Statistical Modeling of Aircraft Takeoff Weight

The Takeoff Weight (TOW) of an aircraft is an important aspect of aircraft performance, and impacts a large number of characteristics, ranging from the trajectory to the fuel burn of the flight. Due to its dependence on factors such as the passenger and cargo load factors as well as operating strategies, the TOW of a particular flight is generally not available to entities outside of the operating airline. The above observations motivate the development of accurate TOW estimates that can be used for fuel burn estimation or trajectory prediction. This paper proposes a statistical approach based on Gaussian Process Regression (GPR) to determine both a mean estimate of the TOW and the associated confidence interval, using observed data from the takeoff ground roll. The predictor variables are chosen by considering both their ease of availability and the underlying aircraft dynamics. The model development and validation are conducted using Flight Data Recorder archives, which also provide ground truth data. The proposed models are found to have a mean TOW error of 3%, averaged across eight different aircraft types, resulting in a nearly 50% smaller error than the models in the Aircraft Noise and Performance (ANP) database. In contrast to the ANP database which provides only point estimates of the TOW, the GPR models quantify the uncertainty in the estimates by providing a probability distribution. Finally, the developed models are used to estimate aircraft fuel flow rate during ascent. The TOW estimated by the GPR models is used as an input to the fuel flow rate estimation. The proposed statistical models of the TOW are shown to enable a better quantification of uncertainty in the fuel flow rate as compared to the deterministic ANP models, or to models that do not use the TOW as an explicit input.