# Modeling Self-Healing of Concrete Using Hybrid Genetic Algorithm–Artificial Neural Network

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Research Significance

## 3. Concept of Neural Network Prediction of Self-Healing in Concrete

_{3}) and/or calcium silicate hydrate (C–S–H). For example, both Özbay et al. [53] and Sahmaran et al. [54] used scanning electron microscopy (SEM) and X-ray diffraction (XRD) to investigate the mineralogy and chemical composition of the healing product observed in the cracked specimens exposed to continuous curing. They reported the formation of both CaCO

_{3}and C–S–H. In addition, a high amount of CaCO

_{3}was reported in the case of using supplementary materials with higher CaO content. Wiktor and Jonkers [27] also reported significant formation of CaCO

_{3}as a healing product due to metabolic conversion of calcium lactate and the reaction of metabolically produced CO

_{2}molecules with Ca(OH)

_{2}minerals present in the concrete. Sisomphon et al. [11] also found that CaCO

_{3}was the major healing product formed in cracks due to the increased release of Ca

^{2+}and high pH of the cement mortar specimens incorporating the healing agents. According to Van Tittelboom and De Belie [52], intrinsic healing can include autogenous healing (further hydration of un-hydrated cement and carbonation of calcium hydroxide) and improved autogenous healing using agents or approaches that promote crystallization and more cementitious hydration reactions. Özbay et al. [53], Sahmaran et al. [54], and Van Tittelboom et al. [17] investigated autogenous self-healing under similar environmental condition and reported practically similar final healing products. Moreover, studies by Sisomphon et al. [11] and Wiktor and Jonkers [27] investigated the improved autogenous self-healing under similar condition and reported similar final healing products. Hence, developing a model based on artificial neural networks to predict the effect of such agents reported in these studies on crack self-healing was considered a suitable approach.

## 4. Artificial Neural Network (ANN)

#### 4.1. Neural Network Approach

#### 4.2. Neural Network Architectures and Parameters

_{n}is the weighted sums of the input component, W

_{nj}is the weight between neurons, x

_{j}is the input, and b is the bias.

_{n}is the output of the neuron and A

_{f}is the activation function.

#### 4.3. Hybrid Genetic Algorithm–Artificial Neural Network (GA–ANN)

_{j}is a vector of current weights and biases; µ is a learning rate; J is the Jacobian matrix; J

^{T}is the transpose matrix of J; I is the identity matrix; and e is a vector of network errors.

#### 4.4. Database Sources and Range of Input and Output Variables

## 5. Performance of GA–ANN Model

^{2}) of model prediction versus experimental data for the training, validation, and test data sets are 0.99765, 0.99773, and 0.99736 respectively. Thus, it can be argued that the proposed GA–ANN model captured the relationships between the provided input and output data with adequate accuracy, which indicates excellent performance.

^{2}), and mean absolute percentage error (MAPE) between the model’s predictions and experimental results, according to Equations (6)–(8). The RMS, R

^{2}, and MAPE values were 10.19 µm, 0.99762, and 10.13%, respectively, which indicates adequate performance of the GA–ANN model.

_{i}is the target output; o

_{i}is the predicted output; and n is the number of data point.

## 6. Conclusions

- The developed GA–ANN model represents a powerful computational tool with high efficiency providing an alternative solution for the modeling procedure of the highly complex self-healing phenomenon in cement-based materials.
- A genetic algorithm was effectively applied in the ANN model to determine the optimal weights and biases that govern the input–output relationship of the model.
- Training the GA–ANN multilayered feed-forward neural network with a back-propagation algorithm showed accurate prediction of the self-healing crack ability in cementitious materials, yielding predictions that were close to the actual experimental values.
- The proposed model was capable of providing accurate predictions for the self-healing ability of a cementitious material, which in return can be used to enhance the durability design of concrete, leading to more durable and sustainable structures.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 4.**Regression plot of GA–ANN predicted change in crack width due to self-healing versus the corresponding experimentally observed change in crack width: (

**a**) training; (

**b**) validation; (

**c**) test; and (

**d**) complete data set.

**Figure 5.**Crack development in mortar specimens tested for self-healing: (

**a**) loading procedure; (

**b**) crack development; and (

**c**) crack width measurement using a microscope.

**Figure 7.**GA–ANN model predictions of crack self-healing (reduction in crack width) of cementitious materials versus corresponding experimentally measured results.

Parameter | GA–ANN |
---|---|

Number of input layer neurons | 11 |

Number of first hidden layer neurons | 14 |

Number of output layer neurons | 1 |

MSE goal | 13 × 10^{−5} |

Source | No. of Data Points | |

Wiktor and Jonkers [27] | 640 | |

Sisomphon et al. [11] | 594 | |

Sahmaran et al. [54] | 36 | |

Van Tittelboom et al. [17] | 182 | |

Özbay et al. [53] | 10 | |

Database Parameter | Maximum | Minimum |

Cement (mR %) | 100 | 15 |

w/c (mR %) | 60 | 25 |

Sand (mR %) | 309 | 200 |

BFS (mR %) | 220 | 0 |

FA (mR %) | 220 | 0 |

Calcium sulfo-aluminate (mR %) | 10 | 0 |

Crystalline additive (mR %) | 4 | 0 |

LWA (mR %) | 76 | 0 |

LWA with bacteria spores (mR %) | 76 | 0 |

Initial crack width (µm) | 400 | 40 |

Healing time (days) | 150 | 0 |

Final crack width (µm) * | 400 | 0 |

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**MDPI and ACS Style**

Ramadan Suleiman, A.; Nehdi, M.L.
Modeling Self-Healing of Concrete Using Hybrid Genetic Algorithm–Artificial Neural Network. *Materials* **2017**, *10*, 135.
https://doi.org/10.3390/ma10020135

**AMA Style**

Ramadan Suleiman A, Nehdi ML.
Modeling Self-Healing of Concrete Using Hybrid Genetic Algorithm–Artificial Neural Network. *Materials*. 2017; 10(2):135.
https://doi.org/10.3390/ma10020135

**Chicago/Turabian Style**

Ramadan Suleiman, Ahmed, and Moncef L. Nehdi.
2017. "Modeling Self-Healing of Concrete Using Hybrid Genetic Algorithm–Artificial Neural Network" *Materials* 10, no. 2: 135.
https://doi.org/10.3390/ma10020135