# Bond Strength Assessment of Concrete-Corroded
## 3 Application of Artificial Neural Network (ANN) Model
### Comparison between ANN and Previous Analytical Models  
Researchers have attempted to develop analytical models for evaluating the bond strength. Some models depend on corrosion level, while others include more parameters such as crack width. In this study, existing models used for the calculation were based on the same database as the one used by the ANN method. As shown in Figures 4-7, the predicted results were compared with the experimental results and the \(R^{2}\) and RMSE were calculated. In Figure 5, the database has 242 series of data collected from existing studies, as mentioned in Section 2; all cases are for specimens without stirrups. The equations from [PERSON] [51] and [PERSON] et al. [52] were adopted for calculation, wherein only the corrosion level is considered as the input. The predicted results from ANN consider the corrosion level as the variable. The ANN shows clear advantages in both \(R^{2}\) and RMSE. In addition, [PERSON] et al. [53] developed a model which considers the crack width as the only variable. In this study, it was adopted for calculation and compared with the results from the ANN, as shown in Figure 6. There are 107 series of data for calculation, which are available from the existing literature. Although the analytical model developed by [PERSON] et al. showed a slightly better \(R^{2}\), the ANN method obtained  
Figure 4: Comparison of the results predicted by ANN using different epochs: (**a**) 100; (**b**) 1000; (**c**) 10,000; and (**d**) 100,000.  
fewer errors as the RMSE was smaller. It seems that the ANN method can achieve better prediction than the existing model considering only the crack width.  
Figure 5: Comparison between the existing analytical models and ANN method considering only corrosion level as an input for specimens without stirrups (unconfined) (note: \(\tau_{u}(\eta)\) is the bond strength of specimen with corrosion level of \(\eta\), \(\tau_{u}(0)\) is the bond strength of the specimen without corrosion damage and \(\eta\) is the corrosion level): (**a**) [PERSON] (1996) [51]; (**b**) [PERSON] et al. (2008) [52]; (**c**) ANN.  
If more variables were considered for bond strength prediction, more accurate results would be obtained. To this end, models that include more parameters as inputs have been developed. For example, [PERSON] et al. [54] considered both the corrosion level and the cover-to-diameter ratio, whereas [PERSON] et al. [55] considered the crack width and cover-to-diameter ratio as variables in their model. Similarly, based on the same database, predictions were obtained using the analytical model and the proposed ANN method, respectively. As shown in Figures 7 and 8, comparisons were made  
Figure 6: Comparison between the existing analytical models and ANN method considering only crack width as input for specimens without stirrups (unconfined) (note: \(\tau_{u}(w)\) is the bond strength of specimen with crack width \(w\), \(\tau_{u}(0)\) is the bond strength of specimen without corrosion damage and \(w\) is the crack width on the surface of specimen): (**a**) [PERSON] et al. (2003) [53]; (**b**) ANN.  
Figure 7: Comparison between the existing analytical models and ANN method considering both corrosion level and cover-to-diameter ratio as inputs for specimens without stirrups (unconfined) (note \(\tau_{u}(\eta)\) is the bond strength of specimen with corrosion level of \(\eta\), \(\tau_{u}(0)\) is the bond strength of specimen without corrosion damage and \(\eta\) is the corrosion level and \(c/d\) is the cover-to-diameter ratio): (**a**) [PERSON] et al. (1999) [54]; (**b**) ANN.  
with respect to \(R^{2}\) and RMSE. The results from the ANN method present higher values of both, verifying the advantage of this method.