# Prediction of Flight Delays at _Beijing_ Capital International Airport Based on Ensemble Methods
###### Abstract  
Predicting flight delays plays a critical role in reducing financial losses and increasing passenger satisfaction. Due to their ability to combine multiple algorithms, ensemble methods have demonstrated strong predictive performance in many research fields. In this paper, ensemble methods are adopted to predict flight delays. First, based on the current studies, two novel explanatory variables, named arrival/departure pressure and cruise pressure, are proposed as factors affecting flight delays. Second, we introduce the ensemble methods and select representative algorithms for the prediction problem. In addition to the ensemble methods, classical algorithms are also used to predict flight delays. Finally, the actual operational data of Beijing Capital International Airport were utilized to conduct a case study. The results show that the stacking method has better prediction performance than other baseline methods. The mean absolute error (MAE) of the stacking method was about 12.58 min on the test dataset. Furthermore, we tested the effect of the two explanatory variables proposed in this paper, and the results show that the MAE was reduced by about 20% by using the stacking method. air traffic; air transport; flight delays prediction; ensemble methods +
Footnote †: journal: Applied  
Operational Databases (AODBs). These databases provide strong support for flight delay predictions. Many methods have been adopted, based on historical operation data, including the econometric model [5], historical data regression [6], and Bayesian network [7]. As machine learning (ML) continues to evolve, more and more researchers are applying it to air traffic, including random forest (RF) [8], support vector regression (SVR) [9], and recurrent neural networks (RNNs) [10]. In recent years, ensemble methods, as a branch of ML, have been applied to study the travel times of vehicles and buses and the estimated time of arrival of flights [11; 12; 13]. To improve prediction performance, ensemble methods combine several weak learners into a strong learner, a method which is applicable in the study of predicting flight delays. Previous researchers have mainly considered macro factors in their models, including weather, laws of delay propagation, and delay causality [14]. We call these macro factors because their impact on delays is not real-time and can only be observed over a long period. Due to difficulties of quantification, more specific micro factors such as airport congestion and route congestion are often ignored. However, these micro factors can have a direct impact on flight delays, and can play an important role in real-time or short-term advance prediction. Therefore, in this paper we propose two novel explanatory variables, named arrival/departure pressure and cruise pressure, for use along with macro factors in prediction of flight delays, and explore their effect within models. In terms of variable processing, previous studies have tended to use the one-hot encoding method for temporal data, including hours of the day, days of the week, and months in a year. However, this type of encoding ignores the unique periodicity of temporal data. Therefore, to retain periodicity, we adopted the sine and cosine functions to convert the temporal data to (x, y) coordinates on a circle, and explored the impact of this encoding method on prediction performance. The main contributions of this paper can be summarized as follows: (1) We applied stacking methods, a type of ensemble technique, to build a model that can reject poorer-performing models and highlight the best-performing ones. (2) We propose new explanatory variables, called arrival/departure pressure and cruise pressure, to describe congestion in the airport and the air-route situation. (3) We combined macro and micro factors as explanatory variables for prediction, which can improve prediction accuracy. (4) To preserve periodicity, we encoded the temporal data using sine and cosine functions.