Abstract
Pile groups are employed in sea and ocean environments in order to support marine and offshore structures. Estimation of scour depth around pile groups is one of the important factors in the design of coastal and marine structures. The scour phenomenon is a serious hazard that threats the structural stability of piles. Data-driven methods are being used more and more for the prediction of scour depth around pile groups due to the complexity of the process involved. The previous studies have indicated that the M5 model tree (M5MT) was able to provide more accurate results for wave-induced scour around pile groups compared to the empirical equations. Recently, multivariate adaptive regression splines (MARS) approach has been used as a relatively novel technique of data-driven methods for modeling and approximating nonlinear civil engineering problems. In this paper, MARS models are developed and used for estimation of the scour depth around pile groups in terms of the most influential dimensionless parameters using experimental data and field observations. Moreover, the classification and regression trees (CART) algorithm as a well-known decision tree algorithm is also used for prediction of the wave-induced scour depth around pile groups. The main feature of MARS is to provide a simple linear regression equation that calculates quickly and easily scour depth. In addition, CART presents decision rules without the need for any mathematical calculations, and it predicts scour depth straightforwardly. Statistical indices demonstrate that MARS with the root mean square error (RMSE) = 0.24 and correlation coefficient (CC) = 0.95 is more accurate than two well-known decision tree algorithms, namely M5MT (RMSE = 0.34 and CC = 0.92) and CART (RMSE = 0.35 and CC = 0.90). In addition, the sensitivity analysis declares that the Keulegan–Carpenter number (KC) is the most important variable that affects the scour depth.
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References
Ayoubloo MK, Etemad-Shahidi A, Mahjoobi J (2010) Evaluation of regular wave scour around a circular pile using data mining approaches. Appl Ocean Res 32(1):34–39. https://doi.org/10.1016/j.apor.2010.05.003
Ayoubloo MK, Azamathulla HM, Jabbari E, Zanganeh M (2011) Predictive model-based for the critical submergence of horizontal intakes in open channel flows with different clearance bottoms using CART, ANN and linear regression approaches. Expert Syst Appl 38(8):10114–10123. https://doi.org/10.1016/j.eswa.2011.02.073
Azimi H, Bonakdari H, Ebtehaj I, Talesh SHA, Michelson DG, Jamali A (2017) Evolutionary Pareto optimization of an ANFIS network for modeling scour at pile groups in clear water condition. Fuzzy Sets Syst 319:50–69. https://doi.org/10.1016/j.fss.2016.10.010
Bayram A, Larson M (2000) Analysis of scour around a group of vertical piles in the field. J Waterw Port Coast Ocean Eng 126(4):215–220. https://doi.org/10.1061/(ASCE)0733-950X(2000)126:4(215)
Breiman L, Friedman J, Olshen R, Stone C (1984) Classification and regression trees. Wadsworth Int Group 37(15):237–251
Chou JS, Pham AD (2014) Hybrid computational model for predicting bridge scour depth near piers and abutments. Autom Constr 48:88–96. https://doi.org/10.1016/j.autcon.2014.08.006
Craven P, Wahba G (1979) Smoothing noisy data with spline functions: estimating the correct degree of smoothing by the method of generalized cross-validation. Numer Math 31:317–403
Etemad-Shahidi A, Ghaemi N (2011) Model tree approach for prediction of pile groups scour due to waves. Ocean Eng 38(13):1522–1527. https://doi.org/10.1016/j.oceaneng.2011.07.012
Friedman JH (1991) Multivariate adaptive regression splines. Ann Stat 19(1):1–67. https://doi.org/10.1214/aos/1176347963
Friedman JH, Roosen CB (1995) An introduction to multivariate adaptive regression splines. Stat Methods Med Res 4:197–217. https://doi.org/10.1177/096228029500400303
Ghaemi N, Etemad-Shahidi A, Ataie-Ashtiani B (2013) Estimation of current-induced pile groups scour using a rule-based method. J Hydroinform 15(2):516–528. https://doi.org/10.2166/hydro.2012.175
Ghazanfari-Hashemi S, Etemad-Shahidi A, Kazeminezhad MH, Mansoori AR (2011) Prediction of pile group scour in waves using support vector machines and ANN. J Hydroinform 13(4):609–620. https://doi.org/10.2166/hydro.2010.107
Guven A, Gunal M (2008) Genetic programming approach for prediction of local scour downstream of hydraulic structures. J Irrig Drain Eng 134(2):241–249. https://doi.org/10.1061/(ASCE)0733-9437(2008)134:2(241)
Haghiabi AH (2016) Prediction of river pipeline scour depth using multivariate adaptive regression splines. J Pipeline Syst Eng Pract 8(1):04016015. https://doi.org/10.1061/(ASCE)PS.1949-1204.0000248
Homaei F, Najafzadeh M (2020) A reliability-based probabilistic evaluation of the wave-induced scour depth around marine structure piles. Ocean Eng 196:106818. https://doi.org/10.1016/j.oceaneng.2019.106818
Kaveh A, Bakhshpoori T, Hamze-Ziabari SM (2017) New model derivation for the bond behavior of NSM FRP systems in concrete. Iran J Sci Technol Trans Civ Eng 41(3):249–262. https://doi.org/10.1007/s40996-017-0058-z
Khan M, Tufail M, Azamathulla HM, Ahmad I, Muhammad N (2018) Genetic functions-based modelling for pier scour depth prediction in coarse bed streams. In: Proceedings of the institution of civil engineers-water management, vol 171, no 5. Thomas Telford Ltd, pp 225–240. https://doi.org/10.1680/jwama.15.00075
Mahjoobi J, Sabzianpoor A, Jabbari E (2010) Application of meta-heuristic models for local scour evaluation. In: AIP conference proceedings, vol 1303, no. 1. AIP, pp 389–397. https://doi.org/10.1063/1.3527177
Mesbahi M, Talebbeydokhti N, Hosseini SA, Afzali SH (2016) Gene-expression programming to predict the local scour depth at downstream of stilling basins. Sci Iran Trans A Civ Eng 23(1):102
Mesbahi M, Talebbeydokhti N, Hosseini SA, Afzali SH (2017) External validation criteria and uncertainty analysis of maximum scour depth at downstream of stilling basins based on EPR and MT approaches. Iran J Sci Technol Trans Civ Eng 41(1):87–99. https://doi.org/10.1007/s40996-016-0025-0
Najafzadeh M (2015) Neuro-fuzzy GMDH systems based evolutionary algorithms to predict scour pile groups in clear water conditions. Ocean Eng 99:85–94. https://doi.org/10.1016/j.oceaneng.2015.01.014
Najafzadeh M, Azamathulla HM (2013) Neuro-fuzzy GMDH to predict the scour pile groups due to waves. J Comput Civ Eng 29(5):04014068. https://doi.org/10.1061/(ASCE)CP.1943-5487.0000376
Najafzadeh M, Barani GA (2011) Comparison of group method of data handling based genetic programming and back propagation systems to predict scour depth around bridge piers. Sci Iran 18(6):1207–1213. https://doi.org/10.1016/j.scient.2011.11.017
Najafzadeh M, Saberi-Movahed F (2019) GMDH-GEP to predict free span expansion rates below pipelines under waves. Mar Georesour Geotechnol 37(3):375–392. https://doi.org/10.1080/1064119X.2018.1443355
Najafzadeh M, Barani GA, Kermani MRH (2013a) GMDH based back propagation algorithm to predict abutment scour in cohesive soils. Ocean Eng 59:100–106. https://doi.org/10.1016/j.oceaneng.2012.12.006
Najafzadeh M, Barani GA, Hessami-Kermani MR (2013b) Group method of data handling to predict scour depth around vertical piles under regular waves. Sci Iran 20(3):406–413
Najafzadeh M, Barani GA, Hessami Kermani MR (2014) Estimation of pipeline scour due to waves by GMDH. J Pipeline Syst Eng Pract 5(3):06014002. https://doi.org/10.1061/(ASCE)PS.1949-1204.0000171
Najafzadeh M, Rezaie Balf M, Rashedi E (2016) Prediction of maximum scour depth around piers with debris accumulation using EPR, MT, and GEP models. J Hydroinform 18(5):867–884. https://doi.org/10.2166/hydro.2016.212
Najafzadeh M, Tafarojnoruz A, Lim SY (2017) Prediction of local scour depth downstream of sluice gates using data-driven models. ISH J Hydraul Eng 23(2):195–202. https://doi.org/10.1080/09715010.2017.1286614
Niazkar M, Afzali SH (2019) Developing a new accuracy-improved model for estimating scour depth around piers using a hybrid method. Iran J Sci Technol Trans Civ Eng 43(2):179–189. https://doi.org/10.1007/s40996-018-0129-9
Pahlavani P, Moghadam MPA, Bigdeli B (2019) Car following prediction based on support vector regression and multi-adaptive regression spline by considering instantaneous reaction time. Iran J Sci Technol Trans Civ Eng 43(1):67–79. https://doi.org/10.1007/s40996-018-0141-0
Parsaie A, Azamathulla HM, Haghiabi AH (2017) Physical and numerical modeling of performance of detention dams. J Hydrol. https://doi.org/10.1016/j.jhydrol.2017.01.018
Parsaie A, Haghiabi AH, Saneie M, Torabi H (2018) Prediction of energy dissipation of flow over stepped spillways using data-driven models. Iran J Sci Technol Trans Civ Eng 42(1):39–53. https://doi.org/10.1007/s40996-017-0060-5
Pourzangbar A, Losada MA, Saber A, Ahari LR, Larroudé P, Vaezi M, Brocchini M (2017) Prediction of non-breaking wave induced scour depth at the trunk section of breakwaters using genetic programming and artificial neural networks. Coast Eng 121:107–118. https://doi.org/10.1016/j.coastaleng.2016.12.008
Rezaie-Balf M (2019) multivariate adaptive regression splines model for prediction of local scour depth downstream of an apron under 2D horizontal jets. Iran J Sci Technol Trans Civ Eng 43(1):103–115. https://doi.org/10.1007/s40996-018-0151-y
Rezaie-Balf M, Kim S, Fallah H, Alaghmand S (2019) Daily river flow forecasting using ensemble empirical mode decomposition based heuristic regression models: application on the perennial rivers in Iran and South Korea. J Hydrol 572:470–485. https://doi.org/10.1016/j.jhydrol.2019.03.046
Roy DK, Datta B (2018) Influence of sea level rise on multi objective management of saltwater intrusion in coastal aquifers. J Hydrol Eng 23(8):04018035. https://doi.org/10.1061/(ASCE)HE.1943-5584.0001680
Salmasi F, Sattari MT (2017) Predicting discharge coefficient of rectangular broad-crested Gabion Weir using M5 tree model. Iran J Sci Technol Trans Civ Eng 41(2):205–212. https://doi.org/10.1007/s40996-017-0052-5
Samadi M, Jabbari E (2012) Assessment of regressions trees and multivariate adaptive regression splines for prediction of scour depth below the skijump bucket spillway. J Hydraul 7(3):73–79 (In persian)
Samadi M, Jabbari E, Azamathulla HM (2014) Assessment of M5′ model tree and classification and regression trees for prediction of scour depth below free overfall spillways. Neural Comput Appl 24(2):357–366. https://doi.org/10.1007/s00521-012-1230-9
Samadi M, Jabbari E, Azamathulla HM, Mojallal M (2015) Estimation of scour depth below free overfall spillways using multivariate adaptive regression splines and artificial neural networks. Eng Appl Comput Fluid Mech 9(1):291–300. https://doi.org/10.1080/19942060.2015.1011826
Samui P, Das S, Kim D (2011) Uplift capacity of suction caisson in clay using multivariate adaptive regression spline. Ocean Eng 38(17–18):2123–2127. https://doi.org/10.1016/j.oceaneng.2011.09.036
Santos VM, Wahl T, Long JW, Passeri DL, Plant NG (2019) Combining numerical and statistical models to predict storm-induced dune erosion. J Geophys Res Earth Surf 124(7):1817–1834. https://doi.org/10.1029/2019JF005016
Sharafati A, Yasa R, Azamathulla HM (2018) Assessment of stochastic approaches in prediction of wave-induced pipeline scour depth. J Pipeline Syst Eng Pract 9(4):04018024. https://doi.org/10.1061/(ASCE)PS.1949-1204.0000347
Sumer BM, Fredsøe J (1998) Wave scour around group of vertical piles. J Waterw Port Coast Ocean Eng 124(5):248–256. https://doi.org/10.1061/(ASCE)0733-950X(1998)124:5(248)
Sumer BM, Fredsøe J, Christiansen N (1992) Scour around vertical pile in waves. J Waterw Port Coast Ocean Eng 118(1):15–31. https://doi.org/10.1061/(ASCE)0733-950X(1992)118:1(15)
Sumer BM, Whitehouse RJ, Tørum A (2001) Scour around coastal structures: a summary of recent research. Coast Eng 44(2):153–190. https://doi.org/10.1016/S0378-3839(01)00024-2
Yasa R, Etemad-Shahidi A (2014) Classification and regression trees approach for predicting current-induced scour depth under pipelines. J Offshore Mech Arct Eng 136(1):011702. https://doi.org/10.1115/1.4025654
Zaji AH, Bonakdari H (2019) Velocity field simulation of open-channel junction using artificial intelligence approaches. Iran J Sci Technol Trans Civ Eng 43(1):549–560. https://doi.org/10.1007/s40996-018-0185-1
Zhang W, Goh AT, Zhang Y (2016) Multivariate adaptive regression splines application for multivariate geotechnical problems with big data. Geotech Geol Eng 34(1):193–204. https://doi.org/10.1007/s10706-015-9938-9
Zounemat-Kermani M, Beheshti AA, Ataie-Ashtiani B, Sabbagh-Yazdi SR (2009) Estimation of current-induced scour depth around pile groups using neural network and adaptive neuro-fuzzy inference system. Appl Soft Comput 9(2):746–755. https://doi.org/10.1016/j.asoc.2008.09.006
Acknowledgements
The first author expresses special thanks to Mrs. Touran Amini for her enormous effort and support of the first author. The first author would like to thank Mr. Mohammad Mojallal for the review of this manuscript. The authors are grateful to Mr. Navid Ghaemi for his help in the preparation of the original datasets.
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Samadi, M., Afshar, M.H., Jabbari, E. et al. Application of Multivariate Adaptive Regression Splines and Classification and Regression Trees to Estimate Wave-Induced Scour Depth Around Pile Groups. Iran J Sci Technol Trans Civ Eng 44 (Suppl 1), 447–459 (2020). https://doi.org/10.1007/s40996-020-00364-2
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DOI: https://doi.org/10.1007/s40996-020-00364-2