# CNN-Based Damage Identification of Submerged Structure-Foundation System Using Vibration Data
## 5 Development of 1-D CNN Models
### 1-D CNN Model Using Time-History Response
#### 5.1.3 Evaluation of 1-D CNN Model Using Time-History Responses  
The 1-D CNN model was evaluated using 20% of the time-history responses from the eight damage levels. As shown in Figure 15, confusion matrices were used to quantify the classification performance. The elements on the diagonal positions represent correct classifications (true positives, TP). The off-diagonal elements indicate incorrect classifications (false negatives, FN, and false positives, FP). True positive rate (TPR, so-called'recall') was calculated as TPR = TP/(TP + FN), while false negative rate (FNR) was calculated as FNR = FN/(FN + TP). Precision was calculated as Precision = TP/(TP + FP), and accuracy was calculated as Accuracy = TP/(TP + FP + FN). F1-score was calculated as F1 = (2 \(\times\) Precision \(\times\) Recall)/(Precision + Recall). Figure 14: Loss values of the 1-D CNN model trained by time-history responses. Figure 13: Visualization of time-history responses for training and evaluation of CNN model. Figure 15(a) plots the damage classification results of the CNN model using the time-history databank for a trained noise level of 1%. The red tick () denotes the correct level of inflicted damage. All data were classified correctly except in damage levels D1 (nine misclassifications) and D3 (one misclassifications), resulting in an overall accuracy of 93.75%. Figure 15(b) plots the damage classification results of the CNN model for a trained noise level of 5%. There were one to six misclassifications in each damage level, and the accuracy of the classification was reduced to 87.50%; nevertheless, the CNN model's reliability was demonstrated, with the majority of classifications being correct. Figure 15(c) shows the damage classification results of the CNN model using time-history databank for an untrained noise level of 6%. Misclassifications appeared in all damage levels except for the intact level (D0). Noticeably, more than half of the data in damage levels D1 and D6 were misclassified. The overall accuracy of classification decreased to 76.88%. For an untrained noise level of 10%, more than half of the data in several damage levels were misclassified, as shown in Figure 15(d). The accuracy of the results dropped to 53.12%. Despite this, most data fell in the nearby neighbor classes of the correct ones, suggesting that the CNN model can handle high noise levels with an acceptable error. However, there is a need to develop a technique that can minimize errors and improve the accuracy of the classification. Figure 15: Damage classification results of the 1-D CNN model using the time-history databank: (**a**) trained 1% noise; (**b**) trained 5% noise; (**c**) untrained 6% noise; (**d**) untrained 10% noise. The red tick () denotes the correct level of inflicted damage. Figure 16 summarizes the accuracy metrics of the CNN model using time-history databank under the effect of noise. Accuracy, false positive rate (FPR), false negative rate (FNR), and F1-score were chosen to be analyzed (see Figure 16a-d). A better damage classification result was indicated by higher accuracy and F1-score value, and lower FPR and FNR. The accuracy values of the CNN model corresponding to noise levels of 0-5% ranged from 94-87%, followed by a constant decrease until they reached 53% at a noise level of 10%. The FPR value ranged from 4-11% for trained noise levels (0-5%) and abruptly increased to 20% at a noise level of 6%. The FPR continued to rise, reaching 41% at a noise level of 10%. Similarly, the FNR value was below 12.5% for noise levels 0-5% and then significantly increased for noise levels of 6-10%, with a maximum error of 47% at a noise level of 10%. The F1-score remained around 0.92 for trained noise levels 1-5%, then constantly decreased in untrained noise levels until reaching 0.79 at a noise level of 10%. The CNN model trained by time-history response data demonstrated its feasibility in damage detection and monitoring. It maintained good performance with high noise levels (up to 5%).