Impact probability under aleatory and epistemic uncertainties
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Impact probability under aleatory and epistemic uncertainties Chiara Tardioli1 · Davide Farnocchia2 · Massimiliano Vasile1 Steve R. Chesley2
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Received: 8 July 2020 / Revised: 21 October 2020 / Accepted: 25 October 2020 / Published online: 25 November 2020 © The Author(s) 2020
Abstract We present an approach to estimate an upper bound for the impact probability of a potentially hazardous asteroid when part of the force model depends on unknown parameters whose statistical distribution needs to be assumed. As case study, we consider Apophis’ risk assessment for the 2036 and 2068 keyholes based on information available as of 2013. Within the framework of epistemic uncertainties, under the independence and non-correlation assumption, we assign parametric families of distributions to the physical properties of Apophis that define the Yarkovsky perturbation and in turn the future orbital evolution of the asteroid. We find IP ≤ 5 × 10−5 for the 2036 keyhole and IP ≤ 1.6 × 10−5 for the 2068 keyhole. These upper bounds are largely conservative choices due to the rather wide range of statistical distributions that we explored. Keywords Epistemic uncertainty · Impact probability · Asteroids
1 Introduction In risk analysis, uncertainties are generally classified into two categories: aleatory and epistemic. Aleatory uncertainty is an inherent variation associated with the physical system or the environment. It may arise from environmental randomness, variation in space, fluctuations in times or other system variability. Given the repetitiveness of the error, it is generally well quantified with a known probability distribution, and in principle, it cannot be eliminated by further observational data, although it may be better characterized (Kolmogorov and Bharucha-Reid 2018). Conversely, epistemic uncertainty is due to a lack of information
The work of C. Tardioli was supported by the Marie Curie FP7-PEOPLE-2012-ITN Stardust, Grant agreement 317185. D. Farnocchia and S. Chesley conducted this research at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with NASA.
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Chiara Tardioli [email protected]
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Department of Mechanical and Aerospace Engineering, University of Strathclyde, Glasgow G1 1XJ, UK
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Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, USA
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about the system or phenomenon under investigation. It may come from a lack of experimental data to characterize new materials and processes, poor understanding of coupled physics phenomena or a lack of knowledge about the model formulation (see, e.g., Helton 1994; Oberkampf et al. 2002; Helton et al. 2004; Zio and Pedroni 2013). In the last decades, there has been an increasing awareness that classical probability theory is inadequate for the treatment of epistemic uncertainty. Therefore, different nonprobabilistic approaches have been developed: imprecise probability, also known as interval analysis, after Walley (1991) and Berger et al. (1994);
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