# Bond Strength Assessment of Concrete-Corroded
## 5 Conclusions  
In this study, to assess the bond strength between concrete and the rebar after corrosion, an ANN was used to examine each parameter correlated to the bond degradation, with respect to the cases with and without confinement. Existing experimental data were collected for calculation and verification. The accuracy of assessment was found to be higher and the method showed more advantages compared to the existing models when more parameters were considered. For the training approach, the error-back-propagation approach using gradient descent and momentum techniques was adopted. Based on the results and discussions, the following conclusions can be drawn:  
1. The proposed scaled FF-BP-ANN method shows higher accuracy than those based on multiple linear regression and multiple nonlinear regression. By inputting the corrosion level, crack width, concrete strength and cover-to-diameter ratio, the ANN method can achieve satisfactory results of bond strength when the rebar is corroded. Besides, the method was validated by comparing with results calculated based on the existing analytical models. The proposed method can be employed for evaluating structural performance in the future. 2. Different epochs were employed for the calculation, and there was an insignificant difference between cases with 1000 and 100,000 epochs. The proposed method was found to be effective in calculating with few epochs, such as 1000, which can help achieve reliable results and ensure efficient and fast calculations. 3. For the unconfined cases, the bond strengths were dominated by the corrosion level and crack width. For cases with a confined condition, in addition to the corrosion level and crack width, other parameters such as concrete strength, cover-to-diameter ratio and stirrups diameter/spacing ratio were also important. The accuracy of the predicted results was not satisfactory without these parameters. It seems that parameters related to confinement such as cover-to-diameter ratio are more important than the materials properties in cases under the confined condition, while the opposite trend is observed in the cases under the unconfined condition. 4. For both cases with and without confinement, if the prediction did not consider the corrosion level, the accuracy would be much lower. However, the results seem acceptable if all other parameters were considered as inputs. This means that it is feasible to predict the bond strength based on the crack width on the surface of concrete, the known configuration information and materials properties. In the parametric analysis, the relative importance of each parameter was preliminarily examined. As indicated by the results, in cases under the unconfined condition, the relative importance was found to be: corrosion level \(>\) crack width \(>\) concrete strength \(>\) cover-to-diameter ratio. While for cases under the confined condition, the relative importance was: crack width \(>\) corrosion level \(>\) cover-to-diameter ratio \(>\) stirrups diameter-to-spacing ratio \(>\) concrete strength. Due to limited available data, these results require further verification. With respect to the ANN model, to overcome the drawbacks of vanishing gradient of the Sigmoid function and local optima, we also plan a future study which improves this part by utilizing a harmony search meta-heuristic algorithm, one of the gradient-free global optimization algorithms, which can directly adopt the original step function representing threshold instead of Sigmoid or ReLU (Rectified Linear Unit). Analysis and writing--original draft preparation, Y.W. ; methodology and supervision Z.W.G. and K.N. ; Conceptualization and writing--review and editing, Z.W.G. and K.N. ; and funding, Y.W. and Z.W.G. All authors have read and agreed to the published version of the manuscript. The first author would like to express his sincere thanks to the Japan Society for the Promotion of Science (JSPS) for providing fellowship (P18348) for his study.