Scouring Depth Assessment Downstream of Weirs Using Hybrid Intelligence Models
Abstract
:1. Introduction
2. Materials and Methods
2.1. Laboratory Data for Estimating Scour Depth
2.2. Adaptive Neuro-Fuzzy Inference System
2.3. Description of the Optimization Methods
- -
- Biogeography based optimization
- -
- Cultural algorithm
- -
- Invasive weeds optimization
- i.
- Generating primary population function: the seeds which are also named as prime solutions are dispersed randomly in search space for finding a fitting solution to tackle problems.
- ii.
- Reproduction function: the IWO employs the minimum and maximum quantity of weeds colony objective functions.
- iii.
- Spatial dispersal function: the primary duty of this function is to provide randomness in the model. This function helps to spread the seed around parental plants. In each iteration, this function measures the standard deviation of new produced results.
- iv.
- Competitive exclusion function: the main task of this function is to increase the chance of surviving for weak plants which contain a low level of fitness function. In this regard, after reaching to maximum number of population, the members of colonies are sorted, and colonies with the highest number of the population are selected for further calculations in the next iteration.
- -
- Teaching Learning Based Optimization
2.4. Optimizing the ANFIS Parameters
- i.
- Divide the dataset into training and testing data with a portion of 66% and 34%, respectively.
- ii.
- Develop a basic ANFIS.
- iii.
- Adopt the optimization algorithms for tuning the parameters of membership functions and fuzzy logic rules.
- iv.
- Select the best hybrid ANFIS model with the highest performance for estimating scour depth downstream of weirs.
2.5. Description of Performance Indices
2.6. Uncertainty Analysis
- i.
- All of the results obtained by the best estimator models (e.g., ANFIS-BBO, ANFIS-TLBO, ANFIS-Cultural, ANFIS-IWO) are considered for each computed scouring depth.
- ii.
- A normal distribution function is assigned to each predicted set.
- iii.
- To quantify the variability of predicted scouring depth, many samples (1000 generation), corresponding each predicted scouring depth, are generated by Monte Carlo simulation using the probability density function (PDF) obtained in step ii.
- iv.
- Using the scouring depths generated in step iii, the 95% confidence interval band, which is the interval between the 2.5% and 97.5% percentiles can be obtained.
- v.
- vi.
3. Results and Discussion
4. Conclusions
Supplementary Materials
Author Contributions
Funding
Conflicts of Interest
References
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Parameters | Training Phase | Testing Phase |
---|---|---|
0.0069–0.9197 | 0.0108–0.866 | |
0.0096–0.362 | 0.00945–0.226 | |
0.179–20.28 | 0.1613–11.344 | |
0.271–2.444 | 0.1359–2.222 |
Parameters | ||||
---|---|---|---|---|
1 | ||||
−0.3604 | 1 | |||
−0.4891 | 0.7218 | 1 | ||
−0.0532 | 0.3810 | 0.5551 | 1 |
Input Combination | Non-Dimensional Variables | ||
---|---|---|---|
M1 | ✓ | ✓ | ✓ |
M2 | ✓ | ✓ | - |
M3 | - | ✓ | - |
No | Predictive Model | Input Combination | Phase | MAE | RMSE | CC | WI |
---|---|---|---|---|---|---|---|
Model 1 | ANFIS-M1 | All parameters | Training | 0.092 | 0.124 | 0.895 | 0.942 |
Testing | 0.133 | 0.192 | 0.883 | 0.916 | |||
Model 2 | ANFIS-CULTURAL-M1 | All parameters | Training | 0.100 | 0.166 | 0.803 | 0.873 |
Testing | 0.151 | 0.260 | 0.816 | 0.800 | |||
Model 3 | ANFIS-BBO-M1 | All parameters | Training | 0.125 | 0.182 | 0.761 | 0.836 |
Testing | 0.167 | 0.276 | 0.829 | 0.735 | |||
Model 4 | ANFIS-IWO-M1 | All parameters | Training | 0.08 | 0.111 | 0.916 | 0.954 |
Testing | 0.108 | 0.148 | 0.932 | 0.955 | |||
Model 5 | ANFIS-TLBO-M1 | All parameters | Training | 0.120 | 0.164 | 0.831 | 0.863 |
Testing | 0.153 | 0.226 | 0.846 | 0.866 | |||
Model 6 | ANFIS-M2 | Without | Training | 0.164 | 0.234 | 0.543 | 0.628 |
Testing | 0.219 | 0.353 | 0.422 | 0.452 | |||
Model 7 | ANFIS-CULTURAL-M2 | Without | Training | 0.161 | 0.240 | 0.507 | 0.622 |
Testing | 0.213 | 0.366 | 0.334 | 0.389 | |||
Model 8 | ANFIS-BBO-M2 | Without | Training | 0.178 | 0.253 | 0.414 | 0.507 |
Testing | 0.226 | 0.366 | 0.355 | 0.365 | |||
Model 9 | ANFIS-IWO-M2 | Without | Training | 0.144 | 0.210 | 0.656 | 0. 760 |
Testing | 0.202 | 0.340 | 0.482 | 0.573 | |||
Model 10 | ANFIS-TLBO-M2 | Without | Training | 0.138 | 0.228 | 0.574 | 0.681 |
Testing | 0.226 | 0.379 | 0.251 | 0.379 | |||
Model 11 | ANFIS-M3 | Only | Training | 0.153 | 0.208 | 0.665 | 0.775 |
Testing | 0.679 | 3.400 | 0.106 | 0.052 | |||
Model 12 | ANFIS-CULTURAL-M3 | Only | Training | 0.179 | 0.272 | 0.214 | 0.242 |
Testing | 0.236 | 0.394 | 0.002 | 0.226 | |||
Model 13 | ANFIS-BBO-M3 | Only | Training | 0.180 | 0.278 | 0.078 | 0.023 |
Testing | 0.234 | 0.392 | 0.000 | 0.214 | |||
Model 14 | ANFIS-IWO-M3 | Only | Training | 0.162 | 0.229 | 0.598 | 0.625 |
Testing | 0.239 | 0.400 | 0.026 | 0.260 | |||
Model 15 | ANFIS-TLBO-M3 | Only | Training | 0.171 | 0.262 | 0.343 | 0.408 |
Testing | 0.246 | 0.411 | 0.000 | 0.225 |
Technique | RMSE | MAE |
---|---|---|
ANFIS-IWO (testing phase) | 0.14755 | 0.107 |
Guan et al. (2016). | 0.4465 | 0.3951 |
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Sharafati, A.; Haghbin, M.; Haji Seyed Asadollah, S.B.; Tiwari, N.K.; Al-Ansari, N.; Yaseen, Z.M. Scouring Depth Assessment Downstream of Weirs Using Hybrid Intelligence Models. Appl. Sci. 2020, 10, 3714. https://doi.org/10.3390/app10113714
Sharafati A, Haghbin M, Haji Seyed Asadollah SB, Tiwari NK, Al-Ansari N, Yaseen ZM. Scouring Depth Assessment Downstream of Weirs Using Hybrid Intelligence Models. Applied Sciences. 2020; 10(11):3714. https://doi.org/10.3390/app10113714
Chicago/Turabian StyleSharafati, Ahmad, Masoud Haghbin, Seyed Babak Haji Seyed Asadollah, Nand Kumar Tiwari, Nadhir Al-Ansari, and Zaher Mundher Yaseen. 2020. "Scouring Depth Assessment Downstream of Weirs Using Hybrid Intelligence Models" Applied Sciences 10, no. 11: 3714. https://doi.org/10.3390/app10113714
APA StyleSharafati, A., Haghbin, M., Haji Seyed Asadollah, S. B., Tiwari, N. K., Al-Ansari, N., & Yaseen, Z. M. (2020). Scouring Depth Assessment Downstream of Weirs Using Hybrid Intelligence Models. Applied Sciences, 10(11), 3714. https://doi.org/10.3390/app10113714