## 4 Results and Discussion
### Method 2: The Fuzzy Boundary Approach  
In method 2, the 'fuzzy boundary' concept is used since the crisp boundaries for processing the ANFIS output values 'z' did not work, as shown in Method 1. Regions 5 to 0 are now representing multiple faults overlapping other regions (Figure 12) instead of representing only the 'defined' faults without any overlaps as in method 1. For example, from Figure 12a, it is seen that the fault F5 comes  
Figure 11: Confusion matrix for the crisp boundary approach. Figure 10: Faulty scenario using the crisp boundary approach. (**a**) EPS performance in faulty scenarios. (**b**) The corresponding results generated by ANFIS monitor using Method 1 approach. under both 'Region 2' and 'Region 3'. This method provides an accurate classification of faults into their regions, as shown in the confusion matrix in Figure 12b. In order to isolate the faults that propagate to other aircraft systems, the second method uses a hybrid combination of causal reasoning with ANFIS. Causal reasoning is a reasoning strategy that draws conclusions based on the cause and effect relationship of the concerned subjects [33]. In general, developing causal reasoning for a system such as EPS is a time-consuming and tedious task due to the large number of interactions between the EPS and other systems. However, with the combination of the ANFIS monitor similar to that in method 1, their results can be used to narrow down the region of search for cause and effect relationships. The algorithm for implementing the method 2 approach is provided in Appendix A. Using the ANFIS monitor, the 'effect' criteria for a particular region of faults is now narrowed down, which is followed by carrying out a certain number of tests to find out the exact 'cause' of the observed effect. This will be done by developing the diagnostic matrix that maps the required tests to be carried out for each region, and once the criteria of the tests are satisfied, the result will lead to the exact fault isolation. The diagnostic matrix for isolating the faults in the EPS is shown in Table 3. For every region identified by the ANFIS monitor, the voltages of the concerned LRUs are checked to isolate the faulty LRU. Carrying out every test in the table during every simulation run will consume a lot of time and memory, especially if the task is only to detect the presence of any fault. Thus, the  
Figure 12: (a) Fuzzy boundaries representing healthy and faulty scenarios based on the power generated. (b) Confusion matrix for method 2 ANFIS rank processing with fuzzy boundaries. application of the ANFIS monitor to detect the presence of a fault, followed by diagnosis using the diagnostic matrix, has the significant advantage of isolating the fault in the EPS in a shorter duration, with lesser memory. An example of the end result, isolating a fault in the EPS, using the ANFIS monitor and the diagnostic matrix, is shown in Figure 13. The variable'monitor_res' in Figure 13 shows the summarized output from the ANFIS monitor, which is then followed by the tests from the diagnostic matrix to isolate the F6 fault. Figure 14 shows the isolation of fault F5. Similarly, with the help of the diagnostic matrix, the tests are able to isolate the LRUs that are propagating faults to the other systems. While the ANFIS rank processing with the fuzzy boundaries classifies the regions of faults accurately, the overall classification accuracy of method 2 is 99.1%. This is due to the slight overlaps between the healthy and DC Valves nominal voltages that are tested in Region 5. The tests carried out from the diagnostic matrix in Table 3 are able to isolate the faults accurately in the rest of the regions. The diagnostic algorithm is tuned in to detect only the steady-state, single fault criteria, and hence, in any case of multiple or intermittent faults, the variable'monitor_res' will give the result as 'Intermittent,' and the further diagnostic tests will be canceled.