N., Hasiotis, Th., Andreadis, O., Psarros, F.: Shoreline variability of an urban beach fronted by a beachrock reef from video imagery. Natural Hazards (2016). doi: 10.1007/s11069-016-2415-9
  9. 9.
    Lowe, R.J., Hart, C., Pattiaratchi, C.B.: Morphological constraints to wave-driven circulation in coastal reef-lagoon systems: a numerical study. J. Geophys. Res. 115, C09021 (2010)CrossRefGoogle Scholar
  10. 10.
    Rigos, A., Tsekouras, G.E., Vousdoukas, M.I., Chatzipavlis, A., Velegrakis, A.F.: A Chebyshev polynomial radial basis function neural network for automated shoreline extraction from coastal imagery. Integr. Comput. Aided Eng. 23, 141–160 (2016)CrossRefGoogle Scholar
  11. 11.
    Ma, L., Khorasani, K.: Constructive feedforward neural networks using Hermite polynomial activation functions. IEEE Trans. Neural Netw. 16(4), 821–833 (2005)CrossRefGoogle Scholar
  12. 12.
    Lee, T.T., Jeng, J.T.: The Chebyshev-polynomials-based unified model neural networks for function approximation. IEEE Trans. Syst. Man Cybern. Part B Cybern. 28(6), 925–935 (1998)CrossRefGoogle Scholar
  13. 13.
    Patra, J.C., Meher, P.K., Chakraborty, G.: Nonlinear channel equalization for wireless communication systems using legendre neural networks. Sig. Process. 89(11), 2251–2262 (2009)CrossRefMATHGoogle Scholar
  14. 14.
    Tsekouras, G.E., Rigos, A., Chatzipavlis, A., Velegrakis, A.: A neural-fuzzy network based on Hermite polynomials to predict the coastal erosion. Commun. Comput. Inf. Sci. 517, 195–205 (2015)CrossRefGoogle Scholar
  15. 15.
    Alexandrakis, G., Ghionis, G., Poulos, S.E.: The Effect of beach rock formation on the morphological evolution of a beach. The case study of an Eastern Mediterranean beach: Ammoudara, Greece. J. Coast. Res. 69(SI), 47–59 (2013)CrossRefGoogle Scholar
  16. 16.
    Bell, W.W.: Special Functions for Scientists and Engineers. D. Van Nostrand Company Ltd., London (1968)MATHGoogle Scholar
  17. 17.
    Moore, R.E.: Interval Analysis. Prentice-Hall, Englewood Cliff (1966)MATHGoogle Scholar
  18. 18.
    Luenberger, D.G., Ye, Y.: Linear and Nonlinear Programming, 3rd edn. Springer, New York (2008)MATHGoogle Scholar
  19. 19.
    Armijo, L.: Minimization of functions having Lipschitz continuous first partial derivatives. Pacific J. Math. 16(1), 1–3 (1966)MathSciNetCrossRefMATHGoogle Scholar
  20. 20.
    Pedrycz, W.: Conditional fuzzy clustering in the design of radial basis function neural networks. IEEE Trans. Neural Netw. 9(4), 601–612 (1998)CrossRefGoogle Scholar

Copyright information

© IFIP International Federation for Information Processing 2016

Authors and Affiliations

  • Anastasios Rigos
    • 1
  • George E. Tsekouras
    • 1
  • Antonios Chatzipavlis
    • 2
  • Adonis F. Velegrakis
    • 2
  1. 1.Department of Cultural Technology and CommunicationUniversity of the AegeanMitiliniGreece
  2. 2.Department of Marine SciencesUniversity of the AegeanMitiliniGreece

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