A Gaussian process regression approach to model aircraft engine fuel flow rate

The problem of building statistical models of cyber-physical systems using operational data is addressed in this paper, using the case study of aircraft engines. These models serve as a complement to physics-based models, which may not accurately reflect the operational performance of systems. The accurate modeling of fuel flow rate is an essential aspect of analyzing aircraft engine performance. In this paper, operational data from Flight Data Recorders are used to model the fuel flow rate. The independent variables are restricted to those which are obtainable from trajectory data. Treating the engine as a statistical system, an algorithm based on Gaussian Process Regression (GPR) is developed to estimate the fuel flow rate during the airborne phases of flight. The algorithm propagates the uncertainty in the estimates in order to determine prediction intervals. The proposed GPR models are evaluated for their predictive performance on an independent set of flights. The resulting estimates are also compared with those given by the Base of Aircraft Data (BADA) model, which is widely used in aircraft performance studies. The GPR models are shown to perform statistically significantly better than the BADA model. The GPR models also provide interval estimates for the fuel flow rate which reflect the variability seen in the data, presenting a promising approach for data-driven modeling of cyber-physical systems.National Science Foundation (U.S.) (Grant 1239054

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.National Science Foundation (U.S.) (Award 0931843

Statistical modeling of aircraft engine fuel burn

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Aeronautics and Astronautics, 2018.Cataloged from PDF version of thesis.Includes bibliographical references (pages 169-177).Fuel burn is a key driver of aircraft performance, and contributes to airline costs and aviation emissions. While the trajectory (ground track) of a flight can be observed using surveillance systems, its fuel consumption is generally not disseminated by the operating airline. Emissions inventories and benefits assessment tools therefore need models that can predict the fuel flow rate profile and fuel burn of a flight, given its trajectory data. Most existing fuel burn estimation tools rely on an architecture that is centered around the Base of Aircraft Data (BADA), an aircraft performance model developed by EUROCONTROL. Operational data (including trajectory data) are generally processed in order to generate the inputs needed by BADA, which then provides an estimate of the fuel flow rate and fuel burn. Although a versatile tool that covers a large number of aircraft types, BADA makes several assumptions that are not representative of real-world operations. Consequently, the reliance on BADA results in errors in the fuel burn estimates. Additionally, existing fuel burn modeling tools provide deterministic predictions, thereby not capturing the operational variability seen in practice. This thesis proposes an alternative model architecture that enables the development of data-driven, statistical models of fuel burn. The parameters of interest are the instantaneous fuel flow rate (that is, the mass of fuel consumed per unit time) and the fuel burn (cumulative mass of fuel consumed over a particular phase or the entire trajectory). The new model architecture uses supervised learning algorithms to directly map aircraft trajectory variables to the fuel flow rate, and subsequently, fuel burn. The models are trained and validated using operational data from flight recorders, and therefore reflect real-world operations. A physical understanding of aircraft and engine performance is leveraged for feature selection. An important characteristic of statistical methods is that they provide both estimates of mean values, as well as predictive distributions reflecting the variability and uncertainty. Locally expert models are developed for each aircraft type and for each of the flight phases. The Bayesian technique of Gaussian Process Regression (GPR) is found to be well-suited for modeling fuel burn. The resulting models are found to be significantly better than state-of-the-art aircraft performance models in predicting the fuel flow rate and fuel burn of a trajectory, giving up to a 63% improvement in total airborne fuel burn prediction over the BADA model. Finally, the Takeoff Weight (TOW) of an aircraft is recognized as an important variable for determining the fuel burn. The thesis therefore develops and evaluates a methodology to estimate the TOW of a flight, using trajectory data from its takeoff ground roll. The proposed statistical models are found to result in up to a 76% smaller error than the Aircraft Noise and Performance (ANP) database, which is used currently for TOW estimation.by Yashovardhan Sushil Chati.Ph. D

Multi-task Gaussian process models for biomedical applications

Gaussian process (GP) models are a flexible means of performing non-parametric Bayesian regression. However, the majority of existing work using GP models in healthcare data is defined for univariate output time-series, denoted as single-task GPs (STGP). Here, we investigate how GPs could be used to model multiple correlated univariate physiological time-series simultaneously. The resulting multi-task GP (MTGP) framework can learn the correlation within multiple signals even though they might be sampled at different frequencies and have training sets available for different intervals. We illustrate the basic properties of MTGPs using a synthetic case-study with respiratory motion data. Finally, two real-world biomedical problems are investigated from the field of patient monitoring and motion compensation in radiotherapy. The results are compared to STGPs and other standard methods in the respective fields. In both cases, MTGPs learned the correlation between physiological time-series efficiently, which leads to improved modelling accuracy. © 2014 IEEE

Multi-task Gaussian process models for biomedical applications

Gaussian process (GP) models are a flexible means of performing non-parametric Bayesian regression. However, the majority of existing work using GP models in healthcare data is defined for univariate output time-series, denoted as single-task GPs (STGP). Here, we investigate how GPs could be used to model multiple correlated univariate physiological time-series simultaneously. The resulting multi-task GP (MTGP) framework can learn the correlation within multiple signals even though they might be sampled at different frequencies and have training sets available for different intervals. We illustrate the basic properties of MTGPs using a synthetic case-study with respiratory motion data. Finally, two real-world biomedical problems are investigated from the field of patient monitoring and motion compensation in radiotherapy. The results are compared to STGPs and other standard methods in the respective fields. In both cases, MTGPs learned the correlation between physiological time-series efficiently, which leads to improved modelling accuracy. © 2014 IEEE