# Estimation of nearshore wave transmission for submerged breakwaters using a data-driven predictive model

## Abstract

The functional design of submerged breakwaters is still developing, particularly with respect to modelling of the nearshore wave field behind the structure. This paper describes a method for predicting the wave transmission coefficients behind submerged breakwaters using machine learning algorithms. An artificial neural network using the radial-basis function approach has been designed and trained using laboratory experimental data expressed in terms of non-dimensional parameters. A wave transmission coefficient calculator is presented, based on the proposed radial-basis function model. Predictions obtained by the radial-basis function model were verified by experimental measurements for a two dimensional breakwater. Comparisons reveal good agreement with the experimental results and encouraging performance from the proposed model. Applying the proposed neural network model for predictions, guidance is given to appropriately calculate wave transmission coefficient behind two dimensional submerged breakwaters. It is concluded that the proposed predictive model offers potential as a design tool to predict wave transmission coefficients behind submerged breakwaters. A step-by-step procedure for practical applications is outlined in a user-friendly form with the intention of providing a simplified tool for preliminary design purposes. Results demonstrate the model’s potential to be extended to three dimensional, rough, permeable structures.

## Keywords

Submerged breakwater Nearshore wave transmission Numerical modeling Artificial neural network Radial-basis function Predictive model## References

- 1.Huang W-P, Chou C-R, Yim J-Z (2005) On reflection and diffraction due to a detached breakwater. Ocean Eng 32(14–15):1762–1779CrossRefGoogle Scholar
- 2.Ilic S, van der Westhuysen AJ, Roelvink JA, Chadwick AJ (2007) Multidirectional wave transformation around detached breakwaters. Coast Eng 54(10):775–789CrossRefGoogle Scholar
- 3.Du Y, Pan S, Chen Y (2010) Modelling the effect of wave overtopping on nearshore hydrodynamics and morphodynamics around shore-parallel breakwaters. Coast Eng 57(9):812–826CrossRefGoogle Scholar
- 4.Kristensen S-E, Drønen N, Deigaard R, Fredsoe J (2013) Hybrid morphological modelling of shoreline response to a detached breakwater. Coast Eng 71:13–27CrossRefGoogle Scholar
- 5.Hur D-S (2004) Deformation of multi-directional random waves passing over an impermeable submerged breakwater installed on a sloping bed. Ocean Eng 31(10):1295–1311CrossRefGoogle Scholar
- 6.Jeng D-S, Schacht C, Lemckert C (2005) Experimental study on ocean waves propagating over a submerged breakwater in front of a vertical seawall. Ocean Eng 32(17–18):2231–2240CrossRefGoogle Scholar
- 7.Tsai C-P, Chen H-B, Lee F-C (2006) Wave transformation over submerged permeable breakwater on porous bottom. Ocean Eng 33(11–12):1623–1643CrossRefGoogle Scholar
- 8.Wang BX, Otta AK, Chadwick AJ (2007) Transmission of obliquely incident waves at low-crested breakwaters: theoretical interpretations of experimental observations. Coast Eng 54(4):333–344CrossRefGoogle Scholar
- 9.Zanuttigh B, Martinelli L, Lamberti A (2008) Wave overtopping and piling-up at permeable low crested structures. Coast Eng 55:484–498CrossRefGoogle Scholar
- 10.Calabrese M, Vicinanza D, Buccino M (2008) 2D wave setup behind submerged breakwaters. Ocean Eng 35(10):1015–1028CrossRefGoogle Scholar
- 11.Zhang J-S, Jeng D-S, Liu PL-F, Zhang C, Zhang Y (2012) Response of a porous seabed to water waves over permeable submerged breakwaters with Bragg reflection. Ocean Eng 43:1–12CrossRefGoogle Scholar
- 12.Sharif Ahmadian A, Simons RR (2014) A 3D numerical model of nearshore wave field behind submerged breakwaters. Coast Eng 83:190–204. doi: 10.1016/j.coastaleng.2013.10.016 CrossRefGoogle Scholar
- 13.Lee T-L, Jeng D-S (2002) Application of artificial neural networks in tide-forecasting. Ocean Eng 29(9):1003–1022CrossRefGoogle Scholar
- 14.Huang W, Murray C, Kraus N, Rosati J (2003) Development of a regional neural network for coastal water level predictions. Ocean Eng 30(17):2275–2295CrossRefGoogle Scholar
- 15.Kim D-H, Park W-S (2005) Neural network for design and reliability analysis of rubble mound breakwaters. Ocean Eng 32(11–12):1332–1349CrossRefGoogle Scholar
- 16.Rao S, Mandal S (2005) Hindcasting of storm waves using neural networks. Ocean Eng 32(5–6):667–684CrossRefGoogle Scholar
- 17.Lee T-L (2006) Neural network prediction of a storm surge. Ocean Eng 33(3–4):483–494CrossRefGoogle Scholar
- 18.van Gent MRA, van den Boogaard HFP, Pozueta B, Medina JR (2007) Neural network modelling of wave overtopping at coastal structures. Coast Eng 54(8):586–593CrossRefGoogle Scholar
- 19.Cha D, Zhang H, Blumenstein M (2011) Prediction of maximum wave-induced liquefaction in porous seabed using multi-artificial neural network model. Ocean Eng 38(7):878–887CrossRefGoogle Scholar
- 20.Kim D-H, Kim Y-J, Hur D-S (2014) Artificial neural network based breakwater damage estimation considering tidal level variation. Ocean Eng 87:185–190CrossRefGoogle Scholar
- 21.Bhaskaran PK, Rajesh Kumar R, Barman Rahul, Ravichandran M (2010) A new approach for deriving temperature and salinity fields in the Indian Ocean using artificial neural networks. J Mar Sci Technol 15(2):160–175CrossRefGoogle Scholar
- 22.Bhaskaran PK, Rajesh Kumar R, Dube SK, Murty TS, Gangopadhyay A, Chaudhuri A, Rao AD (2008) Travel time atlas and the role of neural networks for an early warning system for tsunamis in the Indian Ocean. In: Conference paper, December 2008Google Scholar
- 23.Bhaskaran PK, Rajesh Kumar R, Dube SK, Rao AD, Murty T, Gangopadhyay A, Chaudhuri A (2008) Tsunami early warning system-an Indian Ocean perspective. J Earthq Tsunami 2(3):197–226CrossRefGoogle Scholar
- 24.Barman R, Prasad Kumar B, Pandey PC, Dube SK et al (2006) Tsunami travel time prediction using neural networks. Geophys Res Lett 33:L16612. doi: 10.1029/2006GL026688 CrossRefGoogle Scholar
- 25.van der Meer J, Briganti R, Wang B, Zanuttigh B (2004) Wave transmission at low-crested structures, including oblique wave attack. In: Proceedings of 29th international conference on coastal engineering, ASCE vol 41, pp 52–64Google Scholar
- 26.van der Meer JW, Briganti R, Zanuttigh B, Wang B (2005) Wave transmission and refection at low-crested structures: design formulae, oblique wave attack and spectral change. Coast Eng 52:915–929CrossRefGoogle Scholar
- 27.Panizzo A, Briganti R (2007) Analysis of wave transmission behind low-crested breakwaters using neural networks. Coast Eng 54(9):643–656CrossRefGoogle Scholar
- 28.Buccino M, Calabrese M (2007) Conceptual approach for prediction of wave transmission at low-crested breakwaters. J Waterw Port Coast Ocean Eng 133(3):213–224CrossRefGoogle Scholar
- 29.Goda Y, Ahrens JP (2008) New formulation of wave transmission over and through low-crested structures. In: Proceedings of the 31st international conference of coastal engineering, vol 4Google Scholar
- 30.Kurban T, Beşdok E (2009) A comparison of RBF neural network training algorithms for inertial sensor based terrain classification. Sensors 9:6312–6329. doi: 10.3390/s90806312 CrossRefGoogle Scholar
- 31.Adams C, Sonu C (1987) Wave transmission across submerged near-surface breakwaters. Coast Eng 1986:1729–1738. doi: 10.1061/9780872626003.126 CrossRefGoogle Scholar
- 32.d’Angremond K, van der Meer J, De Jong R (1996) Wave transmission at low-crested structures. In: Proceedings of 25th international conference on coastal engineering, ASCE, vol 24, pp 18–27Google Scholar
- 33.Seabrook S, Hall K (1998) Wave transmission at submerged rubblemound breakwaters. In: Proceedings of 26th international conference on coastal engineering, vol 2, pp 2000–2013Google Scholar
- 34.van Oosten R, Peixo Marco J, van der Meer JW, Verhagen H (2006) Wave transmission at low-crested structures using neural networks. In: International conference on coastal engineering, San Diego, ASCE, pp 4932–4944Google Scholar
- 35.Sharif Ahmadian A, Simons RR (2012) 3-D wave field around submerged breakwater. ASCE, New York. doi: 10.9753/icce.v33.structures.13
- 36.Sharif Ahmadian A (2016) Numerical models for submerged breakwaters. Coastal hydrodynamics and morphodynamics, 1st edn. Elsevier, AmsterdamGoogle Scholar
- 37.Stucky A, Bonnard D (1937) Contribution to the experimental study of marine rock fill dikesbull. Technical report, Technique de Suizze RomandeGoogle Scholar
- 38.Beach-Erosion-Board (1940) A model study of the effect of submerged breakwaters on wave action. Technical memorandum No. 1. Chief of Engineers, U.S. War DepartmentGoogle Scholar
- 39.Morison J (1949) Model study of wave action on underwater barriers. Technical report, Report HE-116-304, Inst. Eng. Res., Univ. Calif., BerkleyGoogle Scholar
- 40.Johnson JW, Fuchs RA, Morison JR (1951) The damping action of submerged breakwaters. Trans Am Geophys Union 32(5):704–718CrossRefGoogle Scholar
- 41.Goda Y, Takeda H, Moriya Y (1967) Laboratory investigation on wave transmission over breakwaters. Report of the port and Harbour Research Institute 13, 38Google Scholar
- 42.Goda Y (1969) Re-analysis of laboratory data on wave transmission over breakwaters. Report of the port and Harbour Research Institute, vol 18(3), pp 3–18Google Scholar
- 43.Seelig W (1980) Two-dimensional tests of wave transmission and reflection characteristics of laboratory breakwaters. Technical report, CERC, Fort Belvoir, Report No. 80-1Google Scholar
- 44.Allsop N (1983) Low-crested breakwaters, studies in random waves. In: Proceedings of coastal structure 83 ASCE, pp 94–107Google Scholar
- 45.Ahrens J (1987) Characteristics of reef breakwaters. Technical report CERC-87-17, 45Google Scholar
- 46.Davies B, Kriebel D (1992) Model testing on wave transmission past low crested breakwaters. In: Proceedings of 23rd international conference on coastal engineering ASCE, pp 1115–1128Google Scholar
- 47.Daemrich K, Kahle W (1985) Schutzwirkung von unterwasser wellen brechern unter dem einfluss unregelmassiger seegangswellen. Technical Report, Franzius Instituts fur Wasserbau und Kusteningenieurswesen, Report Heft 61 (in Germany)Google Scholar
- 48.Powell K, Allsop N (1985) Low-crested breakwaters, hydraulic performance and stability. Technical report SR 57, HR WallingfordGoogle Scholar
- 49.van der Meer J (1988) Rock slopes and gravel beaches under wave attack. Ph.D. thesis, Delft University of Technology, Delft Hydraulics Report No. 396Google Scholar
- 50.Daemen I (1991) Wave transmission at low crested structures. Ph.D. thesis, M.Sc. thesis, Delft University of Technology, Faculty of Civil Engineering, Delft Hydraulics Report H 462Google Scholar
- 51.Seabrook S, Hall K (1997) Effect of crest width and geometry on submerged breakwater performance. In: Proceedings of Canadian coastal conference CCSEA, pp 58–72Google Scholar
- 52.Bleck M, Oumeraci H (2002) Hydraulic performance of artificial reefs: global and local description. In: Proceedings of 28th international conference on coastal engineering ASCE, pp 1778–1790Google Scholar
- 53.Calabrese M, Vicinanza D, Buccino M (2002) Large-scale experiments on the behaviour of low crested and submerged breakwaters in presence of broken waves. In: Proceedings of 28th international conference on coastal engineering ASCE, pp 1900–1912Google Scholar
- 54.Kramer M, Zanuttigh B, Vandermeer J, Vidal C, Gironella F (2005) Laboratory experiments on low-crested breakwaters. Coast Eng 52:867–885CrossRefGoogle Scholar
- 55.van der Meer J (1991) Stability and transmission at low-crested structures. Technical report, Delft Hydraulic, Report No. H 453, 33pGoogle Scholar
- 56.van der Meer J, Daemen I (1994) Stability and wave transmission at low-crested rubble-mound structures. J Waterw Port Coast Ocean Eng. doi: 10.1061/(ASCE)0733-950X(1994)120:1(1) Google Scholar
- 57.Gironella X, Sanchez-Arcilla A, Brigantti R, Sierra JP, Moreno L (2002) Submerged detached breakwaters: towards a functional design. In: Proceedings of 28th coastal engineering conference, Cardiff, Wales, UK, pp 1768–1777Google Scholar
- 58.Garcia N, Lara J, Losada I (2004) 2-d numerical analysis of near-field flow at low-crested permeable breakwaters. J Coast Eng 51:991–1020CrossRefGoogle Scholar
- 59.Melito I, Melby J (2002) Wave runup, transmission, and reflection for structures armored with core-loc. J Coast Eng 42:33–52CrossRefGoogle Scholar
- 60.Hirose N, Watanuki A, Saito M (2002) New type units for artificial reef development of ecofriendly artificial reefs and the effectiveness thereof. In: Proceedings of 30th international navigation congress. PIANC, p Cd ROMGoogle Scholar
- 61.Tanaka N (1976) Wave deformation and beach stabilization capacity of wide-crested submerged breakwaters. In: Proceedings of 23rd Japanese conference coastal engineering, pp 152–157
**(in Japanese)**Google Scholar - 62.Stein R (1993) Selecting data for neural networks. AI Expert 8(2):42–47Google Scholar
- 63.Haykin S (1999) Neural networks, a comprehensive foundation, 2nd edn. Prentice Hall, New JerseyzbMATHGoogle Scholar
- 64.Hagan MT, Demuth HB, Beale MH (1996) Neural network design. PWS Publication, BostonGoogle Scholar
- 65.Wilmott CJ (1981) On the validation of models. Prog Phys Geogr 2:184–194Google Scholar
- 66.Haller MC, Darlymple RA, Svendsen IA (2002) Experimental study of nearshore dynamics on a barred beach with rip channels. J Geophys Res 107(C6):14-1–14-21CrossRefGoogle Scholar
- 67.Draper NR (1984) The Box–Wetz criterion versus R2. J Stat Soc 147:100–103Google Scholar
- 68.Krause P, Boyle DP, Base F (2005) Comparison of different efficiency criteria for hydrological model assessment. Adv Geosci 5:89–97CrossRefGoogle Scholar
- 69.Tukey JW (1977) Box-and-whisker plots. In: Explanatory data analysis. Addison-Wesley, Reading, pp 39–43 Google Scholar
- 70.McGill R, Tukey JW, Larsen WA (1978) Variations of boxplots. Am Stat 32:12–16Google Scholar
- 71.Park J, Sandberg IW (1993) Approximation and radial-basis function networks. Neural Comput 5:305–316CrossRefGoogle Scholar
- 72.Broomhead D, Lowe D (1988) Multivariable functional interpolation and adaptive networks. Complex Syst 2:321–355MathSciNetzbMATHGoogle Scholar
- 73.Poggio T, Girosi F (1990) Networks for approximation and learning. Proc IEEE 78:1481–1497CrossRefzbMATHGoogle Scholar
- 74.Hamadneh N, Sathasivam S, Choon OH (2012) Higher order logic programming in radial basis function neural network. Appl Math Sci 6(3):115–127MathSciNetzbMATHGoogle Scholar
- 75.Robert J, Howlett LCJ (2001) Radial basis function networks 2: new advances in design. Physica-Verlag, HerdelbergzbMATHGoogle Scholar
- 76.Liu Y, Zheng Q, Shi Z, Chen J (2004) Training radial basis function networks with particle swarms. Lecture Notes Computer Science, vol 3173, pp 317–322Google Scholar
- 77.Simon D (2002) Training radial basis neural networks with the extended Kalman filter. Neurocomputing 48:455–475CrossRefzbMATHGoogle Scholar
- 78.Karayiannis NB (1999) Reformulated radial basis neural networks trained by gradient descent. IEEE Trans Neural Netw 10(3):657–671CrossRefGoogle Scholar
- 79.Bullinaria J (2004) Introduction to neural networks. Lecture notesGoogle Scholar