Predicting the Compressive Strength of Environmentally Friendly Concrete Using Multiple Machine Learning Algorithms
Abstract
:1. Introduction
1.1. Literature Review
1.2. Objecitves
- Constructing the predicting model for the compressive strength of concrete containing coal fly ash using six different ML algorithms.
- Synthesizing the standalone models with a PSO algorithm, so as to optimize the hyperparameters of each model automatically.
- Evaluating the applicability of each hybrid ML model using comprehensive statistic indicators.
2. Data Collection
- (1)
- The box chart was used to highlight outliers in the data of each input parameter, and then 23 data sets with abnormal distribution were excluded from the 200 data sets; the statistical characteristics of the remaining 177 data sets are shown in Table 1.
- (2)
- In order to reduce the influence of data scales on the prediction performance and efficiency of the ML algorithm, the data of input parameters were normalized based on Equation (1).
- (3)
- Subsequently, the database was randomly divided into a training set and testing set through the split function in scikit-learn library, and the proportion of division was 75% for training and 25% for testing.
3. Machine Learning Algorithms
3.1. PSO Algorithm
3.2. BP-ANN
3.3. ANFIS
- (1)
- The first layer is the fuzzy layer, which undertakes fuzzy processing of input data by membership function. The selection of the type and number of membership function is usually subjective. When there are more membership functions of each input parameter, there will also be more membership degrees, so more if–then rules will be generated, which may improve the prediction accuracy to a certain level but also significantly increase the requirement of computer performance.
- (2)
- The second layer is to calculate the firing strength of each if–then rule.
- (3)
- The third layer normalizes the firing strength and obtains the trigger intensity of the if–then rule relative to the others.
- (4)
- The fourth layer calculates the output value of each if–then rule by multiplying the original input data and the relative trigger intensity obtained in the third layer.
- (5)
- The fifth layer is the output layer, which weights and sums the output values obtained in the fourth layer and defuzzies them.
3.4. SVR
3.5. XGBoost
3.6. RF
3.7. GP
4. Results and Discussions
4.1. Prediction Performance of Standalone Models
4.2. Prediction Performance of Hybrid Models
4.3. Analysis of Error Distribution
4.4. Accuracy Analysis
5. Conclusions
- (1)
- As a standalone model, the SVR algorithm has the highest R2 of 0.8837 and lowest MSE of 13.9315 with good generalization. In addition, the assembled algorithm outperforms the NN-based algorithm.
- (2)
- The PSO algorithm can effectively improve the prediction accuracy of all the ML models. Among them, the improvement in prediction accuracy of GP is the highest; its MSE decreased by 56.2% and R2 increased by 22.4% after cooperating with PSO. In addition, the R2 of the PSO-RF, PSO-XGBoost and PSO-SVR models are all greater than 0.9.
- (3)
- The absolute error distribution of the PSO-GP and SVR algorithms is relatively uniform, which means that there are fewer large error points in their prediction results, so it is not easy to have a large prediction error under a certain set of features. According to the statistical indicators of each standalone and hybrid algorithm, PSO-XGBoost has the best comprehensive performance.
- (4)
- Given the specificity of each predicting scenario, the same predicting models which have an appropriate accuracy in the fc prediction may not have performed excellently in the other scenarios such as anti-chloride diffusion, carbonization and so forth. Therefore, the applicability of each model should be carefully discussed in the others’ predicting scenarios.
- (5)
- Although six different machine learning algorithms were used to predict the fc of the concrete containing coal fly ash, the kinds of machine learning algorithms are still limited. Future research could discuss the applicability of other machine learning algorithms, even constructing a synthesizing operational interface to improve usability in the field.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Statistic Index | W (kg/m3) | C (kg/m3) | FA (kg/m3) | A (kg/m3) | S (kg/m3) | WR (kg/m3) | fc (MPa) |
---|---|---|---|---|---|---|---|
Count | 177 | 177 | 177 | 177 | 177 | 177 | 177 |
Mean | 157.39 | 380.71 | 45.93 | 1110.27 | 737.49 | 5.55 | 45.54 |
Std | 10.88 | 69.52 | 36.66 | 44.60 | 61.20 | 2.37 | 11.29 |
Minimum | 145.00 | 189.30 | 0 | 999.70 | 572.90 | 0 | 16.30 |
Maximum | 210.00 | 527.60 | 129.00 | 1214.50 | 920.60 | 14.10 | 69.80 |
Skewness | 3.84 | −0.12 | −0.06 | −0.26 | −0.06 | 1.09 | −0.14 |
Mode | 153. | 442. | 0 | 1136.79 | 726.80 | 5.20 | 36.90 |
Kurtosis | 16.33 | −0.42 | −1.19 | −0.53 | −0.53 | 2.96 | −0.61 |
SEM | 0.82 | 5.23 | 2.76 | 3.35 | 4.60 | 0.18 | 0.85 |
ML Model | Value of Hyperparameters |
---|---|
BPNN | Two hidden layers, and the first layer has 18 neurons, the second layer has 12 neurons. |
RF | n_estimate = 15, random state = 45, max_depth = 3 |
SVR | kernel = rbf |
XGBoost | default |
GP | population_size = 5000, generations = 20, stopping_criteria = 0.01, p_crossover = 0.7, p_subtree_mutation = 0.1, p_hoist_mutation = 0.1, p_point_mutation = 0.1, max_samples = 0.9, verbose = 1, parsimony_coefficient = 0.01, random_state = 0 |
ANFIS | membership type = graussf, membership grade = (2, 2, 2, 2, 2, 2, 2, 2) |
PSO Hyperparameters Setting | Predicting Model | Searching Hyperparameters |
---|---|---|
population size = 20 generation = 20 | BPNN | Neurons number of each hidden layer |
RF | n_estimators, random state, max_depth | |
XGBoost | max_depth, learning_rate, n_estimators | |
SVR | C, epsilon, gamma | |
GP | population_size, generations stopping_criteria, max_samples, verbose, parsimony_coefficient, random_state |
ML Model | Evaluating Index | |||
---|---|---|---|---|
R2 | MSE | STD | MAE | |
RF | 0.8309 | 20.885 | 8.8893 | 3.6563 |
PSO-RF | 0.9035 | 11.9172 | 9.8887 | 2.6271 |
SVR | 0.8872 | 13.9315 | 10.7003 | 2.7257 |
PSO-SVR | 0.9038 | 11.8761 | 10.5086 | 2.5996 |
XGBoost | 0.8340 | 20.5032 | 10.3703 | 3.4999 |
PSO-XGBoost | 0.9072 | 11.4594 | 10.6130 | 2.3637 |
GP | 0.7154 | 35.1627 | 11.0829 | 4.6226 |
PSO-GP | 0.8753 | 15.4052 | 10.5057 | 2.9886 |
BP-ANN | 0.8368 | 20.1649 | 11.5004 | 3.6589 |
PSO-BP-ANN | 0.8630 | 16.9292 | 10.7190 | 3.2411 |
Optimized ANFIS | 0.8303 | 26.4208 | 12.3607 | 3.3869 |
ANFIS | 0.7015 | 40.2328 | 11.0996 | 4.1215 |
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Yang, Y.; Liu, G.; Zhang, H.; Zhang, Y.; Yang, X. Predicting the Compressive Strength of Environmentally Friendly Concrete Using Multiple Machine Learning Algorithms. Buildings 2024, 14, 190. https://doi.org/10.3390/buildings14010190
Yang Y, Liu G, Zhang H, Zhang Y, Yang X. Predicting the Compressive Strength of Environmentally Friendly Concrete Using Multiple Machine Learning Algorithms. Buildings. 2024; 14(1):190. https://doi.org/10.3390/buildings14010190
Chicago/Turabian StyleYang, Yanhua, Guiyong Liu, Haihong Zhang, Yan Zhang, and Xiaolong Yang. 2024. "Predicting the Compressive Strength of Environmentally Friendly Concrete Using Multiple Machine Learning Algorithms" Buildings 14, no. 1: 190. https://doi.org/10.3390/buildings14010190