Free Flight Collision Risk Estimation by Sequential MC Simulation

Blom, H.A.P.; Krystul, Jaroslav; Bakker, G.J.

doi:10.1201/9781420008548.ch10

Cited by 35 publications

(44 citation statements)

References 32 publications

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“…Application of this IPS algorithm to air traffic operation may work well for specific scenarios where rare discrete modes are not significantly contributing to the reach probability [12]- [13]. However, there also are relevant scenarios which do not satisfy the latter condition.…”

Section: Factorization Of Reach Probabilitymentioning

confidence: 99%

“…Similar as in the IPS algorithm for an SHS [12][13], a particle is defined as a triplet ( ) Hierarchical Hybrid Interacting Particle System (HHIPS) algorithm estimates these fractions and their product in a recursive way, using the following steps:…”

Section: Hierarchical Hybrid Ips Algorithmmentioning

confidence: 99%

“…in simulating two aircraft there are about 25 10 discrete mode combinations, and the Euclidean state may go up to 336 ℝ [12]. In [12]- [13], [24] we developed a way to cast the air traffic SHS model within the setting of the IPS formulation, and used the IPS to evaluate demanding high risk bearing multi-aircraft scenarios. This IPS approach, however, did not work properly anymore for low risk bearing scenarios.…”

Section: Free Flight Air Traffic Examplementioning

confidence: 99%

“…In [12]- [13], the practical use of the approach of Del Moral [8]- [11] for safety verification of an advanced air traffic operation has already been demonstrated for some specific scenarios. In these scenarios, the main contributions to the reach probability value came from diffusion behavior.…”

Section: Introductionmentioning

confidence: 99%

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Probabilistic reachability analysis for large scale stochastic hybrid systems

Blom

Bakker

Krystul

2007

2007 46th IEEE Conference on Decision and Control

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Abstract-This paper studies probabilistic reachability analysis for large scale stochastic hybrid systems (SHS) as a problem of rare event estimation. In literature, advanced rare event estimation theory has recently been embedded within a stochastic analysis framework, and this has led to significant novel results in rare event estimation for a diffusion process using sequential MC simulation. This paper presents this rare event estimation theory directly in terms of probabilistic reachability analysis of an SHS, and develops novel theory which allows to extend the novel results for application to a large scale SHS where a very huge number of rare discrete modes may contribute significantly to the reach probability. Essentially, the approach taken is to introduce an aggregation of the discrete modes, and to develop importance sampling relative to the rare switching between the aggregation modes. The practical working of this approach is demonstrated for the safety verification of an advanced air traffic control example.

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Section: Factorization Of Reach Probabilitymentioning

confidence: 99%

Section: Hierarchical Hybrid Ips Algorithmmentioning

confidence: 99%

Section: Free Flight Air Traffic Examplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Probabilistic reachability analysis for large scale stochastic hybrid systems

Blom

Bakker

Krystul

2007

2007 46th IEEE Conference on Decision and Control

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“…In this respect, the accelerated Monte Carlo method is similar to recent studies that used rare event Monte Carlo simulation to estimate the collision risk of an uncoordinated airborne self-separation concept. [14][15] Consider failure mode 1. The first step in estimating its probability is to simulate the likelihood that at least one flight is not locatable via ADS-B or SSR in a Monte Carlo simulation.…”

Section: Failure Mode Numbermentioning

confidence: 99%

Accelerated Monte Carlo Simulation for Safety Analysis of the Advanced Airspace Concept

Thipphavong

2010

10th AIAA Aviation Technology, Integration, and Operations (ATIO) Conference

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Safe separation of aircraft is a primary objective of any air traffic control system. An accelerated Monte Carlo approach was developed to assess the level of safety provided by a proposed next-generation air traffic control system. It combines features of fault tree and standard Monte Carlo methods. It runs more than one order of magnitude faster than the standard Monte Carlo method while providing risk estimates that only differ by about 10%. It also preserves component-level model fidelity that is difficult to maintain using the standard fault tree method. This balance of speed and fidelity allows sensitivity analysis to be completed in days instead of weeks or months with the standard Monte Carlo method. Results indicate that risk estimates are sensitive to transponder, pilot visual avoidance, and conflict detection failure probabilities.

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Rare Event Estimation for a Large‐Scale Stochastic Hybrid System with Air Traffic Application

Blom

Bakker²,

Krystul³

2009

Rare Event Simulation Using Monte Carlo Methods

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Embedding of rare event estimation theory within a stochastic analysis framework has recently led to significant novel results in rare event estimation for a diffusion process using sequential MC simulation. This chapter presents this rare event estimation theory for diffusions to a Stochastic Hybrid System (SHS) and extends it in order to handle a large scale SHS where a very huge number of rare discrete modes may contribute significantly to the rare event estimation. Essentially, the approach taken is to introduce a suitable aggregation of the discrete modes, and to develop importance sampling and Rao-Blackwellization relative to these aggregated modes. The practical use of this approach is demonstrated for the estimation of mid-air collision for an advanced air traffic control example.

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Free Flight Collision Risk Estimation by Sequential MC Simulation

Cited by 35 publications

References 32 publications

Probabilistic reachability analysis for large scale stochastic hybrid systems

Probabilistic reachability analysis for large scale stochastic hybrid systems

Accelerated Monte Carlo Simulation for Safety Analysis of the Advanced Airspace Concept

Rare Event Estimation for a Large‐Scale Stochastic Hybrid System with Air Traffic Application

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