Stochastic Orbital Lifetime Analysis

Μέγεθος: px

Εμφάνιση ξεκινά από τη σελίδα:

Download "Stochastic Orbital Lifetime Analysis"

Ἰάειρος Παπακωνσταντίνου
4 χρόνια πριν
Προβολές:

1 Stochastic Orbital Lifetime Analysis Kandyce Goodliff David Cornelius Analytical Mechanics Associates, Inc. Washito Sasamoto NASA Langley Research Center

2 Outline Need for Stochastic Analysis Orbital Lifetime Monte Carlo Tool Key Parameters Sensitivities Conclusions 2

3 Need for Stochastic Analysis Determine the orbital lifetime of a spacecraft Minimum mission goals based on science and/or operational requirements Maximum goals generally defined by spacecraft governing agency Point design analyses Difficult to select appropriate assumptions Ignores probability of occurrence of events Stochastic analyses Simultaneously vary multiple parameters based on probability of occurrence Provides clear, visual representation of probability of meeting a given lifetime 3

4 OLMC Orbital Lifetime Monte Carlo OL Orbital Lifetime Validated heritage Fortran code Long term variations of orbital parameters Limited to altitudes less than 2,500 km Perturbations Atmospheric drag Solar radiation pressure Gravitational effects due to the Earth s oblateness, the Sun, and the Moon MC Monte Carlo New Fortran code Up to 10,000 cases Sets up the key parameter sigma values established for each run 4

5 Products Histogram and Exceedance Probability 9% 8% Frequency % of Total Samples 7% 6% 5% 4% 3% 2% 1% Probability of Exceeding Lifetime 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% 0% Probability of exceeding 60 months lifetime is 72% Lifetime, Months Lifetime, Months 5

6 Key Parameters F10.7 cm solar flux predictions Difficult to predict resulting in significant uncertainty Nominal 11-year cycle but has varied between 9-17 years 250 OLMC factors Solar activity 200 magnitude Timing of the peak 150 OLMC factors modeled as normal distributions Prediction sets NASA MSFC Dr. Kenneth Schatten Custom profiles can be utilized Comparison of prediction sets show difficulty in correctly predicting solar flux magnitude and timing of the peak F10.7 cm SFU Schatten Sigma Schatten Sigma Marshall Sigma Schatten0705 Nominal Schatten0304 Nominal Marshall0705 Nominal 0 9/1/02 5/28/05 2/22/08 11/18/10 8/14/13 5/10/16 2/4/19 10/31/21 7/27/24 4/23/27 1/17/30 Date 6

7 Key Parameters F10.7 cm solar flux predictions Difficult to predict resulting in significant uncertainty Nominal 11-year cycle but has varied between 9-17 years 250 OLMC factors Solar activity 200 magnitude Timing of the peak 150 OLMC factors modeled as normal distributions 100 Prediction sets NASA MSFC 50 Dr. Kenneth Schatten Schatten Sigma Custom profiles can Schatten0705 Nominal be utilized 0 Comparison of prediction sets show difficulty in correctly predicting solar flux magnitude and timing of the peak F10.7 cm SFU 9/1/02 5/28/05 2/22/08 11/18/10 8/14/13 5/10/16 2/4/19 10/31/21 7/27/24 4/23/27 1/17/30 Date 7

8 Key Parameters F10.7 cm solar flux predictions Difficult to predict resulting in significant uncertainty Nominal 11-year cycle but has varied between 9-17 years 250 OLMC factors Solar activity 200 magnitude Timing of the peak 150 OLMC factors modeled as normal distributions Prediction sets NASA MSFC Dr. Kenneth Schatten Custom profiles can be utilized Comparison of prediction sets show difficulty in correctly predicting solar flux magnitude and timing of the peak F10.7 cm SFU Schatten Sigma Marshall Sigma Schatten0705 Nominal Marshall0705 Nominal 0 9/1/02 5/28/05 2/22/08 11/18/10 8/14/13 5/10/16 2/4/19 10/31/21 7/27/24 4/23/27 1/17/30 Date 8

9 Key Parameters F10.7 cm solar flux predictions Difficult to predict resulting in significant uncertainty Nominal 11-year cycle but has varied between 9-17 years 250 OLMC factors Solar activity 200 magnitude Timing of the peak 150 OLMC factors modeled as normal distributions Prediction sets NASA MSFC Dr. Kenneth Schatten Custom profiles can be utilized Comparison of prediction sets show difficulty in correctly predicting solar flux magnitude and timing of the peak F10.7 cm SFU Schatten Sigma Schatten Sigma Schatten0705 Nominal Schatten0304 Nominal 0 9/1/02 5/28/05 2/22/08 11/18/10 8/14/13 5/10/16 2/4/19 10/31/21 7/27/24 4/23/27 1/17/30 Date 9

10 Key Parameters - Continued Launch vehicle dispersions Accuracy with which the launch vehicle is capable of placing a spacecraft into its target orbit Dispersions in OLMC Injection apse Velocity Flight path angle Modeled as normal distributions Launch vehicle manufacturers typically provide injection and non-injection apse errors, the latter being directly related to velocity and flight path angle Nominal Velocity and Flight Path Angle Non-Insertion Apse Insertion Apse Altitude Error Band Nominal Insertion Point 10

11 Key Parameters - Continued Launch delays Based on historical data, if available Modeled as a Weibull distribution Fixed launch delays, if no data available Vary launch date (normal distribution) Ballistic coefficient Defined as: m/(c D A) Uncertainties associated with projected area, drag coefficient, and mass Modeled as a normal distribution 11

12 Sensitivity to Number of MC Runs Frequency % of Total Samples 12% 10% 8% 6% 4% 2% Lifetime Distribution for 525 Km Circular Orbit 100 MC Runs 500 MC Runs 1000 MC Runs 5000 MC Runs MC Runs 0% Lifetime, Months Visual inspection of histograms is recommended to determine the acceptable number of Monte Carlo runs 12

13 Sensitivity to Number of Orbits per Iteration Lifetime Distribution for 300 Km Circular Orbit Frequency % of Total Samples 30% 25% 20% 15% 10% 5% 1 Orbit/iteration 10 Orbits/iteration 100 Orbits/iteration 500 Orbits/iteration 0% Lifetime, Months Lower altitude orbits show a high sensitivity to the number of orbits per iteration 13

14 Sensitivity to Solar Flux Profile 25% 525 Km Circular Orbit Frequency % of Total Samples 20% 15% 10% 5% 0705Schatten 0304Schatten 0705MSAFE 0% Lifetime, Months Multiple profiles should be utilized, given the high sensitivity of lifetime to the solar flux prediction and the intrinsic variability of available predictions 14

15 Conclusions Normal distributions are appropriate for launch vehicle dispersions represented by injection altitude, velocity, and flight path angle Uncertainty distribution for launch delays should be determined based on data available Weibull was appropriate based on data obtained by the authors For any scenario, visual inspection of the lifetime histogram and computation of mean and median variation should be done at multiple settings for orbits per iteration and number of Monte Carlo runs to determine acceptable settings for desired reasonable distribution and repeatability Solar flux predictions are the primary driver for variations in lifetime, therefore caution needs to be exercised when basing analyses on a single prediction 15

16 Acknowledgements Don Avery & Carlos Liceaga Science Support Office, NASA Langley Research Center Larry Green & Jim Dempsey Space Mission Analysis Branch, NASA Langley Research Center Darryl J. Caldwell Analytical Mechanics Associates, Inc. Kristina Zaleski National Institute of Aerospace Paul Baumgartner Orbital Sciences Corporation Warren Frick ATK Barbara Sherman Boeing Launch Services 16

Σχετικά έγγραφα

Bayesian statistics. DS GA 1002 Probability and Statistics for Data Science.

Bayesian statistics. DS GA 1002 Probability and Statistics for Data Science. Bayesian statistics DS GA 1002 Probability and Statistics for Data Science http://www.cims.nyu.edu/~cfgranda/pages/dsga1002_fall17 Carlos Fernandez-Granda Frequentist vs Bayesian statistics In frequentist