# Hybrid Machine Learning-Statistical Method for Anomaly Detection in Flight Data
## 4 Results and Discussion  
A set of flights with the same tail number was analyzed for three different airports, and the LOF score of each set is plotted in Figure 10. From Figure 10, the LOF score of each flight in the set can be seen for three different airports, and highly abnormal flights can be seen from the bar chart. Figure 11 combines the LOF algorithm and [PERSON]'s method. It shows how for each of the three different airports, the LOF threshold is different and dynamic. This plot also shows the median LOF values for each airport and the anomalous flights as outliers for each airport. Detroit (DTW) airport is taken as a case study. From Figures 8 and 11, we can see that DTW has five flights as an outlier. One flight with a LOF score of 1.87 is an extreme outlier. Figure 12 shows the top 10 probable flight parameters responsible for the anomalous behavior. In this plot, flight duration is plotted on the \(x\)-axis,  
Figure 9: LOF score analysis for three airports.  
and abnormal flight parameters are plotted on the \(y\)-axis in the order of how far they were from normal flight parameters. This plot gives a starting point for any investigation or to know what might have caused a flight to be abnormal. From discussions with the human expert, it was concluded that this flight was highly anomalous may be due to flight parameter ABRK (air brakes). Frequent use of air brakes to slow down the aircraft just before touchdown may have caused this anomalous behavior. Similar analyses were performed for the remaining four anomalous flights, and many flight parameters such as engine vibrations, high speed and pitch were found to be some of the contributing factors behind the anomalous behavior.  
Figure 13 shows changing LOF value at each time stamp during the last three minutes of the landing phase. This figure shows how the LOF values change in time as the flight is about to touchdown. The figure shows that the flight became anomalous just 20 s before the touchdown. This plot for any flight can be used to find the time window when this flight was anomalous and to what extent the flight was anomalous. We found that many flights were anomalous during the approach and landing phase, but these flights became normal while touching down. Therefore, any normal flights can also be investigated to check for any instances where these flights might have become anomalous.  
Figure 10: Cont.  
Figure 11: Boxplots for 3 different airports showing outliers using hybrid LOF–Tukey method.  
Figure 12: Top 10 flight parameters responsible for an anomalous flight during last 3 min before touchdown.  
Figure 10: LOF analysis for three different airports.  
These results were verified and validated by the industry expert. Flights labeled anomalous for each airport were also anomalous, as per the human expert. [PERSON]'s method reduced the number of false positives given by the LOF algorithm. All the points exceeded [PERSON]'s threshold, but one was found to be anomalous and exerting an unstabilized approach, which is of safety concern. The one flight which was established to be anomalous but was later found to be a false positive was due to the aircraft taking a completely different approach route from the rest of the dataset under investigation. Therefore, while still anomalous, this was not found to be of any safety concerns.