Non-parametric high confidence interval prediction: application to aircraft trajectory prediction

Air traffic in Europe represents about 30,000 flights each day and forecasts from Eurocontrol predict a growth of 70% by 2020 (50,000 flights per day). The airspace, made up of numerous control sectors, will soon be saturated given the current planification and control methods. In order to make the system able to cope with the predicted traffic growth, the air traffic controllers workload has to be reduced by automated systems that help them handle the aircraft separation task. Based on the traffic demand by airlines, this study proposes a new planning method for 4D trajectories that provides conflict-free traffic to the controller. This planning method consists of two successive steps, each handling a unique flight parameter : a flight level allocation phase followed by a ground holding scheme.We present constraint programming models and an evolutionary algorithm to solve these large scale combinatorial optimization problems, as well as techniques for improving the robustness of the model by handling uncertainties of takeoff times and trajectory prediction. Simulations carried out over the French airspace successfully solved all conflicts, with a mean of one minute allocated delay (80 to 90 minutes for the most delayed flight) and a discrepancy from optimal altitude of one flight level for most of the flights. Handling uncertainties with a static method leads to a dramatic increase in the cost of the previous non-robust solutions. However, we propose a dynamic model to deal with this matter, based on a sliding time horizon, which is likely to be able to cope with a few minutes of uncertainty with reasonable impact on the cost of the solutions

High Confidence Intervals Applied to Aircraft Altitude Prediction

International audienceThis paper describes the application of high confidence interval prediction methods to the aircraft trajectory prediction problem, more specifically to the altitude prediction during climb. We are interested in methods for finding twosided intervals that contain, with a specified confidence, at least a desired proportion of the conditional distribution of the response variable. This paper introduces Two-sided Bonferroni-Quantile Confidence Intervals (TBQCI), which is a new method for obtaining high confidence two-sided intervals in quantile regression. The paper also uses the Bonferroni inequality to propose a new method for obtaining tolerance intervals in least-squares regression. This latter has the advantages of being reliable, fast and easy to calculate. We compare physical point-mass models to the introduced models on an Air Traffic Management (ATM) dataset composed of traffic at major French airports. Experimental results show that the proposed interval prediction models perform significantly better than the conventional pointmass model currently used in most trajectory predictors. When comparing with a recent state-of-the-art point-mass model with adaptive mass estimation, the proposed methods giv

Representing uncertainty by possibility distributions encoding confidence bands, tolerance and prediction intervals

For a given sample set, there are already different methods for building possibility distributions encoding the family of probability distributions that may have generated the sample set. Almost all the existing methods are based on parametric and distribution free confidence bands. In this work, we introduce some new possibility distributions which encode different kinds of uncertainties not treated before. Our possibility distributions encode statistical tolerance and prediction intervals (regions). We also propose a possibility distribution encoding the confidence band of the normal distribution which improves the existing one for all sample sizes. In this work we keep the idea of building possibility distributions based on intervals which are among the smallest intervals for small sample sizes. We also discuss the properties of the mentioned possibility distributions

Building possibility distribution based on confidence intervals of parameters of Gaussian mixtures

International audienceIn parametric methods, building a probability distribution from data requires an a priori knowledge about the shape of the distribution. Once the shape is known, we can estimate the optimal parameters value from the data set. However, there is always a gap between the estimated parameters from the sample sets and true parameters, and this gap depends on the number of observations. Even if an exact estimation of parameters values might not be performed, confidence intervals for these parameters can be built. One interpretation of the quantitative possibility theory is in terms of families of probabilities that are upper and lower bounded by the associated possibility and necessity measure. In this paper, we assume that the data follow a Gaussian distribution, or a mixture of Gaussian distributions. We propose to use confidence interval parameters (computed from a sample set of data) in order to build a possibility distribution that upper approximate the family of probability distributions whose parameters are in the confidence intervals. Starting from the case of a single Gaussian distribution, we extend our approach to the case of Gaussian mixture models

A new approach in compatibilization of the poly(lactic acid)/thermoplastic starch (PLA/TPS) blends

tIn this study, a new compatibilizer was synthesized to improve the compatibility of the poly(lacticacid)/thermoplastic starch blends. The compatibilizer was based on maleic anhydride grafted poly-ethylene glycol grafted starch (mPEG-g-St), and was characterized using Fourier transform infraredspectroscopy (FTIR), dynamic mechanical thermal analysis (DMTA) and back titration techniques. Theresults indicated successful accomplishment of the designed reactions and formation of a starch coredstructure with many connections to m-PEG chains. To assess the performance of synthesized compati-bilizer, several PLA/TPS blends were prepared using an internal mixer. Consequently, their morphology,dynamic-mechanical behavior, crystallization and mechanical properties were studied. The compatibi-lizer enhanced interfacial adhesion, possibly due to interaction between free end carboxylic acid groupsof compatibilizer and active groups of TPS and PLA phases. In addition, biodegradability of the sampleswas evaluated by various methods consisting of weight loss, FTIR-ATR analysis and morphology. Theresults revealed no considerable effect of compatibilizer on biodegradability of samples

Statistical prediction of aircraft trajectory : regression methods vs point-mass model

International audienceGround-based aircraft trajectory prediction is a critical issue for air traffic management. A safe and efficient prediction is a prerequisite for the implementation of automated tools that detect and solve conflicts between trajectories. Moreover, regarding the safety constraints, it could be more reasonable to predict intervals rather than precise aircraft positions . In this paper, a standard point-mass model and statistical regression method is used to predict the altitude of climbing aircraft. In addition to the standard linear regression model, two common non-linear regression methods, neural networks and Loess are used. A dataset is extracted from two months of radar and meteorological recordings, and several potential explanatory variables are computed for every sampled climb segment. A Principal Component Analysis allows us to reduce the dimensionality of the problems, using only a subset of principal components as input to the regression methods. The prediction models are scored by performing a 10-fold cross-validation. Statistical regression results method appears promising. The experiment part shows that the proposed regression models are much more efficient than the standard point-mass model. The prediction intervals obtained by our methods have the advantage of being more reliable and narrower than those found by point-mass model

Ground-based prediction of aircraft climb : point-mass model vs regression methods

Predicting aircraft trajectories with great accuracy is central to most operational concepts ([1], [2]) and automated tools that are expected to improve the air traffic management (ATM) in the near future. On-board flight management systems predict the aircraft trajectory using a point-mass model describing the forces applied to the center of gravity. This model is formulated as a set of differential algebraic equations that must be integrated over a time interval in order to predict the successive aircraft positions in this interval. The point-mass model requires knowledge of the aircraft state (mass, thrust, etc), atmospheric conditions (wind, temperature), and aircraft intent (target speed or climb rate, for example)

Comparison of Two Ground-based Mass Estimation Methods on Real Data

International audienceThis paper focuses on the estimation of the aircraft mass in ground-based applications. Mass is a key parameter for climb prediction. It is currently not available to groundbased trajectory predictors because it is considered a competitive parameter by many airlines. There is hope that the aircraft mass might become widely available someday, but in the meantime it is possible to estimate an equivalent mass from the data already available, assuming the thrust to be known (maximum or reduced climb thrust for example). In a previous paper ([1]), two mass estimation methods were compared using simulated data. In this paper, we compare these two mass estimation methods using Mode-C radar data. Both methods estimate the aircraft mass by fitting the modeled energy rate (i.e. the power of the forces acting on the aircraft) with the energy rate observed at several points of the past trajectory. The first method, proposed by Schultz et al. ([2]), dynamically adjusts the weight parameter so as to fit the energy rate, using an adaptive sensitivity parameter to weight each observation. The second method, introduced in one of our previous publications ([1]), estimates the mass by minimizing the quadratic error on the observed energy rate, taking advantage of the polynomial expression of the modeled power when using the BADA model. The actual mass is unavailable in our radar data. However, we can use the estimated mass to compute a trajectory prediction. This prediction is then compared to the actual trajectory giving us some insight on the accuracy of the estimated mass. We have compared the obtained predictions with the ones obtained using the BADA reference mass. The root mean square error on the predicted altitude is reduced by 45 % using the least squares method. With the adaptive method this error is divided by two