Probabilistic Analysis of Airborne Collision Risk by Data Driven Approach

Aviation safety relies on maintaining adequate spacing between aircraft. While uncertainties are common, this study employs approaches that account for small uncertainties and deviations in aircraft positions. The objective is to assess the likelihood of airborne collision risks using data from the Aviation Risk Identification and Assessment (ARIA) developed by MITRE. To achieve this, we utilize a model that integrates probability density functions (PDFs), convolution integrals, and engineering dynamics. The study validates results from the convolution approach using a logit model for binary outcome data, where 1 indicates a collision event if the spacing is less than or equal to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>λ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>xy</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> , and 0 otherwise. Predictions from both the convolution and logit models show similarities in the horizontal dimension, with parameters derived exclusively from data-driven methods. Total collision risks are calculated by multiplying probabilities across horizontal, vertical, and time intervention dimensions. Notably, vertical spacing data exhibit considerable volatility, leading to a wider probability range and discussions on threshold crossings. Reliability theory is also applied to analyze the impact of timely interventions. This study highlights the correlation between collision probabilities and ARIA scores, while Bayesian Monte Carlo simulations reveal underlying data patterns. Additionally, the research addresses the strengths and limitations of the analytical models. For instance, navigation system errors and deviations in paired aircraft positions are often dynamic and unknown, and ARIA data may not fully capture the complexities of potential collisions. These factors underscore the need for further data-driven efforts to obtain more accurate estimates of uncertainties and overlap probabilities.