Uncertainty propagation for statistical impact prediction of space debris

Hoogendoorn, Raymond; Mooij, Erwin; Geul, Jacco

doi:10.1016/j.asr.2017.10.009

Cited by 9 publications

(5 citation statements)

References 19 publications

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“…Indeed, this model is representative of the phenomena encountered but with a reduced simulation cost (e.g., use of mass point model) while remaining challenging enough regarding the use of advanced rare event estimation techniques and sensitivity analysis methods. For more realistic problems, one can refer to [36,37]. In these studies, other parameters are considered and investigated concerning the dynamics of the vehicle (e.g., perturbation of atmospheric density, winds).…”

Section: Resultsmentioning

confidence: 99%

Global Reliability‐oriented Sensitivity Analysis under Distribution Parameter Uncertainty

Chabridon

Balesdent

Perrin

et al. 2021

Mechanical Engineering Under Uncertainties

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Section: Resultsmentioning

confidence: 99%

Global Reliability‐oriented Sensitivity Analysis under Distribution Parameter Uncertainty

Chabridon

Balesdent

Perrin

et al. 2021

Mechanical Engineering Under Uncertainties

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“…Thus, the volume of this support approaches 0 over time. Consequently, in order to conserve probability mass, sup P S f → ∞, leading directly to numerical overflow in computer implementations [13].…”

Section: The Koopman Expectationmentioning

confidence: 99%

The Koopman Expectation: An Operator Theoretic Method for Efficient Analysis and Optimization of Uncertain Hybrid Dynamical Systems

Gerlach¹,

Leonard²,

Rogers³

et al. 2020

Preprint

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For dynamical systems involving decision making, the success of the system greatly depends on its ability to make good decisions with incomplete and uncertain information. By leveraging the Koopman operator and its adjoint property, we introduce the Koopman Expectation, an efficient method for computing expectations as propagated through a dynamical system. Unlike other Koopman operator-based approaches in the literature, this is possible without an explicit representation of the Koopman operator. Furthermore, the efficiencies enabled by the Koopman Expectation are leveraged for optimization under uncertainty when expected losses and constraints are considered. We show how the Koopman Expectation is applicable to discrete, continuous, and hybrid non-linear systems driven by process noise with non-Gaussian initial condition and parametric uncertainties. We finish by demonstrating a 1700x acceleration for calculating probabilistic quantities of a hybrid dynamical system over the naive Monte Carlo approach with many orders of magnitudes improvement in accuracy. * For example, systems without explicit differential equations, i.e., data-driven models

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“…For each bin, the density is computed as the mean of the density values of the data points contained in it. This method can be used if the PDF data are uniformly distributed in each bin in all dimensions and if the enclosed volume of the scattered data in each bin is equal [36]. However, even if the initial distribution of samples is uniform, its evolution in time does not necessarily remain uniform, and the enclosed volume of the data in each bin does not remain equal.…”

Section: Introductionmentioning

confidence: 99%

“…However, even if the initial distribution of samples is uniform, its evolution in time does not necessarily remain uniform, and the enclosed volume of the data in each bin does not remain equal. Therefore, such a methodology generates results which present poor agreement with corresponding Monte Carlo simulations [32,36]. In addition, such a methodology still uses a number of samples comparable to Monte Carlo methods.…”

Section: Introductionmentioning

confidence: 99%

Propagation and Reconstruction of Reentry Uncertainties Using Continuity Equation and Simplicial Interpolation

Trisolini

Colombo

2021

Journal of Guidance, Control, and Dynamics

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This Paper proposes a continuum-based approach for the propagation of uncertainties in the initial conditions and parameters for the analysis and prediction of spacecraft reentries. Using the continuity equation together with the reentry dynamics, the joint probability distribution of the uncertainties is propagated in time for specific sampled points. At each time instant, the joint probability distribution function is then reconstructed from the scattered data using a gradient-enhanced linear interpolation based on a simplicial representation of the state space. Uncertainties in the initial conditions at reentry and in the ballistic coefficient for three representative test cases are considered: a three-state and a six-state steep Earth reentry and a six-state unguided lifting entry at Mars. The Paper shows the comparison of the proposed method with Monte Carlo-based techniques in terms of quality of the obtained marginal distributions and runtime as a function of the number of samples used.

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Uncertainty propagation for statistical impact prediction of space debris

Cited by 9 publications

References 19 publications

Global Reliability‐oriented Sensitivity Analysis under Distribution Parameter Uncertainty

Global Reliability‐oriented Sensitivity Analysis under Distribution Parameter Uncertainty

The Koopman Expectation: An Operator Theoretic Method for Efficient Analysis and Optimization of Uncertain Hybrid Dynamical Systems

Propagation and Reconstruction of Reentry Uncertainties Using Continuity Equation and Simplicial Interpolation

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