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Arriving air traffic separations generalized model identification

Pawełek Adrian, Lichota Piotr

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2022

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Vol. 70, nr 2

art. no. e140694

EN

Quick development of computer techniques and increasing computational power allow for building high-fidelity models of various complex objects and processes using historical data. One of the processes of this kind is an air traffic, and there is a growing need for traffic mathematical models as air traffic is increasing and becoming more complex to manage. This study concerned the modelling of a part of the arrival process. The first part of the research was air separation modelling by using continuous probability distributions. Fisher information matrix was used for the best fit selection. The second part of the research consisted of applying regression models that best match the parameters of representative distributions. Over a dozen airports were analyzed in the study and that allowed to build a generalized model for aircraft air separation in function of traffic intensity. Results showed that building a generalized model which comprises traffic from various airports is possible. Moreover, aircraft air separation can be expressed by easy to use mathematical functions. Models of this kind can be used for various applications, e.g.: air separation management between aircraft, airports arrival capacity management, and higher-level air traffic simulation or optimization tasks.

2

Comparison of Two Nonstationary Flood Frequency Analysis Methods within the Context of the Variable Regime in the Representative Polish Rivers

Strupczewski W. G., Kochanek K., Bogdanowicz E., Markiewicz I., Feluch W.

Acta Geophysica

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2016

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Vol. 64, no. 1

206--236

EN

Changes in river flow regime resulted in a surge in the number of methods of non-stationary flood frequency analysis. Common assumption is the time-invariant distribution function with time-dependent location and scale parameters while the shape parameters are time-invariant. Here, instead of location and scale parameters of the distribution, the mean and standard deviation are used. We analyse the accuracy of the two methods in respect to estimation of time-dependent first two moments, time-invariant skewness and time-dependent upper quantiles. The method of maximum likelihood (ML) with time covariate is confronted with the Two Stage (TS) one (combining Weighted Least Squares and L-moments techniques). Comparison is made by Monte Carlo simulations. Assuming parent distribution which ensures the asymptotic superiority of ML method, the Generalized Extreme Value distribution with various values of linearly changing in time first two moments, constant skewness, and various time-series lengths are considered. Analysis of results indicates the superiority of TS methods in all analyzed aspects. Moreover, the estimates from TS method are more resistant to probability distribution choice, as demonstrated by Polish rivers’ case studies.

3

Optimization of the maximum likelihood estimator for determining the intrinsic dimensionality of high-dimensional data

Karbauskaitė R., Dzemyda G.

International Journal of Applied Mathematics and Computer Science

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2015

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Vol. 25, no. 4

895--913

EN

One of the problems in the analysis of the set of images of a moving object is to evaluate the degree of freedom of motion and the angle of rotation. Here the intrinsic dimensionality of multidimensional data, characterizing the set of images, can be used. Usually, the image may be represented by a high-dimensional point whose dimensionality depends on the number of pixels in the image. The knowledge of the intrinsic dimensionality of a data set is very useful information in exploratory data analysis, because it is possible to reduce the dimensionality of the data without losing much information. In this paper, the maximum likelihood estimator (MLE) of the intrinsic dimensionality is explored experimentally. In contrast to the previous works, the radius of a hypersphere, which covers neighbours of the analysed points, is fixed instead of the number of the nearest neighbours in the MLE. A way of choosing the radius in this method is proposed. We explore which metric—Euclidean or geodesic—must be evaluated in the MLE algorithm in order to get the true estimate of the intrinsic dimensionality. The MLE method is examined using a number of artificial and real (images) data sets.