Sector status and dynamic density

A quick presentation

The main steps and results of the project are described here: [DASC presentation (2006)]


The S2D2 project deals with air traffic complexity. It started as a collaboration between the LEEA and the LOG, and was continued within the POM team. The idea of S2D2 was initially motivated by the results of a previous project ( CASSOS) which allowed us to implement efficient algorithms that computed optimal airspace sectors configurations, taking as input the incoming flows, and according to sector capacity constraints. However, the incoming flows did not seem highly related to the actual controller's workload. There remained to find a set of indicators, with the corresponding threshold values, which would be more relevant than the incoming flows and sector capacities.

Much research has been conducted over the last decade to help understanding air traffic complexity and controller workload. Many studies propose a variety of indicators, sometimes combined in a densité dynamique (using a linear regression), and there also exist many validation methods. The term air traffic complexity , widely used lately, covers in fact a great variety of underlying ideas. The Eurocontrol Performance Review Unit (PRU, project COCA) uses indicators defined over a whole day. The aims are to compare several control centers, and to find a sector typology. This study is not concerned with how each sector is operated. In many other studies, complexity is considered in light of the controller's workload at time t . It is then often subjective, in the sense that it is assessed by air traffic controllers during simulations, or real traffic, most often replayed. Some experiments use physiologic indicators of the controller's stress facing a given traffic situation, or take account of the nature and the frequency of the human-computer interactions. These experiments are relatively costly (in time and effort, at least), and should involve a wide set of sectors, and a significant population of controllers, to provide general results .

The main idea of the S2D2 project is to consider the complexity indicators, in light of the sector status evolution throughout the day, in order to find out which indicators, or combination of indicators, is actually relevant. We consider that the decisions to merge control sectors (that is to assign these sectors to a single working position), or on the contrary to split a sector, are statistically related to the controller workload, althouqh we must keep aware of the possible biases (controllers training, team shifts, harware failures,...). Air traffic complexity is here envisionned at an intermediate scale, between the general PRU indicators and the instant workload. We are looking for a relationship between complexity indicators and how each sector is actually operated, with a time granularity around the minute.

Our goal is to find out how the sector status (merged, armed, or split) is correlated with some basic indicators (aircraft count, incoming flows,...) or with some more synthetic indicators that are supposed to reflect the air traffic complexity. Several methods are likely to tackle this problem:

==Neural net figure==

The originality and the advantage of the method we propose to select the most relevant indicators, is that it uses recorded data (radar tracks, sector configurations), relatively cheap to collect, and that reflect the operational reality. However, we must keep aware that this data may be noisy: not all splitting/merging decisions are motivated by controller workload. But we may expect that, by selecting traffic samples within the peak period of the year, the noise will remain low.


The project started with the following, rather painstaking, necessary steps:

The descriptive analysis comprised a principal component analysis (PCA), allowing to identify 6 main components, with eigenvalue above 1, from the 27 indicators we have implemented.

We have then applied neural networks to these components, to which we have added the sector volume, and to the sector status data. We adress a classification problem, where the aim is to assign each vector of values of the explanatory variables (components, or sector volume) to a class corresponding to a sector status (merged, armed, or split). So we used multi-layer perceptrons, with a softmax transfer function applied to the output layer, in order to minimize the cross entropy (instead of the quadratic error).

Several combinations of components were tried. The components were successively added, in the order suggested by the PCA. The sector volume was also used as input of the neural network. For each combination, the network's training is made on a randomly chosen subset of the available input data. Once the network is trained, the rest of this data is used to assess its predictions on fresh data. As the goal is to select a statistical model which best explains the sector status (the target variable) from a combination of components and the sector volume (the explanatory variables), we have chosen the following selection criteria: the Akaike information criterion (AIC), and the Schwartz Bayesian information criterion (BIC, or SIC).


The best model found by this selection method uses a subset of only 5 explanatory variables: the sector volume and the first four components, that is C1, highly related to the number of aircraft within the sector, C2, corresponding to the ground speed variance and the vertical evolutions, C3, which groups the incoming traffic flows, with various time horizons, and C4, linked to the convergence of flows, and the anticipation of conflicts.

The correct classification rates obtained with this best model are around 84%, on test data as well as train data. If we detail the results by class, we have success rates of about 89% for the merged sector class, 67% for the armed sector class, and 91% for the split sector class.

The following step of our work was to evaluation the individual metrics of each relevant component, using neural networks once again. The most relevant metrics we have found are:

However, let us keep in mind that we only detect the combined effects of the various indicators. Adding or removing some metrics from the initial set may change the picture.

In the end, we obtain a simple and direct relationship between the relevant metrics and the sector status.

The future work on the subject may deal with:


The data pre-processing in S2D2 is written in Objective Caml. This code is not public domain. The descriptive analysis was made with R tools. For the neural networks, we first used SNNS, and then switched to the nnet package of the R environnment. More recently, we have implemented a some neural network softare (see the software page), written in Ocaml.


Main publications

All publications of the POM team may be found in here.

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