# A Study on PF-IFF-Based Diagnosis Model of Plant Equipment Failure
## 4 Case Study
### Evaluation  
The performance of the proposed PF-IFF-based approach was evaluated by comparing the performance with and without PF-IFF when the SVM classifier was applied to classify the failure modes. In this study, the actual state of the equipment was given in order to evaluate the performance of the SVM. The state of the actual equipment corresponding to each feature vector was set to the state of the equipment failure mode from the point  
Figure 11: Classification model learning through SVM classifier. Figure 10: Scatter diagrams of equipment state. of time when the history was recorded in the specific type of equipment to the specific point of time. Figure 12 depicts scatter plots showing the actual state of the equipment for 3 of the 13 variables in the test data. The PF-IFF-based method was used to find anomalies associated with the type of equipment failure and to assign the state of the equipment to each feature vector. In Figure 12, the red color represents the state for leakage, green represents misalignment, black represents bearing damage, and blue represents the steady state. The vertical line shown in Figure 12 indicates the time when each type of failure occurred. However, when the PF-IFF is not used, it is necessary to allocate the state of the equipment to each feature vector when learning the classifier. To this end, we assigned the state of the equipment to each feature vector with the failure mode or normal identifier using the equipment status data during a certain period before the occurrence of the specific failure mode. For certain periods, we used 1, 2, 3, and 4 days for the computational tests, respectively, in order to know which day was more suitable for classification. In the experiment using PF-IFF, performance was evaluated for the cases where the number of abnormal patterns associated with the failure mode was different, as mentioned in Section 4.3.3. The performance criterion was set as Area Under the Curve (AUC) in the Receiver Operating Characteristic (ROC) Curve. ROC Curve is a technique for evaluating the performance of classification using sensitivity and specificity. For example, sensitivity refers to the probability of being correctly classified as leakage when there is actual leakage, and specificity means the probability that the leakage is correctly classified as not leakage. The ROC curve and the AUC were calculated using the above two values for each state of  
Figure 12: Scatter plots of actual states of the equipment. Table 5 shows the experimental results using SVM when PF-IFF was not used. As the test results show, when the failure mode was assigned with the equipment status data one day before the occurrence of the specific failure mode, the result is the best. It shows that AUC was 0.722 (normal), 0.593 (bearing damage), 0.739 (leakage), and 0.689 (misalignment), respectively. Table 6 shows the AUC of each state of the equipment when the number of abnormal patterns associated with the failure mode was changed. We endeavored to know whether the optimum performance is achieved at a certain setting by comparing the AUC and the comparison result when the PF-IFF was not used. The number of abnormal patterns associated with each type of failure was increased up to 3, and the experiment was conducted 27 times to evaluate the performance of the PF-IFF-based method with the SVM classifier. For example, Table 7 shows that the AUC for each state of the equipment (normal, bearing damage, leakage, misalignment) was 0.957, 0.977, 0.930, and 0.765 when there were three, two, and one abnormal pattern/s corresponding to bearing damage, leakage, and misalignment, which is the best performance case. In this case, the abnormal patterns in each failure mode were pattern 9, pattern 12, and pattern 17 in the case of bearing damage, pattern 3 and pattern 10 in the case of leakage, and pattern 5, pattern 14, and pattern 15 in the case of misalignment. Table 7 compares the performance of the model according to the use of PF-IFF based on AUC.