# Self-Healing Performance Assessment of Bacterial-Based Concrete Using Machine Learning Approaches

^{1}

^{2}

^{*}

## Abstract

**:**

^{2}) and root mean square error (RMSE) are applied to evaluate the prediction ability, including the prediction performance and accuracy of the ML models. The results exhibit that the GBR model has better prediction ability (R

^{2}

_{GBR}= 0.956, RMSE

_{GBR}= 6.756%) than other ML models. Finally, the influence of the variables on the HP is investigated by employing the sensitivity analysis in the GBR model.

## 1. Introduction

^{2}and RMSE, which can indicate the prediction ability of the ML models, are obtained by training the ML models with five algorithms. Then, the optimal ML model for predicting the HP of BSHC is defined according to the R

^{2}and RMSE. Moreover, the 10-fold cross validation method is applied to validate the prediction ability of the optimal ML model. Finally, a sensitivity analysis is also conducted on the optimal ML model to investigate the primary influencing variables.

#### 1.1. Types of BSHC

#### 1.1.1. Ureolytic Bacterial Healing Concrete (UBHC)

#### 1.1.2. Aerobic Bacterial Healing Concrete (ABHC)

#### 1.1.3. Nitrifying Bacterial Healing Concrete (NBHC)

#### 1.2. Types of Bacteria

#### 1.3. Influencing Factors of HP

#### 1.4. Healing Performance Determination

## 2. Materials and Methods

#### 2.1. Data Preparation

#### 2.2. Machine Learning Algorithms

^{2}value of 0.9226, which was dramatically higher than that of the MLR model (R

^{2}

_{MLR}= 0.7456). Furthermore, R

^{2}values of 0.951 and 0.929 for predicting the compressive and splitting tensile strength were demonstrated by employing GBR models [24,39,40,41,42,43,44,45,46,47,48,49,50,51]. In this paper, the prediction ability of the five types of ML models for predicting the HP of BSHC is studied. To achieve the best prediction ability, here a hyper-parameter tuning method named GSA is utilised to determine the optimal parameters of the ML models [52]. The reason why GSA is a reliable hyper-parameter tuning method can be attributed to its ability to find the optimal hyper-parameters combination according to an exhaustive analysis [53,54,55,56].

#### 2.3. Prediction Ability Evaluation

#### 2.4. Data Splitting

## 3. Results

#### Prediction Ability of ML Models

^{2}and RMSE values) of the training and testing data sets by the five types of ML models demonstrating the relationship between the predicted and experimental HP of BSHC is exhibited in Figure 2. R

^{2}and RMSE values are applied to inspect the prediction performance and accuracy of the ML models. The horizontal and vertical axes indicate the experimental and predicted HP, respectively. Furthermore, the results of the ML models are demonstrated in Table 2 to show the differences in the prediction ability. Moreover, the optimal parameters of the ML models defined by GSA are listed in Table 3.

^{2}than the other four ML models. The R

^{2}and RMSE of GBR are 0.956 and 6.756%, respectively. Furthermore, the R

^{2}and RMSE values of DNN, DTR, RF and SVR are (0.870, 14.145%), (0.882, 12.766%), (0.899, 11.760%) and (0.871, 13.352%), respectively, which are lower than that of the GBR model (Figure 2c,j). According to the results, the following can be concluded. Firstly, the GBR model is the optimal model for predicting the HP of BSHC due to the highest R

^{2}(0.956) and lowest RMSE (6.756%). Secondly, the GBR model is reliable because of the similar R

^{2}results of the training and testing sets, indicating no underfitting or overfitting problem. Thirdly, the RMSE (6.756%) of the GBR model demonstrates that the prediction deviation is low and robust.

## 4. Discussion

#### 4.1. K-Fold Cross Validation

^{2}and RMSE values of all GBR models [59].

^{2}and RMSE values) of the GBR models validated by different folds of the data sets is shown in Figure 3. Slight differences in R

^{2}and RMSE values of the GBR models can be noticed in Figure 3a,b. For instance, 0.947 is the maximum R

^{2}value of the GBR model at Fold 8, while 0.937 is the minimum R

^{2}value of the GBR model at Fold 1. The rest of the R

^{2}values are maintained at approximately 0.944. Furthermore, the RMSE value dramatically decreases from 6.864% to 6.039% between Fold 1 and Fold 2, followed by a slight growth to 6.210% at Fold 3. Subsequently, it keeps constant at 6.218% until Fold 6. It then fluctuates between 6.067% and 6.218% from Fold 7 to Fold 10. Moreover, the average R

^{2}and RMSE values and the standard deviations (SDs) of the GBR models are listed in Table 4. The average R

^{2}and RMSE values of the GBR models with different folds of the data sets are 0.9438 and 6.2342%, respectively. Additionally, the SDs of the R

^{2}and RMSE values are 0.0029 and 0.2208, respectively, which can be concluded that the coefficient of variations (COVs) of the values are relatively low, only 0.31% and 3.54%, respectively. Regarding the R

^{2}, RMSE and the statistical results of the GBR models, it can be concluded that the promising prediction ability of the GBR model for predicting the HP of BSHC is reliable.

#### 4.2. Sensitivity Analysis

## 5. Conclusions

- The ${\mathrm{R}}^{2}$ and RMSE values of the GBR model were 0.956 and 6.756%, respectively, which means that the prediction performance is excellent, and the prediction deviation is relatively low and reasonable. The GBR model was also compared to other ML algorithms, such as DTR, SVR, DNN and RF, and it showed an outstanding superiority to these ML models. Thus, it can be concluded that GBR is the optimal ML model that can accurately predict the HP of BSHC with the 22 variables.
- Concerning the results of the 10-fold cross validation, the average R
^{2}and RMSE values were 0.9438 and 6.2342%, respectively. Thus, it can be concluded that the robust prediction ability of the GBR model is convincing. - All variables in the GBR model were studied to inspect the influence on the HP of BSHC. It was observed that CW, FA, CM, W/B, HT and DB are key variables and have relatively higher effects on the HP of BHSC, which means that they cannot be neglected during the ML-aided self-healing concrete design.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

Number | Representation |
---|---|

0 | No carrier |

1 | Expanded clay |

2 | Expanded perlite |

3 | Graphene nanoplatelets |

4 | Coir |

5 | Flax |

6 | Jute |

7 | Low alkali calcium sulphoaluminate |

8 | Recycled brick aggregate |

Number | Representation |
---|---|

0 | No bacteria |

1 | Bacillus subtilis |

2 | Bacillus cohnii |

3 | Bacillus alkalinitrilicus |

4 | Bacillus pasteurii |

5 | Bacillus sphaericus |

6 | Bacillus megaterium |

Number | Representation |
---|---|

1 | Ambient water condition |

2 | Ambient air condition |

3 | Wet–dry cycles |

Number | Representation |
---|---|

0 | Autogenous healing |

1 | ABHC |

2 | UBHC |

Number | Representation |
---|---|

1 | Peptone |

2 | Yeast |

3 | Beef extract |

Number | Representation |
---|---|

0 | Water |

1 | Air |

2 | Calcium lactate |

Number | Representation |
---|---|

1 | CEM I 42.5N |

2 | CEM II 42.5N |

3 | CEM I 52.5N |

Number | Representation |
---|---|

1 | Calcium nitrate |

2 | Calcium lactate |

3 | Ca(OH)_{2} |

Number | Representation |
---|---|

1 | Cracking width measurement |

2 | Cracking area measurement |

3 | Ultrasound pulse velocity measurement |

4 | Regained strength measurement |

5 | Anti-seepage repairing measurement |

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**Figure 2.**Experimental vs. predicted HP for the models: (

**a**) GBR-training; (

**b**) GBR-testing; (

**c**) DTR-training; (

**d**) DTR-testing; (

**e**) DNN-training; (

**f**) DNN-testing; (

**g**) SVR-training; (

**h**) SVR-testing; (

**i**) RF-training; and (

**j**) RF-testing, with the corresponding R

^{2}and RMSE.

**Figure 3.**(

**a**) R

^{2}results and (

**b**) RMSE results of GBR models with the 10-fold cross validation for predicting HP of BSHC.

Types of Variables | Symbol | Unit | Minimum | Maximum |
---|---|---|---|---|

Inputs | C | - | 0 | 8 |

TC | - | 1 | 3 | |

B | - | 0 | 6 | |

DB | cells/g | 0 | 2.6 × 10^{9} | |

TBSHC | - | 0 | 2 | |

TCIS | - | 1 | 3 | |

DCI | g/g | 0 | 0.034 | |

TCS | - | 0 | 2 | |

DC | g/g | 0 | 0.034 | |

TN | - | 1 | 3 | |

DN | g/L | 0 | 4 | |

DU | g/L | 0 | 0.024 | |

FA | g/g | 0.204 | 0.666 | |

CA | g/g | 0 | 0.522 | |

CM | g/g | 0.156 | 0.222 | |

W/B | - | 0.4 | 0.599 | |

S | g/g | 0 | 1.564 | |

CD | days | 3 | 56 | |

CW | mm | 0.027 | 1.152 | |

HC | - | 1 | 3 | |

HT | days | 3 | 100 | |

HTM | - | 1 | 5 | |

Output | HP | % | 0 | 100.76 |

Algorithm | Dataset | HP Prediction Ability | |
---|---|---|---|

R^{2} | RMSE (%) | ||

GBR | Training | 0.978 | 4.371 |

Testing | 0.956 | 6.756 | |

DTR | Training | 0.935 | 10.038 |

Testing | 0.882 | 12.766 | |

DNN | Training | 0.898 | 13.583 |

Testing | 0.870 | 14.145 | |

SVR | Training | 0.928 | 10.683 |

Testing | 0.871 | 13.352 | |

RF | Training | 0.941 | 9.797 |

Testing | 0.899 | 11.760 |

Algorithms | Parameters | Setting |
---|---|---|

DNN | Hidden layers | 4 |

Hidden neurons | 30-30-30-30 | |

Learning rate | 0.0010 | |

Activation function | Maxout | |

GBR | Depth_{max} | 21 |

Split_{min} | 0.001 | |

Learning rate | 0.9001 | |

Number of trees | 21 | |

DTR | Depth_{max} | 10 |

Split_{min} | 1.000 | |

Leaf_{min} | 1 | |

Gain_{min} | 0.0010 | |

SVR | C_{penalty} | 1 |

Epsilon | 0.001 | |

Gamma | 5000 | |

Kernel type | Radial | |

RF | Depth_{max} | 60 |

Split_{min} | 100.000 | |

Leaf_{min} | 60 | |

Gain_{min} | 0.3007 | |

Number of trees | 11 |

Folds | HP Prediction Ability | |
---|---|---|

R^{2} | RMSE (%) | |

Fold 1 | 0.937 | 6.864 |

Fold 2 | 0.945 | 6.039 |

Fold 3 | 0.940 | 6.210 |

Fold 4 | 0.944 | 6.218 |

Fold 5 | 0.945 | 6.218 |

Fold 6 | 0.946 | 6.218 |

Fold 7 | 0.944 | 6.067 |

Fold 8 | 0.947 | 6.206 |

Fold 9 | 0.946 | 6.084 |

Fold 10 | 0.944 | 6.218 |

Average | 0.9438 | 6.2342 |

SD | 0.0029 | 0.2208 |

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**MDPI and ACS Style**

Huang, X.; Sresakoolchai, J.; Qin, X.; Ho, Y.F.; Kaewunruen, S.
Self-Healing Performance Assessment of Bacterial-Based Concrete Using Machine Learning Approaches. *Materials* **2022**, *15*, 4436.
https://doi.org/10.3390/ma15134436

**AMA Style**

Huang X, Sresakoolchai J, Qin X, Ho YF, Kaewunruen S.
Self-Healing Performance Assessment of Bacterial-Based Concrete Using Machine Learning Approaches. *Materials*. 2022; 15(13):4436.
https://doi.org/10.3390/ma15134436

**Chicago/Turabian Style**

Huang, Xu, Jessada Sresakoolchai, Xia Qin, Yiu Fan Ho, and Sakdirat Kaewunruen.
2022. "Self-Healing Performance Assessment of Bacterial-Based Concrete Using Machine Learning Approaches" *Materials* 15, no. 13: 4436.
https://doi.org/10.3390/ma15134436