# A Hybrid Intelligence Approach to Enhance the Prediction Accuracy of Local Scour Depth at Complex Bridge Piers

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## Abstract

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## 1. Introduction

_{s}), a few empirical methods have been proposed including the FHWA design methodology, Hydraulic Engineering Circular No. 18. (HEC-18) [9], the Florida Department of Transportation (FDOT) bridge mechanisms scour manual [2,10,11]. In addition, a procedure was proposed by Amini and Mohammad [7] which, based on field data, gives reasonable estimates of the scour depth at CPs [12]. For calculations of scour depth, the HEC-18 and FDOT methods apply a superposition procedure to combine the effect of each element of CPs. However, the methods presented by Lee and Hong [1], Amini et al. [6], and Arneson et al. [9] provided relations for an equivalent width (b

_{e}) for that around a CP to be used in simple pier equations where b

_{e}is the diameter of a circular simple pier that produces scour depth equal to the CP, for the same sediment and flow conditions. Apart from HEC-18 and FDOT methods, Mueller and Wagner [13] used field data to examine the efficacy of 20 bridge pier scour depth estimation methods and found that these methods predict the scour depth inaccurately with a large number of overestimations.

## 2. Methodology

#### 2.1. Data Acquisition

_{50}, flow depth, h, and contraction effects on LSCP became insignificant. The flow intensity, U/U

_{c}, was selected so that in all tests the clear water condition was maintained, where U is mean velocity of the approach flow and U

_{c}is critical mean velocity for sediment motion.

#### 2.2. Dimensional Analysis

_{s}, most of the empirical methods use of dimensional analysis, a functional relationship, based on an equivalent pier width, be, at CPs, from an existing equation for single piers [7,9,10,11]. The b

_{e}is defined as the diameter of a simple pile for the same flow and sediment characteristics that would produce the same scour depth as the CPs. Depending on the pile cap location (Y) with respect to the undisturbed streambed, y

_{s}or b

_{e}is a function of flow and sediment properties and CPs’ geometries. Therefore, a functional relationship for presenting LSCP may be written as Equation (1) using dimensional analysis:

_{c}is the column width; b

_{pc}is the pile cap width; h is flow depth, d

_{50}is median particle size of the bed sediment, U

_{c}is critical value of U associated with initiation of motion of bed sediments, Fr is Froude number, T is the thickness of the pile cap; L

_{u}and L

_{f}are extensions of the pile cap upstream of and sides of the column; k

_{sc}and k

_{spc}are the shape factors for the column and pile cap; b

_{pg}is the pile diameter; m and n are the number of piles in line and normal with the flow; S

_{l}and S

_{b}are the pile spacing in line and normal with the flow, and Y is pile cap elevation with respect to the undisturbed streambed. A schematic drawing for flow-induced scour around a CP and the corresponding parameters are shown in Figure 1.

#### 2.3. Empirical Equations

_{scol}is scour of column, y

_{spc}is the scour of pile cap, and y

_{spg}is the scour of pile group. The FDOT method calculates the equivalents single cylindrical pier that would produce the same scour depth as that complex pier component. Then, the equivalent diameter of the CPs is calculated by adding the equivalent diameters of the CP components and expressed as Equation (3):

_{se}, D

_{ecol}, D

_{epc}, and D

_{epg}are equivalent diameters of the CPs, column, pile cap, and pile group, respectively. Finally, the scour depth at CPs can be calculated using the methods presented for scouring calculation at simple piers.

#### 2.4. Machine Learning Algorithms

#### 2.4.1. Artificial Neural Networks

#### 2.4.2. M5P Model Tree

_{1}, S

_{2}, …, S

_{n}as the sets that result from splitting of the node according to the chosen attribute [64].

#### 2.4.3. Support Vector Machine

#### 2.4.4. REP Tree

_{i}: i = 1, 2, …, n in consecutive pruning stages. Since complex decision-trees could lead to over-fitting and the reduced-interpretability of a model, REP helps in decreasing the complexity, by removing leaves and branches of the DT structure [17,71,73,74].

#### 2.4.5. Random Subspace Ensemble Algorithm

#### 2.5. Evaluation and Comparison

#### 2.5.1. Statistical Metrics

#### 2.5.2. Non-Parametric Statistical Tests

#### 2.6. Sensitivity Analysis

## 3. Results and Analysis

#### 3.1. Optimal Selection of Modeling Parameters

#### 3.2. Model Validation and Comparison

#### 3.3. Sensitivity Analysis

_{pc}). The rest factors have slight effect for modeling process by the proposed ensemble model (Figure 9).

## 4. Discussion

## 5. Conclusions

- The machine learning algorithms have the powerful capability to predict LSCP and the hybrid models can improve the performance of separate models in predicting LSCP.
- Computing benchmark algorithms presented in this research have the potential to alter the LSCP prediction in comparison with the most well-known empirical methods, namely HEC-18 and FDOT methods.
- The state-of-the-art RS-REPTree ensemble model, with the highest accuracy of the REPTree, is proposed as a classifier for the prediction of the LSCP.
- The pile cap location (Y) was a more sensitive factor for LSCP among other factors based on the availability of data.

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

RMSE | Root Mean Squared Error |

LSCP | Local Scour Depth at Complex Piers |

RS | Random Subspace |

ANN | Artificial Neural Network |

R | Correlation Coefficient |

d_{50} | Median Sediment Size |

Y_{s} | Scour Depth |

h | Water Depth |

b_{c} | Column Width |

lc | Column Length |

b_{pc} | Pile Cap Width |

l_{pc} | Pile Cap Length |

T | Pile Cap Thickness |

Lu | Extension length of pile cap out from the column face |

Lf | Extension width of pile cap out from the column |

k_{sc} | Shape factor for the column |

k_{spc} | Shape factor for the pile cap |

b_{pg} | Pile diameter |

F_{r} | Froude number |

m | Number of piles in line with the flow |

n | Number of piles normal with the flow |

S_{l} | Pile spacing in line with the flow |

S_{b} | Pile spacing normal with the flow |

Y | Pile cap elevation in respect to undisturbed streamflow |

b_{e} | Equivalent width/diameter |

y_{scol} | Column’s scour |

y_{spc} | Pile cap’s scour |

y_{spg} | Scour of pile group |

D_{se} | Equivalent diameters of the complex pier |

D_{ecol} | Equivalent diameters of the column |

D_{epc} | Equivalent diameters of the pile cap |

D_{epg} | Equivalent diameters of the pile group |

X | Training dataset |

S | Subset of training dataset |

U_{c} | Critical velocity for the beginning of sediment motion |

U | Mean approach flow velocity |

## References

- Lee, S.O.; Hong, S.H. Turbulence Characteristics before and after Scour Upstream of a Scaled-Down Bridge Pier Model. Water
**2019**, 11, 1900. [Google Scholar] [CrossRef][Green Version] - Melville, B.W.; Coleman, S.E. Bridge Scour; Water Resources Publication: Littleton, CO, USA, 2000. [Google Scholar]
- Ghodsi, H.; Khanjani, M.; Beheshti, A. Evaluation of harmony search optimization to predict local scour depth around complex bridge piers. Civ. Eng. J.
**2018**, 4, 402–412. [Google Scholar] [CrossRef][Green Version] - Ghazvinei, P.T.; Mohamed, T.A.; Ghazali, A.H.; Huat, B.K. Scour hazard assessment and bridge abutment instability analysis. Electron. J. Geotech. Eng.
**2012**, 17, 2213–2224. [Google Scholar] - Wardhana, K.; Hadipriono, F.C. Analysis of recent bridge failures in the United States. J. Perform. Constr. Facil.
**2003**, 17, 144–150. [Google Scholar] [CrossRef][Green Version] - Amini, A.; Melville, B.W.; Ali, T.M. Local scour at piled bridge piers including an examination of the superposition method. Can. J. Civ. Eng.
**2014**, 41, 461–471. [Google Scholar] [CrossRef] - Amini, A.; Mohammad, T.A. Local scour prediction around piers with complex geometry. Mar. Georesour. Geotechnol.
**2017**, 35, 857–864. [Google Scholar] [CrossRef] - Baghbadorani, D.A.; Ataie-Ashtiani, B.; Beheshti, A.; Hadjzaman, M.; Jamali, M. Prediction of current-induced local scour around complex piers: Review, revisit, and integration. Coast. Eng.
**2018**, 133, 43–58. [Google Scholar] [CrossRef] - Arneson, L.; Zevenbergen, L.; Lagasse, P.; Clopper, P. Evaluating Scour at Bridges; U.S. Department of TransportationFederal Highway Administration: Washington, DC, USA, 2012.
- Coleman, S.E. Clearwater local scour at complex piers. J. Hydraul. Eng.
**2005**, 131, 330–334. [Google Scholar] [CrossRef] - Sheppard, D.; Renna, R. Bridge Scour Manual; Florida Department of Transportation: Tallahassee, FL, USA, 2005. [Google Scholar]
- Jannaty, M.; Eghbalzadeh, A.; Hosseini, S. Using field data to evaluate the complex bridge piers scour methods. Can. J. Civ. Eng.
**2015**, 43, 218–225. [Google Scholar] [CrossRef] - Mueller, D.S.; Wagner, C.R. Field Observations and Evaluations of Streambed Scour at Bridges; U.S. Department of TransportationFederal Highway Administration: Washington, DC, USA, 2005.
- Chen, W.; Xie, X.; Wang, J.; Pradhan, B.; Hong, H.; Bui, D.T.; Duan, Z.; Ma, J. A comparative study of logistic model tree, random forest, and classification and regression tree models for spatial prediction of landslide susceptibility. Catena
**2017**, 151, 147–160. [Google Scholar] [CrossRef][Green Version] - Thai Pham, B.; Prakash, I.; Dou, J.; Singh, S.K.; Trinh, P.T.; Trung Tran, H.; Minh Le, T.; Tran, V.P.; Kim Khoi, D.; Shirzadi, A. A novel hybrid approach of landslide susceptibility modeling using rotation forest ensemble and different base classifiers. Geocarto Int.
**2018**, 14, 1–38. [Google Scholar] - Shafizadeh-Moghadam, H.; Valavi, R.; Shahabi, H.; Chapi, K.; Shirzadi, A. Novel forecasting approaches using combination of machine learning and statistical models for flood susceptibility mapping. J. Environ. Manag.
**2018**, 217, 1–11. [Google Scholar] [CrossRef] [PubMed][Green Version] - Pham, B.T.; Prakash, I.; Singh, S.K.; Shirzadi, A.; Shahabi, H.; Bui, D.T. Landslide susceptibility modeling using Reduced Error Pruning Trees and different ensemble techniques: Hybrid machine learning approaches. Catena
**2019**, 175, 203–218. [Google Scholar] [CrossRef] - Wang, Y.; Hong, H.; Chen, W.; Li, S.; Panahi, M.; Khosravi, K.; Shirzadi, A.; Shahabi, H.; Panahi, S.; Costache, R. Flood susceptibility mapping in dingnan county (China) using adaptive neuro-fuzzy inference system with biogeography based optimization and imperialistic competitive algorithm. J. Environ. Manag.
**2019**, 247, 712–729. [Google Scholar] [CrossRef] [PubMed] - Ahmadlou, M.; Karimi, M.; Alizadeh, S.; Shirzadi, A.; Parvinnejhad, D.; Shahabi, H.; Panahi, M. Flood susceptibility assessment using integration of adaptive network-based fuzzy inference system (ANFIS) and biogeography-based optimization (BBO) and BAT algorithms (BA). Geocarto Int.
**2019**, 34, 1252–1272. [Google Scholar] [CrossRef] - Khosravi, K.; Shahabi, H.; Pham, B.T.; Adamowski, J.; Shirzadi, A.; Pradhan, B.; Dou, J.; Ly, H.-B.; Gróf, G.; Ho, H.L. A comparative assessment of flood susceptibility modeling using Multi-Criteria Decision-Making Analysis and Machine Learning Methods. J. Hydrol.
**2019**, 573, 311–323. [Google Scholar] [CrossRef] - Chen, W.; Hong, H.; Li, S.; Shahabi, H.; Wang, Y.; Wang, X.; Ahmad, B.B. Flood susceptibility modelling using novel hybrid approach of reduced-error pruning trees with bagging and random subspace ensembles. J. Hydrol.
**2019**, 575, 864–873. [Google Scholar] [CrossRef] - Tien Bui, D.; Khosravi, K.; Shahabi, H.; Daggupati, P.; Adamowski, J.F.; M Melesse, A.; Thai Pham, B.; Pourghasemi, H.R.; Mahmoudi, M.; Bahrami, S. Flood spatial modeling in northern Iran using remote sensing and gis: A comparison between evidential belief functions and its ensemble with a multivariate logistic regression model. Remote Sens.
**2019**, 11, 1589. [Google Scholar] [CrossRef][Green Version] - Bui, D.T.; Panahi, M.; Shahabi, H.; Singh, V.P.; Shirzadi, A.; Chapi, K.; Khosravi, K.; Chen, W.; Panahi, S.; Li, S. Novel hybrid evolutionary algorithms for spatial prediction of floods. Sci. Rep.
**2018**, 8, 15364. [Google Scholar] [CrossRef][Green Version] - Tien Bui, D.; Khosravi, K.; Li, S.; Shahabi, H.; Panahi, M.; Singh, V.; Chapi, K.; Shirzadi, A.; Panahi, S.; Chen, W. New hybrids of anfis with several optimization algorithms for flood susceptibility modeling. Water
**2018**, 10, 1210. [Google Scholar] [CrossRef][Green Version] - Chen, W.; Pradhan, B.; Li, S.; Shahabi, H.; Rizeei, H.M.; Hou, E.; Wang, S. Novel hybrid integration approach of bagging-based fisher’s linear discriminant function for groundwater potential analysis. Nat. Resour. Res.
**2019**, 28, 1–20. [Google Scholar] [CrossRef][Green Version] - Miraki, S.; Zanganeh, S.H.; Chapi, K.; Singh, V.P.; Shirzadi, A.; Shahabi, H.; Pham, B.T. Mapping groundwater potential using a novel hybrid intelligence approach. Water Resour. Manag.
**2019**, 33, 281–302. [Google Scholar] [CrossRef] - Rahmati, O.; Naghibi, S.A.; Shahabi, H.; Bui, D.T.; Pradhan, B.; Azareh, A.; Rafiei-Sardooi, E.; Samani, A.N.; Melesse, A.M. Groundwater spring potential modelling: Comprising the capability and robustness of three different modeling approaches. J. Hydrol.
**2018**, 565, 248–261. [Google Scholar] [CrossRef] - Rahmati, O.; Choubin, B.; Fathabadi, A.; Coulon, F.; Soltani, E.; Shahabi, H.; Mollaefar, E.; Tiefenbacher, J.; Cipullo, S.; Ahmad, B.B. Predicting uncertainty of machine learning models for modelling nitrate pollution of groundwater using quantile regression and uneec methods. Sci. Total Environ.
**2019**, 688, 855–866. [Google Scholar] [CrossRef] [PubMed] - Chen, W.; Li, Y.; Xue, W.; Shahabi, H.; Li, S.; Hong, H.; Wang, X.; Bian, H.; Zhang, S.; Pradhan, B. Modeling flood susceptibility using data-driven approaches of naïve Bayes tree, alternating decision tree, and random forest methods. Sci. Total Environ.
**2020**, 701, 134979. [Google Scholar] [CrossRef] - Khosravi, K.; Melesse, A.M.; Shahabi, H.; Shirzadi, A.; Chapi, K.; Hong, H. Flood susceptibility mapping at Ningdu catchment, China using bivariate and data mining techniques. In Extreme Hydrology and Climate Variability; Elsevier: Amsterdam, The Netherlands, 2019; pp. 419–434. [Google Scholar]
- He, Q.; Shahabi, H.; Shirzadi, A.; Li, S.; Chen, W.; Wang, N.; Chai, H.; Bian, H.; Ma, J.; Chen, Y. Landslide spatial modelling using novel bivariate statistical based Naïve Bayes, RBF Classifier, and RBF Network machine learning algorithms. Sci. Total Environ.
**2019**, 663, 1–15. [Google Scholar] [CrossRef] - Tien Bui, D.; Shirzadi, A.; Shahabi, H.; Chapi, K.; Omidavr, E.; Pham, B.T.; Talebpour Asl, D.; Khaledian, H.; Pradhan, B.; Panahi, M. A Novel Ensemble Artificial Intelligence Approach for Gully Erosion Mapping in a Semi-Arid Watershed (Iran). Sensors
**2019**, 19, 2444. [Google Scholar] [CrossRef][Green Version] - Tien Bui, D.; Shahabi, H.; Omidvar, E.; Shirzadi, A.; Geertsema, M.; Clague, J.J.; Khosravi, K.; Pradhan, B.; Pham, B.T.; Chapi, K. Shallow landslide prediction using a novel hybrid functional machine learning algorithm. Remote Sens.
**2019**, 11, 931. [Google Scholar] [CrossRef][Green Version] - Tien Bui, D.; Shirzadi, A.; Chapi, K.; Shahabi, H.; Pradhan, B.; Pham, B.T.; Singh, V.P.; Chen, W.; Khosravi, K.; Bin Ahmad, B. A Hybrid Computational Intelligence Approach to Groundwater Spring Potential Mapping. Water
**2019**, 11, 2013. [Google Scholar] [CrossRef][Green Version] - Tien Bui, D.; Shahabi, H.; Shirzadi, A.; Chapi, K.; Hoang, N.-D.; Pham, B.; Bui, Q.-T.; Tran, C.-T.; Panahi, M.; Bin Ahamd, B. A novel integrated approach of relevance vector machine optimized by imperialist competitive algorithm for spatial modeling of shallow landslides. Remote Sens.
**2018**, 10, 1538. [Google Scholar] [CrossRef][Green Version] - Chen, W.; Peng, J.; Hong, H.; Shahabi, H.; Pradhan, B.; Liu, J.; Zhu, A.-X.; Pei, X.; Duan, Z. Landslide susceptibility modelling using GIS-based machine learning techniques for Chongren County, Jiangxi Province, China. Sci. Total Environ.
**2018**, 626, 1121–1135. [Google Scholar] [CrossRef] [PubMed] - Granata, F.; de Marinis, G. Machine learning methods for wastewater hydraulics. Flow Meas. Instrum.
**2017**, 57, 1–9. [Google Scholar] [CrossRef] - Parasuraman, K.; Elshorbagy, A.; Si, B.C. Estimating saturated hydraulic conductivity in spatially variable fields using neural network ensembles. Soil Sci. Soc. Am. J.
**2006**, 70, 1851–1859. [Google Scholar] [CrossRef][Green Version] - Pham, B.T.; Hoang, T.-A.; Nguyen, D.-M.; Bui, D.T. Prediction of shear strength of soft soil using machine learning methods. Catena
**2018**, 166, 181–191. [Google Scholar] [CrossRef] - Prasad, R.; Deo, R.C.; Li, Y.; Maraseni, T. Soil moisture forecasting by a hybrid machine learning technique: ELM integrated with ensemble empirical mode decomposition. Geoderma
**2018**, 330, 136–161. [Google Scholar] [CrossRef] - Kazemi, S.; Minaei Bidgoli, B.; Shamshirband, S.; Karimi, S.M.; Ghorbani, M.A.; Chau, K.-W.; Kazem Pour, R. Novel genetic-based negative correlation learning for estimating soil temperature. Eng. Appl. Comput. Fluid Mech.
**2018**, 12, 506–516. [Google Scholar] [CrossRef][Green Version] - Chen, W.; Shahabi, H.; Shirzadi, A.; Hong, H.; Akgun, A.; Tian, Y.; Liu, J.; Zhu, A.-X.; Li, S. Novel hybrid artificial intelligence approach of bivariate statistical-methods-based kernel logistic regression classifier for landslide susceptibility modeling. Bull. Eng. Geol. Environ.
**2019**, 78, 4397–4419. [Google Scholar] [CrossRef] - Jaafari, A.; Zenner, E.K.; Panahi, M.; Shahabi, H. Hybrid artificial intelligence models based on a neuro-fuzzy system and metaheuristic optimization algorithms for spatial prediction of wildfire probability. Agric. For. Meteorol.
**2019**, 266, 198–207. [Google Scholar] [CrossRef] - Alizadeh, M.; Alizadeh, E.; Asadollahpour Kotenaee, S.; Shahabi, H.; Beiranvand Pour, A.; Panahi, M.; Bin Ahmad, B.; Saro, L. Social vulnerability assessment using artificial neural network (ANN) model for earthquake hazard in Tabriz city, Iran. Sustainability
**2018**, 10, 3376. [Google Scholar] [CrossRef][Green Version] - Chen, W.; Shirzadi, A.; Shahabi, H.; Ahmad, B.B.; Zhang, S.; Hong, H.; Zhang, N. A novel hybrid artificial intelligence approach based on the rotation forest ensemble and naïve Bayes tree classifiers for a landslide susceptibility assessment in Langao County, China. Geomat. Nat. Hazards Risk
**2017**, 8, 1955–1977. [Google Scholar] [CrossRef][Green Version] - Cheng, M.-Y.; Cao, M.-T. Hybrid intelligent inference model for enhancing prediction accuracy of scour depth around bridge piers. Struct. Infrastruct. Eng.
**2015**, 11, 1178–1189. [Google Scholar] [CrossRef] - Najafzadeh, M.; Barani, G.-A.; Azamathulla, H.M. GMDH to predict scour depth around a pier in cohesive soils. Appl. Ocean. Res.
**2013**, 40, 35–41. [Google Scholar] [CrossRef] - Zounemat-Kermani, M.; Beheshti, A.-A.; Ataie-Ashtiani, B.; Sabbagh-Yazdi, S.-R. Estimation of current-induced scour depth around pile groups using neural network and adaptive neuro-fuzzy inference system. Appl. Soft Comput.
**2009**, 9, 746–755. [Google Scholar] [CrossRef] - Hosseini, R.; Fazloula, R.; Saneie, M.; Amini, A. Bagged neural network for estimating the scour depth around pile groups. Int. J. River Basin Manag.
**2018**, 16, 401–412. [Google Scholar] [CrossRef] - Amini, A.; Ali, T.M.; Ghazali, A.H.; Aziz, A.A.; Akib, S.M. Impacts of land-use change on streamflows in the Damansara Watershed, Malaysia. Arab. J. Sci. Eng.
**2011**, 36, 713–720. [Google Scholar] [CrossRef] - Amini, A.; Mohammad, T.A.; Aziz, A.A.; Ghazali, A.H.; Huat, B.B. A local scour prediction method for pile caps in complex piers. In Proceedings of the Institution of Civil Engineers-Water Management; ICE: Washington, DC, USA, 2019; pp. 73–80. [Google Scholar]
- Ataie-Ashtiani, B.; Baratian-Ghorghi, Z.; Beheshti, A. Experimental investigation of clear-water local scour of compound piers. J. Hydraul. Eng.
**2010**, 136, 343–351. [Google Scholar] [CrossRef] - Rumelhart, D.E.; McClelland, J.L. Parallel Distributed Processing: Explorations in the Microstructure of Cognition, Volume 1. Foundations; MIT Press: Cambridge, MA, USA, 1986. [Google Scholar]
- Haykin, S. Support vector machines. Neural Netw. A Compr. Found.
**1999**, 12, 318–350. [Google Scholar] - Dreiseitl, S.; Ohno-Machado, L. Logistic regression and artificial neural network classification models: A methodology review. J. Biomed. Inform.
**2002**, 35, 352–359. [Google Scholar] [CrossRef][Green Version] - Tian, Y.; Xu, C.; Hong, H.; Zhou, Q.; Wang, D. Mapping earthquake-triggered landslide susceptibility by use of artificial neural network (ANN) models: An example of the 2013 Minxian (China) Mw 5.9 event. Geomat. Nat. Hazards Risk
**2019**, 10, 1–25. [Google Scholar] [CrossRef][Green Version] - Shirzadi, A.; Shahabi, H.; Chapi, K.; Bui, D.T.; Pham, B.T.; Shahedi, K.; Ahmad, B.B. A comparative study between popular statistical and machine learning methods for simulating volume of landslides. Catena
**2017**, 157, 213–226. [Google Scholar] [CrossRef] - Bateni, S.M.; Borghei, S.; Jeng, D.-S. Neural network and neuro-fuzzy assessments for scour depth around bridge piers. Eng. Appl. Artif. Intell.
**2007**, 20, 401–414. [Google Scholar] [CrossRef] - Kia, M.B.; Pirasteh, S.; Pradhan, B.; Mahmud, A.R.; Sulaiman, W.N.A.; Moradi, A. An artificial neural network model for flood simulation using GIS: Johor River Basin, Malaysia. Environ. Earth Sci.
**2012**, 67, 251–264. [Google Scholar] [CrossRef] - Kaya, A. Artificial neural network study of observed pattern of scour depth around bridge piers. Comput. Geotech.
**2010**, 37, 413–418. [Google Scholar] [CrossRef] - Choi, S.U.; Cheong, S. Prediction of local scour around bridge piers using artificial neural networks 1. J. Am. Water Resour. Assoc.
**2006**, 42, 487–494. [Google Scholar] [CrossRef] - Pal, M.; Singh, N.; Tiwari, N. Support vector regression based modeling of pier scour using field data. Eng. Appl. Artif. Intell.
**2011**, 24, 911–916. [Google Scholar] [CrossRef] - Quinlan, J.R. Learning with continuous classes. In Proceedings of the 5th Australian Joint Conference on Artificial Intelligence, Hobart, Tasmania, 16–18 November 1992; pp. 343–348. [Google Scholar]
- Balouchi, B.; Nikoo, M.R.; Adamowski, J. Development of expert systems for the prediction of scour depth under live-bed conditions at river confluences: Application of different types of ANNs and the M5P model tree. Appl. Soft Comput.
**2015**, 34, 51–59. [Google Scholar] [CrossRef] - Etemad-Shahidi, A.; Mahjoobi, J. Comparison between M5′ model tree and neural networks for prediction of significant wave height in Lake Superior. Ocean Eng.
**2009**, 36, 1175–1181. [Google Scholar] [CrossRef] - Solomatine, D.P.; Siek, M.B.L. Flexible and optimal M5 model trees with applications to flow predictions. In Hydroinformatics: (In 2 Volumes, with CD-ROM); World Scientific: Singapore, 2004; pp. 1719–1726. [Google Scholar]
- Bhattacharya, B.; Solomatine, D.P. Neural networks and M5 model trees in modelling water level–discharge relationship. Neurocomputing
**2005**, 63, 381–396. [Google Scholar] [CrossRef] - Vapnik, V. The Nature of Statistical Learning Theory; Jordan, M., Lauritzen, S.L., Lawless, J.L., Nair, V., Eds.; Springer: NewYork, NY, USA, 1995. [Google Scholar]
- Micheletti, N.; Foresti, L.; Robert, S.; Leuenberger, M.; Pedrazzini, A.; Jaboyedoff, M.; Kanevski, M. Machine learning feature selection methods for landslide susceptibility mapping. Math. Geosci.
**2014**, 46, 33–57. [Google Scholar] [CrossRef][Green Version] - Vapnik, V. Pattern recognition using generalized portrait method. Autom. Remote Control
**1963**, 24, 774–780. [Google Scholar] - Quinlan, J.R. Simplifying decision trees. Int. J. Man-Mach. Stud.
**1987**, 27, 221–234. [Google Scholar] [CrossRef][Green Version] - Khosravi, K.; Pham, B.T.; Chapi, K.; Shirzadi, A.; Shahabi, H.; Revhaug, I.; Prakash, I.; Bui, D.T. A comparative assessment of decision trees algorithms for flash flood susceptibility modeling at Haraz watershed, northern Iran. Sci. Total Environ.
**2018**, 627, 744–755. [Google Scholar] [CrossRef] - Mohamed, W.N.H.W.; Salleh, M.N.M.; Omar, A.H. A comparative study of reduced error pruning method in decision tree algorithms. In Proceedings of the Control System, Computing and Engineering (ICCSCE), 2012 IEEE International Conference on, Penang, Malaysian, 23 November 2012; pp. 392–397. [Google Scholar]
- Galathiya, A.; Ganatra, A.; Bhensdadia, C. Improved decision tree induction algorithm with feature selection, cross validation, model complexity and reduced error pruning. Int. J. Comput. Sci. Inf. Technol.
**2012**, 3, 3427–3431. [Google Scholar] - Ho, T.K. The random subspace method for constructing decision forests. IEEE Trans. Pattern Anal. Mach. Intell.
**1998**, 20, 832–844. [Google Scholar] - Skurichina, M.; Duin, R.P. Bagging, boosting and the random subspace method for linear classifiers. Pattern Anal. Appl.
**2002**, 5, 121–135. [Google Scholar] [CrossRef] - Shirzadi, A.; Bui, D.T.; Pham, B.T.; Solaimani, K.; Chapi, K.; Kavian, A.; Shahabi, H.; Revhaug, I. Shallow landslide susceptibility assessment using a novel hybrid intelligence approach. Environ. Earth Sci.
**2017**, 76, 60. [Google Scholar] [CrossRef] - Chai, T.; Draxler, R.R. Root mean square error (RMSE) or mean absolute error (MAE)?–Arguments against avoiding RMSE in the literature. Geosci. Model. Dev.
**2014**, 7, 1247–1250. [Google Scholar] [CrossRef][Green Version] - Willmott, C.J.; Matsuura, K. Advantages of the mean absolute error (MAE) over the root mean square error (RMSE) in assessing average model performance. Clim. Res.
**2005**, 30, 79–82. [Google Scholar] [CrossRef] - Veerasamy, R.; Rajak, H.; Jain, A.; Sivadasan, S.; Varghese, C.P.; Agrawal, R.K. Validation of QSAR models-strategies and importance. Int. J. Drug Des. Discov.
**2011**, 3, 511–519. [Google Scholar] - Bonadonna, C.; Costa, A. Estimating the volume of tephra deposits: A new simple strategy. Geology
**2012**, 40, 415–418. [Google Scholar] [CrossRef] - Taylor, K.E. Summarizing multiple aspects of model performance in a single diagram. J. Geophys. Res. Atmos.
**2001**, 106, 7183–7192. [Google Scholar] [CrossRef] - Sigaroodi, S.K.; Chen, Q.; Ebrahimi, S.; Nazari, A.; Choobin, B. Long-term precipitation forecast for drought relief using atmospheric circulation factors: A study on the Maharloo Basin in Iran. Hydrol. Earth Syst. Sci.
**2014**, 18, 1995–2006. [Google Scholar] [CrossRef][Green Version] - Barnston, A.G. Correspondence among the correlation, RMSE, and Heidke forecast verification measures; refinement of the Heidke score. Weather Forecast.
**1992**, 7, 699–709. [Google Scholar] [CrossRef][Green Version] - Chapi, K.; Singh, V.P.; Shirzadi, A.; Shahabi, H.; Bui, D.T.; Pham, B.T.; Khosravi, K. A novel hybrid artificial intelligence approach for flood susceptibility assessment. Environ. Model. Softw.
**2017**, 95, 229–245. [Google Scholar] [CrossRef] - Najafzadeh, M.; Rezaie Balf, M.; Rashedi, E. Prediction of maximum scour depth around piers with debris accumulation using EPR, MT, and GEP models. J. Hydroinform.
**2016**, 18, 867–884. [Google Scholar] [CrossRef] - Beasley, T.M.; Zumbo, B.D. Comparison of aligned Friedman rank and parametric methods for testing interactions in split-plot designs. Comput. Stat. Data Anal.
**2003**, 42, 569–593. [Google Scholar] [CrossRef] - Lee, S.O.; Hong, S.H. Reproducing Field Measurements Using Scaled-Down Hydraulic Model Studies in a Laboratory. Adv. Civ. Eng.
**2018**, 2018, 1–11. [Google Scholar] [CrossRef][Green Version] - Moreno, M.; Maia, R.; Couto, L. Effects of relative column width and pile-cap elevation on local scour depth around complex piers. J. Hydraul. Eng.
**2015**, 142, 04015051. [Google Scholar] [CrossRef] - Ferraro, D.; Tafarojnoruz, A.; Gaudio, R.; Cardoso, A.H. Effects of pile cap thickness on the maximum scour depth at a complex pier. J. Hydraul. Eng.
**2013**, 139, 482–491. [Google Scholar] [CrossRef] - Amini, A.; Solaimani, N. The effects of uniform and nonuniform pile spacing variations on local scour at pile groups. Mar. Georesour. Geotechnol.
**2018**, 36, 861–866. [Google Scholar] [CrossRef] - Shirzadi, A.; Soliamani, K.; Habibnejhad, M.; Kavian, A.; Chapi, K.; Shahabi, H.; Chen, W.; Khosravi, K.; Thai Pham, B.; Pradhan, B. Novel GIS based machine learning algorithms for shallow landslide susceptibility mapping. Sensors
**2018**, 18, 3777. [Google Scholar] [CrossRef] [PubMed] - Shirzadi, A.; Solaimani, K.; Roshan, M.H.; Kavian, A.; Chapi, K.; Shahabi, H.; Keesstra, S.; Ahmad, B.B.; Bui, D.T. Uncertainties of prediction accuracy in shallow landslide modeling: Sample size and raster resolution. Catena
**2019**, 178, 172–188. [Google Scholar] [CrossRef]

**Figure 1.**The various components of the composite pier and the corresponding parameters; (

**a**) Upstream view, (

**b**) Side view, and (

**c**) Plan view.

**Figure 4.**Determination of the number of optimal values of iteration and seed in the modeling process based on the RMSE and R; (

**a**) number of seed by RMSE, (

**b**) number of iteration using RMSE, (

**c**) number of iteration using R and (

**d**) number of seed using R.

**Figure 5.**Comparison between actual and predicted scour depth using training dataset; (

**a**) FDOT model, (

**c**) HEC-18, (

**e**) ANNMLP, (

**g**) M5P, (

**i**) SVM, (

**k**) REPTree, (

**m**) RS-REPTree, and Testing dataset; (

**b**) FDOT, (

**d**) HEC-18, (

**f**) ANNMLP, (

**h**) M5P, (

**j**) SVM, (

**l**) REPTree and (

**n**) RS-REPTree.

**Figure 6.**Analysis of correlation between actual and predicted values of LSCP (m) for empirical models and machine learning algorithms.

**Figure 7.**Taylor diagram for displaying the correlation between the observed and predicted LSCP by different machine learning models.

**Figure 9.**Sensitivity analysis graphically based on the proposed ensemble model to predict local scour depth.

Algorithms | Parameters |
---|---|

ANN | Number of hidden layer: 7; learning rate: 0.3; momentue: 0.2; Number of seed: 3; training time: 500; validation threshold: 20; validation set size: default |

M5P | Build regression tree: True; minimum number of instance: 4 |

SVM | C: 0.95; filter type: normalized training data; regOptimizer: RegSMO improved; number of seed: 1; tolerance: 0.001 |

REPTree | Maximum depth: −1; minimum number: 2; minimum variance probability: 0.001; number of fold: 2; number of seed: 1 |

RS-REPTree | Classifier: REPTree; Number of iteration: 10; number of seed: 6; subspace size: 0.5 |

Models | MAE | RMSE | R | |||
---|---|---|---|---|---|---|

Training | Validation | Training | Validation | Training | Validation | |

FDOT | 0.045 | 0.058 | 0.032 | 0.062 | 0.736 | 0.726 |

HEC-18 | 0.053 | 0.051 | 0.067 | 0.064 | 0.625 | 0.620 |

ANN | 0.012 | 0.016 | 0.015 | 0.021 | 0.954 | 0.907 |

M5P | 0.014 | 0.017 | 0.020 | 0.022 | 0.943 | 0.912 |

SVM | 0.015 | 0.016 | 0.020 | 0.024 | 0.924 | 0.918 |

REPTree | 0.013 | 0.018 | 0.021 | 0.025 | 0.931 | 0.885 |

RS-REPTree | 0.013 | 0.014 | 0.019 | 0.018 | 0.946 | 0.945 |

No | Scour Depth Models | Mean Ranks | χ^{2} | Sig. |
---|---|---|---|---|

1 | FDOT | 6.53 | 158.012 | 0.000 |

2 | HEC-18 | 6.49 | ||

3 | ANN | 3.77 | ||

4 | M5P | 3.62 | ||

5 | SVM | 4.18 | ||

6 | REPTree | 3.58 | ||

7 | RS-REPTree | 3.38 |

**Table 4.**Performance of the RS-REPTree model compared to other LSCP models using Wilcoxon signed-rank test (two-tailed).

NO | Pairwise Comparison | NND | NPD | z-Value | p-Value | Significance |
---|---|---|---|---|---|---|

1 | Actual-FDOT | 9 | 65 | −6.608 | 0.000 | Yes |

2 | Actual-HEC18 | 14 | 68 | −6.732 | 0.000 | Yes |

3 | Actual-ANN | 39 | 44 | −0.409 | 0.683 | No |

4 | Actual-M5P | 45 | 39 | −0.085 | 0.932 | No |

5 | Actual-SVM | 37 | 38 | −0.481 | 0.631 | No |

6 | Actual-REPTree | 45 | 39 | −0.112 | 0.911 | No |

7 | Actual-RSREPTree | 41 | 40 | −0.443 | 0.658 | No |

8 | HEC18-FDOT | 40 | 24 | −0.994 | 0.320 | No |

9 | HEC18-ANN | 68 | 14 | −6.619 | 0.000 | Yes |

10 | HEC18-M5P | 74 | 10 | −6.927 | 0.000 | Yes |

11 | HEC18-SVM | 68 | 16 | −6.442 | 0.000 | Yes |

12 | HEC18-REPTree | 70 | 15 | −6.806 | 0.000 | Yes |

13 | HEC18-RSREPTree | 71 | 13 | −6.848 | 0.000 | Yes |

14 | FDOT-ANN | 78 | 10 | −6.799 | 0.000 | Yes |

15 | FDOT-M5P | 73 | 12 | −6.768 | 0.000 | Yes |

16 | FDOT-SVM | 67 | 18 | −6.536 | 0.000 | Yes |

17 | FDOT-REPTree | 78 | 7 | −7.072 | 0.000 | Yes |

18 | FDOT-RSREPTree | 67 | 13 | −6.799 | 0.000 | Yes |

19 | ANN-M5P | 40 | 39 | −0.364 | 0.716 | No |

20 | ANN-SVM | 32 | 50 | −1.371 | 0.170 | No |

21 | ANN-REPTree | 49 | 32 | −0.393 | 0.694 | No |

22 | ANN-RSREPTree | 37 | 47 | −0.116 | 0.908 | No |

23 | M5P-SVM | 36 | 46 | −1.318 | 0.188 | No |

24 | M5P-REPTree | 42 | 36 | −0.416 | 0.677 | No |

25 | M5P-RSREPTree | 35 | 49 | −0.989 | 0.323 | No |

26 | SVM-REPTree | 46 | 39 | −0.734 | 0.463 | No |

27 | SVM-RSREPTree | 47 | 36 | −01.115 | 0.265 | No |

28 | RSREPTree-RSREPTree | 43 | 37 | −0.187 | 0.852 | No |

**NND**: Number of negative differences;

**NPD**: Number of positive differences; “the standard

**p value**is 0.05”.

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Tien Bui, D.; Shirzadi, A.; Amini, A.; Shahabi, H.; Al-Ansari, N.; Hamidi, S.; Singh, S.K.; Thai Pham, B.; Ahmad, B.B.; Ghazvinei, P.T. A Hybrid Intelligence Approach to Enhance the Prediction Accuracy of Local Scour Depth at Complex Bridge Piers. *Sustainability* **2020**, *12*, 1063.
https://doi.org/10.3390/su12031063

**AMA Style**

Tien Bui D, Shirzadi A, Amini A, Shahabi H, Al-Ansari N, Hamidi S, Singh SK, Thai Pham B, Ahmad BB, Ghazvinei PT. A Hybrid Intelligence Approach to Enhance the Prediction Accuracy of Local Scour Depth at Complex Bridge Piers. *Sustainability*. 2020; 12(3):1063.
https://doi.org/10.3390/su12031063

**Chicago/Turabian Style**

Tien Bui, Dieu, Ataollah Shirzadi, Ata Amini, Himan Shahabi, Nadhir Al-Ansari, Shahriar Hamidi, Sushant K. Singh, Binh Thai Pham, Baharin Bin Ahmad, and Pezhman Taherei Ghazvinei. 2020. "A Hybrid Intelligence Approach to Enhance the Prediction Accuracy of Local Scour Depth at Complex Bridge Piers" *Sustainability* 12, no. 3: 1063.
https://doi.org/10.3390/su12031063