Aircraft Weight Estimation During Take-off Using Declarative Machine Learning

Aircraft sensors measure physical quantities to help pilots and flight automation systems with situational awareness and decision making. Unfortunately, some important quantities of interest (QoI), e.g., aircraft weight, cannot be directly measured by sensors. This may lead to accidents, exemplified by Tuninter 1153 and Cessna 172R N4207P, where the airplanes were underweight (not enough fuel) and overweight (6% over maximum gross weight) respectively. Learning models to infer QoI from other aircraft sensor data is thus critical to safety through analytical redundancy. In this paper, we extend PILOTS, our declarative programming language for stream analytics, to learn models from data. We illustrate the supervised machine learning extensions to PILOTS with an example where we use take-off speed profiles under different density altitudes and runway conditions to estimate aircraft weight. Using data collected from the X-Plane flight simulator for a Cessna 172SP, we compare the results of several models on accuracy and timeliness. We also consider ensemble learning to improve the accuracy of weight estimation during takeoff from 94.3% (single model) to 97% (multiple models). Given that the average length of a take-off is 26.75s, this model was able to converge within 10% of the correct weight after 10.7s and converge within 5% after 17.7s. On August 25th, 2014, a Cessna 172R, N4207P, crashed killing the pilot and three passengers. The National Transportation Safety Board (NTSB) report calculated the aircraft to be 1.06 times the maximum gross weight. We simulated the take-off in X-Plane using information from the report. We were able to estimate within 5% error after 8s, which is less than 200ft down the runway, and at the point of take-off, 27s, had an error of 3%. This implies that our model could have alerted the pilot of an overweight condition well before the aircraft became airborne, leaving more than 2000ft of runway to come to a stop. If this system were to be implemented in any fixed wing aircraft, it would create a larger safety net. Pilots would have a greater chance of catching errors thus increasing the probability of survival for crew and passengers.