A Constitutive Model Study of Chemical Corrosion Sandstone Based on Support Vector Machine and Artificial Bee Colony Algorithm
Abstract
:1. Introduction
2. Methods
2.1. SVM Algorithm
2.2. ABC Algorithm
2.3. ABC-SVM
- (1)
- The data set is established and randomly divided into a training set and test set.
- (2)
- The parameters of the ABC algorithm are initialized and produce the initial solution.
- (3)
- The SVM with the initial solution as the parameter combination is used to establish the model on the training set and back-judge to obtain the results. At the same time, the K-fold cross-validation method (K = 5 in this paper) is used to calculate the performance of the model (the mean square error is used as the evaluation index in this paper).
- (4)
- Honey bees search for new nectar sources using the neighbor search method. Repeat step 3 and compare it with the original outcome, to compare the performance of SVM under different combinations of two parameters. The combination of SVM parameters with the better performance will be retained.
- (5)
- The observed bee takes the position of the retained nectar source, i.e., (c, g) combination, as the new initial solution, and then repeats step 4.
- (6)
- Repeat the above steps and record the global optimal solution and the corresponding performance index.
- (7)
- When the bee passes through the limit cycle, it is judged whether the condition is satisfied. If it is satisfied, the new solution is used instead of the old solution.
- (8)
- Determine whether the termination condition is satisfied. If it is satisfied, the optimal solution of the output is used as the optimal parameter combination; if it is not satisfied, turn to step 4 until the end condition is satisfied.
- (9)
- The optimal (c, g) combination obtained by the ABC algorithm is brought into SVM to establish the ABC-SVM model, which is applied to the test set to analyze its performance and generalization ability.
- (1)
- The training set is randomly divided into five subsets with the same number of samples in each; four of those are selected as the sub-training set, and the remaining subset is the validation set.
- (2)
- Based on the initial parameters and sub-training sets of the ABC algorithm, the model is established and then applied to the validation set, and the performance of the model on the validation set is calculated.
- (3)
- Step 2 is repeated five times, in which the validation set is changed in each cycle to ensure that each set of samples in the training set can be used to train and validate the model.
- (4)
- The results of the above five cycles are recorded and the average value is calculated.
- (5)
- Based on the new set of parameters of the bee colony near search, repeat steps 2–4.
- (6)
- Carry out steps 4–5 of the artificial bee colony algorithm, in which the new parameter performance calculation in step 5 repeats steps 1–5 of the 5-fold cross-validation, and then move on to steps 6–9 of the artificial bee colony algorithm.
3. Rock Constitutive Model Based on ABC-SVM Model
3.1. Data Analysis
3.2. Establishment and Verification of Model
3.3. Comparison with the Statistical Damage Constitutive Model of Sandstone
3.3.1. Establishment of Statistical Damage Constitutive Model for Sandstone
3.3.2. Comparison
4. Discussion
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Hydrating Condition | Confining Pressure /MPa | Porosity /% | Uniaxial Compressive Strength/MPa |
---|---|---|---|
H2SO4 | 20 | 10.86 | 52.45 |
Distilled water | 5 | 5.96 | 63.13 |
NaOH | 10 | 8.57 | 55.74 |
Natural state | 0 | 5.02 | 65.16 |
Model | R2 | RMSE | MAPE |
---|---|---|---|
Statistical damage constitutive model | 0.990 | 2.5822 | 4.96 |
ABC-SVM model | 0.998 | 0.7730 | 1.51 |
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Lin, Y.; Li, C.; Zhou, K.; Guo, Z.; Zang, C. A Constitutive Model Study of Chemical Corrosion Sandstone Based on Support Vector Machine and Artificial Bee Colony Algorithm. Sustainability 2023, 15, 13415. https://doi.org/10.3390/su151813415
Lin Y, Li C, Zhou K, Guo Z, Zang C. A Constitutive Model Study of Chemical Corrosion Sandstone Based on Support Vector Machine and Artificial Bee Colony Algorithm. Sustainability. 2023; 15(18):13415. https://doi.org/10.3390/su151813415
Chicago/Turabian StyleLin, Yun, Chong Li, Keping Zhou, Zhenghai Guo, and Chuanwei Zang. 2023. "A Constitutive Model Study of Chemical Corrosion Sandstone Based on Support Vector Machine and Artificial Bee Colony Algorithm" Sustainability 15, no. 18: 13415. https://doi.org/10.3390/su151813415