Modeling and Parameter Identification of Shipping Water Events: A Numerical Evaluation with Non-Integer Derivatives

Resumen: In this article, we explore the use of a generalized diffusion equation (GDE) for modeling shipping water (SW) events, which are bodies of water that flood the deck of marine structures during extreme weather conditions. The GDE is obtained by substituting the first-order time derivative of the standard diffusion equation by a generalized derivative of non-integer order. The GDE, which in this contribution is formulated using the Caputo fractional derivative, may permit to approximate the behavior between diffusion and wave propagation observed in SW events. We present numerical results to demonstrate the agreement between the response of the GDE and the standard advection-difussion equation, which has been previously used to describe SW events.

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Marcos A. Gonzalez-Olvera, Lizeth Torres & Jassiel Vladimir Hernández-Fontes. Modeling and Parameter Identification of Shipping Water Events: A Numerical Evaluation with Non-Integer Derivatives. Memorias del Congreso Nacional de Control Automático, pp. 1-6, 2020.

Palabras clave

Shipping Water Events, Fractional-Time Difussion Equation, System Identification

• Buchner, B. (2002). Green water on ship-type offshore structures. PhD Thesis. Delft University of Technology, Delft, The Netherlands. Ph.D. thesis, Delft University of Technology Delft, The Netherlands.
• Caputo, M. (1967). Linear models of dissipation whose q is almost frequency independent—ii. Geophysical Journal International, 13(5), 529–539.
• Chuang, W.L., Chang, K.A., and Mercier, R. (2018). Kinematics and dynamics of green water on a fixed platform in a large wave basin in focusing wave and random wave conditions. Experiments in Fluids, 59(6), 100.
• Diethelm, K. and Freed, A.D. (1998). The fracpece subroutine for the numerical solution of differential equations of fractional order. Forschung und wissenschaftliches Rechnen, 1999, 57–71.
• Goda, K. and Miyamoto, T. (1976). A study of shipping water pressure on deck by two-dimensional ship model tests. Journal of The Society of Naval Architects of Japan, 1976(140), 16–22.
• González-Olvera, M.A. and Tang, Y. (2016). Identification of incommensurate state-space fractional systems. In 2016 IEEE 13th International Conference on Networking, Sensing, and Control (ICNSC), 1–4. IEEE.
• Gorenflo, R. and Mainardi, F. (1997). Fractional calculus. In Fractals and fractional calculus in continuum mechanics, 223–276. Springer. Greco, M., Faltinsen, O., and Landrini, M. (2005). Shipping of water on a two-dimensional structure. Journal of Fluid Mechanics, 525, 309.
• Hernández-Fontes, J.V., Esperança, P.T., Silva, R., Mendoza, E., and Sphaier, S.H. (2020a). Violent waterstructure interaction: Overtopping features and vertical loads on a fixed structure due to broken incident flows. Marine Structures, 74, 102816.
• Hernández-Fontes, J.V., Hernández, I.D., Mendoza, E., and Silva, R. (2020b). Green water evolution on a fixed structure induced by incoming wave trains. Mechanics Based Design of Structures and Machines, 1–29.
• Hernández-Fontes, J.V., Vitola, M.A., Paulo de Tarso, T.E., and Sphaier, S.H. (2019a). Analytical convolution model for shipping water evolution on a fixed structure. Applied Ocean Research, 82, 415–429.
• Hernández-Fontes, J.V., Vitola, M.A., Paulo de Tarso, T.E., and Sphaier, S.H. (2019b). Assessing shipping water vertical loads on a fixed structure by convolution model and wet dam-break tests. Applied Ocean Research, 82, 63–73.
• Hernández-Fontes, J., Torres, L., Mendoza, E., and Escudero, M. (2020c). Identification of the advectiondiffusion equation for predicting green water propagation. Ocean Engineering, 214, 107658.
• Huang, F. and Liu, F. (2005). The time fractional diffusion equation and the advection-dispersion equation. The ANZIAM Journal, 46(3), 317–330.
• Lorenzo, C.F. and Hartley, T.T. (2001). Initialization in fractional order systems. In 2001 European Control Conference (ECC), 1471–1476. IEEE.
• Mainardi, F. (2010). Fractional calculus and waves in linear viscoelasticity: an introduction to mathematical models. World Scientific.
• Pakozdi, C., Östman, A., Ji, G., Stansberg, C.T., Reum, O., Ovrebo, S., Vestbøstad, T., Sorvaag, C., and Ersland, J. (2016). Estimation of wave loads due to green water events in 10000-year conditions on a tlp deck structure. In International Conference on Offshore Mechanics and Arctic Engineering, volume 49927, V001T01A050. American Society of Mechanical Engineers.
• Silva, D.F., Esperança, P.T., and Coutinho, A.L. (2017). Green water loads on fpsos exposed to beam and quartering seas, part ii: Cfd simulations. Ocean Engineering, 140, 434–452.
• Tang, Y., Liu, H., Wang, W., Lian, Q., and Guan, X. (2015). Parameter identification of fractional order systems using block pulse functions. Signal Processing, 107, 272–281.
• Zhang, X., Draper, S., Wolgamot, H., Zhao, W., and Cheng, L. (2019). Eliciting features of 2d greenwater overtopping of a fixed box using modified dam break models. Applied Ocean Research, 84, 74–91.