# Predicting the Compressive Strength of Environmentally Friendly Concrete Using Multiple Machine Learning Algorithms

^{1}

^{2}

^{*}

## Abstract

**:**

^{2}and MSE equal to 0.9072 and 11.4546, respectively.

## 1. Introduction

#### 1.1. Literature Review

#### 1.2. Objecitves

^{2}and MSE. The highlight of the research was the comparison of the prediction performance of various machine learning algorithms and the synthesizing of the PSO algorithm with each predicting model. The objectives of this research were as follows:

- 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).

_{i}is the data in one input parameter, and max(x) and min(x) are the maximum and minimum value in the corresponding input parameter.

- (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

_{ij}of the I neuron of the k layer to the j neuron of the k + 1 layer (k is the number of the layers, including the input layer and the hidden layers), and the bias b

_{i}of the k layer neuron. The received data of the k + 1 layer will be processed by the activation function; then, the data will be transformed to the k + 2 layer.

#### 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

^{2}, MSE, MAE and explanatory variance were used to evaluate the prediction accuracy of the constructed algorithms. The statistic indexes were calculated using the r2_score, mean_absolute_error, mean_squared_error and sm.taylor functions in the sklearn.metrics library.

^{2}indicates the fitness of prediction of the model. As can be seen from the figure, the R

^{2}of the predicted and experimental values is generally around 0.8, indicating the selected ML algorithms have a good predicting performance. However, the R

^{2}of AFNIS and GP are only 0.7015 and 0.7154, respectively. The prediction ability of the GP model is dependent on variability, just like genetic variation [26]. Therefore, the variation direction of branches is highly controlled by the hyperparameter settings. In contrast, SVR has the highest R

^{2}by virtue of its excellent generalization. As for RF and XGBoost models, their fitting goodness showed a certain fluctuation, and this is because of their random splitting of tree branches and the formation of data subsets of each sub-tree integrated in them, and all of this results in a decisive dependency on the hyperparameter setting. As a contrast, the SVR model will map the lower dimension problem to the higher one and simplify the calculation through kernel function, performing little randomness. Therefore, the SVR model is outperformed. The ANFIS showed a worse R

^{2}; this may because the database has six features, resulting in the requirement of many more membership degrees (MDs), and the MDs only default at two for each feature, resulting in the poor performance of the ANFIS model.

#### 4.2. Prediction Performance of Hybrid Models

^{2}of PSO-RF are 11.9172 and 0.9035, respectively, which are 42.9% lower and 8.7% higher than that of RF, respectively; while for PSO-SVR, the MSE and R

^{2}are reduced 14.8% and increased 1.9% compared with its standalone model; for XGBoost, the results are 44.1% and 8.9%; for GP, they are 56.2% and 22.4%; and for BP-ANN, they are 16% and 2.9%.

^{2}of 0.9072. In addition, the assembled and SVR algorithms have better prediction performance than the NN-based algorithms.

^{2}was increased by 18.4%. As aforementioned, the predicting performance of RF and XGBoost is highly dependent on the hyperparameter setting. Therefore, the predicting accuracy is significantly increased.

#### 4.3. Analysis of Error Distribution

^{2}and lower MSE after PSO optimization, they have more large error points, which may lead to larger prediction errors in practical applications. Therefore, SVR and PSO-GP are more suitable for regression prediction of this data set.

#### 4.4. Accuracy Analysis

^{2}of the optimized ANFIS is only 4.5% and 0.7% lower than XGBoost and RF, respectively, but the MSE is 29.6% and 27.7% higher. In addition, the change rates of R

^{2}and MSE of each model are significantly different after PSO optimization. The reason is that different statistic indicators have different sensitivity to the errors. Therefore, it is difficult to fully reflect the prediction accuracy of the model through a single statistical indicator.

## 5. Conclusions

- (1)
- As a standalone model, the SVR algorithm has the highest R
^{2}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 R
^{2}increased by 22.4% after cooperating with PSO. In addition, the R^{2}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 f
_{c}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 f
_{c}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

- Sahoo, S.; Mahapatra, T.R. ANN Modeling to study strength loss of Fly Ash Concrete against Long term Sulphate Attack. Mater. Today Proc.
**2018**, 5, 24595–24604. [Google Scholar] [CrossRef] - Mohamed, O.; Kewalramani, M.; Ati, M.; Hawat, W.A. Application of ANN for prediction of chloride penetration resistance and concrete compressive strength. Materialia
**2021**, 17, 101123. [Google Scholar] [CrossRef] - Mohamed, O.A.; Najm, O.F. Compressive strength and stability of sustainable self-consolidating concrete containing fly ash, silica fume, and GGBS. Front. Struct. Civ. Eng.
**2017**, 11, 406–411. [Google Scholar] [CrossRef] - Huang, H.; Yuan, Y.J.; Zhang, W.; Zhu, L. Property Assessment of High-Performance Concrete Containing Three Types of Fibers. Int. J. Concr. Struct. Mater.
**2021**, 15, 39. [Google Scholar] [CrossRef] - Zheng, Z.; Tian, C.; Wei, X.; Zeng, C. Numerical investigation and ANN-based prediction on compressive strength and size effect using the concrete mesoscale concretization model. Case Stud. Constr. Mater.
**2022**, 16, e01056. [Google Scholar] [CrossRef] - Ullah, H.S.; Khushnood, R.A.; Farooq, F.; Ahmad, J.; Vatin, N.I.; Ewais, D.Y. Prediction of Compressive Strength of Sustainable Foam Concrete Using Individual and Ensemble Machine Learning Approaches. Materials
**2022**, 15, 3166. [Google Scholar] [CrossRef] [PubMed] - Khan, M.A.; Farooq, F.; Javed, M.F.; Zafar, A.; Ostrowski, K.A.; Aslam, F.; Malazdrewicz, S.; Maślak, M. Simulation of Depth of Wear of Eco-Friendly Concrete Using Machine Learning Based Computational Approaches. Materials
**2022**, 15, 58. [Google Scholar] [CrossRef] - Petković, D.; Ćojbašić, Ž.; Nikolić, V.; Shamshirband, S.; Mat Kiah, M.L.; Anuar, N.B.; Abdul Wahab, A.W. Adaptive neuro-fuzzy maximal power extraction of wind turbine with continuously variable transmission. Energy
**2014**, 64, 868–874. [Google Scholar] [CrossRef] - Shamshirband, S.; Petković, D.; Amini, A.; Anuar, N.B.; Nikolić, V.; Ćojbašić, Ž.; Mat Kiah, M.L.; Gani, A. Support vector regression methodology for wind turbine reaction torque prediction with power-split hydrostatic continuous variable transmission. Energy
**2014**, 67, 623–630. [Google Scholar] [CrossRef] - Petković, B.; Agdas, A.S.; Zandi, Y.; Nikolić, I.; Denić, N.; Radenkovic, S.D.; Almojil, S.F.; Roco-Videla, A.; Kojić, N.; Zlatković, D.; et al. Neuro fuzzy evaluation of circular economy based on waste generation, recycling, renewable energy, biomass and soil pollution. Rhizosphere
**2021**, 19, 100418. [Google Scholar] [CrossRef] - Nguyen, T.-D.; Cherif, R.; Mahieux, P.-Y.; Lux, J.; Aït-Mokhtar, A.; Bastidas-Arteaga, E. Artificial intelligence algorithms for prediction and sensitivity analysis of mechanical properties of recycled aggregate concrete: A review. J. Build. Eng.
**2023**, 66, 105929. [Google Scholar] [CrossRef] - Taffese, W.Z.; Sistonen, E.; Puttonen, J. CaPrM: Carbonation prediction model for reinforced concrete using machine learning methods. Constr. Build. Mater.
**2015**, 100, 70–82. [Google Scholar] [CrossRef] - Adeli, H.; Cheng, N.T. Integrated Genetic Algorithm for Optimization of Space Structures. J. Aerosp. Eng.
**1993**, 6, 315–328. [Google Scholar] [CrossRef] - Xu, J.; Wang, Y.; Ren, R.; Wu, Z.; Ozbakkaloglu, T. Performance evaluation of recycled aggregate concrete-filled steel tubes under different loading conditions: Database analysis and modelling. J. Build. Eng.
**2020**, 30, 101308. [Google Scholar] [CrossRef] - Dantas, A.T.A.; Batista Leite, M.; de Jesus Nagahama, K. Prediction of compressive strength of concrete containing construction and demolition waste using artificial neural networks. Constr. Build. Mater.
**2013**, 38, 717–722. [Google Scholar] [CrossRef] - Huang, W.; Zhou, L.; Ge, P.; Yang, T. A Comparative Study on Compressive Strength Model of Recycled Brick Aggregate Concrete Based on PSO-BP and GA-BP Neural Networks. Mater. Rep.
**2021**, 35, 15026–15030. (In Chinese) [Google Scholar] - Ahmadi, M.; Kioumarsi, M. Predicting the elastic modulus of normal and high strength concretes using hybrid ANN-PSO. Mater. Today Proc.
**2023**, in press. [Google Scholar] [CrossRef] - Kim, S.; Choi, H.-B.; Shin, Y.; Kim, G.-H.; Seo, D.-S. Optimizing the Mixing Proportion with Neural Networks Based on Genetic Algorithms for Recycled Aggregate Concrete. Adv. Mater. Sci. Eng.
**2013**, 2013, 527089. [Google Scholar] [CrossRef] - Zheng, W.; Zaman, A.; Farooq, F.; Althoey, F.; Alaskar, A.; Akbar, A. Sustainable predictive model of concrete utilizing waste ingredient: Individual alogrithms with optimized ensemble approaches. Mater. Today Commun.
**2023**, 35, 105901. [Google Scholar] [CrossRef] - Ababneh, A.; Alhassan, M.; Abu-Haifa, M. Predicting the contribution of recycled aggregate concrete to the shear capacity of beams without transverse reinforcement using artificial neural networks. Case Stud. Constr. Mater.
**2020**, 13, e00414. [Google Scholar] [CrossRef] - Jin, L.; Dong, T.; Fan, T.; Duan, J.; Yu, H.; Jiao, P.; Zhang, W. Prediction of the chloride diffusivity of recycled aggregate concrete using artificial neural network. Mater. Today Commun.
**2022**, 32, 104137. [Google Scholar] [CrossRef] - Hiew, S.Y.; Teoh, K.B.; Raman, S.N.; Kong, D.; Hafezolghorani, M. Prediction of ultimate conditions and stress–strain behaviour of steel-confined ultra-high-performance concrete using sequential deep feed-forward neural network modelling strategy. Eng. Struct.
**2023**, 277, 115447. [Google Scholar] [CrossRef] - Minaz Hossain, M.; Nasir Uddin, M.; Abu Sayed Hossain, M. Prediction of compressive strength ultra-high steel fiber reinforced concrete (UHSFRC) using artificial neural networks (ANNs). Mater. Today Proc.
**2023**, in press. [Google Scholar] [CrossRef] - Allouzi, R.; Almasaeid, H.; Alkloub, A.; Ayadi, O.; Allouzi, R.; Alajarmeh, R. Lightweight foamed concrete for houses in Jordan. Case Stud. Constr. Mater.
**2023**, 18, e01924. [Google Scholar] [CrossRef] - Kursuncu, B.; Gencel, O.; Bayraktar, O.Y.; Shi, J.; Nematzadeh, M.; Kaplan, G. Optimization of foam concrete characteristics using response surface methodology and artificial neural networks. Constr. Build. Mater.
**2022**, 337, 127575. [Google Scholar] [CrossRef] - Salami, B.A.; Iqbal, M.; Abdulraheem, A.; Jalal, F.E.; Alimi, W.; Jamal, A.; Tafsirojjaman, T.; Liu, Y.; Bardhan, A. Estimating compressive strength of lightweight foamed concrete using neural, genetic and ensemble machine learning approaches. Cem. Concr. Compos.
**2022**, 133, 104721. [Google Scholar] [CrossRef] - Asteris, P.G.; Lourenço, P.B.; Roussis, P.C.; Elpida Adami, C.; Armaghani, D.J.; Cavaleri, L.; Chalioris, C.E.; Hajihassani, M.; Lemonis, M.E.; Mohammed, A.S.; et al. Revealing the nature of metakaolin-based concrete materials using artificial intelligence techniques. Constr. Build. Mater.
**2022**, 322, 126500. [Google Scholar] [CrossRef] - Bhuva, P.; Bhogayata, A.; Kumar, D. A comparative study of different artificial neural networks for the strength prediction of self-compacting concrete. Mater. Today Proc.
**2023**. [Google Scholar] [CrossRef] - Gao, X.; Yang, J.; Zhu, H.; Xu, J. Estimation of rubberized concrete frost resistance using machine learning techniques. Constr. Build. Mater.
**2023**, 371, 130778. [Google Scholar] [CrossRef] - Naseri Nasab, M.; Jahangir, H.; Hasani, H.; Majidi, M.-H.; Khorashadizadeh, S. Estimating the punching shear capacities of concrete slabs reinforced by steel and FRP rebars with ANN-Based GUI toolbox. Structures
**2023**, 50, 1204–1221. [Google Scholar] [CrossRef] - Bardhan, A.; Biswas, R.; Kardani, N.; Iqbal, M.; Samui, P.; Singh, M.P.; Asteris, P.G. A novel integrated approach of augmented grey wolf optimizer and ANN for estimating axial load carrying-capacity of concrete-filled steel tube columns. Constr. Build. Mater.
**2022**, 337, 127454. [Google Scholar] [CrossRef] - Zhao, B.; Li, P.; Du, Y.; Li, Y.; Rong, X.; Zhang, X.; Xin, H. Artificial neural network assisted bearing capacity and confining pressure prediction for rectangular concrete-filled steel tube (CFT). Alex. Eng. J.
**2023**, 74, 517–533. [Google Scholar] [CrossRef] - Concha, N.C. Neural network model for bond strength of FRP bars in concrete. Structures
**2022**, 41, 306–317. [Google Scholar] [CrossRef] - Huang, L.; Chen, J.; Tan, X. BP-ANN based bond strength prediction for FRP reinforced concrete at high temperature. Eng. Struct.
**2022**, 257, 114026. [Google Scholar] [CrossRef] - Zhang, F.; Wang, C.; Liu, J.; Zou, X.; Sneed, L.H.; Bao, Y.; Wang, L. Prediction of FRP-concrete interfacial bond strength based on machine learning. Eng. Struct.
**2023**, 274, 115156. [Google Scholar] [CrossRef] - You, X.; Yan, G.; Al-Masoudy, M.M.; Kadimallah, M.A.; Alkhalifah, T.; Alturise, F.; Ali, H.E. Application of novel hybrid machine learning approach for estimation of ultimate bond strength between ultra-high performance concrete and reinforced bar. Adv. Eng. Softw.
**2023**, 180, 103442. [Google Scholar] [CrossRef] - Sun, L.; Wang, C.; Zhang, C.W.; Yang, Z.Y.; Li, C.; Qiao, P.Z. Experimental investigation on the bond performance of sea sand coral concrete with FRP bar reinforcement for marine environments. Adv. Struct. Eng.
**2023**, 26, 533–546. [Google Scholar] [CrossRef] - Gehlot, T.; Dave, M.; Solanki, D. Neural network model to predict compressive strength of steel fiber reinforced concrete elements incorporating supplementary cementitious materials. Mater. Today Proc.
**2022**, 62, 6498–6506. [Google Scholar] [CrossRef] - Fakharian, P.; Rezazadeh Eidgahee, D.; Akbari, M.; Jahangir, H.; Ali Taeb, A. Compressive strength prediction of hollow concrete masonry blocks using artificial intelligence algorithms. Structures
**2023**, 47, 1790–1802. [Google Scholar] [CrossRef] - Owusu-Danquah, J.S.; Bseiso, A.; Allena, S.; Duffy, S.F. Artificial neural network algorithms to predict the bond strength of reinforced concrete: Coupled effect of corrosion, concrete cover, and compressive strength. Constr. Build. Mater.
**2022**, 350, 128896. [Google Scholar] [CrossRef] - Rehman, F.; Khokhar, S.A.; Khushnood, R.A. ANN based predictive mimicker for mechanical and rheological properties of eco-friendly geopolymer concrete. Case Stud. Constr. Mater.
**2022**, 17, e01536. [Google Scholar] [CrossRef] - Sadowski, Ł.; Hoła, J. ANN modeling of pull-off adhesion of concrete layers. Adv. Eng. Softw.
**2015**, 89, 17–27. [Google Scholar] [CrossRef] - Imran Waris, M.; Plevris, V.; Mir, J.; Chairman, N.; Ahmad, A. An alternative approach for measuring the mechanical properties of hybrid concrete through image processing and machine learning. Constr. Build. Mater.
**2022**, 328, 126899. [Google Scholar] [CrossRef] - Nikolić, V.; Mitić, V.V.; Kocić, L.; Petković, D. Wind speed parameters sensitivity analysis based on fractals and neuro-fuzzy selection technique. Knowl. Inf. Syst.
**2017**, 52, 255–265. [Google Scholar] [CrossRef] - Wang, Q.; Xia, C.; Alagumalai, K.; Thanh Nhi Le, T.; Yuan, Y.; Khademi, T.; Berkani, M.; Lu, H. Biogas generation from biomass as a cleaner alternative towards a circular bioeconomy: Artificial intelligence, challenges, and future insights. Fuel
**2023**, 333, 126456. [Google Scholar] [CrossRef] - Cao, B.T.; Obel, M.; Freitag, S.; Mark, P.; Meschke, G. Artificial neural network surrogate modelling for real-time predictions and control of building damage during mechanised tunnelling. Adv. Eng. Softw.
**2020**, 149, 102869. [Google Scholar] [CrossRef] - Felix, E.F.; Carrazedo, R.; Possan, E. Carbonation model for fly ash concrete based on artificial neural network: Development and parametric analysis. Constr. Build. Mater.
**2021**, 266, 121050. [Google Scholar] [CrossRef] - Payton, E.; Khubchandani, J.; Thompson, A.; Price, J.H. Parents’ Expectations of High Schools in Firearm Violence Prevention. J. Community Health
**2017**, 42, 1118–1126. [Google Scholar] [CrossRef] - Çevik, A.; Kurtoğlu, A.E.; Bilgehan, M.; Gülşan, M.E.; Albegmprli, H.M. Support vector machines in structural engineering: A review. J. Civ. Eng. Manag.
**2015**, 21, 261–281. [Google Scholar] [CrossRef]

**Figure 5.**Prediction results of RF model for test set: (

**a**) Error and (

**b**) correlation between predicted value and experimental value.

**Figure 6.**Prediction results of SVR model for test set: (

**a**) Error and (

**b**) correlation between predicted value and experimental value.

**Figure 7.**Prediction results of XGBoost model for test set: (

**a**) Error and (

**b**) correlation between predicted value and experimental value.

**Figure 8.**Prediction results of GP model for test set: (

**a**) Error and (

**b**) correlation between predicted value and experimental value.

**Figure 9.**Prediction results of BP-ANN model for test set: (

**a**) Error and (

**b**) correlation between predicted value and experimental value.

**Figure 10.**Prediction results of ANFIS model for test set: (

**a**) Error and (

**b**) correlation between predicted value and experimental value.

**Figure 11.**Prediction results of PSO-RF model for test set: (

**a**) Error and (

**b**) correlation between predicted value and experimental value.

**Figure 12.**Prediction results of PSO-SVR model for test set: (

**a**) Error and (

**b**) correlation between predicted value and experimental value.

**Figure 13.**Prediction results of PSO-XGBoost model for test set: (

**a**) Error and (

**b**) correlation between predicted value and experimental value.

**Figure 14.**Prediction results of PSO-GP model for test set: (

**a**) Error and (

**b**) correlation between predicted value and experimental value.

**Figure 15.**Prediction results of PSO-BP-ANN model for test set: (

**a**) Error and (

**b**) correlation between predicted value and experimental value.

**Figure 16.**Prediction results of optimized ANFIS model for test set: (

**a**) Error and (

**b**) correlation between predicted value and experimental value.

Statistic Index | W (kg/m ^{3}) | C (kg/m ^{3}) | FA (kg/m ^{3}) | A (kg/m ^{3}) | S (kg/m ^{3}) | WR (kg/m ^{3}) | f_{c} (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 | |||
---|---|---|---|---|

R^{2} | 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 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2024 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 (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

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

**AMA Style**

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 Style**

Yang, 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