## 5 Conclusions  
This paper discussed the importance of developing diagnostics for an Electrical Power System to isolate faults, including those that affect other systems like the engine, the fuel system, and the Environmental Control System of an aircraft. The development of an EPS digital twin, along with its simulation of healthy and faulty states, are presented. An ANFIS monitor is developed to detect the presence of faults in the EPS based on the power generated. Isolation of faults to particular LRUs is attempted by processing the ANFIS ranks in two methods: (i) a crisp boundary approach, and (ii) a fuzzy boundary approach. While the former provided a very high misclassification rate of 67%, the second method was able to classify the faults to their regions accurately. This fuzzy boundary method is combined with causal reasoning by developing tests for every region through a diagnostic matrix, through which the faults that propagate to LRUs of other aircraft systems are isolated. The developed diagnostic algorithm with ANFIS is tunable to monitor the power generated at desired time windows and is also capable of identifying the intermittency during the simulation run.  
With these results from EPS diagnostics, it is possible to pinpoint the location and time where a fault has occurred, thus reducing the time taken to troubleshoot the root cause of faults effectively. This method will help in preventing ambiguous scenarios like the aircraft incidents presented in  
Figure 15: (**a**) Diagnostics for one intermittent fault (F6). (**b**) Diagnostics of multiple intermittent faults (F5, F8).  
Section 1, where the effect is significantly observed in the interacting system rather than the system of origin. As the combination of the ANFIS monitor with causal reasoning does not take much time to isolate the faults during the simulation run, this diagnostic method could be tried in both ground systems as well as onboard highly electrified aircraft for rapid diagnosis in the case of real-time fault scenarios. As this diagnostic method is not heavy on computation requirements, it is also helpful for monitoring the health of the aircraft at the vehicle level, considering the interaction between its multiple systems. A framework of digital twins of multiple interacting systems like the EPS, the engine, the ECS, and the fuel system, along with their system-level diagnostics isolating the interacting faults, would help in monitoring the overall health of the aircraft [5].  
Conceptualization, C.M.E., and I.K.J.; Methodology, C.M.E.; Software, C.M.E.; Validation, C.M.E.; Formal analysis, C.M.E.; Investigation, C.M.E.; Resources, I.K.J.; Data curation, C.M.E.; Writing--original draft preparation, C.M.E.; Writing--review and editing, C.M.E. and I.K.J.; Visualization, C.E.; Supervision, I.K.J.; Project administration, I.K.J.; Funding acquisition, I.K.J. All authors have read and agreed to the published version of the manuscript. This work has been funded by The Boeing Company as part of their collaboration with Cranfield University's IVHM Centre. The authors would like to thank Boeing for their support of this project.  
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.