## 4 Pipeline System Modeling
### Damage, Load and Support Identification Using CNN
C1 has 156 tuned parameters (each filter has 16 \(\times\) 16 unit parameters and a bias parameter, 6 filters in total, so (16 \(\times\) 16 + 1) \(\times\) 6 = 1542 parameters in total). One kernel is used between input and C1, so 1542 \(\times\) (196 \(\times\) 196) = 59,237,472 connections in total. S2 is a sub-sampling layer. According to the local correlation principle of image, sub-sampling can be applied to images, thus decreasing data processing ability and retaining useful information. Two 98 \(\times\) 98 feature maps are used. Each unit of feature map is connected with 8 \(\times\) 8 neighborhood of C1. Sixteen inputs of each unit of S2 are added, multiplied by a tuned parameter with a tuned bias. The result can be calculated by sigmoid function. Tuned parameters and bias control the non-linearity of the sigmoid function. If these parameters are relatively small, the operation is as similar as linear operation. Sub-sampling is equivalent to fuzzy images by decreasing the pixels of the images. If these parameters are relatively larger, sub-sampling can be regarded as \"or\" or \"and\" operations with noise. 8 \(\times\) 8 receptive field is not overlapped for each unit, therefore the size of each feature map in S2 is 1/4 of that of C1. S2 has (1 + 1) \(\times\) 2 = 4 tuned parameters and (8 \(\times\) 8 + 1) \(\times\) 2 \(\times\) (98 \(\times\) 98) = 1,248,520 connections. C3 and S4 have similar architectures, and output layers are composed of Euclidean radial basis function units. Images are fed into the network and the output \(O_{p}=F_{n}\Big{(}\cdots\Big{(}F_{2}\Big{(}F_{1}\Big{(}X_{p}W^{(1)}\Big{)}W^{ (2)}\Big{)}\Big{)}\cdots W^{(n)}\Big{)}\), and the error between practical output \(O_{p}\) and desired output \(Y_{p}\) can be calculated by back propagation with tuned weight parameters. Table 3 labels all the cases regarding two supports, excitation loads and different damage cases (D0-D3). Table 4 displays all the label settings for 10 strain gauge strain in the longitudinal direction for different damage cases. Table 5 shows the damage, load and support identification results for seven labels with respect to true positive rate (TPR), true negative rate (TNR), false positive rate (FPR) and false negative rate (FNR). Images are scaled to the same size 900 \(\times\) 1200 \(\times\) 3 and then 256 \(\times\) 256 \(\times\) 1 without any annotation. For labeled dataset, the location for the specific case (Support 1, Support 2, Excitation, D0, D1, D2, D3) is labeled 1 while other locations are labeled 0. Different evaluation rates can be calculated by:  
1. True positive rate (TPR) = TP/(TP + FN),
2. True negative rate (TNR) = TN/(TN + FP),
3. False positive rate (FPR) = FP/(FP + TN),
4. False negative rate (FNR) = FN/(TP + FN). Eight hundred testing datasets are employed to verify the effectiveness of convolutional neural network, and it is promising to apply CNN to the identification of different extents of damage, load excitation location and support location. For engineering applications, to the best of the authors' knowledge, most work presented in the literature use artificial neural network-related methods to process images taken from bridges, tunnels, pipes. The disadvantages of this method include the fact that images may not inherently reflect the structural health status, and even if these images are fed into convolutional neural network, the trained images may not have a good generalization ability to evaluate the test samples. By combining the modal macro strain method and convolutional neural network, the sensitive strain distribution information can be extracted and then fed it into convolutional neural network for training and testing. The combination of these two methods can be used effectively to solve actual practical problems in complex civil engineering structures based on the numerical and analytical results shown in this study.