11th AIAA / ISSMO MAO Conference, 6-9 September 2006, Portsmouth, VA
Analysis, Optimization and
Probabilistic Assessment of an
Airbag Landing System for the
ExoMars Space Mission
Richard Slade, EADS Astrium, Stevenage, UK
Royston Jones and Paul Sharp, Altair Engineering Ltd, Coventry, UK
and
Vassili Toropov, University of Leeds
(with Altair Engineering until April 2006), UK
Design of Airbag Landing System for the ExoMars Space Mission, 11 AIAA-ISSMO MAO Conference
ExoMars Space Mission
• ESA Aurora exploration
programme
• 240kg mobile robotic exobiology laboratory
• To search for extinct or extant
microbial life on Mars
• Supporting geology and
meteorology experiments
• Launch in 2011 or 2013
• Currently in Phase B – mission
planning and concept design
phase
Design of Airbag Landing System for the ExoMars Space Mission, 11 AIAA-ISSMO MAO Conference
Airbags for Space Landers
• Un-vented Type
–
–
–
–
Multiple bounces
Established Heritage
High Mass
Vulnerable to rupture
Mars Pathfinder
NASA/JPL
Beagle 2
Beagle2
• Vented Type
–
–
–
–
–
Active control
Single stroke
No space heritage
Low Mass
Vulnerable to overturning
Kistler Booster
Irvin
ExoMars
ESA
Design of Airbag Landing System for the ExoMars Space Mission, 11 AIAA-ISSMO MAO Conference
Airbag Landing Design Concept
• Design concept
considers vented (or
“Dead-Beat”) airbag
coming to rest on
second bounce
• Inflated with N2 during
descent under main
parachute
Design of Airbag Landing System for the ExoMars Space Mission, 11 AIAA-ISSMO MAO Conference
Airbag Configuration
• Six identical vented chambers
• One “anti-bottoming” un-vented toroidal
Design of Airbag Landing System for the ExoMars Space Mission, 11 AIAA-ISSMO MAO Conference
Optimization and reliability assessment of ExoMars lander
Failure modes:
–
–
–
–
Roll-over (payload overturns),
Dive-through (payload impacts rock)
Rupture (fabric tears)
Full-scale terrestrial testing is difficult / expensive
Design of Airbag Landing System for the ExoMars Space Mission, 11 AIAA-ISSMO MAO Conference
Software Tools
• LS-DYNA
– Dynamic Relaxation (steady-state free fall condition)
– Airbag functionality (Wang Nefske inflation model)
– Advanced contact (internal fabric contact etc.)
• HyperMesh
– Advanced LS-DYNA model build support
– Comprehensive interface
• HyperView
– Time dependent LS-DYNA animations
– Multi results type environment (animations, X-Y data)
• HyperMorph
– Airbag parameterisation
– Rock height, pitch angle variation in reliability assessment
• HyperStudy
– Airbag size optimisation
– Reliability assessment
Design of Airbag Landing System for the ExoMars Space Mission, 11 AIAA-ISSMO MAO Conference
Landing Scenarios
Two Landing Scenarios – Flat Bottom & Inclined Rock
Impacts
Mars Environment:
• Gravity 3.7 m/s2 = 0.38g
• Pressure 440Pa = 0.4% of Earth air pressure at sea level
= at 36.5 km altitude on Earth
• Temperature 187K = - 86º C
Design of Airbag Landing System for the ExoMars Space Mission, 11 AIAA-ISSMO MAO Conference
Landing Scenarios
Landing scenarios are chosen to give conflicting
design requirements
•Flat Bottomed Impact
•Vertical Velocity 25m/s
•Favours ‘Tall’ airbag designs
•Favours ‘Narrow’ airbag designs
•Tall, Narrow airbag makes most
effective vertical energy absorber
•Inclined Rock Impact
•Vertical Velocity 25m/s
•Lateral ‘Wind’ Velocity 16.3m/s
•Favours ‘Wide’ Airbag designs
•Wide airbag makes most effective
rock intrusion absorber
Design of Airbag Landing System for the ExoMars Space Mission, 11 AIAA-ISSMO MAO Conference
Baseline Response : Flat Bottom Impact
• Peak Filtered Deceleration 66g (Target <70g)
• Peak Airbag Material Stresses 135MPa (Target <533MPa)
• Constraints Satisfied by Baseline
Design of Airbag Landing System for the ExoMars Space Mission, 11 AIAA-ISSMO MAO Conference
Baseline Response : Inclined Rock Impact
•
•
•
•
Peak Filtered Deceleration 980g (Target <70g
Peak Filtered Deceleration 980g (Target <70g)
Peak Airbag Material Stresses 281MPa (Target <533MPa)
Deceleration Constraint Exceeded Due to ‘Dive Through’
Design of Airbag Landing System for the ExoMars Space Mission, 11 AIAA-ISSMO MAO Conference
Baseline Response : Inclined Rock Impact ‘Dive Through’
• Critical to prevent ‘direct’ payload to Rock/Ground impact
• Such type of impact guarantees violation of deceleration
constraint
Direct Payload to
Rock impact due
to ‘dive through’
Design of Airbag Landing System for the ExoMars Space Mission, 11 AIAA-ISSMO MAO Conference
ExoMars Lander: LS-DYNA Simulation
Design of Airbag Landing System for the ExoMars Space Mission, 11 AIAA-ISSMO MAO Conference
Optimization: Set-up
Design Objective
- Minimise System Mass (Airbag + Payload + Gas + System)
Design Constraints
- Payload Acceleration (<70g)
- Global Bag Von Mises Stress (<533MPa)
- Re-bound and “roll over” inversion kinematics
Design Objective and Constraint Responses Evaluated for each Landing Case
Design Variables
▲
- Airbag Base Diameter (HyperMorph)
- Airbag Height (HyperMorph)
- Airbag Venting Area
- Airbag Steady-State Pressure (Mass of Gas)
Minimise Design Objective by varying the Design Variables whilst satisfying
the Design Constraints
Design of Airbag Landing System for the ExoMars Space Mission, 11 AIAA-ISSMO MAO Conference
Design Parameterization
Design Variables : Airbag Height and Diameter
• Airbag geometry defined by dimensional relationships between height (H)
and diameter (D) of cross-section, curves are elliptical sections
• Geometric factors a, b, c are constant
¼ ellipse
¼ ellipse
¼ ellipse
Design of Airbag Landing System for the ExoMars Space Mission, 11 AIAA-ISSMO MAO Conference
Metamodelling
▲
Need for metamodelling
•One LS DYNA analysis of 0.2s after touchdown takes
10 hours of computing
▲
Unifying approach
•Both optimization and reliability study utilise metamodels
▲
Accuracy of metamodels
•Optimization and reliability studies based on metamodels
•High quality metamodel is required
Design of Airbag Landing System for the ExoMars Space Mission, 11 AIAA-ISSMO MAO Conference
DOEs for metamodel building
• Main requirements to DOE are:
– maximum quantity of information
– achieved with minimum computational effort (number
of numerical experiments)
Design of Airbag Landing System for the ExoMars Space Mission, 11 AIAA-ISSMO MAO Conference
Optimal Latin Hypercube DOEs
• Optimal Latin Hypercube (OLH) DOEs specify the sample
points such that as much of the design space is sampled
as possible, with the minimum number of response
evaluations - especially useful when the evaluations are
expensive.
• OLH DOEs are highly structured in a way that:
– They provide an optimal uniform distribution of sample points.
– They spread out the sample points efficiently (space filling)
through out the design space.
• OLH can also be used to specify sampling points in robust
design, reliability analysis.
Design of Airbag Landing System for the ExoMars Space Mission, 11 AIAA-ISSMO MAO Conference
LH DOE – conventional (random) and optimal
Random Latin hypercube Optimal Latin hypercube
random points
distribution
optimal uniformity of the
points distribution
Design of Airbag Landing System for the ExoMars Space Mission, 11 AIAA-ISSMO MAO Conference
Optimization: Objective function (Audze-Eglais 1977)
• Physical analogy: a system consisting of points of unit
mass exert repulsive forces on each other causing the
system to have potential energy. When the points are
released from an initial state, they move. They will reach
equilibrium when the potential energy of the repulsive
forces between the masses is at a minimum. If the
magnitude of the repulsive forces is inversely
proportional to the distance squared between the points
then minimize:
P
min
U
= min
P

p 1 q  p 1
Potential energy
(objective function)
1
2
L pq
Distance between points p and q
Design of Airbag Landing System for the ExoMars Space Mission, 11 AIAA-ISSMO MAO Conference
permGA iteration history for 2 design variables & 10 points
Design of Airbag Landing System for the ExoMars Space Mission, 11 AIAA-ISSMO MAO Conference
permGA iteration history for 2 design variables & 50 points
Design of Airbag Landing System for the ExoMars Space Mission, 11 AIAA-ISSMO MAO Conference
permGA iteration history for 2 design variables & 400 points
Design of Airbag Landing System for the ExoMars Space Mission, 11 AIAA-ISSMO MAO Conference
permGA iteration history for 2 design variables & 999 points
Design of Airbag Landing System for the ExoMars Space Mission, 11 AIAA-ISSMO MAO Conference
Metamodelling: DoE
Four Design Variables – 40 Test Plan Points (EULH) / Landing Scenario
Design of Airbag Landing System for the ExoMars Space Mission, 11 AIAA-ISSMO MAO Conference
Metamodel building using Moving Least Squares Method (MLSM)
• Suggested for generation of surfaces given by points
• Used in meshless (mesh-free) form of FEM
• Useful for metamodel building
• Simple – can be explained to (and understood by) an
engineer within 5 minutes
Design of Airbag Landing System for the ExoMars Space Mission, 11 AIAA-ISSMO MAO Conference
Moving Least Squares Method
Generalization of a weighted least squares method
where weights do not remain constant but are
functions of Euclidian distance rk from a k-th sampling
point to a point x where the surrogate model is
evaluated.
DoE point
xj
Evaluation point x
rk
xi
Design of Airbag Landing System for the ExoMars Space Mission, 11 AIAA-ISSMO MAO Conference
Moving Least Squares Method
The weight wi , associated with a sampling point xi ,
decays as a point x moves away from xi .
Because the weights wi are functions of x, the
polynomial basis function coefficients are also
dependent on x.
G a ( x )  
 w p ( x ) F  x p 
P
p 1

~
 F x p ,a

2

min
This means that it is not possible to obtain an
analytical form of the approximation function but its
evaluation is still computationally inexpensive.
Design of Airbag Landing System for the ExoMars Space Mission, 11 AIAA-ISSMO MAO Conference
Gaussian weight decay function
wi = exp(-ri2)
where  is “closeness of fit parameter”
=1
 = 10
 = 100
Design of Airbag Landing System for the ExoMars Space Mission, 11 AIAA-ISSMO MAO Conference
Example: six-hump camel back function
F(x1,x2) = (4 - 2.1 x12 + x14 / 3) x12+x1x2+(- 4 + 4x22) x22,
-2 ≤ x1 ≤ 2, -1 ≤ x2 ≤ 1.
5.5-6
5-5.5
4.5-5
4-4.5
3.5-4
3-3.5
2.5-3
2-2.5
1.5-2
6
1-1.5
5.5
5
0.5-1
0-0.5
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
-0.5
-1
-1.5
-0.5-0
-1--0.5
-1.5--1
-2
x2
x1
-1
Design of Airbag Landing System for the ExoMars Space Mission, 11 AIAA-ISSMO MAO Conference
Example: six-hump camel back function
5.5-6
5-5.5
4.5-5
4-4.5
3.5-4
3-3.5
6-6.5
2.5-3
5.5-6
2-2.5
1.5-2
6
1-1.5
5.5
5
0.5-1
0-0.5
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
-0.5
-1
-1.5
-0.5-0
-1--0.5
-1.5--1
4.5-5
4-4.5
3.5-4
3-3.5
2.5-3
2-2.5
1.5-2
1-1.5
0.5-1
0-0.5
-0.5-0
-1--0.5
x2
-1.5--1
-2
-2
x2
5-5.5
6.5
6
5.5
5
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
-0.5
-1
-1.5
x1
-1
x1
-1
Original function
Approximation on 100 sampling
points,  = 120
Design of Airbag Landing System for the ExoMars Space Mission, 11 AIAA-ISSMO MAO Conference
Example:
Computing and Rendering Point Set Surfaces by M. Alexa et al. 2001
larger 
smaller 
Design of Airbag Landing System for the ExoMars Space Mission, 11 AIAA-ISSMO MAO Conference
Metamodel Generation using MLSM
• MLSM provides a high quality response surface to accurately
approximate a highly nonlinear system.
• Important feature of MLSM is efficient handling of numerical noise
by adjusting “closeness of fit” parameter to provide close fit to a
low noise situation or loose fit when the response exhibits a larger
amount of noise
• Direct Payload to Rock/Ground Impact Resulting in High Payload
Accelerations (>100g) occurred at high percentage of Test Plan
Points
• These high results ‘swamp’ the responses of interest in the
approximation
Design of Airbag Landing System for the ExoMars Space Mission, 11 AIAA-ISSMO MAO Conference
MLSM Test Example : Rosenbrock’s Banana Valley Function
2
45
40
35
30
25
20
15
2
10
40-45
35-40
30-35
25-30
20-25
1
15-20
10-15
1-2
0-1
5-10
0-5
5
0
0
2
0
0
Noise Outside Area of Interest
Function Capped
• To minimise this function, a good quality approximation of the valley
should be obtained whilst ignoring numerical noise outside the valley
Design of Airbag Landing System for the ExoMars Space Mission, 11 AIAA-ISSMO MAO Conference
MLSM Test Example : Rosenbrock’s Banana Valley Function
3
3
2.5
2.5
2.5-3
2
2
2.5-3
2-2.5
1.5
1.5-2
1-1.5
1
0.5-1
0-0.5
2-2.5
1.5-2
1.5
1-1.5
0.5-1
1
2
0-0.5
2
0.5
0.5
0
0
0
0
0
0
2
2
Least Squares approximation of capped function, 100 Sampling
points, quadratic polynomial (left) and cubic polynomial (right),
still give poor approximation of function
Design of Airbag Landing System for the ExoMars Space Mission, 11 AIAA-ISSMO MAO Conference
MLSM Test Example : Rosenbrock’s Banana Valley Function
2
2
1
1-2
1
0-1
1-2
0-1
2
0
0
0
0
Capped function
MLSM approximation of capped
function, 100 sampling points gives
good approximation of function
Design of Airbag Landing System for the ExoMars Space Mission, 11 AIAA-ISSMO MAO Conference
Optimization results
• On review of the response data set obtained from the Test Plan points
it was observed that there was a high percentage of runs that failed to
meet the constraints
• This was reflected in the approximations and resulted in a very small
‘sweet spot’ on the response surface where the constraints could be
met
• Model mass varied very little (<0.25%) within this area (all runs in this
area had more mass than baseline run)
• Because of the minimal mass penalty, instead of optimising for mass it
was decided at this stage to optimise for payload deceleration and
residual energy in order to achieve the best model to carry forward to
the reliability analysis. Note that the same approximation models could
be used for the reformulated optimization problem.
Design of Airbag Landing System for the ExoMars Space Mission, 11 AIAA-ISSMO MAO Conference
Optimization results
•Optimised
mass selected was 403.5kg (baseline 392.8kg)
•Flat
Bottom Impact Payload Acceleration increased from
65.5g to 67.7g
•Rock
Impact Payload Acceleration decreased from 980.3g
to 69.1g
•Maximum
Material Stresses were reduced from 281MPa to
157MPa
•While
3 variables are in middle of range, Vent Area pushes
limit
Design of Airbag Landing System for the ExoMars Space Mission, 11 AIAA-ISSMO MAO Conference
Reliability assessment of ExoMars lander
• Ultimately, the reliability figure gives the probability of
a successful landing for a given design under a range of
conditions
• Alternatively it can be used to establish an envelope of
conditions for a given success probability
• For this project, the limited number of variables (4)
considered, results in a reliability index 'figure of merit',
rather than an overall probability of success
• Establishing this 'figure of merit', index for the reliability
of a design gives a useful comparison with alternative
designs
Design of Airbag Landing System for the ExoMars Space Mission, 11 AIAA-ISSMO MAO Conference
Reliability assessment: Model definitions
• Adopt airbag design variables determined by optimization study
• Consider only rock impact loadcase (though rock height may be zero, i.e.
flat surface)
• Failure defined by exceeding similar constraints to optimisation study
– Resultant deceleration < 80g
– Kinematic metrics, re-bound, roll-over
– No bag tearing
• Environment Variables
Design
Variable#
DV1
DV2
DV3
DV4
Description
Lower Bound Upper Bound
Lateral Wind Velocity
0 m/s
20 m/s
Rock Height
0m
0.8 m
Lander Pitch Attitude
-20 º
20 º
Lander Pitch Rate
-30 º/s
30 º/s
Design of Airbag Landing System for the ExoMars Space Mission, 11 AIAA-ISSMO MAO Conference
Stochastic Variables & PDFs
•
Wind Velocity - Weibull distribution, Determined from European
Mars Environmental Model Project
Design of Airbag Landing System for the ExoMars Space Mission, 11 AIAA-ISSMO MAO Conference
Stochastic Variables & PDFs
• Rock Height -Exponential distribution, Determined from past mission data
P ro b a b ility D e n s ity F u n c tio n f(H )
7 .0 0 0 0
k = 10%
6 .0 0 0 0
k = 20%
k = 30%
P ro b ab ility D en sity (m ^ -1)
5 .0 0 0 0
4 .0 0 0 0
3 .0 0 0 0
2 .0 0 0 0
1 .0 0 0 0
0 .0 0 0 0
0 .0 0 0
0 .2 0 0
0 .4 0 0
0 .6 0 0
0 .8 0 0
1 .0 0 0
1 .2 0 0
1 .4 0 0
1 .6 0 0
1 .8 0 0
R o c k H e ig h t H (m )
• Pitch Attitude – Normal distribution - Variation from mean at ±3σ is ±30°
• Pitch Rate – Normal distribution - Variation from mean at ±3σ is ±20°/sec
Design of Airbag Landing System for the ExoMars Space Mission, 11 AIAA-ISSMO MAO Conference
Reliability assessment of ExoMars lander: Metamodel generation
•Test Plan – Uniform Latin HyperCube with Extremities Extension
•Eighty Test Points – 80 LS-DYNA runs executed (single load case)
•Advanced metamodelling using moving least squares method
•Process is the same as used to generate optimization metamodel, but with
different variables
Design of Airbag Landing System for the ExoMars Space Mission, 11 AIAA-ISSMO MAO Conference
Reliability assessment of ExoMars lander
Objective: avoid this…
Design of Airbag Landing System for the ExoMars Space Mission, 11 AIAA-ISSMO MAO Conference
Result of reliability assessment of ExoMars lander
• Metamodel generation methodology successfully used to
perform optimization and assess reliability in Altair’s
HyperStudy
• The optimization study arrived at a design that satisfies the
requirements with only a small increase in mass
• Reliability analysis proved that the concept is viable
• Reliability analysis uncovered failure modes that had
not previously been considered
Design of Airbag Landing System for the ExoMars Space Mission, 11 AIAA-ISSMO MAO Conference
Conclusions
• The suggested airbag optimization & reliability assessment
process can be employed in future phases of the ExoMars
project, with:
- Further design improvements by increasing design variable
space (vent areas, trigger accelerations, more complex
differential venting strategies, changes in the un-vented
toroidal, etc.)
- More comprehensive reliability assessment, with aim of
determining the overall airbag reliability
Design of Airbag Landing System for the ExoMars Space Mission, 11 AIAA-ISSMO MAO Conference
Astrium Mars Lander: LS-DYNA Simulation
Design of Airbag Landing System for the ExoMars Space Mission, 11 AIAA-ISSMO MAO Conference
Questions?
Any questions?
Design of Airbag Landing System for the ExoMars Space Mission, 11 AIAA-ISSMO MAO Conference