3-D WAVE FIELD AROUND SUBMERGED BREAKWATER. Amir Sharif Ahmadian 1 and Richard Simons 1

Transcription

1 3-D WAVE FIELD AROUD SUBMERGED BREAKWATER Ar Sharf Ahadan 1 and Rhard Sons 1 Methods for desgnng suberged breakwaters are stll beng developed, partularly n respet of the 3D nature of wave-breakwater nteraton. Many of the avalable desgn tools are neffent as they are not able to provde any nforaton on the spatal dstrbuton of the wave feld around breakwaters, and annot therefore guarantee relablty and auray for the engneer. There s thus a need for an engneerng desgn tool wth the ablty to odel spatal varaton of wave heght. Ths paper proposes a ethod based on ahne learnng algorths for predtng the nearshore wave feld behnd a suberged breakwater that nludes both D and 3D effets. The proposed nueral odel has been valdated by varous sales of laboratory data. Coparsons reveal the ablty of the proposed odel to predt the wave feld around suberged breakwater. Keywords: Suberged Breakwaters; Wave feld; 3D; Wave transsson; Artfal eural etworks; ueral odelng ITRODUCTIO Construtng suberged breakwaters s nreasngly preferred as a eans to redue eroson, trap natural sedents and restore beahes. Ths s beause of ther lower onstruton osts and sgnfant nfluene on dsspaton of ndent wave energy. owever, shorelne response to suberged breakwaters s partularly nfluened by the wave feld behnd the struture drven by oastal proesses, partularly wave overtoppng and dffraton, whh obvously nludes both D and 3D effets. The D aspets of wave transsson behnd suberged breakwaters and spefally wave transsson oeffent K have been studed extensvely by researhers (Johnson et al. 1951; Adas t and Sonu 1986; Losada et al. 1996; d'angreond et al. 1996; Seabrook and all 1998; Shlurann and Ouera 00; Panzzo et al. 003; Brgant et al. 003; Wasley and Ahrens 003; van der Meer et al. 005; Buno and Calabrese 007; Panzzo and Brgant 007; Goda and Ahrens 008). owever, very few studes have foused on the 3D effets of suberged breakwaters (Bellott 004; Johnson et al. 005; Zanuttgh and Martnell 008; ur et al. 01) and even fewer on the spatal varaton of nearshore wave feld behnd ths type of oastal struture (Kraer et al. 005; Caeres et al. 008; Vnanza et al. 009; Buno et al. 009). Avalable D engneerng desgn tools are neffent n breakwater desgn as they are not able to provde any nforaton on the spatal dstrbuton of wave feld around the breakwater. Also, the few reent studes of 3D effets on ths knd of detahed breakwater are ostly restrted to low-rested strutures whh are not fully suberged and therefore not applable to fully suberged breakwaters. There s thus a need for a proper desgn tool to provde full nforaton of spatal nearshore wave varaton around suberged breakwaters. Ths fat enouraged authors to start the present study, ntendng to ontrbute to ths ajor researh top and ts future applaton not only to wave transsson odelng but also to drvng fores requred for oastal area flow rulaton, sedent transport and orphodyna odelng systes (anson and Kraus 1991). The spatal dstrbuton of the nearshore wave feld around a suberged breakwater onsderng obned dffraton-overtoppng s nvestgated nuerally based on the data-drven algorths known as Artfal eural etworks (hereafter: As). Coputatonal predton odels of As have proven to be useful n any felds of engneerng to solve oplated nonlnear probles suh as regresson where any relatons are nvolved. As have prevously been appled suessfully n researh related to oastal engneerng (Mase et al. 1995; Van Gent and van den Boogaard 1998; Medna 1999; Medna et al. 00; Kabekar and Deo 003; Verhaeghe 005; Panzzo and Brgant 007; Verhaeghe et al. 008). In ths study, an A odel has been desgned and traned usng experental data olleted fro tests perfored at dfferent sales. The wave transsson oeffents alulated by the proposed odel were opared wth the easured experental data. Coparson of alulated and easured wave data reveals the auray of the proposed odel and ts apablty of predtng the wave feld around suberged breakwaters. The agreeent wth experental data s enouragng. 1 Cvl, Envronental and Geoat Engneerng Departent, UCL, Gower Street, London, WC1E 6BT, UK 1

2 COASTAL EGIEERIG 01 ARTIFICIAL EURAL ETWORKS Artfal neural networks onsst of a assve nuber of oputatonal unts postoned n ordered layers and lnked together wth network weghts. A supervsed feed-forward shee known as a Mult-Layer Pereptrons (MLPs) network s eployed n ths study and wll be dsussed further below. owever, for ore nforaton about ths approah, please see: (aykn 1998). Basally, supervsed feed-forward networks eploy a atheatal ethod for the learnng proess (here, a bak-propagaton (BP) algorth) to fnd a non-lnear relatonshp between nput data. Through the learnng proess network paraeters suh as nterlayer weghts and bas values are odfed and adapted so as to nze an overall error E produed over all the patterns n the tranng set s as follows: E s ( t y ) (1) th where t and y and are respetvely target response and oputed output by the network for saple. MLPs nlude an nput layer, one or ore hdden layers and an output layer of neurons. MLPs are usually traned by the BP algorth n two phases (Ruelhart et al. 1986; Werbos 1988). Frst, the network s paraeters are seleted and the nput sgnal s propagated through the layers. MLP networks apply transfer funtons whh opute the nner produt of the network s weghts and the nput vetors. An overall error E s oputed at the end by oparng the network s response wth the desred output. Then, n the seond phase, the alulated error E s propagated bakward through the network. The network s paraeters are adjusted so as to nze the overall error E and tranng s opleted. EXPERIMETAL SETUP AD DATA SAMPLIG Ths seton desrbes the experental setup, equpent, data saplng and test ondtons. The tests were arred out n a 0x1.x1 wave flue. The sde walls of the flue were onstruted wth glass to provde lear vsualzaton panels to ontor wave transforaton around the breakwater durng the tests. The horzontal botto of the flue was ade of glass wth a 1V:15 slopng artfal stanless steel beah at the end for wave absorpton. The length of the beah was 5.5. The effetveness of the wave absorpton by the beah was nvestgated for all test ondtons n the flue wthout any breakwater. A sngle absorbng pston type wave-aker was used to generate onohroat waves n the flue. A round head breakwater wth trapezodal body setons was onstruted and tested n the wave flue. The breakwater was onstruted wth horzontal top and sde slopes of 1V:1 n all dretons and ade of sooth arne plywood. The breakwaters were fxed to the botto of the flue so that the shoreward toe was loated at a dstane of 10 onshore of the wave paddle. Offshore water depth was antaned at 300 for all experents. Measureents were ade n dfferent loatons around the breakwater nludng front, sde and behnd. Wave heght and water level hanges along the flue and partularly behnd the breakwater were easured by 1 wave gauges. The data saplng rate of water surfae elevaton usng these wave gauges was set at 100 saples per seond for eah probe. The tests were onduted n the wave flue wth dfferent wave ondtons and subergene depths. A total of 176 tests was perfored under dfferent obnatons of 44 onohroat wave lates nludng 11 wave heghts and 4 wave perods wth 4 dfferent water depths. 35 tests were also arred out n the flue wth the sae water depth and slar wave ondtons wthout the breakwater to exane the ndent wave heghts and beah refletons. The range of test ondtons (water depth, wave perod and target wave heghts) are presented n Table 1. All the tests were ontored wth vdeo aeras nstalled on the top and sde of the flue and the observatons reorded on tapes for further analyss. In ths table, s the ndent wave heght, L offshore wave length, o hs water depth over the breakwater rest, h water depth n the toe of breakwater, θ and r are polar oordnates. Fg. 1 shows a sheat plan and seton of the suberged breakwater llustratng the physal paraeters entoned above.

3 COASTAL EGIEERIG 01 3 Table 1. Range of paraeters used to desrbe spatal wave transsson oeffent Varable L o h s h Θ r () () () () (rad) () Mean Standard devaton Maxu Mnu Fgure 1. Paraeters used for spatal wave transsson behnd suberged breakwater EXPERIMETAL DATA PROCESSIG AD AALYSIS An portant aspet of experental studes s the proessng and analyzng of the data olleted fro the laboratory easureents to enhane ts nterpretaton. Water surfae elevaton data, olleted by wave probes along the wave flue, were used to alulate ndent and refleted wave heght, transtted wave heght behnd breakwater and transsson oeffents. The ethod of Goda and Suzuk 1976 was pleented to alulate ndent and refleted wave heght. Ths ethod s basally a tehnque to deopose the ndent and refleted wave heghts by analyzng the apltudes of Fourer oponents of reorded data fro two wave probes loated n front of the breakwater at an approprate dstane fro eah other and fro any refletve surfae. The wave transtted onshore of the suberged breakwater vares spatally. Ths phenoenon was learly observed throughout the laboratory tests. The average root ean squared wave heght ( Ĥ rs ) fro the probes behnd the struture was alulated and used for analyss. Table presents the range of non-densonal data used n the neural network odelng, nludng nu, axu, ean and standard devaton of eah ndvdual paraeter. Table. on-densonal nput paraeters eployed n A odel h ondensonal s h s paraeters θ Lo h h L o Mean Standard devaton Maxu Mnu r

4 4 COASTAL EGIEERIG 01 Therefore, K t wll be deterned as: hs hs r K t f,,,, Lo h h L o () A MODEL SETUP AD PERFORMACE The MLP odel n ths researh was desgned wth three layers of neurons nludng nput, hdden and output layers as well as bases n the hdden and output layers. An optu network should be seleted durng the odel desgn. A ross-valdaton ethod (aykn 1998) whh proeeds as follows was eployed for generalzaton. The entre olleted laboratory data was dvded nto two an subsets for tranng and for testng. The set of tranng saples tself was splt nto two parts: estaton and valdaton subsets. The estaton subset ontaned data that were used to tran the A odel, whle the valdaton subset was used to evaluate the odel perforane and ontor the tranng proess. The network, tuned by the entre set of tranng data set, was fnally verfed aganst test data not used before. The phlosophy behnd eployng test data s to test the traned neural network by data never used before, the network experenng those nputs for the frst te. Ths exanes the perforane and apablty of the odel under new ondtons to ensure the odel works properly and that generalzaton probles do not our as new data are gven to the odel. The sze of these three subsets s presented n Table 3. Table 3. Sze of dfferent data sets used for A odel tranng and testng Data sets Tranng Estaton (Set 1) Valdaton (Set ) Sze Testng (Set 3) To perfor learnng ost effetvely, the tranng saples were set to be opletely rando. Aong dfferent transfer funtons, n MLP odel, an antsyetr hyperbol tangent atvaton funton was used for ts better perforane n BP learnng n oparson wth other funtons suh as the unsyetral logst transfer funton. To solve the salng proble durng the tranng, valdaton and testng as well as future applaton of the A odel, a noralzaton proess s essental. Ths goal ght be aheved by Eq. 3: x n x n( x) ax( x) n( x) (3) where x s the value to be noralzed. Eployng a BP algorth nreases the tranng te, although nreasng the nuber of hdden layers ay prove the generalzaton. Therefore, n ths researh, t s assued that one hdden layer s suffent to be able to approxate the underlyng unknown funton properly. For a ore detaled desrpton see (agan et al. 1996) or (aykn 1998). One the nuber of hdden layers of the network s deterned, the nuber of hdden neurons n ths layer should be deterned. To aheve ths, slar networks but wth dfferent nubers of hdden neurons were bult and traned and the optu nuber of hdden unts then deterned fro the network whh produed the least error n the valdaton subset. Fg. presents the RMSE (Eq. 1) error for 5 networks. As an be seen, both the estaton and valdaton error dereases durng the ntal phase of tranng. owever, ths reduton n oputed error s offset to soe extent, and wth an nrease n the hdden unts, overlearnng s ntrodued and onsequently the error n the valdaton set begns to rse. In all ases, tranng was ternated one ether the nuber of teratons reahed ts axu lt or the oputed response error was redued to a value less than the target value. The network weghts and bases were seleted as the fnal odel paraeters at the pont where nu error n the valdaton subset was aheved. As an be seen n Fg., the odel wth 7 nodes gves the least errors; hene 7 hdden neurons were hosen for the hdden layer of the odel.

5 COASTAL EGIEERIG 01 5 Fgure. Root ean square error oputed for the sae A odels but wth dfferent nubers of oputatonal unts n the hdden layer of the network The predtons obtaned fro the MLP odel are shown n Fg. 3, along wth the orrespondng observed data for two densonal and non-densonal ases. Two separate odels have been desgned, one based on the densonal tranng data set (Table 1) and the other usng non-densonal tranng data (Table ). Fgure 3. Satter plot between predted and easured transsson oeffent K t and oparson between two A odels: (a). Model based on densonal data set, (b) Model based on non -densonal data set. Correlaton oeffent R s estated usng Equaton 5. Coparson of the two odels aganst the experental data was also ade usng two statstal paraeters: Root Mean Squared Error (RMSE) and the squared ultple orrelaton oeffent R : RMSE 1 X X X 1 (4)

6 6 COASTAL EGIEERIG 01 R 1 X X X X X X X X 1 1 (5) Table 4 shows the statstal oparsons of the two MLP odels. The non-densonal MLP odel gves a better perforane n predtng wave transsson oeffent opared wth the densonal odel. Ths an be observed fro the graphs and fro the statstal ndexes (.e. low er RMS error and hgher R ). Table 4. Statstal oparson of two A odels Statstal ndexes RMSE R Densonal odel on-densonal odel Based on these oparsons, the non-densonal neural network odel was adopted and used to predt wave transsson oeffents around the suberged breakwater. Valdaton of the odel aganst testng data set and ts overall perforane wll be assessed n detal n the followng setons. MODEL VERIFICATIO Auray Analyss The proposed A odel n ths paper has been valdated usng experental data easured n the wave flue whh were not used durng the tranng proess. The oparson of the proposed odel wth the experental data was ade by oparng fve statstal paraeters, nludng the Root Mean Square Error (RMSE ) and the squared ultple orrelaton oeffent R as defned n prevous seton together wth three addtonal paraeters: Wlott ndex (Wlott, 1981), bas or dstorton β, and error funton (aller et al., 00): I w I w 1 X X X X 1 1 X X (6) 1 X X (7) 1 X 1 X X 1 (8) where represents the nuber of data and where X are the alulated values, X are the easured values and the barred paraeters deonstrate the average values of the paraeters. Perfet agreeent s aheved f R and Wlott ndex are 1.0 and the error funton s zero; also, the values

7 COASTAL EGIEERIG 01 7 of dstorton lose to 1.0 and the lower values of RMSE show better agreeent n the results. R s onsdered unsatsfatory as a easure of the goodness of ft for a ultvarate regresson relatonshp (Draper, 1984) and thus the valdty of the odel wll be assessed ostly by the other paraeters. The values of the fve statstal paraeters are presented n Table 5. The values of the statstal ndators ndate that the A odel s able to deterne wave transsson oeffent wth very hgh auray. The values alulated usng the A provde hgh R (95%) and Wlot nuber Iw (75%) and low values of ε (0.4) and RMSE (0.07) as well as value of dstorton very lose to 1.0, ndatng very good auray of results. Table 5. Statstal oparson of on-densonal A odel aganst easured testng data Statstal ndex on-densonal A odel I w R β RMSE Investgaton of the odel perforane also has been ade graphally. Fg. 4 shows the orrelaton between values predted by the A odel and values easured n the flue for the test subset. Fgure 4. Measured vs. predted values of the wave transsson oeffent 50, r = 500, θ = 1.05rad ) K t (Set 3; h s = 60, h = Fg. 5 shows a ontour ap of the error n the wave transsson alulated by A, gvng a graphal llustraton of the dfferenes between alulated and easured wave heghts n dfferent regons around the suberged breakwater. Ths graph llustrates learly the error at dfferent ponts, thus provdng valuable spatal nforaton about the perforane of the A odel. As an been seen n ths graph, the A odel perfors very well wth very low error (ostly less than %5) n ost regons nludng that behnd the breakwater and around the head. gher values n error, between 5% and 10%, an be seen n soe sall areas.

8 8 COASTAL EGIEERIG 01 Fgure 5. Contour ap of oputed absolute error of predted opared wth easured values (Set 3; 68, T = 1se, h s = 60, h = 50) = All these evaluatons reveal reasonable onssteny between the easured data and results fro the proposed odel n the ase of wave transsson oeffent predton. It s evdent that the traned non-densonal A odel s powerful enough to predt wave transsson oeffents spatally behnd the suberged breakwater for a wde range of water depths and wave lates. Table 5. Senstvty analyss of the on-densonal A odel h Otted s h s paraeters θ L o h h L o R RMSE r COCLUSIOS Coparsons reveal the aurate perforane and relable predtons of A odels. The followng onlusons an be drawn: the perforane of the A odel wth non-densonal paraeters was better than the one wth densonal paraeters n the predton of wave transsson oeffent around a suberged breakwater. Auray analyss llustrates very good results fro the A-MLP odel for spatal predton of K over a wde range of water depths and wave ondtons. Senstvty t analyss showed that the non-densonal paraeter θ was the ost effetve paraeter aong all the effetve paraeters nvolved n the proess. The paraeters Lo and r Lo also have a onsderable nfluene on the results. Wthout these paraeters as nputs to the network n the test data, the nu orrelaton oeffent and the ost error was obtaned. All these evaluatons reveal onssteny between the easured data and results fro the proposed odel. It s evdent that the traned A odel s powerful enough to predt wave transsson oeffents.

9 COASTAL EGIEERIG 01 9 REFERECES Adas, C.B. and C.J. Sonu, Wave Transsson Aross Suberged ear-surfae Breakwaters. In ASCE, pp Bellott, G., 004. A splfed odel of rp urrents systes around dsontnuous suberged barrers. Coastal Engneerng, 51 (4), pp Brgant R, J.W. Van der Meer, M. Buno, M. Calabrese, 003. Wave transsson behnd low rested strutures. Pro 3rd Coastal Strutures Conferene. Buno M., D.I. Vnanza, C.M. Caeres, D wave feld behnd pereable low rested strutures. Journal of Coastal Researh, 56, pp Buno, M and M. Calabrese, 007. Coneptual approah for predton of wave transsson at lowrested breakwaters. Journal of Waterway, Port, Coastal and Oean Engneerng, 133(3), pp Caeres I., M.J.F. Stve, A. Sanhez-Arlla, L.. Trung, 008., Quantfaton of hanges n urrent ntenstes ndued by wave overtoppng around low rested strutures. Coastal Engneerng, 55, p d'angreond K., J.W. Van der Meer, R.J. De Jong, Wave transsson at low-rested strutures. Proeedngs of the th Internatonal Conferene on Coastal Engneerng Orlando, FL, USA, pp Goda Y., and J.P. Ahrens, 008. ew forulaton of wave transsson over and through low-rested strutures. Proeedngs of the 31st Internatonal Conferene of Coastal Engneerng, 4. Goda, Y. and Y. Suzuk, Estaton of ndent and refleted waves n rando wave experents. In Pro. 15th Int. Conf. on Coastal Engneerng, ASCE. pp agan, M.T.,.B. Deuth, M.. Beale, eural network desgn, PWS Pub. anson,. and.c. Kraus, ueral Sulaton of Shorelne Change at Loran, Oho. Journal of Waterway, Port, Coastal, and Oean Engneerng, 117(1), pp aykn, S., eural etworks: A Coprehensve Foundaton by Son aykn (1998, ardover, Subsequent Edton): A Coprehensve Foundaton, Prente all. ur D.S., W.D. Lee. W.C. Cho, 01. Three-densonal flow haratersts around pereable suberged breakwaters wth open nlet. Oean Engneerng, 44, pp Johnson,.K., T.V. Karabas, I. Avgers, B. Zanuttgh,, D. Gonzalez Maro, and I. Caeres, 005. Modellng of waves and urrents around suberged breakwaters. Journal of Coastal Engneerng, 5, Johnson, J.W., R.A. Fuhs, and J.R. Morson, The dapng aton of suberged breakwaters. Transatons, Aeran Geophysal Unon, Vol. 3, o. 5, Kabekar A.R., and Deo M.C. 003, Estaton of ple group sour usng neural networks, Appled Oean Researh, Elsever, Oxford, UK, 5(4) Kraer, M., B. Zanuttgh, J.W van der Meer, C. Vdal,, F.X. Gronella, 005. Laboratory experents on low-rested breakwaters. Coastal Engneerng. 5, Losada, I.J., R. Slva, M.A. Losada, D non-breakng regular wave nteraton wth suberged breakwaters. Coastal Engneerng, 8, pp Mase,., M. Sakaoto, T. Saka, eural etwork for Stablty Analyss of Rubble-Mound Breakwaters. Journal of Waterway, Port, Coastal, and Oean Engneerng, 11(6), pp Medna, J.R., J.A., GonzÃlez-EsrvÃ, J.M.Garrdo, J. De Rouk, 00. Overtoppng analyss usng neural networks. Proeedngs of the 8th Internatonal Conferene on Coastal Engneerng, ASCE, pp Medna, J.R., eural network odellng of runup and overtoppng. ASCE Pro Coastal Strutures Santander, 1, p Panzzo, A, R. Brgant, 007. Analyss of wave transsson behnd low-rested breakwaters usng neural networks. Coastal Engneerng, 54(9), pp Panzzo, A., R. Brgant,, J.W. Van der Meer, L. Frano, 003. Analyss of wave transsson behnd low rested strutures usng neural networks, Pro. 4th Int. Coastal Strutures Conferene, Portland, Oregon. Ruelhart, D.E., G.E. nton, R.J. Wllas, Learnng representatons by bak-propagatng errors., 33(6088), pp Shlurann, T., M. Blek, and. Ouera, 00. Wave transforaton at artfal reefs desrbed by the lbert-uang transforaton. Proeedngs of the 8th Internatonal Conferene on Coastal Engneerng,, pp

10 10 COASTAL EGIEERIG 01 Seabrook, S.R., K.R. all, Wave transsson at suberged rubbleound breakwaters. Proeedngs of the Coastal Engneerng Conferene,, pp van der Meer, J.W., R. Brgant,, B. Zanuttgh, and B. Wang, 005. Wave transsson at low-rested strutures, nludng oblque wave attak. Journal of Coastal Engneerng, 5, van Gent, M.R.A.,.F.P. van den Boogaard, eural network odellng of fores on vertal strutures. Proeedngs of the Internatonal Conferene on Coastal Engneerng, 1(6). pp Verhaeghe,., J.D. Rouk and J. van der Meer, 008, Cobned lassfer-quantfer odel: A - phases neural odel for predton of wave overtoppng at oastal strutures, Coastal Engneerng, Elsever, 55 (008) Verhaeghe,., 005. eural network predton of wave overtoppng at oastal strutures. Ph.D. Thess, Unverstet Gent, Gent, Belgu, ISB Vnanza D., I. Caeres, M. Buno, X. Gronella. and M. Calabrese, 009. Wave dsturbane behnd low-rested strutures: Dffraton and overtoppng effets. Coastal Engneerng, 56, pp Wasley, T.V., J.P. Ahrens, 003. Coputaton of Wave Transsson Coeffents at Detahed Breakwaters for Shorelne Response Modelng. ASCE Conferene Proeedngs, 147(40733), p.49. Werbos, P.J., Bakpropagaton: past and future. In eural etworks, 1988., IEEE Internatonal Conferene on. vol.1 pp Zanuttgh, B., L. Martnell, 008. Transsson of wave energy at pereable low rested strutures. Coastal Engneerng, 55(1), pp