# Prediction of Self-Healing of Engineered Cementitious Composite Using Machine Learning Approaches
###### Abstract  
Engineered cementitious composite (ECC) is a unique material, which can significantly contribute to self-healing based on ongoing hydration. However, it is difficult to model and predict the self-healing performance of ECC. Although different machine learning (ML) algorithms have been utilized to predict several properties of concrete, the application of ML on self-healing prediction is considerably rare. This paper aims to provide a comparative analysis on the performance of various machine learning models in predicting the self-healing capability of ECC. These models include four individual methods, linear regression (LR), back-propagation neural network (BPNN), classification and regression tree (CART), and support vector regression (SVR). To improve prediction accuracy, three ensemble methods, namely bagging, AdaBoost, and stacking, were also studied. A series of experimental works on the self-healing performance of ECC samples was conducted, and the results were used to develop and compare the accuracy among the ML models. The comparison results showed that the Stack_LR model had the best predictive performance, showing the highest coefficient of determination (\(R^{2}\)), the lowest root-mean-squared error (RMSE), and the smallest prediction error (MAE). Among all individual models studies, the BPNN model performed the best in terms of the RMSE and \(R^{2}\), while SVR performed the best in terms of the MAE. Furthermore, SVR had the smallest prediction error (MAE) for crack widths less than 60 \(\upmu\)m or greater than 100 \(\upmu\)m, while CART had the smallest prediction error (MAE) for crack widths between 60 \(\upmu\)m and 100 \(\upmu\)m. The study concluded that the individual and ensemble methods can be used to predict the self-healing of ECC. Ensemble models were able to improve the accuracy of prediction compared to the individual model used as their base learner, i.e., a 2.3% to 4.9% reduction in MAE. However, selecting an appropriate individual and ensemble method is critical. To improve the performance accuracy, researchers should employ different ensemble methods to compare their effectiveness with different ML models. engineering cementitious composites; self-healing; machine learning; ensemble method +
Footnote †: journal: Applied Sciences  
problems associated with concrete cracking and thereby reducing the maintenance costs over a structure's lifetime [1]. The inspiration of self-healing comes from the biomimicry concept and the healing process in living nature [3]. For example, the skin of humans or animals can biologically repair itself from simple injuries. In cement-based materials, the process of crack self-healing can be categorized into two major mechanisms, i.e., autogenous healing and autonomous healing [4]. The former indicates the self-healing ability results from the physical and/or chemical composition of the cementitious matrix, whereas the self-healing mechanism of the latter is triggered by some biological agents, such as bacteria that are deliberately introduced into the cementitious matrix. Generally, the autogenous self-healing of concrete is mainly controlled by two mechanisms including (1) further hydration of cement particles and/or swelling of calcium silicate hydrate and (2) calcium hydroxide carbonation [5, 6]. It has been reported that crack widths of 10 \(\upmu\)m [7], 100 \(\upmu\)m [8], 200 \(\upmu\)m [9], 205 \(\upmu\)m [5], and 300 \(\upmu\)m [10] of engineered cementitious composite (ECC) can be self-healed completely [11]. ECC is a high-performance fiber-reinforced cementitious composite, and its matrix design is strongly associated with the autogenous self-healing mechanism [12]. ECC features high tensile ductility with a typical fiber volume fraction of 2% [13, 14] to promote the self-healing ability [4].