Seepage Analysis in Short Embankments Using Developing a Metaheuristic Method Based on Governing Equations
Abstract
:1. Introduction
- (1)
- Investigating different conditions of the seepage rate in the environment;
- (2)
- Implementing the equations governing the seepage rate and different generating models;
- (3)
- Developing neural models;
- (4)
- Presenting new approaches to evaluating the seepage rate as alternative solutions to the equations previously presented in the literature.
2. Research Methodology
2.1. Theory and Data Collection
2.1.1. Dupuit’s Method
2.1.2. Schafferank and van Iterson Method
2.2. Prediction Models
2.2.1. Artificial Neural Network (ANN)
2.2.2. Invasive Weed Optimization (IWO)
- (1)
- First, at the “population initialization” step, several seeds are randomly distributed within the search space.
- (2)
- At the “reproduction” step, every plant is poured into a flowering plant; after that, the system can produce seeds that are worth their proportion. Then, the quantity of the seeds is linearly reduced from Smax to Smin with the use of the following equation:
- (3)
- At the third step, a new position of the seeds within the search space is determined. At this step, the child’s seeds are positioned nearby their parents.
- (4)
- At the fourth step, which is referred to as the competitive elimination step, the best seeds are created based on their merit. It takes place in the case that a certain number (Pmax) of seeds have been created.
- (5)
- Finally, at the fifth step, if the termination criterion is not satisfied yet, the whole process is repeated from the second step to the end. It continues until the termination criterion is met, and the algorithm operation will then end. Figure 4 illustrates a general diagram showing the steps involved in an IWO operation.
2.2.3. Hybrid Algorithms
3. Simulation Models
3.1. Initial Model
3.2. Hybrid Model Development
4. Results and Discussion
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Parameter | Abbreviation | Unit | Min | Max | Average | Std |
---|---|---|---|---|---|---|
Soil permeability coefficient | K | cm/s | 1 × 10−10 | 1 × 10−4 | 1.59 × 10−5 | 3.45 × 10−5 |
Height water | HW | m | 10 | 48 | 29 | 10.89 |
Freeboard | FB | m | 2 | 5 | 4 | 1.12 |
Upstream slopes | β | degree | 15 | 30 | 23 | 5.59 |
downstream slopes | α | degree | 15 | 30 | 23 | 5.59 |
Width crest | WC | m | 8 | 12 | 10 | 1.63 |
Seepage rate | Q | m3/s | 7.81 × 10−11 | 1.48 × 10−3 | 8.82 × 10−5 | 2.22 × 10−5 |
Model No. | Structure | The Best R2 | |
---|---|---|---|
Training | Testing | ||
T1 | 6-1-1 | 0.7925 | 0.8050 |
T2 | 6-2-1 | 0.9126 | 0.9068 |
T3 | 6-3-1 | 0.8738 | 0.8633 |
T4 | 6-4-1 | 0.9018 | 0.9184 |
T5 | 6-5-1 | 0.9378 | 0.9333 |
T6 | 6-6-1 | 0.9140 | 0.9050 |
T7 | 6-7-1 | 0.8919 | 0.8998 |
T8 | 6-8-1 | 0.9071 | 0.9199 |
T9 | 6-9-1 | 0.9155 | 0.9143 |
T10 | 6-10-1 | 0.9241 | 0.9077 |
Model No. | Structure | The Best R2 | |
---|---|---|---|
Training | Testing | ||
E1 | 6-1-1 | 0.8460 | 0.8391 |
E2 | 6-2-1 | 0.9025 | 0.8954 |
E3 | 6-3-1 | 0.9257 | 0.9261 |
E4 | 6-4-1 | 0.9059 | 0.9064 |
E5 | 6-5-1 | 0.8648 | 0.8660 |
E6 | 6-6-1 | 0.8813 | 0.8956 |
E7 | 6-7-1 | 0.9103 | 0.9213 |
E8 | 6-8-1 | 0.9052 | 0.9149 |
E9 | 6-9-1 | 0.8666 | 0.8926 |
E10 | 6-10-1 | 0.8860 | 0.8722 |
Model No. | Structure | The Best R2 | |
---|---|---|---|
Training | Testing | ||
S1 | 6-1-1 | 0.8571 | 0.8600 |
S2 | 6-2-1 | 0.8708 | 0.8924 |
S3 | 6-3-1 | 0.9231 | 0.8874 |
S4 | 6-4-1 | 0.8962 | 0.9053 |
S5 | 6-5-1 | 0.8862 | 0.9113 |
S6 | 6-6-1 | 0.9055 | 0.8813 |
S7 | 6-7-1 | 0.8834 | 0.9075 |
S8 | 6-8-1 | 0.9017 | 0.8825 |
S9 | 6-9-1 | 0.8876 | 0.9175 |
S10 | 6-10-1 | 0.8668 | 0.8925 |
Model No. | Structure | The Best R2 | |
---|---|---|---|
Training | Testing | ||
L1 | 6-1-1 | 0.8513 | 0.8643 |
L2 | 6-2-1 | 0.8757 | 0.8875 |
L3 | 6-3-1 | 0.8521 | 0.8432 |
L4 | 6-4-1 | 0.8852 | 0.8946 |
L5 | 6-5-1 | 0.9023 | 0.8904 |
L6 | 6-6-1 | 0.8938 | 0.8849 |
L7 | 6-7-1 | 0.8759 | 0.9009 |
L8 | 6-8-1 | 0.9052 | 0.8944 |
L9 | 6-9-1 | 0.8707 | 0.8712 |
L10 | 6-10-1 | 0.8802 | 0.8934 |
The Parameters | Equation | R2 |
---|---|---|
Water height | Y = 9 × 10−5 | 0.9944 |
Freeboard | Y = −8 × 10−6 x + 0.0002 | 0.9994 |
Upstream slope | Y = 2 × 10−6 x + 0.0001 | 0.9997 |
Downstream slope | Y = 8 × 10−6 | 0.9998 |
Width crest | Y = −3 × 10−6 x + 0.0002 | 0.9996 |
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Tang, D.; Gordan, B.; Koopialipoor, M.; Jahed Armaghani, D.; Tarinejad, R.; Thai Pham, B.; Huynh, V.V. Seepage Analysis in Short Embankments Using Developing a Metaheuristic Method Based on Governing Equations. Appl. Sci. 2020, 10, 1761. https://doi.org/10.3390/app10051761
Tang D, Gordan B, Koopialipoor M, Jahed Armaghani D, Tarinejad R, Thai Pham B, Huynh VV. Seepage Analysis in Short Embankments Using Developing a Metaheuristic Method Based on Governing Equations. Applied Sciences. 2020; 10(5):1761. https://doi.org/10.3390/app10051761
Chicago/Turabian StyleTang, Dongchun, Behrouz Gordan, Mohammadreza Koopialipoor, Danial Jahed Armaghani, Reza Tarinejad, Binh Thai Pham, and Van Van Huynh. 2020. "Seepage Analysis in Short Embankments Using Developing a Metaheuristic Method Based on Governing Equations" Applied Sciences 10, no. 5: 1761. https://doi.org/10.3390/app10051761
APA StyleTang, D., Gordan, B., Koopialipoor, M., Jahed Armaghani, D., Tarinejad, R., Thai Pham, B., & Huynh, V. V. (2020). Seepage Analysis in Short Embankments Using Developing a Metaheuristic Method Based on Governing Equations. Applied Sciences, 10(5), 1761. https://doi.org/10.3390/app10051761