# 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 |

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**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