Abstract
This paper extends the overbounding technique for univariate error monitoring to the multivariate error domain while using modeling techniques based on the extreme value theory. It derives an overbounding condition called norm overbounding by using hyperspherical coordinates to define errors in the multivariate domain as a vector norm, which in turn can be compared to a scalar threshold probability (such as an alert limit). This new approach provides an overbound model that bounds the probabilities of any norm exceeding any value. In particular, this method employs a constant lower bound for the marginal angular distribution and a Gaussian-Pareto hybrid distribution to bound the conditional radial distribution. In this case, a half-Gaussian distribution is used to overbound the region of the distribution near zero, and a Pareto distribution is used for the tail. This is motivated by results from extreme value theory for modeling heavy-tailed distributions. Furthermore, this approach uses a hypercone partitioning approach to estimate the norm overbounds from sampled data. The entire technique is demonstrated through a twodimensional example.
Original language | English (US) |
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Pages (from-to) | 148-161 |
Number of pages | 14 |
Journal | Journal of Aerospace Information Systems |
Volume | 16 |
Issue number | 4 |
DOIs | |
State | Published - 2019 |
Bibliographical note
Funding Information:This material is based upon work supported by the National Science Foundation under grant no. NSF/CNS-1329390 entitled CPS: Breakthrough: Collaborative Research: Managing Uncertainty in the Design of Safety-Critical Aviation Systems.
Funding Information:
This material is based upon work supported by the National Science Foundation under grant no. NSF/CNS-1329390 entitled “CPS: Breakthrough: Collaborative Research: Managing Uncertainty in the Design of Safety-Critical Aviation Systems.”
Publisher Copyright:
Copyright © 2019 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.