Development of Stability Formulas for Rock Armor and Tetrapods Using Multigene Genetic Programming
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 146, Issue 1
Abstract
Stability formulas for rock armor and Tetrapods were developed using multigene genetic programming, which is one of the machine learning methods. The developed formulas are shown to be more accurate than previous empirical formulas and neural network models. They are also compared against a few independent data that were not used in the development of the formulas. To give an idea of the confidence of the formulas, the equations for 90% prediction error band are presented. The formula for Tetrapods is somewhat less accurate than that for rock armor, probably because the experimental data for rock armor were produced by a single author, whereas those for Tetrapods were produced by several authors, so the data were inhomogeneous. The formula for rock armor includes the crest freeboard of the structure, which was not considered in previous studies, so it can be used for low-crested structures as well.
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Acknowledgments
This study was performed by the project of ‘‘Investigation of large swell waves and rip currents and development of the disaster response system (No. 20140057)’’ sponsored by the Ministry of Oceans and Fisheries, Republic of Korea. The first author was also supported by the research project of the Korea Institute of Ocean Science and Technology (Project No. PE99731). The Institute of Construction and Environmental Engineering at Seoul National University provided research facilities for this work.
References
Balas, C. E., and L. Balas. 2002. “Risk assessment of some revetments in southwest Wales, United Kingdom.” J. Waterway, Port, Coastal, Ocean Eng. 128 (5): 216–223. https://doi.org/10.1061/(ASCE)0733-950X(2002)128:5(216).
Balas, C. E., M. L. Koc, and R. Tür. 2010. “Artificial neural networks based on principal component analysis, fuzzy systems and fuzzy neural networks for preliminary design of rubble mound breakwaters.” Appl. Ocean Res. 32 (4): 425–433. https://doi.org/10.1016/j.apor.2010.09.005.
Bonakdar, L., and A. Etemad-Shahidi. 2011. “Predicting wave run-up on rubble mound structures using M5 model tree.” Ocean Eng. 38 (1): 111–118. https://doi.org/10.1016/j.oceaneng.2010.09.015.
Burcharth, H. F., and S. A. Hughes. 2002. “Fundamentals of design.” In Vol. VI-5 of Coastal engineering manual, 1–327, edited by S. A. Hughes. Washington, DC: USACE.
CIRIA (Construction Industry Research and Information Association), CUR (Civieltechnisch Centrum Uitvoering Research en Regelgeving), and CETMEF (Centre d’Etudes Techniques Maritimes et Fluviales). 2007. The rock manual. The use of rock in hydraulic engineering. 2nd ed. London: CIRIA.
De Jong, R. J. 1996. “Wave transmission at low-crested structure, Stability of tetrapods at front, crest and rear of a low-crested breakwater.” Master’s thesis, Dept. of Civil Engineering and Geosciences, Delft Univ. of Technology.
Erdik, T. 2009. “Fuzzy logic approach to conventional rubble mound structures design.” Expert Syst. Appl. 36 (3): 4162–4170. https://doi.org/10.1016/j.eswa.2008.06.012.
Erdik, T., M. E. Savci, and Z. Sen. 2009. “Artificial neural network for predicting maximum wave runup on rubble mound structures.” Expert Syst. Appl. 36 (3): 6403–6408. https://doi.org/10.1016/j.eswa.2008.07.049.
Etemad-Shahidi, A., and L. Bonakdar. 2009. “Design of rubble-mound breakwaters using M5′ machine learning method.” Appl. Ocean Res. 31 (3): 197–201. https://doi.org/10.1016/j.apor.2009.08.003.
Etemad-Shahidi, A., and E. Jafari. 2014. “New formulae for prediction of wave overtopping at inclined structures with smooth impermeable surface.” Ocean Eng. 84 (Jul): 124–132. https://doi.org/10.1016/j.oceaneng.2014.04.011.
Etemad-Shahidi, A., S. Shaeri, and E. Jafari. 2016. “Prediction of wave overtopping at vertical structures.” Coastal Eng. 109 (Mar): 42–52. https://doi.org/10.1016/j.coastaleng.2015.12.001.
Formentin, S. M., B. Zanuttigh, and J. W. Van der Meer. 2017. “A neural network tool for predicting wave reflection, overtopping, and transmission.” Coastal Eng. J. 59 (1): 1750006. https://doi.org/10.1142/S0578563417500061.
Hanzawa, M., H. Sato, S. Takahashi, K. Shimosako, T. Takayama, and K. Tanimoto. 1996. “New stability formula for wave-dissipating concrete blocks covering horizontally composite breakwaters.” In Proc., 25th Int. Conf. on Coastal Engineering (ICCE), 1665–1678. New York: ASCE.
Hudson, R. Y. 1959. “Laboratory investigation of rubble-mound breakwaters.” J. Waterw. Harbors Div. 85 (WW3): 93–121.
Kim, D. H., and W. S. Park. 2005. “Neural network for design and reliability analysis of rubble mound breakwaters.” Ocean Eng. 32 (11–12): 1332–1349. https://doi.org/10.1016/j.oceaneng.2004.11.008.
Kim, S.-W., and K.-D. Suh. 2013. “Development of a stability formula for Tetrapod using M5′ model tree.” [In Korean.] J. Korean Soc. Coastal Ocean Eng. 25 (3): 138–146. https://doi.org/10.9765/KSCOE.2013.25.3.138.
Koza, J. R. 1992. Genetic programming: On the programming of computers by means of natural selection. Cambridge, MA: MIT Press.
Lee, A., Z. Geem, and K.-D. Suh. 2016a. “Determination of optimal initial weights of an artificial neural network by using the harmony search algorithm: Application to breakwater armor stones.” Appl. Sci. 6 (6): 164. https://doi.org/10.3390/app6060164.
Lee, A., S. E. Kim, and K.-D. Suh. 2016b. “An easy way to use artificial neural network model for calculating stability number of rock armors.” Ocean Eng. 127 (Nov): 349–356. https://doi.org/10.1016/j.oceaneng.2016.10.013.
Lee, D. S., S.-H. Oh, and B. S. Cho. 2016c. “Experimental investigation on the change of stability coefficient of Tetrapod according to difference in density.” [In Korean.] J. Korean Soc. Coastal Ocean Eng. 28 (3): 124–131. https://doi.org/10.9765/KSCOE.2016.28.3.124.
Lee, J. S. 2017. “Development of stability formulas for Tetrapods and rock armors using multigene genetic programming.” Master’s thesis, Dept. of Civil and Environmental Engineering, Seoul National Univ.
Lee, S. B., and K.-D. Suh. 2019. “Development of wave overtopping formulas for inclined seawalls using GMDH algorithm.” KSCE J. Civ. Eng. 23 (5): 1899–1910. https://doi.org/10.1007/s12205-019-1298-1.
Mase, H., M. Sakamoto, and T. Sakai. 1995. “Neural network for stability analysis of rubble-mound breakwaters.” J. Waterway, Port, Coastal, Ocean Eng. 121 (6): 294–299. https://doi.org/10.1061/(ASCE)0733-950X(1995)121:6(294).
Melby, J. A., and N. Kobayashi. 1998. “Progression and variability of damage on rubble mound breakwaters.” J. Waterway, Port, Coastal, Ocean Eng. 124 (6): 286–294. https://doi.org/10.1061/(ASCE)0733-950X(1998)124:6(286).
Melby, J. A., and N. Kobayashi. 2000. “Damage progression and variability on breakwater trunks.” In Proc., Coastal Structures ’99, 309–315, edited by I. J. Losada. Rotterdam, Netherlands: A.A. Balkema.
Pullen, T., N. W. H. Allsop, T. Bruce, A. Kortenhaus, H. Schüttrumph, and J. W. Van der Meer. 2007. EurOtopmanual. Scharsterbrug, Netherlands: SkarWeb.
Searson, D. P., D. E. Leahy, and M. J. Willis. 2010. “GPTIPS: An open source genetic programming toolbox for multigene symbolic regression.” In Proc., Int. Multiconf. of Engineers and Computer Scientists, 77–80. Hong Kong: Newswood.
Smith, W. G., N. Kobayashi, and S. Kaku. 1992. “Profile changes of rock slopes by irregular waves.” In Proc., 23rd Int. Conf. on Coastal Engineering (ICCE), 1559–1572. Reston, VA: ASCE.
Smits, G., and M. Kotanchek. 2004. “Pareto-front exploitation in symbolic regression.” In Genetic programming theory and practice II, 283–299. Berlin: Springer.
Suh, K. D., H.-M. Kweon, and H. D. Yoon. 2002. “Reliability design of breakwater armor blocks considering wave direction in computation of wave transformation.” Coastal Eng. J 44 (4): 321–341. https://doi.org/10.1142/S0578563402000585.
Suh, K.-D., and J. Kang. 2012. “Stability formula for Tetrapods.” J. Waterway, Port, Coastal, Ocean Eng. 138 (3): 261–266. https://doi.org/10.1061/(ASCE)WW.1943-5460.0000124.
Suh, K.-D., M. Kim, and S.-W. Kim. 2013. “Comparison of calculation methods of cumulative damage to breakwater armor layer.” J. Waterway, Port, Coastal, Ocean Eng. 139 (4): 277–285. https://doi.org/10.1061/(ASCE)WW.1943-5460.0000181.
Thompson, D. M., and R. M. Shuttler. 1975. Riprap design for wind wave attack. A laboratory study in random waves. Wallingford, UK: H. R. Wallingford.
Van der Meer, J. W. 1987a. “Stability of breakwater armor layers–Design formulae.” Coastal Eng. 11 (3): 93–121. https://doi.org/10.1016/0378-3839(87)90013-5.
Van der Meer, J. W. 1987b. Stability of rubble mound breakwaters, stability formula for breakwaters armoured with tetrapods. Delft, Netherlands: Delft Hydraulics Laboratory.
Van der Meer, J. W. 1988a. Rock slopes and gravel beaches under wave attack. Delft, Netherlands: Delft Hydraulics.
Van der Meer, J. W. 1988b. “Stability of cubes, tetrapods and accropode.” In Design of breakwaters, 71–80. London: Thomas Telford.
Van der Meer, J. W. 2000. “Design of concrete armour layers.” In Proc., Coastal structures ’99, 213–221. Rotterdam, Netherlands: A.A. Balkema.
Van Gent, M. R. A., H. F. P. Van den Boogaard, B. Pozueta, and J. R. Medina. 2007. “Neural network modeling of wave overtopping at coastal structures.” Coastal Eng. 54 (8): 586–593. https://doi.org/10.1016/j.coastaleng.2006.12.001.
Van Gent, M. R. A., and H. F. P. Van den Boogaard. 1998. “Neural network modelling of forces on vertical structures.” In Proc., 26th Int. Conf. on Coastal Engineering (ICCE), 2096–2109. Reston, VA: ASCE.
Verhaeghe, H. 2005. “Neural network prediction of wave overtopping at coastal structures.” Ph.D. thesis, Dept. of Civil Engineering, Univ. of Gent.
Willmott, C. J. 1981. “On the validation of models.” Phys. Geogr. 2 (2): 184–194. https://doi.org/10.1080/02723646.1981.10642213.
Zanuttigh, B., S. M. Formentin, and J. W. Van der Meer. 2016. “Prediction of extreme and tolerable wave overtopping discharges through an advanced neural network.” Ocean Eng. 127 (Nov): 7–22. https://doi.org/10.1016/j.oceaneng.2016.09.032.
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Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 146 • Issue 1 • January 2020
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©2019 American Society of Civil Engineers.
History
Received: Aug 3, 2018
Accepted: May 1, 2019
Published online: Oct 3, 2019
Published in print: Jan 1, 2020
Discussion open until: Mar 3, 2020
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