Monte-Carlo Analysis of Object Reentry in Earth s Atmosphere Based on Taguchi Method

Transcription

1 Monte-Carlo Analysis of Object Reentry in Earth s Atmosphere Based on Taguchi Method Bastien Plazolles, R.Tech France Martin Spel, R.Tech France Vincent Rivola, R.Tech France Didier El Baz, LAAS-CNRS France 8 th European Symposium on Aerothermodynamics for Space Vehicles 5 march

2 Overview Context Taguchi Method Calima Application Conclusion/Perspective

3 Context It is a crucial point to predict the casualty area of a reentering object in order to avoid human casualty This is why space agencies have developed several numerical tools to predict this casualty area 3

4 Context - Actual atmospheric reentry tools are deterministic - Problem: deterministic approach does not allow to consider uncertainties on simulations: - Uncertainties on the models used: - Aerodynamic : simplified models - Thermodynamic: simplified models - Material properties : not well characterized at very high temperature - Trajectography : Atmospheric model - Uncertainties on the initial conditions: - Reentry point

5 Context - Atmospheric reentry is a very chaotic system => a slight modification of any initial condition can dramatically change the result - Because of these uncertainties => the tools use very conservative models that can be limiting for industrial - A solution to avoid these conservative models => perform statistical analysis on less conservative models 06/03/2015 5

6 Context - Possible to develop scripts around tools to perform Monte-Carlo analysis: - Impractical for user - Time consuming: a lot of parameters to perturb, limited computing means - Two questions: - How to minimize the amount of parameters to perturb - How to reduce computing time - A solution: Calima

7 Context - Calima permits to: restrain the amount of input parameters for a Monte-Carlo simulation via the Taguchi Method Easily perform a Monte-Carlo simulation Reduce computing time: Using Graphics Processing Unit (GPU) to parallelize computations (possibility to perform computations on CPU but currently sequential) Each parallel thread : completes simulation from the initial point to the ground

8 Taguchi Method - Aim : Find the relationship between various perturbed input parameters of a model and how the model respond to them - Means : - Generate combinations of «representative» values of the perturbed input parameters thanks to Orthogonal Array - Process the results with the Analysis of Variance (ANOVA) - Interest: With few computations permits one to identify which parameter influence the value of the result and which do not. - The Taguchi method also provides a confidence level of its result. Identify pertinent parameters for a Monte-Carlo simulation

9 Calima - Calima : 6 DoF, object oriented, atmospheric reentry simulation tool - Interest: Performs statistical analysis of atmospheric reentry debris to determine casualty area - Currently only 11 parameters can be perturbed: - Mass - Altitude - Latitude - Longitude - Azimuth - Speed - Angle of attack - Angle of yaw - Angle of roll - Flight Path Angle - Choose the perturbation method : random, Gaussian, fixed step, imposed values or Taguchi analysis - The tool ensures the correct coverage of the input parameters space

10 Application: initial conditions - Considering a sphere with a diameter of 1,0 m - The other input parameters with a normal uncertainty Parameter Mean value μ Standard deviation σ Mass (kg) 247,224 4,12 Altitude (km) 120,0 0,25 Latitude ( ) 0,0 0,05 Longitude ( ) 0,0 0,1 Azimuth ( ) 45,0 0,15 Speed (m.s -1 ) 7272,582 48,51 Flight Path Angle ( ) -2,612 0,01 - Taguchi method uses representative values : μ, μ- 1,5σ and μ + 1,5σ

11 Application: ANOVA table - ANOVA table of Impact Energy Parameter DoF: f Sum of Square: SS Variance: V Variance Ratio: F Pure Sum of Square: SS Percent Contribution : P Mass e e e e+02 92,3810 Radius e e e e-02 0,0387 Latitude e e e e-03 0,0001 Longitude e e e e-04 0,0002 Azimuth e e e e+00 0,4541 Speed e e e e+01 7,1131 F.P.A e e e e-03 0,0008 Error e e e e-03 0,001 - The parameter that has the biggest impact on the variation of the impact energy is the mass, with more than 99,5% of confidence - Initial Latitude, Longitude, Azimuth and Flight Path Angle have no impact

12 Application: ANOVA table - The same manner for impact latitude and longitude: - Parameters having the most impact : intital latitude and longitude - Parameters having the less impact: Mass, Flight Path Angle and the Azimuth - These results are dependents on the uncertainty on the input parameters

13 Application: Monte-Carlo Analysis - We can now reduce our input space parameter, and perform Monte-Carlo analysis of latitude, longitude dispersion - The nominal impact point : Latitude = 0.0, Longitude= The 3 sigma area = ,41 km² simulations performed in around 88s on the GPU: NVIDIA K40 With Debrisk : performed in around 300 hours 13

14 Conclusion - The Taguchi Method is a good alternative to classic Monte-Carlo analysis - It permits to determine with few computations parameters that really influence the variation of a results (ex: demise altitude, impact energy, impact point dispersion) - This method is applicable to every existing reentry simulation tools 14

15 Conclusion - Calima : new atmospheric reentry simulation tool (in development) - Permits to perform automated Monte-Carlo analysis - Takes advantage of Taguchi Method, to study only pertinent input parameters - Reasonable computing time thanks to GPU parallelism 15

16 Perspective - Increase amount of parameters to perturb (short term) - Improve physical models in Calima (ablation, shapes, ) (mid term) - Transition from object oriented to spacecraft oriented (long term) - Possibility to compute simultaneously several objects and their interactions : wake, (long term) 16