## 6 An Alternative TL-Based Fault Diagnosis Process for Unlabelled Target Domain Using TCA  
Following a close inspection of all the confusion matrices of the TCA results in Section 5, one major finding is that the prediction of the healthy cases is particularly accurate for all transfer scenarios. Table 7 demonstrates this point by the predictive accuracy and precision for target domain healthy cases, where the predictive accuracy is calculated by the true positive rate (TPR) for healthy cases, and the precision is calculated by the positive predictive rate (PPV) for the healthy cases. PPV is of interest, since it calculates the proportion of true healthy cases among all healthy cases predicted. From Table 7, both predictive accuracy and precision are high for TCA after averaging over all transfer scenarios, at 98.30% and 94.56%, respectively. Furthermore, the minimum precision, 69.70%, stands above 50%, which means the correct healthy cases can be found in larger proportion than the incorrect healthy cases in the worst performing scenario. In 95% of all transfer scenarios tested, the precision is found to be above 80%, which indicates the true healthy case dominates in all the predicted healthy cases. Consequently, it is safe to conclude that TCA predicts healthy labels accurately and reliably across all transfer scenarios on Table 7.  
This feature of TCA is of particular interest because, with the identification of the healthy label in the target domain, an alternative solution for the fault diagnosis for the unlabelled target domain can now be designed and tested if it can deliver better results than TCA. It is a common practice to use deviation from the healthy baseline as the basis for fault diagnosis in engineering scenarios. While this was not possible by the assumption of only unlabelled data in target domain, the accurate prediction of healthy labels enables this approach for the problem of interest. Existing works in ECS fault diagnosis also adopt deviation data from a healthy baseline, such as the work by [PERSON] et al. (2018) and the work of [PERSON] et al. (2018), who used the deviation between the measured signal and baseline data to diagnose ECS faults effectively in multiple flight phases, the identification of the healthy label in the target domain enables the establishment of baseline data, so that deviation from the baseline can be used instead of nominal data in order to allow better fault identification. The architecture of the alternative solution is shown in Figure 15. First, TCA was performed as normal, and at the end of the TCA loop, a healthy case could be identified from the target domain. In contrast to the TCA approach, the other labels predicted by TCA are not considered as the final label prediction. At the end of the first step, the target domain no longer has only unlabelled data because it has one healthy case labelled. In the second step, a healthy case is chosen as the baseline case in the source domain, and the case labelled healthy from step 1 serves as the target domain counterpart. All cases in the source domain and the target domain are then subtracted from the respective baseline healthy case in each domain. This step should help to reduce the domain shift between the source and target domain, since all cases now bear the deviation data from the healthy baseline case. The cases with deviation data in the source and target domains should share a similar pattern when they are in the same health state, which would make a classifier trained in the source domain accurate when directly applied to the target domain. For instance, it is clear from Figure 2 that a PHX fault can be identified by rising temperature at PHX outlet and SHX inlet than the healthy case, and this trend is invariant across the operating conditions. In the last step, the k-NN trained by the source domain deviation data is applied directly to the target domain deviation data for label prediction. Figure 15: The architecture of an alternative solution enabled by TCA.