An Offline/Online DDDAS Capability for Self-Aware Aerospace Vehicles

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Nov 15, 2013 (3 years and 11 months ago)

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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)
MuDi-1


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