# Explainable Ensemble Learning Models for the Rheological Properties of Self-Compacting Concrete

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Test Procedures

#### 2.1.1. Slump Flow Test

#### 2.1.2. V-Funnel Test

#### 2.1.3. L-Box Test

#### 2.2. Ensemble Machine Learning Process

#### 2.3. Gradient Boosting Algorithms

**,**where K is the total number of the decision trees in the model [49].

## 3. Results

#### SHAP Analysis

## 4. Discussion and Conclusions

- The XGBoost model performed best on the test set during the prediction of shear stress as a function of the variables D, t, PA, and $\mathsf{\mu},$ with an ${\mathrm{R}}^{2}$ score of 0.9802, followed by random forest (${\mathrm{R}}^{2}$ = 0.9797), CatBoost (${\mathrm{R}}^{2}$ = 0.9779), and LightGBM (${\mathrm{R}}^{2}$ = 0.9111).
- The CatBoost model performed best on the test set during the prediction of plastic viscosity as a function of D, t, PA, and $\tau ,$ with an ${\mathrm{R}}^{2}$ score of 0.9654, followed by random forest (${\mathrm{R}}^{2}$ = 0.9570), LightGBM (${\mathrm{R}}^{2}$ = 0.9387), and XGBoost (${\mathrm{R}}^{2}$ = 0.9132).
- Shear strength and plastic viscosity features were found to have the highest impact on the predictive model output during prediction of each other, based on the SHAP analysis. In the prediction of both shear stress and plastic viscosity, the slump flow diameter was found to have the lowest impact on the model output.
- In the prediction of shear stress, the most consistent predictions were made by the CatBoost model, whereas the LightGBM model was most consistent in predicting plastic viscosity.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**V-funnel test equipment [1].

**Figure 3.**L-Box test setup [11].

**Figure 5.**The correlation matrix with variable distributions (three stars indicate the significance of correlation).

**Figure 6.**Learning curves of the (

**a**) XGBoost, (

**b**) random forest, (

**c**) LightGBM, and (

**d**) CatBoost models.

**Figure 9.**Comparison of the experimental and predicted shear stress values for (

**a**) XGBoost, (

**b**) random forest, (

**c**) LightGBM, and (

**d**) CatBoost models.

**Figure 10.**(

**a**) Predictions of the shear stress, (

**b**) error percentages, (

**c**) error distribution of the training set, and (

**d**) error distribution of the test set for the XGBoost model.

**Figure 11.**Comparison of the experimental and predicted plastic viscosity values for (

**a**) XGBoost, (

**b**) random forest, (

**c**) LightGBM, and (

**d**) CatBoost models.

**Figure 12.**(

**a**) Predictions of the plastic viscosity, (

**b**) error percentages, (

**c**) error distribution of the training set, and (

**d**) error distribution of the test set for the CatBoost model.

**Figure 13.**SHAP (SHapley Additive exPlanation) values [53].

**Figure 16.**Feature dependence plots for the variables in the prediction of τ: (

**a**) D, (

**b**) t, (

**c**) PA, and (

**d**) μ.

**Figure 17.**Feature dependence plots for the variables in the prediction of $\mu $: (

**a**) D, (

**b**) t, (

**c**) PA, and (

**d**) $\tau $.

**Figure 18.**Prediction consistency plots for the variables in the prediction of $\tau $: (

**a**) D, (

**b**) t, (

**c**) PA, and (

**d**) $\tau $.

**Figure 19.**Prediction consistency plots for the variables in the prediction of $\mu $: (

**a**) D, (

**b**) t, (

**c**) PA, and (

**d**) $\tau $.

**Figure 20.**Individual conditional expectation (ICE) plots for the variables in the prediction of $\tau $: (

**a**) D, (

**b**) t, (

**c**) PA, and (

**d**) $\mu $.

**Figure 21.**Individual conditional expectation (ICE) plots for the variables in the prediction of $\mu $: (

**a**) D, (

**b**) t, (

**c**) PA, and (

**d**) $\tau $.

Dataset | Property | D | t | PA | $\mathit{\mu}$ | $\mathit{\tau}$ |
---|---|---|---|---|---|---|

Training (119 samples) | Unit | cm | s | - | $\left[\mathrm{Pa}\cdot \mathrm{s}\right]$ | $\left[\mathrm{Pa}\cdot \mathrm{s}\right]$ |

Min | 52.4 | 7.0 | 0.5 | 18.2 | 0.2 | |

Max | 88.0 | 60.0 | 1.0 | 296.3 | 98.6 | |

Mean | 68.19 | 18.10 | 0.83 | 107.40 | 29.23 | |

SD | 9.08 | 9.94 | 0.11 | 67.34 | 21.54 | |

As | 0.65 | 1.30 | −0.69 | 0.57 | 1.18 | |

K | −0.54 | 2.09 | 0.35 | −0.10 | 1.28 | |

Test (51 samples) | Min | 54.0 | 7.0 | 0.52 | 18.3 | 0.8 |

Max | 88.0 | 60.0 | 1.0 | 274.65 | 97.8 | |

Mean | 69.30 | 16.04 | 0.85 | 93.26 | 25.34 | |

SD | 9.12 | 9.57 | 0.11 | 58.22 | 20.71 | |

As | 0.59 | 2.38 | −0.83 | 0.81 | 1.63 | |

K | −0.55 | 7.45 | 0.99 | 0.52 | 2.78 |

Model | Parameter | Value |
---|---|---|

Random Forest | Number of estimators (n_estimators) | 5 |

Minimum samples for split (min_samples_split) | 3 | |

Minimum samples of leaf node (min_samples_leaf) | 1 | |

Maximum tree depth (max_depth) | None | |

Number of features (max_features) | “sqrt” | |

XGBoost | Number of estimators (n_estimators) | 50 |

Step size shrinkage (eta) | 0 | |

Learning rate | 0.1 | |

Subsample ratio of the training instances (subsample) | 0.5 | |

Maximum depth of a tree | 6 | |

LightGBM | Number of estimators (n_estimators) | 500 |

Maximum number of decision leaves (num_leaves) | 5 | |

Maximum depth of a tree (max_depth) | 4 | |

Learning rate | 0.2 | |

use extremely randomized trees (extra_trees) | True | |

CatBoost | Bagging temperature (bagging_temperature) | 10 |

Learning rate | 0.3 | |

Depth | 8 | |

Tree growing policy (grow_policy) | “Depthwise” |

Algorithm | R^{2} | MAE | VAF | RMSE | Duration [s] | ||||
---|---|---|---|---|---|---|---|---|---|

Train | Test | Train | Test | Train | Test | Train | Test | ||

XGBoost | 0.9997 | 0.9802 | 0.094 | 1.712 | 99.99 | 97.04 | 0.397 | 2.885 | 4.54 |

Random Forest | 0.9977 | 0.9797 | 0.658 | 1.795 | 99.76 | 98.05 | 1.037 | 2.924 | 3.24 |

LightGBM | 0.8968 | 0.9111 | 4.104 | 3.624 | 90.08 | 90.80 | 6.888 | 6.114 | 4.04 |

CatBoost | 0.9988 | 0.9779 | 0.572 | 2.120 | 99.92 | 97.98 | 0.747 | 3.047 | 22.69 |

Algorithm | R^{2} | MAE | VAF | RMSE | Duration [s] | ||||
---|---|---|---|---|---|---|---|---|---|

Train | Test | Train | Test | Train | Test | Train | Test | ||

XGBoost | 0.9999 | 0.9132 | 0.041 | 8.274 | 99.99 | 91.56 | 0.084 | 16.986 | 4.66 |

Random Forest | 0.9896 | 0.9570 | 3.665 | 7.703 | 98.74 | 95.44 | 6.846 | 11.961 | 3.15 |

LightGBM | 0.9324 | 0.9387 | 9.527 | 9.286 | 93.61 | 93.18 | 17.437 | 14.270 | 3.65 |

CatBoost | 0.9986 | 0.9654 | 1.764 | 7.602 | 99.95 | 96.32 | 2.487 | 10.727 | 19.82 |

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**MDPI and ACS Style**

Cakiroglu, C.; Bekdaş, G.; Kim, S.; Geem, Z.W.
Explainable Ensemble Learning Models for the Rheological Properties of Self-Compacting Concrete. *Sustainability* **2022**, *14*, 14640.
https://doi.org/10.3390/su142114640

**AMA Style**

Cakiroglu C, Bekdaş G, Kim S, Geem ZW.
Explainable Ensemble Learning Models for the Rheological Properties of Self-Compacting Concrete. *Sustainability*. 2022; 14(21):14640.
https://doi.org/10.3390/su142114640

**Chicago/Turabian Style**

Cakiroglu, Celal, Gebrail Bekdaş, Sanghun Kim, and Zong Woo Geem.
2022. "Explainable Ensemble Learning Models for the Rheological Properties of Self-Compacting Concrete" *Sustainability* 14, no. 21: 14640.
https://doi.org/10.3390/su142114640