D R A F T. P. G. Hänninen 1 M. Lavagna 1 Dipartimento di Ingegneria Aerospaziale

Transcription

1 Multi-Disciplinary Optimisation for space vehicles during Aero-assisted manoeuvres: an Evolutionary Algorithm approach P. G. Hänninen 1 M. Lavagna 1 p.g.hanninen@ .it, lavagna@aero.polimi.it 1 POLITECNICO DI MILANO D R A F T Dipartimento di Ingegneria Aerospaziale

2 The toolbox Fast tool for a preliminary multi-disciplinary multi-objective optimization in terms of Guidance and Shape for a space vehicle involved in atmospheric manoeuvres The default settlement of the toolbox supplies: pre phase-a solutions in a multidisciplinary environment that can be further investigated in detail and locally refined first guess solutions to be given to analytical optimizers (Astos, etc ) global optimum in a broad search space R 27 according to an objective vector in 3 R This tool is easily reconfigurable: well-suited for solving broad class of problems in different scenarios according to given gravitational/atmospheric models for the selected planet

3 Problem Statement Multidisciplinary Optimisation of shape and 3 DOF optimum control for atmospheric manoeuvres, in terms of either final State or dynamic related specific quantities for different scenarios: - Entry problems - Aerocapture - AGA (Aeroassisted Gravity Assists Wave Riders) Closed orbit around the planet Atmospheric phase Hyperbolic Orbit R 0,V 0 R f,v f Aerocapture

4 Problem Statement Default cost functions: Min f (m 0 /m pl, S?V, ) Constraints: inequality: structural loads equality: final absolute velocity landing site error heat load, heat flux Vehicle dynamics Free variables: X opt = [? 0, bank, t 1 t i, Vehicle configuration parameters, trim angle,?v, t i+1 t fin, m pl ] Input parameters: target planet initial energy (hyperbolic arrival orbit) atmospheric model (Universal interpolators) gravitational model selected materials for the vehicle Outputs: space vehicle shape Angle of attack/bank Guidance internal Volume 3D visualisation of configuration and trajectory

5 Selected Approach Requirements: - global optimisation - discrete and continuous domains Selected approach: Genetic algorithms + Non-Dominance Pareto ranking Benefits: - set of different well-spread final optimal solutions - objective vector domain-independent worse better Non Dominance Approach to find the final set of solutions

6 Physical Model Simulation model: - 3 DOF - rotation of the planet is considered - trimmed vehicle - discrete bank control profile - Modified Newton method to derive aerodynamics coefficients for conic shape (hypersonic flow) Environment: - atmosphere and gravitational field modelled through an universal approximators on real data Parameters: - user-selected materials for structure and heat shield - target planet, entry absolute velocity and position [ V 0, R 0 ] The dynamics of the atmospheric path has been validated with Traj3D code.

7 NDGA Toolbox The Genetic Algorithm Optimiser (NDGA) has been designed on the specific problem to: avoid the genetic drift through a Twins control that kills identical individuals have the individuals spread throughout the Optimal Pareto Front obtain a faster convergence To assure the convergence to the optimum the proposed tool has been tested on Pareto fronts available in literatures: continuous concave/convex, discontinuous fronts

8 NDGA Toolbox Test case: NDGA vs NSGA [Deb 2000] Bi-objective vector Solutions are spread trough the whole front NDGA: 80 generations [76s Intel C. 1.5 Mhz] NSGA: 300 generations 200 individuals 200 individuals

9 NDGA Constraint handling The aeroassisted manoeuvres give rise to different forms of infeasibilities: the generated shape of the vehicle is not feasible trajectory brings the vehicle to crash to the ground exceeded Q,, g max Q max max final orbit is hyperbolic (not for AGA) minimum altitude during the atmospheric pass is too low the final constrained orbit is not reached Infeasibilities have been treated both in terms of - satisfaction / non-satisfaction - amount of violation The selection process allows the infeasible individuals to evolve too, to maintain sensitivity on the active constraints zone, often in proximity of the global constrained optimum Moreover such an approach speeds up the convergence and helps finding global and sparse Pareto fronts.

10 Architecture NDGA block MDO blocks switching: MATLAB environment Crossover Population Fitness Function Mutation Blcone: aerodynamic data (Modified Newtonian) Monocoque: Structural module Simulink module: Dynamics/loads computation Qmax g max max Q User available data Pareto Ranking Selection Fitness/constraint evaluation: Constraint check Graphical Graphical Visualisation Visualisation of of output output & results results Convergence Test Fitness evaluation Solution

11 Results Selected planet: Mars Objective vector: min [? a,? e,? i ] Final orbit Keplerian parameter errors minimisation Initial Population shows the infeasibility in eccentricity (could be solution for an AGA) Initial population e Final populations?a e 5 generations?a 25 generations 35 generations Pareto Fronts TARGET: [a, e] = [ 4 e6 m, 0 ]

12 Results Studied case: Mars Aerocapture solutions in terms of trajectory, shape, ballistic coefficient, heat flux, load, tof g max = ~ 6 g earths Q = ~ 1 e8 J/m 2 Q max = ~ 2 e6 W/m 2 Tof = ~ 700 s H min = ~ 30 Km? 0 = ~ -10

13 Results Studied case: Mars Aerocapture Pareto solutions g max = ~ 8 g earths Q = ~ 8 e7 J/m 2 Q = ~ 2 e6 W/m 2 max Tof = ~ 300 s H min = ~ 20 Km? 0 = ~ -16

14 Results The achieved solutions show the trade off between: high loads / low altitude / short time of flight / thinner shape and lower loads / high altitude / long time of flight / bulkier shape Similar approach has been used to find solutions for the entry problem optimising also the configuration sequence (IBD inflation, drogue-parachute deployment) to achieve the target landing site.

15 Work in progress Objective vector enlargement Uncertainty management, possible approaches: - Use of Interval Computation - Robust approach by criteria vector enlargement different techniques to deal with different parameters uncertainties (entry, atmospheric, aerodynamics database) Modelling a continuous bank profile through an universal approximator (Neural Network - spline interpolator) Identification of the most sensitive variables in the criteria vector trough a Response Surfaces and Taguchi method analysis. Man machine interface implementation thanks to a user friendly graphical interface

16 Conclusions The proposed tool permits to have fast and global optimisation of both Guidance and Shape Works on huge research spaces Graphical representation of solutions: shape, trajectory, loads Parameterised to easily reconfigure the tool to solve different type of problems in different scenarios