An Offline/Online DDDAS Capability for
Self

Aware Aerospace Vehicles
MIT:
Douglas Allaire
, Karen
Willcox
, Marc
Lecerf
, Laura
Mainini
,
Demet
Ulker
, Harriet Li
UT Austin:
George Biros, Omar
Ghattas
Aurora Flight Sciences:
Jeffrey Chambers, David
Kordonowy
,
Raghvendra
Cowlagi
International Conference on Computational Science
Barcelona, Spain
June 6, 2013
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Motivation and Goals
2
A
self

aware aerospace vehicle
can
dynamically adapt the way it performs
missions by gathering information
about itself and its surroundings and
responding intelligently.
Research Goal: Create a
multifidelity framework for the DDDAS paradigm
.
•
DDDAS process draws on multiple modeling options and data sources to
evolve models, sensing strategies, and predictions as the flight proceeds
•
Dynamic data inform online adaptation of structural damage models and
reduced

order models
•
Dynamic guidance of sensing strategies
•
Dynamic, online management of multifidelity structural response models
and sensor data, ensuring that predictions have sufficient confidence
Leading to
dynamic health

aware mission re

planning
with
quantifiable benefits in reliability, maneuverability and survivability.
Outline
•
Approach Overview
•
Modeling capabilities
•
Offline approach
•
Online approach
•
Demonstration
•
Next steps
3
Approach Overview
Offline
Generate libraries of damage states, kinematic
states, and capability states using high fidelity
information
Online
Dynamically collect data from sensors to
classify vehicle damage and capability states
4
Baseline UAV
•
Wing span: 55
ft
•
Cruise velocity: 140 knots
•
Cruise altitude: 25,000
ft
•
Payload: 500
lb
•
Range 2500
nmi
5
Source: www.aurora.aero
ASWING model
Matlab
model
Orion
Composite Panel Application
•
Demonstrating our methodology
on a composite panel
–
Panel located 260” outboard
–
Sized for strength
•
Consists of 4 plies
–
[45,0,0,45] quasi

isotropic layup
–
Meets FAR 23 loading
requirements
•
Model offline with NASTRAN
•
Enables the generation of
experimental results
6
18” x 18” Panel
NASTRAN model
Damage Considered
•
Damage type we consider is delamination
–
Low speed impacts,
interlaminar
separation
–
Can be designed into a specimen for experimentation
•
Model delamination in NASTRAN by reducing
stiffness
•
Enables analysis of offline damage library content
via design of experiments
7
Offline Approach
8
Online Approach: Motion Planning
•
Planning Task: Get from A to B as quickly as
possible subject to a constraint on the probability
of failure
•
Prior to the first turn, we must assess the
capability of the vehicle with online data
9
1
Online Approach
10
Damage
“Cluster ”
Current AC
Kinematic
State
Panel Strain
Field
Strain gages
Failure Index
Requirements
AC
Kinematic
Constraints
R
2
R
1
1.
Quickly
evaluate current “damage cluster” of aircraft
structure based on strain sensors and current
maneuver
2
Online Approach
11
Damage
“Cluster ”
Current AC
Kinematic
State
Panel Strain
Field
Strain gages
Failure Index
Requirements
AC
Kinematic
Constraints
R
2
R
1
1.
Quickly
evaluate current “damage cluster” of aircraft structure
based on strain sensors and current
maneuver
2.
Use
damage cluster estimate to predict current limits on
aircraft maneuvers given a prescribed failure index
threshold
Online Approach: Bayes Classifier
•
Assumed fixed number of sensors
•
Assumed damage library is complete
•
For a given maneuver (e.g., sustained turn):
12
1
(  ) (  )
S
j i i j
i
L X p d X
d
( ) (  )
(  )
( ) (  )
j j
j
j j
j
P X L X
P X
P X L X
d
d
d
1 2
( ,,, )
j j S j
G X G X G X
2
,
 (,)
i j i j g
G X g
N
,,,max
,max
i j i j
j
n
g g
n
2
,max
(,),
j j C
C n
N
2
(,)
N
N n
N
(  )(  )
fail j fail j
j
P P X P X
d
 ({ }) 0
fail j j
P X P N C
Sensors
Sensor outputs
Capability
Load
Demonstration: Problem Setup
13
Objective:
Get from A to B in minimum time
Subject to:
Probability of failure < 1x10

9
Maneuver:
Sustained rate turn
Offline damage library:
Pristine Moderate Severe
Demonstration: Offline Data
14
Pristine
Model

based sensor outputs
Moderate
Severe
Demonstration: Online Data
•
Perform a gentle, 500m radius turn for data
collection
•
Three cases
–
Case 1: Aircraft not damaged
–
Case 2: Aircraft moderately damaged
–
Case 3: Aircraft severely damaged
15
Online data collected for each damage case
Demonstration: Failure Probability
•
Uncertainty assumptions
–
Straing
gauge outputs:
–
Capability estimates:
–
Load estimate:
•
Case 1 (pristine):
–
Tight turn:
–
Wide turn:
•
Case 2 (moderate):
–
Tight turn:
–
Wide turn:
•
Case 3 (severe):
–
Tight turn:
–
Wide turn:
16
2
0.01
C
2
(,),
N
N n
N
2
,
 (,),
i j i j g
G X g
N
5
3.5 10
fail
P
2
0.0001
g
2
0.02
N
2
,max
(,),
j j C
C n
N
mod
(  ) 1,(  ) 0,(  ) 0
prist severe
P X P X P X
d d d
0
fail
P
mod
(  ) 0,(  ) 1,(  ) 0
prist severe
P X P X P X
d d d
1
fail
P
0
fail
P
mod
(  ) 0,(  ) 0,(  ) 1
prist severe
P X P X P X
d d d
1
fail
P
7
1.6 10
fail
P
Demonstration: Failure Probability
•
Uncertainty assumptions
–
Straing
gauge outputs:
–
Capability estimates:
–
Load estimate:
•
Case 1 (pristine)
–
Tight turn
:
–
Wide turn
:
•
Case 2 (moderate)
–
Tight turn
:
–
Wide turn
:
•
Case 3 (severe)
–
Tight turn
:
–
Wide turn
:
17
5
3.5 10
fail
P
0
fail
P
1
fail
P
0
fail
P
1
fail
P
7
1.6 10
fail
P
2
0.02
C
2
(,),
N
N n
N
2
,
 (,),
i j i j g
G X g
N
2
0.0001
g
2
0.02
N
2
,max
(,),
j j C
C n
N
Demonstration: Maneuver Envelope
•
Maneuver envelope for
each damage case
–
Offline calculations
•
Updated maneuver
envelope
–
Computed online from data
18
Conclusions
•
Demonstrated an offline/online DDDAS approach
–
Incorporates online data to map from data to capability state
–
By constructing offline libraries of damage and capability states
the vehicle may encounter during a mission
•
Our approach can be used to support mission
replanning
–
Go/no

go decisions
–
Full mission
replan
•
Next steps:
–
Reduced

order models to augment offline libraries with online
calculations
–
Sensor placement driven by vehicle usage
–
Sensor allocation driven by online data
–
Offline motion planning
–
Resource allocation
–
Experimentation
19
Example damage scenarios caused by ply
delamination. Yellow indicates
delamination sites.
An offline/online DDDAS
a
pproach
•
Test case
:
composite
panel on a
UAV
20
•
Offline
: develop libraries of panel strain information, under different load/damage
scenarios under
uncertainty.
Develop
data

driven reduced

order
models to
map from
sensed strain to damage state, capability state, and mission
decision

making.
•
Online
:
information management strategy for
dynamic
sensor and model

based data
acquisition, damage and capability state updates, and dynamic mission
re

planning.
0
50
100
150
200
250
300
350
300
200
100
0
100
200
300
Fuselage Station (in)
Wing Span Station (in)
MuDi1
Sweep Angle=4.3deg
Wing Spars
Wing OML
Engines
Pylons
Fuselage OML
Front Landing Gear
Main Landing Gear
Payload
Sweep Angle=5deg
Wing Spars
Wing OML
Airplane Center of Gravity
Airplane Neutral Point
Sensor
information
Strain field
estimation
Damage state
estimation
Capability state
estimation
Mission
decision

making
Arrows represent mapping capabilities from sensor data to mission decision

making,
and feedback for resource allocation
Offline Stage
21
AC Structure
(ASW format)
T
wp
AC Loads
(ASW format)
Panel BC’s
(NAS format)
Panel Structure
(NAS format)
Damage
Model
Modified AC
Structural
Properties
Max FI
Calc
ASWING
NASTRAN
T
ap
AC
Kinematic
State
Damage
Description
Pristine AC
Structural
Properties
T
aw
•
Toolset to build simulation
library relating damage
description, AC kinematic
states, strain, and internal
panel failure index
•
T
aw
: Derivation of ASWING
aircraft structural model from
top

level aircraft model
•
T
ap
: Derivation of NASTRAN
panel structural model from
top

level aircraft model
•
T
wp
: Conversion of ASWING
beam loads to panel
boundary distributed loads
Max FI
Panel
Strain
Field
Offline Stage
22
AC
Kinematic
State
Damage
“Clusters”
•
Use simulation library to
generate probabilistic
relationships
•
Simplify damage domain
into clusters that
correspond to common
impact on AC
performance
•
R
1
: Relationship between
damage, aircraft state,
and approximations of
strain field within wing
panel
•
R
2
: Relationship between
approximations of strain
field and corresponding
structural failure
indices
Max FI
Panel
Strain
Field
R
2
R
1
1
Online Stage
23
Damage
“Cluster ”
Current AC
Kinematic
State
Panel Strain
Field
Strain gages
Failure Index
Requirements
AC
Kinematic
Constraints
R
2
R
1
1.
Quickly
evaluate current “damage cluster” of aircraft
structure based on strain sensors and current
maneuver
2
Online Stage
24
Damage
“Cluster ”
Current AC
Kinematic
State
Panel Strain
Field
Strain gages
Failure Index
Requirements
AC
Kinematic
Constraints
R
2
R
1
1.
Quickly
evaluate current “damage cluster” of aircraft structure
based on strain sensors and current
maneuver
2.
Use
damage cluster estimate to predict current limits on
aircraft maneuvers given a prescribed failure index
threshold
Multifidelity
data driven analysis for self

aware
aerospace vehicles
Wing panel
OFFLINE Complete High
Fidelity analysis
POD & RS based surrogate model
Built offline

Used online
Failure Index/
Capability Factor
Strategy:
Surrogate modeling and data reconstruction involving
•
Proper Orthogonal Decomposition (POD)
•
Response Surfaces (RS)
Given a set of
m
strain fields characterized by
different damage, a new strain field
u
is
approximated as
m
= number of snapshots
d
= chosen to capture the desired level of
energy (
<<
m
)
j
i
= i

th POD basis vector
a
i
= POD coefficients, function of the
characteristic parameters
x
x
= {x
1
,…,x
n
}, vector of the characteristic
parameters defining damage size,
damage location, maneuver and load case
POD coefficients
a
i
approximated as
1
d
i i
i
a
u
φ
2
0
1 1
n n n
i j j jk j k jj j
j j k j
b b x b x x b x
a
x
ONLINE Sensor data
Incomplete High
Fidelity information
In flight
reconstruction
Surrogate
modeling
Damage
26
Planning
–
Problem Setup
•
Informal problem statement:
“Satisfy mission objectives subject to
uncertain structural capability constraints”
•
Mission objectives
Typically specified in terms of logic formulae
Standard algorithms available to find a plan to “satisfy mission objectives”
•
Structural capability constraint
Main constraint relevant for motion planning: maximum allowable load factor,
or (equivalently) minimum radius of turn
Estimation of maximum load factor is inherently uncertain
•
Notion of
“satisfaction”
of mission objectives becomes inherently
probabilistic
“
Satisfy
”
=
“
Ensure
𝑃
𝑓𝑎𝑖𝑙
<
1
−
,
” where
is specified by the user
Planning algorithm must terminate and report failure if no solution exists
27
Algorithmic Tools
•
𝐻

Cost motion planning algorithm
Cell

decomposition

based algorithm that finds a plan to “satisfy mission
objectives” while satisfying vehicle dynamical constraints, arising due to e.g.,
max load factor, max bank angle, max speed, damaged ailerons, etc.
Cornerstone idea: capture
a geometric
signature of dynamical constraints, e.g.,
max curvature
(min radius of turn)
derived from dynamical constraints
Cowlagi &
Tsiotras
, IEEE Trans. Robot., 28(2), pp. 379
–
395
Computationally efficient,
multi

resolution version:
Cowlagi &
Tsiotras
, IEEE
Trans. Sys. Man Cy. B., 42(5), pp. 1455
–
1469
•
Curvature

bounded
traversability
analysis
Geometric analysis of geometric structures (called
tiles
) arising from cell

decomposition
Critical link between planning algorithm and vehicle dynamical constraint
Cowlagi &
Tsiotras
, IEEE Trans. Robot, article in review
•
Toolkit in literature:
Planner finds a mission plan that is guaranteed
to be within vehicle’s operational constraints …
… for
deterministic
constraints
28
Progress and Expected Results
•
Current research: extend
𝐻

Cost motion planning approach for
uncertain lower bound on radius of turn
Expected additional algorithmic capability:
Multiple results if multiple
plans
satisfy
𝑃
𝑓𝑎𝑖𝑙
<
1
−
•
Approach
Geometric aspect:
Calculate for each tile
𝑅
=
max
(
𝑅
)
such that the tile is
traversable with a path with min radius of turn
𝑅
Algorithmic aspect:
Calculate
𝑃
(
𝑓𝑎𝑖𝑙
)
for each tile,
𝐻

Cost algorithm uses
𝑃
(
𝑓𝑎𝑖𝑙
)
info for each tile and calculates
𝑃
𝑓𝑎𝑖𝑙
for overall plan
𝑃
𝑓
𝑎𝑖𝑙
=
1
−
𝑓
𝑅
0
•
Preliminary results
𝐻

Cost algorithm modified, tested with placeholder values of
𝑅
Geometric analysis to compute
𝑅
in progress
𝑅
PDF of uncertain turn
radius constraint related
to structural capability
29
Benchmark Example
•
Mission objective: start from Cell 10, loiter in Cell 29, return to Cell 1
•
Above result for deterministic constraints, similar proof

of

concept
results are available for uncertain constraints with placeholders for
𝑅
and
𝑓
Yellow

colored cells indicate cells searched by planner for potential plans
•
Development of planner with actual
𝑅
and
𝑓
in progress
“Pristine” structural condition; high max load factor (low min turn radius)
“Damaged” structural condition; low max load factor (high min turn radius)
Adaptive
Multifidelity
Structural Response Models
•
High Fidelity Response Model: Finite Element Method (FEM)
–
Set of elements
e
interconnected at nodes
–
Element stiffness matrices
k
e
used to solve nodal displacements
–
Strain

displacement matrix
B
to transform nodal displacements to
strains
–
Elasticity matrix
E
that transforms effective strains to stresses
•
Unique element properties
–
Stiffness, Strength, thickness, layup (for composite materials),
constituent material orientation(s), failure modes, etc.
•
Examples of failure modes: mechanical overload (maximum stress/strain
criteria), buckling, fatigue, yield
•
Major advantages to using FEM approach:
–
Use of existing solvers for complex system with external work
applied
–
Finite discretization of sensor information and degradation modes
allows discrete adaptation of individual elements
•
Sensor information can be applied to specific elements to modify the
stiffness or strength properties or modify the mesh (e.g.
remesh
, element
elimination) of a subset of elements to reflect the inferred change
30
Vehicle State Space
31
•
Vehicle maneuver library defines motion primitives used
to plan flight, set flight limits, and create missions
Motion #
Motion Primitive
Constraint
Parametrized
by
different
1
Steady level
𝛾
=
0
𝜓
=
𝑎
𝜙
=
0
(
𝑎
)
2
Steady climb/descent
𝛾
=
𝑎
𝜓
=
𝑎
𝜙
=
0
(
𝑎
)
𝐿
3
Steady level turn
𝛾
=
0
𝜓
=
𝑎
𝜙
=
𝑎
=
𝑎
𝐿
4
Steady
climbing/descending
turn
𝛾
=
𝑎
𝜓
=
𝑎
𝜙
=
𝑎
=
𝑎
𝐿
Defining Sensors
32
•
“Truth data” to replace physics (i.e. strains,
pressures, temperatures, damage)
•
Sensor models will sense truth data with
possible uncertainties built in
–
E.g. include sensor failures, drifts, errors
•
Model parameters are adjustable “in

situ”
33
Experimental Aspects
•
Sensors provide real

time structural
and environmental data
Multi

fidelity models incorporate real

time sensor data
Uncertainties associated with sensor
data
•
Magnitude of loading and function of
current maneuver
Update path planner will change the
applied loading
•
Composite test specimens to include
pristine and ‘damaged’ specimens
Nominal mission will adapt to perceived
structural state
–
applied experimentally
via changes in tensile loading
34
Actuator
–
Load Control
•
Machine screw actuator will apply uniaxial
tension.
A Duff

Norton worm gear actuator is used to impart
load into the system. Actuator is rated for 5 tons
(10,000
lbf
). Actuator
driven via DC motor
.
•
Leeson
21 Amp, 12 V electric motor drives
actuator.
•
Elmo Motion Controller (DC

WHISTLE 20/60)
controls the DC motor. Motion controller interfaces
with PC to send control signals.
•
LabVIEW
VI under development to provide motor
control signals. Control will permit either ‘load
control’ or ‘displacement control’ based on real

time
data from the load cell or the LVDT, respectively.
Controller feedback provided via encoder (attached
to actuator worm gear), LVDT, and/or load cell.
•
Flight profile determined from path planner will set
the ‘load path’ (load history). The load path will be
executed in real

time, with real

time sensor data
provided to the multi

fidelity models.
35
Test Specimen
•
Geometry
: Square panel, 18” long x 18” wide (thickness
determined by number of plies, see next bullet)
•
Material: Carbon
fiber reinforced plastic (CFRP)
–
the
strength of the panel will be matched to the load capability
of the load frame (i.e. number of CFRP plies (layers) will
provide a strength no greater than the capacity of the load
frame). This will permit the test panel to be loaded to
‘failure’.
•
Multiple panels will be manufactured/tested. Some panels
will be manufactured with pre

existing ‘damage’, such as
delaminations or matrix cracks.
Initial panels to
be
manufactured at
Aurora this summer.
36
Sensors
•
LVDT
–
MacroSensors
DC750

500 (axial displacement)
•
Load Cell
–
Sensor Development 10188

014, 10 kip
threaded rod load cell (uniaxial tensile load)
•
Multiple Strain gages
–
350 Ohm, bonded foil strain gages
(uniaxial strain at specific points on the surface of the
panel)
•
Thermocouple
–
K

type (panel temperature
–
assumed
constant across the entire panel)
•
Encoder
–
Accu

Coder (
actuator
position
–
secondary
axial displacement reading)
37
Experimental Updates
•
Components in

hand:
Actuator, motor, power

supply, motor controller
Load cell, LVDT, thermocouples, strain gages
Couplers and load triangles have been machined
PC with
LabView
, NI
cDAQ
with necessary modules
•
Out

standing components:
Finalize selection of self

reacting frame
Modifications of frame to integrate our system
Control system
Fabricate composite panels
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