Estimation of Rare Event Probabilities in Complex Aerospace and Other Systems: A Practical Approach

Rare event probability (10-4 and less) estimation has become a large area of research in the reliability engineering and system safety domains. A significant number of methods have been proposed to reduce the computation burden for the estimation of rare events from advanced sampling approaches to extreme value theory. However, it is often difficult in practice to determine which algorithm is the most adapted to a given problem. Estimation of Rare Event Probabilities in Complex Aerospace and Other Systems: A Practical Approach provides a broad up-to-date view of the current available techniques to estimate rare event probabilities described with a unified notation, a mathematical pseudocode to ease their potential implementation and finally a large spectrum of simulation results on academic and realistic use cases.

• 1 Introduction to rare event probability estimation - Jerome Morio and Mathieu Balesdent
• 2 Basics of probability and statistics - Jerome Morio and Mathieu Balesdent
• 3 The formalism of rare event probability estimation in complex systems - Jerome Morio and Mathieu Balesdent
• 4 Introduction - Mathieu Balesdent and Jerome Morio
• 5 Simulation techniques - Mathieu Balesdent, Jerome Morio, Christelle Verge and Rudy Pastel
• 6 Statistical techniques - Jerome Morio, Damien Jacquemart and Mathieu Balesdent
• 7 Reliability based approaches - Jerome Morio and Mathieu Balesdent
• 8 Methods for high dimensional and computationally intensive models - Mathieu Balesdent, Loic Brevault, Sylvain Lacaze, Samy Missoum and Jerome Morio
• 9 Special developments for time-variant systems - Damien Jacquemart, Jerome Morio, Francois Le Gland and Mathieu Balesdent
• 10 Estimation of launch vehicle stage fallout zone - Loic Brevault, Mathieu Balesdent and Jerome Morio
• 11 Estimation of collision probability between space debris and satellite - Jerome Morio, Juan Carlos Dolado Perez, Christelle Verge, Rudy Pastel and Mathieu Balesdent
• 12 Analysis of extreme aircraft wake vortex circulations - Jerome Morio, Ivan De Visscher, Matthieu Duponcheel, Gregoire Winckelmans, Damien Jacquemart and Mathieu Balesdent
• 13 Estimation of conflict probability between aircraft - Jerome Morio and Damien Jacquemart
• 14 Synthesis of rare event probability estimation methods for input-output systems - Jerome Morio and Mathieu Balesdent
• 15 Synthesis for time-variant systems - Damien Jacquemart, Jerome Morio, Mathieu Balesdent and Francois Le Gland