## 4 Evaluation of Hollow Slab Girders Based on Surface Damage and Neural Networks  
### Evaluation Using Neural Network  
It is costly and time-consuming to perform the truck load test and cutting off process in order to evaluate the hinge joint damage and the durability of the hollow slab bridges in the entire highway system. As the bending moment and stiffness of a single girder are greatly affected by its condition state and the load distribution under the joints, the cracking of the bottom plates at different locations of the bridge is a critical parameter under the external load. The surface cracks can be clearly observed in the visual inspection. If a relationship between the surface cracks and the damage index (hinge joint damage \(\mu\) or the durability result \(R_{d}\)) can be found, the evaluation of the bridge is more convenient with a much lower inspection cost. Therefore, the artificial neural networks (ANN) method is employed to establish the correlation between the damage index and cracks. As a powerful machine-learning tool, the ANN method can fit the nonlinear mapping relations well and has been widely used in the bridge performance evaluation [18]. The backpropagation network used in this study is shown in Figure 16 with a single hidden layer. The network structure includes the input layer, hidden layer, and output layer. The set of raw data obtained from the visual inspections is used in the input layer. Based on the transfer function, weight of the input, and bias, an artificial neuron produces an output in the hidden layer. The desired results in the output layer are then calculated by summing up the weighted inputs in the hidden layer. As such, a feedforward calculation ends, and the prediction error of the results is obtained. The training phase then starts by adjusting the weights and biases in each layer with the backward error propagation. The training ends until the errors or the termination condition met the requirements. Based on the statistical analysis of the surface damage in different locations and the concrete cracking under the degradation of the mechanical performance, the maximum crack width was selected as the critical parameter in the input data set, as shown in Figure 16. For a hollow slab concrete bridge in the Wu-He highway system, there are eight single girders and seven hinge joints. Each girder was equally divided into six segments in the longitudinal direction, i.e., 0-1/3 span, 1/3-2/3 span, and 2/3-1 span, and the maximum crack width on the bottom plates of three girder segments was recorded. The maximum crack width of 24 segments and seven hinge joints was recorded, and a total of 31 parameters were considered in the input layer for one bridge. As two cases were studied including the hinge joint damage and girder durability, there were seven output results for the hinge joint damage \(\mu\) and eight output results for the durability evaluation result \(R_{d}\). As the data in the field test are limited, an updated FE model was used to obtain the additional  
Figure 16: Backpropagation network. data set with different damage conditions. A reduction factor calculated by the maximum crack width was used in the elastic modulus to account for the decrease of the bending stiffness. The status of the virtual beams and the boundary condition were adjusted to simulate the weakening of the hinge joints. A total of 115 samples were obtained from the field test and the FE simulation which included 25 bridges. A total of 100 samples from 21 bridges were used in the training of the network, and 15 samples from four bridges were used for verification. A single hidden layer is employed as two or more hidden layers may lead to over-fitting of the data and an increase in training time. The sigmoid function was employed in the transfer function, and gradient descent algorithm is used in the training phase. The maximum number of iterations in the training phase was set to be 500.