A Dynamic Data-Driven Approach to Multiple Task Capability ...
A Dynamic Data-Driven Approach to Multiple Task Capability Estimation for Self-Aware Aerospace Vehicles! ! Brian Burrows, Benson Isaac, Douglas Allaire! Department of Mechanical Engineering! Texas A&M University! ! ! 17th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference! Washington, D.C.! June 16, 2016! ! Supported by AFOSR grant FA9550-11-1-0339 and FA9550-16-1-0108, under the Dynamic Data-Driven Application Systems Program, Program Manager Dr. Frederica Darema.!
!
Research Team!
2
Project Overview! • A self-aware unmanned aircraft! Re-plan Mission!
Estimate Capability!
062LR Micro-Measurements
General Purpose Strain Gages - Rectangular Rosette
Offline PhysicsBased Models!
GAGE PATTERN DATA GAGE DESIGNATION
RESISTANCE (OHMS)
OPTIONS AVAILABLE
Change Sensing Strategy!
See Note 1 L2A-XX-062LR-120 L2A-XX-062LR-350 C2A-XX062LR-120 C2A-XX-062LR-350
Sensors!
120 ± 0.6% 350 ± 0.6% 120 ± 0.6% 350 ± 0.6%
DESCRIPTION Small 45° rectangular single-plane rosette.
actual size GAGE DIMENSIONS
Legend:
Gage Length
Overall Length
0.062
0.185
1.52
4.70
GAGE SERIES DATA Series
ES = Each Section
CP = Complete Pattern
S = Section (S1 = Sec 1)
M = Matrix
inch millimeter
Grid Width
Overall Width
Matrix Length
Matrix Width
0.050
0.260
0.277
0.410
1.27
6.60
7.04
10.41
See Gage Series data sheet for complete specifications. Strain Range
Temperature Range
L2 A
Encapsulated constantan gages with preattached ribbon leads.
±3%
–100° to +250°F [–75° to +120°C]
C2 A
Encapsulated constantan gages with preattached ready-to-use cables.
Description
±3%
–60° to +180°F [–50° to +80°C]
Example of an L2A Construction
Graphics:! Vishay Precision Group! AeroVironment! Microbotics!
Example of a C2A Construction
Note 1: Insert desired S-T-C number in spaces marked XX.
Document Number: 11095 Revision: 02-Feb-10
For technical questions, contact: [email protected]
www.micro-measurements.com 85
3
Today’s Focus! An approach for combining offline computation with online sensor data to provide a time-constrained, updated estimate of UAV flight capability! Re-plan Mission!
Estimate Capability!
062LR Micro-Measurements
General Purpose Strain Gages - Rectangular Rosette
Offline PhysicsBased Models!
GAGE PATTERN DATA GAGE DESIGNATION
RESISTANCE (OHMS)
OPTIONS AVAILABLE
Change Sensing Strategy!
See Note 1 L2A-XX-062LR-120 L2A-XX-062LR-350 C2A-XX062LR-120 C2A-XX-062LR-350
Sensors!
120 ± 0.6% 350 ± 0.6% 120 ± 0.6% 350 ± 0.6%
DESCRIPTION Small 45° rectangular single-plane rosette.
actual size GAGE DIMENSIONS
Legend:
ES = Each Section
CP = Complete Pattern
S = Section (S1 = Sec 1)
M = Matrix
inch millimeter
Gage Length
Overall Length
Grid Width
Overall Width
Matrix Length
Matrix Width
0.062
0.185
0.050
0.260
0.277
0.410
1.52
4.70
1.27
6.60
7.04
10.41
GAGE SERIES DATA Series
See Gage Series data sheet for complete specifications. Strain Range
Temperature Range
L2 A
Encapsulated constantan gages with preattached ribbon leads.
±3%
–100° to +250°F [–75° to +120°C]
C2 A
Encapsulated constantan gages with preattached ready-to-use cables.
Description
±3%
–60° to +180°F [–50° to +80°C]
Example of an L2A Construction
Graphics:! Vishay Precision Group! AeroVironment! Microbotics!
Example of a C2A Construction
Note 1: Insert desired S-T-C number in spaces marked XX.
Document Number: 11095
For technical questions, contact: [email protected]
www.micro-measurements.com
4
Outline! 1. Model Aircraft Behavior!
2. Quantify Flight Capability!
Background prior work!
3. Infer Capability from Sensors!
4. Extend to Multiple Maneuvers!
5. Online Estimation Enhancement!
New contributions!
6. Demonstration! 5
Aircraft Capability Definition! The ability of an aircraft to perform steady level turning maneuvers of a certain maximal curvature, as well as pull up maneuvers, as it pertains to the limits on loads applied to the wing structure.! ! Directly related to the airspeed (V) and load factor (n) of the aircraft in flight:! L
!
FR
mV 2 V2 ∑ F = R ⇒ Rturn = 2 g n −1 turn
L n= W
W = mg Graphic: AeroVironment!
6
Extension to Multiple Maneuver Types! • Prior work: Developed offline/online procedure for dynamic online capability estimation in the context of a pull up maneuver (Lecerf et al. 2015, Allaire et al. 2013)! ! ! • Current work: Incorporate multiple maneuvers (steady left turn, steady right turn, pull up)!
• Future work: incorporate all maneuver types for complete dynamic flight envelope updating for use in dynamic mission replanning!
7
Global Aircraft Behavior with ASWING!
Global Kinematics! • Airspeed! • Load Factor!
Wing Structure! • Forces! • Moments! • Strains!
Cruise Speed! 140 KEAS! Cruise Altitude! 25000 ft! Range! 2500 nmi!
• Baseline aircraft using derivative of TASOPT design methodology (Ref. N+3 report, Greitzer E.M. et al, 2010)! • Conforms to FAR 23 guidelines!
References:! • http://web.mit.edu/drela/Public/web/aswing! • AIAA SDM Paper, M. Drela, 1999!
Payload Sizing! 500 lbs!
8
How to Represent Damage?! Stiffness modification in ASWING to capture effects of damage on aircraft behavior.! ! • “Smeared” effect!
Bending stiffness along wing about axis! parallel to airfoil chord!
EIcc!
(left wing tip)!
(right wing tip)!
(exaggerated)!
Location on span!
9
Model Damage with VABS! Wing Structure! • Forces! • Moments! • Strains!
Local Wing Structure! • Damage! • Sensors! • Failures!
• Variational Asymptotic Beam cross-Sectional Analysis (VABS)! • Substitute for full 3dimensional FEM! • Slender, thin-walled beams!
Influence coefficients! Stiffness properties!
Reference: Palacios and Cesnik, 2005!
1D Beam Solver!
Reference line forces and moments! 10
Aircraft Model using ASWING and VABS! 1. Model Aircraft Behavior! 2!
Maneuver!
Coupled ASWING and VABS!
Damage!
Strain Sensor Readings !
45°!
1!
Maximum Failure Index!
Baseline Aircraft!
11
Finding Capability using Model! 2. Quantify Flight Capability! Flight Capability is boundary between:! Red ó Unsafe !ó max FI > 1 ! Blue ó Safe !ó max FI < 1!
(V held constant, capability with respect to nmax)! Maximum load factor change due to damage VIAS = 260 ft/s at 25 kft Damaged [location,width] on span: [+0.35,0.075] Damaged region stiffness loss: 95%
Classification using FI
max
VIAS = 260 ft/s at 25 kft Damaged [location,width] on span: [+0.35,0.075] Damaged region stiffness loss: 95%
3.34
3.4 Safe Unsafe
3.38
3.45
A
3.36
3.33
A
3.4
3.32
n
3.32
B
3.3
nmax
3.34
3.35
3.31
3.3 3.3
3.28
3.25
3.26
3.29
3.2 0
3.24
B
0.02
3.22
3.28 0.2
0.04 3.2
0
0.01
0.02
0.03
0.04
0.05
0.06
Chord Width
0.07
0.08
0.09
0.1
0.06
0.24 0.26
0.08
Chord Width
0.22
0.1
0.3
0.28
Chord Location
3.27 3.26
nmax
12
Offline Procedure Summary (following Lecerf et al., 2015)! • We have a database with features:! – – – – –
1. Model Aircraft Behavior!
Damage conditions XD! Maneuver conditions XM! Maneuver type XF! Strain sensor readings XS! Flight capability Rmin via classification using failure index Fimax for each maneuver type!
• Size constrained by memory and/or lookup limitations! XD s
ws
XM c
2. Quantify Flight Capability!
4. Extend to Multiple Maneuvers!
XF
…
V
n 1
0.35
0.075 0.20
…
260
0.35
0.075 0.28
…
260 3.3
XS e111
2e121
e221
… Rmin,LT Rmin,PU
PU
-1.13e+03
6.15
63.2 …
608
658
627
PU
-6.79e+03
366
378
615
674
649
…
Rmin,RT
13
Online Maximum Likelihood Estimation! XD
Use library from offline phase!
s
! ! ! Notation:!
Cases stored in library!
ws
XM c
XF
…
V
n 1
0.35
0.075 0.20
…
260
0.35
0.075 0.28
…
260 3.3
XS e111
2e121
e221
PU
-1.13e+03
6.15
63.2 …
… Rmin,LT Rmin,PU 608
658
627
PU
-6.79e+03
366
378
615
674
649
…
Rmin,RT
3. Infer Capability from Sensors!
4. Extend to Multiple Maneuvers!
XM 2 {m1 , m2 , . . . , mK } = M XD 2 {d1 , d2 , . . . , dJ } = D XF 2 {LT, PU, RT} = F
Library lookup functions!
C : D ! RN F
S : M ⇥ D ⇥ F ! RN S
14
Online Maximum Likelihood Estimation! 3. Infer Capability from Sensors!
1. Likelihood of seeing sensor readings conditioned on the maneuver, damage, and maneuver type!
pXS |XM ,XD ,XF (·|mk , dj , f ) ⇠ N (S(mk , dj , f ),
2
I)
2. Maximize the likelihood over all possible damage cases in library!
✓
ˆ min (s, mk , f ) = C argmax p R XS |XM ,XD ,XF (s|mk , dj , f ) dj 2D
◆ 15
Improving Capability Estimates Online! 5. Online Estimation Enhancement!
• The James-Stein estimator for sensor average estimation! ! ! • Conjunctive filtering to exploit different misclassifications by different sources!
16
A Closer Look at Maximizing the Likelihood ! 5. Online Estimation Enhancement! 1. Letting!
L(s|mk , dj , f ) , pXS |XM ,XD ,XF (s|mk , dj , f )
17
A Closer Look at Maximizing the Likelihood ! 5. Online Estimation Enhancement! 1. Letting!
L(s|mk , dj , f ) , pXS |XM ,XD ,XF (s|mk , dj , f )
2. Taking the logarithm results in!
ln L(s|mk , dj , f ) =
NS ln(2⇡ 2
2
)
2
NS X 1 2
(si
S(mk , dj , f ))2
i=1
18
A Closer Look at Maximizing the Likelihood ! 5. Online Estimation Enhancement! 1. Letting!
L(s|mk , dj , f ) , pXS |XM ,XD ,XF (s|mk , dj , f )
2. Taking the logarithm results in!
ln L(s|mk , dj , f ) =
NS ln(2⇡ 2
2
)
2
NS X 1
3. Thus,!
argmax L(s|mk , dj , f ) = arg min dj 2D
dj 2D
2
(si
S(mk , dj , f ))2
i=1
NS X
(si
S(mk , dj , f ))2
i=1
19
Mitigating Sensor Noise! 5. Online Estimation Enhancement! 1. Online, we accumulate noisy data from our sensors and can use Nd at a time ! j j j 1 2 Nd j T where!
{ˆs , ˆs , . . . , ˆs
}
ˆs = (ˆ s1 , sˆ2 , . . . , sˆNS )
20
Mitigating Sensor Noise! 5. Online Estimation Enhancement! 1. Online, we accumulate noisy data from our sensors and can use Nd at a time ! j j j 1 2 Nd j T where!
{ˆs , ˆs , . . . , ˆs
}
ˆs = (ˆ s1 , sˆ2 , . . . , sˆNS )
2. To mitigate the impacts of noise we could do the usual thing and let! ! Nd ! j ! ! d j=1 ! prior to implementing the maximum likelihood capability estimator!
1 X ˆs s=s, N
21
Mitigating Sensor Noise! 5. Online Estimation Enhancement! 1. Online, we accumulate noisy data from our sensors and can use Nd at a time ! j j j 1 2 Nd j T where!
{ˆs , ˆs , . . . , ˆs
}
ˆs = (ˆ s1 , sˆ2 , . . . , sˆNS )
2. To mitigate the impacts of noise we could do the usual thing and let! ! Nd ! j ! ! d j=1 ! prior to implementing the maximum likelihood capability estimator!
1 X ˆs s=s, N
Recall:!
argmax L(s|mk , dj , f ) = arg min dj 2D
dj 2D
NS X i=1
(si
S(mk , dj , f ))2 22
The James-Stein Estimator (James and Stein, 1961)! 5. Online Estimation Enhancement! 1. James-Stein Estimator!
✓ˆJS =
✓
1
(NS
2
2) /Nd ksk2
◆
s
Statistically dominates the sample average for NS greater than 2. ! ! ! Trial! MSE – JamesMSE – Sample Demo:! Stein Estimator! Mean!
ND = 100! NS = 12! N (0, 400I)
1!
0.01!
32.69!
2!
0.29!
30.35!
3!
5.07!
49.11!
4!
6.83!
52.22!
5!
0.46!
37.49! 23
The James-Stein Estimator (James and Stein, 1961)! 5. Online Estimation Enhancement! 1. James-Stein Estimator!
✓ˆJS =
✓
1
(NS
2
2) /Nd ksk2
◆
s
Statistically dominates the sample average for NS greater than 2. ! ! ! Trial! MSE – JamesMSE – Sample Demo:! Stein Estimator! Mean!
ND = 100! NS = 12! N (0, 400I) Recall:!
1!
0.01!
32.69!
2!
0.29!
30.35!
3!
5.07! NS X 6.83!
49.11!
4!
argmax L(s|mk , dj , f )5!= arg min dj 2D
(si 0.46! dj 2D i=1
52.22! 2 S(mk ,37.49! dj , f )) 24
Demonstration! 6. Demonstration!
Damage Parameter!
Trial Levels!
ls!
0.15!
ws!
0.05!
lc!
0.1, 0.2, 0.3, 0.4, 0.5, 0.6!
wc!
0.1, 0.2, 0.3, 0.4, 0.5!
dt!
0.5, 0.6 ,0.7, 0.8, 0.9!
df!
0.95!
Online Simulation Parameters! ND = 1000, NS = 12! Moving window with 100 stored MLE capability estimates! Noise at 400 µstrain!
25
Demonstration – James-Stein Estimator! Online Simulation Explanation! Moderate, in-library damage case! Performing low-stress LT maneuver! Estimating capability for LT!
Performing Left Turn Maneuver! 0.03
James−Stein Estimator Sample Average Direct Stain Data (no averaging)
0.025
Density
0.02
0.015
0.01
0.005
0
380
400
420
440
460
480
500
520
Minimum Turn Radius − Left Turn
540
560
26
Demonstration – Multiple Maneuver Capability Estimates! Online Simulation Explanation! Moderate, in-library damage case! Performing low-stress LT, PU, RT maneuvers! Estimating capability for LT, PU, RT!
Maneuver Capability Estimates 0.05
0.05 True µ Left Turn Pull Up Right Turn
Density!
0.04
0.04
‘
0.05 True µ Left Turn Pull Up Right Turn
0.04
0.03
0.03
0.03
0.02
0.02
0.02
0.01
0.01
0.01
0 400
450
500
550
600
650
Minimum Turn Radius – Left Turn!
0 400
450
500
True µ Left Turn Pull Up Right Turn
550
600
650
Minimum Turn Radius – Pull Up!
0 400
450
500
550
600
650
Minimum Turn Radius – Right Turn!
27
Conjunctive Filtering! 5. Online Estimation Enhancement!
Use the idea that data gathered during different maneuver types will lead to different misclassifications! Estimate!
RT(LT) !
RT(PU)!
RT(RT)!
1!
510.99!
510.99!
510.99!
2!
513.31 !
510.99!
510.99!
3!
513.31!
510.99!
510.99 !
4!
513.31!
510.99!
512.00 !
5!
514.78 !
513.31!
512.00 !
6!
514.78!
513.55!
512.00 !
7!
514.78 !
514.75!
513.31!
8!
517.07!
514.75!
513.55 !
9!
520.49!
514.78!
514.75! 28
Conjunctive Filtering! 5. Online Estimation Enhancement!
Use the idea that data gathered during different maneuver types will lead to different misclassifications! Estimate!
RT(LT) !
RT(PU)!
RT(RT)!
1!
510.99!
510.99!
510.99!
Conjunction RT(LT,PU)!
2!
513.31 !
510.99!
510.99!
510.99!
3!
513.31!
510.99!
510.99 !
513.31!
4!
513.31!
510.99!
512.00 !
514.78!
5!
514.78 !
513.31!
512.00 !
6!
514.78!
513.55!
512.00 !
7!
514.78 !
514.75!
513.31!
8!
517.07!
514.75!
513.55 !
9!
520.49!
514.78!
514.75! 29
Conjunctive Filtering! 5. Online Estimation Enhancement!
Use the idea that data gathered during different maneuver types will lead to different misclassifications! Estimate!
RT(LT) !
RT(PU)!
RT(RT)!
1!
510.99!
510.99!
510.99!
Conjunction RT(LT,PU,RT)!
2!
513.31 !
510.99!
510.99!
510.99!
3!
513.31!
510.99!
510.99 !
513.31!
4!
513.31!
510.99!
512.00 !
5!
514.78 !
513.31!
512.00 !
6!
514.78!
513.55!
512.00 !
7!
514.78 !
514.75!
513.31!
8!
517.07!
514.75!
513.55 !
9!
520.49!
514.78!
514.75! 30
Conjunctive Filtering ! c˜CF =
|C1r,s |
X
di,1 di,2
P|C1r,s |
i=1
2 ˜CF
i=1
= P|C r,s | 1 i=1
di,1 di,2 |C1r,s |
1
di,1 di,2
1
X
ci
!
di,1 di,2 (ci
Mean! Variance!
c˜CF )2
i=1
Estimate!
RT(LT) !
RT(PU)!
1!
510.99!
510.99!
2!
513.31 !
510.99!
3!
513.31!
510.99!
4!
513.31!
510.99!
5!
514.78 !
513.31!
Conjunction RT(LT,PU,RT)! 510.99! 513.31!
31
Conjunctive Filtering ! c˜CF =
|C1r,s |
X
di,1 di,2
P|C1r,s |
i=1
2 ˜CF
i=1
= P|C r,s | 1 i=1
di,1 di,2 |C1r,s |
1
di,1 di,2
1
X
ci
Number of nonrepeated entries in first information source that are also in the second information source!
!
di,1 di,2 (ci
c˜CF )2
i=1
Estimate!
RT(LT) !
RT(PU)!
1!
510.99!
510.99!
2!
513.31 !
510.99!
3!
513.31!
510.99!
4!
513.31!
510.99!
5!
514.78 !
513.31!
Conjunction RT(LT,PU,RT)! 510.99! 513.31!
Here:!
r,s |C1 |
=2 32
Conjunctive Filtering ! c˜CF =
|C1r,s |
X
di,1 di,2
P|C1r,s |
i=1
2 ˜CF
i=1
= P|C r,s | 1 i=1
di,1 di,2 |C1r,s |
1
di,1 di,2
1
X
ci
!
Number of times the ith element in the intersection between the two sources occurs!
di,1 di,2 (ci
c˜CF )2
i=1
Estimate!
RT(LT) !
RT(PU)!
1!
510.99!
510.99!
2!
513.31 !
510.99!
3!
513.31!
510.99!
4!
513.31!
510.99!
5!
514.78 !
513.31!
Conjunction RT(LT,PU,RT)! 510.99! 513.31!
Here:!
d1,1 = 1, d2,1 = 3 33
Conjunctive Filtering ! c˜CF =
|C1r,s |
X
di,1 di,2
P|C1r,s |
i=1
2 ˜CF
i=1
= P|C r,s | 1 i=1
di,1 di,2 |C1r,s |
1
di,1 di,2
1
X
ci
!
ith element of the intersection of the two sources without repeats !
di,1 di,2 (ci
c˜CF )2
i=1
Estimate!
RT(LT) !
RT(PU)!
1!
510.99!
510.99!
2!
513.31 !
510.99!
3!
513.31!
510.99!
4!
513.31!
510.99!
5!
514.78 !
513.31!
Conjunction RT(LT,PU,RT)! 510.99! 513.31!
Here:!
c1 = 510.99, c2 = 513.31 34
Demonstration with Conjunctive Filtering! Online Simulation Explanation! Moderate, in-library damage case! Performing low-stress LT, PU, RT maneuvers! Estimating capability for LT, PU, RT!
Maneuver Capability Estimates with Conjunctive Filtering 0.08
0.08 True µ 1st estimate st 1 update nd 2 update
0.07
Density!
0.06
0.07 0.06
0.08 True µ 1st estimate st 1 update nd 2 update
0.06
0.05
0.05
0.05
0.04
0.04
0.04
0.03
0.03
0.03
0.02
0.02
0.02
0.01
0.01
0.01
0 400
450
500
550
600
650
Minimum Turn Radius – Left Turn!
0 400
450
500
True µ 1st estimate st 1 update nd 2 update
0.07
550
600
650
Minimum Turn Radius – Pull Up!
0 400
450
500
550
600
650
Minimum Turn Radius – Right Turn!
35
Demonstration Comparison! Maneuver Capability Estimates ‘
0.08
0.08 True µ Left Turn Pull Up Right Turn
Density!
0.07 0.06
0.07 0.06
0.08 True µ Left Turn Pull Up Right Turn
0.06
0.05
0.05
0.05
0.04
0.04
0.04
0.03
0.03
0.03
0.02
0.02
0.02
0.01
0.01
0.01
0 400
450
500
550
600
650
Minimum Turn Radius – Left Turn!
0 400
450
500
True µ Left Turn Pull Up Right Turn
0.07
550
600
650
Minimum Turn Radius – Pull Up!
0 400
450
500
550
600
650
Minimum Turn Radius – Right Turn!
Maneuver Capability Estimates with Conjunctive Filtering 0.08
0.08 True µ st 1 estimate 1st update nd 2 update
0.07
Density!
0.06
0.07 0.06
0.08 True µ st 1 estimate 1st update nd 2 update
0.06
0.05
0.05
0.05
0.04
0.04
0.04
0.03
0.03
0.03
0.02
0.02
0.02
0.01
0.01
0.01
0 400
450
500
550
600
650
Minimum Turn Radius – Left Turn!
0 400
450
500
True µ st 1 estimate 1st update nd 2 update
0.07
550
600
650
0 400
450
500
550
600
650
Minimum Turn Radius – Pull Up! Minimum Turn Radius – Right Turn!36
Conclusions & Future Work! • Extended the offline/online DDDAS paradigm for enabling self-aware UAVs to incorporate multiple maneuvers! • Implemented and defined enhancements to online capability estimation approach! • Using information from multiple tasks has the potential to mitigate misclassification in online stage! Future Work! • Study the conjunctive filter and implement robustness features! • Incorporate online reduced-order models as another source of information! • Heterogeneous sensing capabilities! • Online sensor “placement”! • Out-of-library classification confidence metrics! 37
38
References! • • •
• •
•
•
•
• •
Dynamic Data Driven Application Systems community website: http://www.dddas.org! Drela, M. (1999). Integrated Simulation Model for Preliminary Aerodynamic , Structural , and Control-Law Design of Aircraft. In 40th AIAA SDM Conference (pp. 1–13).! Greitzer, E., M.; Bonnefoy, P., A.; Blanco, E., De la Rosa; Dorbian, C., S.; Drela, M.; Hall, D., K.; Hansman, R., J.; Hileman, J., I.; Liebeck, R., H.; Lovegren, J.; Mody, P.; Pertuze, J., A.; Sato, S.; Spakovszky, Z., S.; Tan, C., S.; Hollman, J., S.; Duda, J., E.; Fitzgerald, N.; Houghton, J.; Kerrebrock, J., L.; Kiwada, G., F.; Kordonowy, D.; Parrish, J., C.; Tylko, J.; Wen, E., A.; Lord, W., K. (2010). N + 3 Aircraft Concept Designs and Trade Studies , Final Report Volume 1 (Vol. 1, pp. 1–187).! Willis, S. (2009). OLM : A HANDS-ON APPROACH. In 25th ICAF Symposium (pp. 1199–1214). Rotterdam.! Fox, J. J., & Glass, B. J. (n.d.). Impact of integrated vehicle health management (IVHM) technologies on ground operations for reusable launch vehicles (RLVs) and spacecraft. In 2000 IEEE Aerospace Conference. Proceedings (Vol. 2, pp. 179–186). IEEE. doi:10.1109/AERO.2000.878223! Mehr, A. F., Tumer, I., & Barszcz, E. (2005). Optimal Design of Integrated Systems Health Management ( ISHM ) for Improving the Safety of NASA ’ s Exploration Missions : A Multidisciplinary Design Approach. In 6th World Congresses on Structural and Multidisciplinary Optimization. Rio de Janeiro.! Glaessgen, E. H., & Stargel, D. S. (2012). The Digital Twin Paradigm for Future NASA and U.S. Air Force Vehicles. In the 53rd American Institute of Aeronautics and Astronautics Structures, Structural Dynamics, and Materials Conference.! Saxena, A., Celaya, J., Balaban, E., Goebel, K., Saha, B., Saha, S., & Schwabacher, M. (2008). Metrics for evaluating performance of prognostic techniques. In 2008 International Conference on Prognostics and Health Management (pp. 1–17). Ieee. doi:10.1109/PHM.2008.4711436! Palacios, R., & Cesnik, C. E. S. (2005). Cross-sectional analysis of nonhomogeneous anisotropic active slender structures. AIAA journal, 43(12), 2624–2638.! Lecerf, M., Allaire, D., and Willcox, K., “Methodology for Dynamic Data-Driven Online Flight Capability Estimation,” AIAA Journal, Vol. 53, No. 10, 2015, pp. 3073-3087.!
39
References! • • • • • • • • • • • • • •
Cacuci, D., “Sensitivity and Uncertainty Analysis: Theory, Sensitivity and Uncertainty Analysis”, Chapman & Hall/CRC, 2003.! McDonald, R. A., “Error Propagation and Metamodeling for a Fidelity Tradeoff Capability in Complex Systems Design”, Ph.D. thesis, Georgia Institute of Technology, 2006.! Martin, J. D., “A methodology for evaluating system-level uncertainty in the conceptual design of complex multidisciplinary systems”, Ph.D. thesis, Dept. of Mechanical Engineering, The Pennsylvania State University, May 2005.! Liu, H., Chen, W., Kokkolaras, M., Papalambros, P. Y., and Kim, H. M., “Probabilistic Analytical Target Cascading: A Moment Matching Formulation for Multilevel Optimization Under Uncertainty," Journal of Mechanical Design, Vol. 128, No. 4, 2006, pp. 991-1000. ! Du, X. and Chen, W., “Collaborative Reliability Analysis for Multidisciplinary Systems Design," 2002.! Rubin, D. B., “Using the SIR algorithm to simulate posterior distributions,“ Bayesian Statistics 3 , edited by M. H. Bernardo, K. M. Degroot, D. V. Lindley, and A. F. M. Smith, Oxford University Press, 1988.! Scott, D., “Multivariate Density Estimation: Theory, Practice, and Visualization”. John Wiley & Sons, Inc. 1992.! Grimmett, G.R., Strizaker, D., “Probability and Random Process”, Texts from Oxford University Press, 2001.! Weibach, R. and Wied, D., “Consistency of the kernel density estimator-a survey”, HT014602036 , 2009.! Peherstorfer, B., Pflüger D., Bungartz H.J.: “Clustering Based on Density Estimation with Sparse Grids”, Proceedings of German Conference on Artificial Intelligence (KI 2012), (2012). ! MacKay, D., Information theory, inference and learning algorithms, Cambridge University Press, 2003, p 370.! March, A. and Willcox, K., “A Provably Convergent Multifidelity Optimization Algorithm not Requiring HighFidelity Derivatives,” Proceedings of the 3rd MDO Specialists Conference, Orlando, FL, AIAA-2010-2912.! James, W. and Stein, C., “Estimation with Quadratic Loss,” Proceedings of the 4th Berkeley Symposium on Mathematical Statistics and Probability, Vol. 1, 1961, pp. 361-379.! Allaire, D., Kordonowy, D., Cowlagi, R., Chambers, J., Mainini, L., Ulker, F., Lecerf, M., and Willcox, K., “An Offline/Online Dynamic Data-Driven Capability for Self-Aware Aerospace Vehicles," Procedia Computer Science, 18:1959-1968, 2013.!
40
Fusing Information from Multiple Maneuvers! 5. Online Estimation Enhancement! 1. Bayesian approach with two information sources!
µupdated =
2 2 µ1 2 1
+ +
2 1 µ2 2 2
2 updated
=
2 2 1 2 2 1
+
2 2
2. Graphically! Combine Similar Trust Sources with Combine Similar Trust Sources Combine Similar Trust Sources with Combine Similar Trust Sources withwith Combine Similar Trust Sources with Sources! Lower Variance! Sources! Lower Variance! Sources! Lower Variance! Sources! Lower Variance! Sources! Lower Variance!
(Adapted from March and Willcox, 2010)!
Estimate! Updated Estimate! Source Source 1! Source 2!2!Updated Updated Estimate! Estimate! Updated Estimate! Source 1! 1! 2! 2! Source 1! Source Source 2! Updated Source 1! Source
41
Demonstration with Bayesian Fusion ! Online Simulation Explanation! Moderate, in-library damage case! Performing low-stress LT, PU, RT maneuvers! Estimating capability for LT, PU, RT!
Maneuver Capability Estimates with Bayesian Fusion 0.08
0.08 True µ 1st estimate 1st update 2nd update
0.07
Density!
0.06
0.07 0.06
0.08 True µ 1st estimate 1st update 2nd update
0.07 0.06
0.05
0.05
0.05
0.04
0.04
0.04
0.03
0.03
0.03
0.02
0.02
0.02
0.01
0.01
0.01
0 400
450
500
550
600
650
Minimum Turn Radius – Left Turn!
0 400
450
500
True µ 1st estimate 1st update 2nd update
550
600
650
Minimum Turn Radius – Pull Up!
0 400
450
500
550
600
650
Minimum Turn Radius – Right Turn!
42
Demonstration Comparison! Maneuver Capability Estimates with Bayesian Fusion 0.08
0.08 True µ 1st estimate 1st update 2nd update
0.07
Density!
0.06
0.07 0.06
0.08 True µ 1st estimate 1st update 2nd update
0.06
0.05
0.05
0.05
0.04
0.04
0.04
0.03
0.03
0.03
0.02
0.02
0.02
0.01
0.01
0.01
0 400
450
500
550
600
650
Minimum Turn Radius – Left Turn!
0 400
450
500
True µ 1st estimate 1st update 2nd update
0.07
550
600
650
Minimum Turn Radius – Pull Up!
0 400
450
500
550
600
650
Minimum Turn Radius – Right Turn!
Maneuver Capability Estimates with Conjunctive Filtering 0.08
0.08 True µ st 1 estimate 1st update nd 2 update
0.07
Density!
0.06
0.07 0.06
0.08 True µ st 1 estimate 1st update nd 2 update
0.06
0.05
0.05
0.05
0.04
0.04
0.04
0.03
0.03
0.03
0.02
0.02
0.02
0.01
0.01
0.01
0 400
450
500
550
600
650
Minimum Turn Radius – Left Turn!
0 400
450
500
True µ st 1 estimate 1st update nd 2 update
0.07
550
600
650
0 400
450
500
550
600
650
Minimum Turn Radius – Pull Up! Minimum Turn Radius – Right Turn!43
Literature Review! Operation Loads Monitoring (OLM), [Willis, 2009]! • •
On-board aircraft sensors gather structural loading! Identify damage and fatigue (post-flight)!
Prognostics Health Management (PHM), [NASA Ames ISD Saxena et al, 2008]!
• •
System Characterization
System Health Monitoring
Integrated System/Vehicle Health Monitoring (ISHM/ISVM), [Fox and Glass, System 2000 and NASA Ames, Mehr et al, 2005] :! Diagnosis of possible problems, Health automatic detection and correction! Increase safety, Increase reliability and Reduce cost!
Monitoring
“Digital Twin” [Glaessgen and Stargel, 2012]!
Machine
• •
Physics-physics-based models of aircraft with operational data! Integrates multi-level Operational Based data: On-board ISVHM, maintenance Learning history and /historical data!
•
machine learning in the physics-based modeling sense to capture failure modes (SVMs), reliability-based MDO !
Statistical Modeling Learning Response Surface Methods for reliability analysis [Hurtado, 2004] • Unified statistical framework for System all regression, classification and probability density estimation in system reliability analysis! Reliability Reliability Based Multi Disciplinary Optimization and Design Space Analysis Decomposition [Basudhar and Missoum, 2010]!
Dynamic Data-Driven Application Systems (DDDAS)! • Real-time modeling of Composite Damage [Prudencio & Oden et al., 2013]! • Dynamic Data Driven Methods for Self-aware Aerospace Vehicles, [Allaire et al. 2012]! • Surrogate Modeling Approach for Real-time Structural Assessment [Mainini, Willcox, 2015]!
Physics Based Modeling
Incorporates probabilistic uncertainty estimates from prognostic algorithms Machine Learning \ Statistical Learning
•
44
!
Research Team!
2
Project Overview! • A self-aware unmanned aircraft! Re-plan Mission!
Estimate Capability!
062LR Micro-Measurements
General Purpose Strain Gages - Rectangular Rosette
Offline PhysicsBased Models!
GAGE PATTERN DATA GAGE DESIGNATION
RESISTANCE (OHMS)
OPTIONS AVAILABLE
Change Sensing Strategy!
See Note 1 L2A-XX-062LR-120 L2A-XX-062LR-350 C2A-XX062LR-120 C2A-XX-062LR-350
Sensors!
120 ± 0.6% 350 ± 0.6% 120 ± 0.6% 350 ± 0.6%
DESCRIPTION Small 45° rectangular single-plane rosette.
actual size GAGE DIMENSIONS
Legend:
Gage Length
Overall Length
0.062
0.185
1.52
4.70
GAGE SERIES DATA Series
ES = Each Section
CP = Complete Pattern
S = Section (S1 = Sec 1)
M = Matrix
inch millimeter
Grid Width
Overall Width
Matrix Length
Matrix Width
0.050
0.260
0.277
0.410
1.27
6.60
7.04
10.41
See Gage Series data sheet for complete specifications. Strain Range
Temperature Range
L2 A
Encapsulated constantan gages with preattached ribbon leads.
±3%
–100° to +250°F [–75° to +120°C]
C2 A
Encapsulated constantan gages with preattached ready-to-use cables.
Description
±3%
–60° to +180°F [–50° to +80°C]
Example of an L2A Construction
Graphics:! Vishay Precision Group! AeroVironment! Microbotics!
Example of a C2A Construction
Note 1: Insert desired S-T-C number in spaces marked XX.
Document Number: 11095 Revision: 02-Feb-10
For technical questions, contact: [email protected]
www.micro-measurements.com 85
3
Today’s Focus! An approach for combining offline computation with online sensor data to provide a time-constrained, updated estimate of UAV flight capability! Re-plan Mission!
Estimate Capability!
062LR Micro-Measurements
General Purpose Strain Gages - Rectangular Rosette
Offline PhysicsBased Models!
GAGE PATTERN DATA GAGE DESIGNATION
RESISTANCE (OHMS)
OPTIONS AVAILABLE
Change Sensing Strategy!
See Note 1 L2A-XX-062LR-120 L2A-XX-062LR-350 C2A-XX062LR-120 C2A-XX-062LR-350
Sensors!
120 ± 0.6% 350 ± 0.6% 120 ± 0.6% 350 ± 0.6%
DESCRIPTION Small 45° rectangular single-plane rosette.
actual size GAGE DIMENSIONS
Legend:
ES = Each Section
CP = Complete Pattern
S = Section (S1 = Sec 1)
M = Matrix
inch millimeter
Gage Length
Overall Length
Grid Width
Overall Width
Matrix Length
Matrix Width
0.062
0.185
0.050
0.260
0.277
0.410
1.52
4.70
1.27
6.60
7.04
10.41
GAGE SERIES DATA Series
See Gage Series data sheet for complete specifications. Strain Range
Temperature Range
L2 A
Encapsulated constantan gages with preattached ribbon leads.
±3%
–100° to +250°F [–75° to +120°C]
C2 A
Encapsulated constantan gages with preattached ready-to-use cables.
Description
±3%
–60° to +180°F [–50° to +80°C]
Example of an L2A Construction
Graphics:! Vishay Precision Group! AeroVironment! Microbotics!
Example of a C2A Construction
Note 1: Insert desired S-T-C number in spaces marked XX.
Document Number: 11095
For technical questions, contact: [email protected]
www.micro-measurements.com
4
Outline! 1. Model Aircraft Behavior!
2. Quantify Flight Capability!
Background prior work!
3. Infer Capability from Sensors!
4. Extend to Multiple Maneuvers!
5. Online Estimation Enhancement!
New contributions!
6. Demonstration! 5
Aircraft Capability Definition! The ability of an aircraft to perform steady level turning maneuvers of a certain maximal curvature, as well as pull up maneuvers, as it pertains to the limits on loads applied to the wing structure.! ! Directly related to the airspeed (V) and load factor (n) of the aircraft in flight:! L
!
FR
mV 2 V2 ∑ F = R ⇒ Rturn = 2 g n −1 turn
L n= W
W = mg Graphic: AeroVironment!
6
Extension to Multiple Maneuver Types! • Prior work: Developed offline/online procedure for dynamic online capability estimation in the context of a pull up maneuver (Lecerf et al. 2015, Allaire et al. 2013)! ! ! • Current work: Incorporate multiple maneuvers (steady left turn, steady right turn, pull up)!
• Future work: incorporate all maneuver types for complete dynamic flight envelope updating for use in dynamic mission replanning!
7
Global Aircraft Behavior with ASWING!
Global Kinematics! • Airspeed! • Load Factor!
Wing Structure! • Forces! • Moments! • Strains!
Cruise Speed! 140 KEAS! Cruise Altitude! 25000 ft! Range! 2500 nmi!
• Baseline aircraft using derivative of TASOPT design methodology (Ref. N+3 report, Greitzer E.M. et al, 2010)! • Conforms to FAR 23 guidelines!
References:! • http://web.mit.edu/drela/Public/web/aswing! • AIAA SDM Paper, M. Drela, 1999!
Payload Sizing! 500 lbs!
8
How to Represent Damage?! Stiffness modification in ASWING to capture effects of damage on aircraft behavior.! ! • “Smeared” effect!
Bending stiffness along wing about axis! parallel to airfoil chord!
EIcc!
(left wing tip)!
(right wing tip)!
(exaggerated)!
Location on span!
9
Model Damage with VABS! Wing Structure! • Forces! • Moments! • Strains!
Local Wing Structure! • Damage! • Sensors! • Failures!
• Variational Asymptotic Beam cross-Sectional Analysis (VABS)! • Substitute for full 3dimensional FEM! • Slender, thin-walled beams!
Influence coefficients! Stiffness properties!
Reference: Palacios and Cesnik, 2005!
1D Beam Solver!
Reference line forces and moments! 10
Aircraft Model using ASWING and VABS! 1. Model Aircraft Behavior! 2!
Maneuver!
Coupled ASWING and VABS!
Damage!
Strain Sensor Readings !
45°!
1!
Maximum Failure Index!
Baseline Aircraft!
11
Finding Capability using Model! 2. Quantify Flight Capability! Flight Capability is boundary between:! Red ó Unsafe !ó max FI > 1 ! Blue ó Safe !ó max FI < 1!
(V held constant, capability with respect to nmax)! Maximum load factor change due to damage VIAS = 260 ft/s at 25 kft Damaged [location,width] on span: [+0.35,0.075] Damaged region stiffness loss: 95%
Classification using FI
max
VIAS = 260 ft/s at 25 kft Damaged [location,width] on span: [+0.35,0.075] Damaged region stiffness loss: 95%
3.34
3.4 Safe Unsafe
3.38
3.45
A
3.36
3.33
A
3.4
3.32
n
3.32
B
3.3
nmax
3.34
3.35
3.31
3.3 3.3
3.28
3.25
3.26
3.29
3.2 0
3.24
B
0.02
3.22
3.28 0.2
0.04 3.2
0
0.01
0.02
0.03
0.04
0.05
0.06
Chord Width
0.07
0.08
0.09
0.1
0.06
0.24 0.26
0.08
Chord Width
0.22
0.1
0.3
0.28
Chord Location
3.27 3.26
nmax
12
Offline Procedure Summary (following Lecerf et al., 2015)! • We have a database with features:! – – – – –
1. Model Aircraft Behavior!
Damage conditions XD! Maneuver conditions XM! Maneuver type XF! Strain sensor readings XS! Flight capability Rmin via classification using failure index Fimax for each maneuver type!
• Size constrained by memory and/or lookup limitations! XD s
ws
XM c
2. Quantify Flight Capability!
4. Extend to Multiple Maneuvers!
XF
…
V
n 1
0.35
0.075 0.20
…
260
0.35
0.075 0.28
…
260 3.3
XS e111
2e121
e221
… Rmin,LT Rmin,PU
PU
-1.13e+03
6.15
63.2 …
608
658
627
PU
-6.79e+03
366
378
615
674
649
…
Rmin,RT
13
Online Maximum Likelihood Estimation! XD
Use library from offline phase!
s
! ! ! Notation:!
Cases stored in library!
ws
XM c
XF
…
V
n 1
0.35
0.075 0.20
…
260
0.35
0.075 0.28
…
260 3.3
XS e111
2e121
e221
PU
-1.13e+03
6.15
63.2 …
… Rmin,LT Rmin,PU 608
658
627
PU
-6.79e+03
366
378
615
674
649
…
Rmin,RT
3. Infer Capability from Sensors!
4. Extend to Multiple Maneuvers!
XM 2 {m1 , m2 , . . . , mK } = M XD 2 {d1 , d2 , . . . , dJ } = D XF 2 {LT, PU, RT} = F
Library lookup functions!
C : D ! RN F
S : M ⇥ D ⇥ F ! RN S
14
Online Maximum Likelihood Estimation! 3. Infer Capability from Sensors!
1. Likelihood of seeing sensor readings conditioned on the maneuver, damage, and maneuver type!
pXS |XM ,XD ,XF (·|mk , dj , f ) ⇠ N (S(mk , dj , f ),
2
I)
2. Maximize the likelihood over all possible damage cases in library!
✓
ˆ min (s, mk , f ) = C argmax p R XS |XM ,XD ,XF (s|mk , dj , f ) dj 2D
◆ 15
Improving Capability Estimates Online! 5. Online Estimation Enhancement!
• The James-Stein estimator for sensor average estimation! ! ! • Conjunctive filtering to exploit different misclassifications by different sources!
16
A Closer Look at Maximizing the Likelihood ! 5. Online Estimation Enhancement! 1. Letting!
L(s|mk , dj , f ) , pXS |XM ,XD ,XF (s|mk , dj , f )
17
A Closer Look at Maximizing the Likelihood ! 5. Online Estimation Enhancement! 1. Letting!
L(s|mk , dj , f ) , pXS |XM ,XD ,XF (s|mk , dj , f )
2. Taking the logarithm results in!
ln L(s|mk , dj , f ) =
NS ln(2⇡ 2
2
)
2
NS X 1 2
(si
S(mk , dj , f ))2
i=1
18
A Closer Look at Maximizing the Likelihood ! 5. Online Estimation Enhancement! 1. Letting!
L(s|mk , dj , f ) , pXS |XM ,XD ,XF (s|mk , dj , f )
2. Taking the logarithm results in!
ln L(s|mk , dj , f ) =
NS ln(2⇡ 2
2
)
2
NS X 1
3. Thus,!
argmax L(s|mk , dj , f ) = arg min dj 2D
dj 2D
2
(si
S(mk , dj , f ))2
i=1
NS X
(si
S(mk , dj , f ))2
i=1
19
Mitigating Sensor Noise! 5. Online Estimation Enhancement! 1. Online, we accumulate noisy data from our sensors and can use Nd at a time ! j j j 1 2 Nd j T where!
{ˆs , ˆs , . . . , ˆs
}
ˆs = (ˆ s1 , sˆ2 , . . . , sˆNS )
20
Mitigating Sensor Noise! 5. Online Estimation Enhancement! 1. Online, we accumulate noisy data from our sensors and can use Nd at a time ! j j j 1 2 Nd j T where!
{ˆs , ˆs , . . . , ˆs
}
ˆs = (ˆ s1 , sˆ2 , . . . , sˆNS )
2. To mitigate the impacts of noise we could do the usual thing and let! ! Nd ! j ! ! d j=1 ! prior to implementing the maximum likelihood capability estimator!
1 X ˆs s=s, N
21
Mitigating Sensor Noise! 5. Online Estimation Enhancement! 1. Online, we accumulate noisy data from our sensors and can use Nd at a time ! j j j 1 2 Nd j T where!
{ˆs , ˆs , . . . , ˆs
}
ˆs = (ˆ s1 , sˆ2 , . . . , sˆNS )
2. To mitigate the impacts of noise we could do the usual thing and let! ! Nd ! j ! ! d j=1 ! prior to implementing the maximum likelihood capability estimator!
1 X ˆs s=s, N
Recall:!
argmax L(s|mk , dj , f ) = arg min dj 2D
dj 2D
NS X i=1
(si
S(mk , dj , f ))2 22
The James-Stein Estimator (James and Stein, 1961)! 5. Online Estimation Enhancement! 1. James-Stein Estimator!
✓ˆJS =
✓
1
(NS
2
2) /Nd ksk2
◆
s
Statistically dominates the sample average for NS greater than 2. ! ! ! Trial! MSE – JamesMSE – Sample Demo:! Stein Estimator! Mean!
ND = 100! NS = 12! N (0, 400I)
1!
0.01!
32.69!
2!
0.29!
30.35!
3!
5.07!
49.11!
4!
6.83!
52.22!
5!
0.46!
37.49! 23
The James-Stein Estimator (James and Stein, 1961)! 5. Online Estimation Enhancement! 1. James-Stein Estimator!
✓ˆJS =
✓
1
(NS
2
2) /Nd ksk2
◆
s
Statistically dominates the sample average for NS greater than 2. ! ! ! Trial! MSE – JamesMSE – Sample Demo:! Stein Estimator! Mean!
ND = 100! NS = 12! N (0, 400I) Recall:!
1!
0.01!
32.69!
2!
0.29!
30.35!
3!
5.07! NS X 6.83!
49.11!
4!
argmax L(s|mk , dj , f )5!= arg min dj 2D
(si 0.46! dj 2D i=1
52.22! 2 S(mk ,37.49! dj , f )) 24
Demonstration! 6. Demonstration!
Damage Parameter!
Trial Levels!
ls!
0.15!
ws!
0.05!
lc!
0.1, 0.2, 0.3, 0.4, 0.5, 0.6!
wc!
0.1, 0.2, 0.3, 0.4, 0.5!
dt!
0.5, 0.6 ,0.7, 0.8, 0.9!
df!
0.95!
Online Simulation Parameters! ND = 1000, NS = 12! Moving window with 100 stored MLE capability estimates! Noise at 400 µstrain!
25
Demonstration – James-Stein Estimator! Online Simulation Explanation! Moderate, in-library damage case! Performing low-stress LT maneuver! Estimating capability for LT!
Performing Left Turn Maneuver! 0.03
James−Stein Estimator Sample Average Direct Stain Data (no averaging)
0.025
Density
0.02
0.015
0.01
0.005
0
380
400
420
440
460
480
500
520
Minimum Turn Radius − Left Turn
540
560
26
Demonstration – Multiple Maneuver Capability Estimates! Online Simulation Explanation! Moderate, in-library damage case! Performing low-stress LT, PU, RT maneuvers! Estimating capability for LT, PU, RT!
Maneuver Capability Estimates 0.05
0.05 True µ Left Turn Pull Up Right Turn
Density!
0.04
0.04
‘
0.05 True µ Left Turn Pull Up Right Turn
0.04
0.03
0.03
0.03
0.02
0.02
0.02
0.01
0.01
0.01
0 400
450
500
550
600
650
Minimum Turn Radius – Left Turn!
0 400
450
500
True µ Left Turn Pull Up Right Turn
550
600
650
Minimum Turn Radius – Pull Up!
0 400
450
500
550
600
650
Minimum Turn Radius – Right Turn!
27
Conjunctive Filtering! 5. Online Estimation Enhancement!
Use the idea that data gathered during different maneuver types will lead to different misclassifications! Estimate!
RT(LT) !
RT(PU)!
RT(RT)!
1!
510.99!
510.99!
510.99!
2!
513.31 !
510.99!
510.99!
3!
513.31!
510.99!
510.99 !
4!
513.31!
510.99!
512.00 !
5!
514.78 !
513.31!
512.00 !
6!
514.78!
513.55!
512.00 !
7!
514.78 !
514.75!
513.31!
8!
517.07!
514.75!
513.55 !
9!
520.49!
514.78!
514.75! 28
Conjunctive Filtering! 5. Online Estimation Enhancement!
Use the idea that data gathered during different maneuver types will lead to different misclassifications! Estimate!
RT(LT) !
RT(PU)!
RT(RT)!
1!
510.99!
510.99!
510.99!
Conjunction RT(LT,PU)!
2!
513.31 !
510.99!
510.99!
510.99!
3!
513.31!
510.99!
510.99 !
513.31!
4!
513.31!
510.99!
512.00 !
514.78!
5!
514.78 !
513.31!
512.00 !
6!
514.78!
513.55!
512.00 !
7!
514.78 !
514.75!
513.31!
8!
517.07!
514.75!
513.55 !
9!
520.49!
514.78!
514.75! 29
Conjunctive Filtering! 5. Online Estimation Enhancement!
Use the idea that data gathered during different maneuver types will lead to different misclassifications! Estimate!
RT(LT) !
RT(PU)!
RT(RT)!
1!
510.99!
510.99!
510.99!
Conjunction RT(LT,PU,RT)!
2!
513.31 !
510.99!
510.99!
510.99!
3!
513.31!
510.99!
510.99 !
513.31!
4!
513.31!
510.99!
512.00 !
5!
514.78 !
513.31!
512.00 !
6!
514.78!
513.55!
512.00 !
7!
514.78 !
514.75!
513.31!
8!
517.07!
514.75!
513.55 !
9!
520.49!
514.78!
514.75! 30
Conjunctive Filtering ! c˜CF =
|C1r,s |
X
di,1 di,2
P|C1r,s |
i=1
2 ˜CF
i=1
= P|C r,s | 1 i=1
di,1 di,2 |C1r,s |
1
di,1 di,2
1
X
ci
!
di,1 di,2 (ci
Mean! Variance!
c˜CF )2
i=1
Estimate!
RT(LT) !
RT(PU)!
1!
510.99!
510.99!
2!
513.31 !
510.99!
3!
513.31!
510.99!
4!
513.31!
510.99!
5!
514.78 !
513.31!
Conjunction RT(LT,PU,RT)! 510.99! 513.31!
31
Conjunctive Filtering ! c˜CF =
|C1r,s |
X
di,1 di,2
P|C1r,s |
i=1
2 ˜CF
i=1
= P|C r,s | 1 i=1
di,1 di,2 |C1r,s |
1
di,1 di,2
1
X
ci
Number of nonrepeated entries in first information source that are also in the second information source!
!
di,1 di,2 (ci
c˜CF )2
i=1
Estimate!
RT(LT) !
RT(PU)!
1!
510.99!
510.99!
2!
513.31 !
510.99!
3!
513.31!
510.99!
4!
513.31!
510.99!
5!
514.78 !
513.31!
Conjunction RT(LT,PU,RT)! 510.99! 513.31!
Here:!
r,s |C1 |
=2 32
Conjunctive Filtering ! c˜CF =
|C1r,s |
X
di,1 di,2
P|C1r,s |
i=1
2 ˜CF
i=1
= P|C r,s | 1 i=1
di,1 di,2 |C1r,s |
1
di,1 di,2
1
X
ci
!
Number of times the ith element in the intersection between the two sources occurs!
di,1 di,2 (ci
c˜CF )2
i=1
Estimate!
RT(LT) !
RT(PU)!
1!
510.99!
510.99!
2!
513.31 !
510.99!
3!
513.31!
510.99!
4!
513.31!
510.99!
5!
514.78 !
513.31!
Conjunction RT(LT,PU,RT)! 510.99! 513.31!
Here:!
d1,1 = 1, d2,1 = 3 33
Conjunctive Filtering ! c˜CF =
|C1r,s |
X
di,1 di,2
P|C1r,s |
i=1
2 ˜CF
i=1
= P|C r,s | 1 i=1
di,1 di,2 |C1r,s |
1
di,1 di,2
1
X
ci
!
ith element of the intersection of the two sources without repeats !
di,1 di,2 (ci
c˜CF )2
i=1
Estimate!
RT(LT) !
RT(PU)!
1!
510.99!
510.99!
2!
513.31 !
510.99!
3!
513.31!
510.99!
4!
513.31!
510.99!
5!
514.78 !
513.31!
Conjunction RT(LT,PU,RT)! 510.99! 513.31!
Here:!
c1 = 510.99, c2 = 513.31 34
Demonstration with Conjunctive Filtering! Online Simulation Explanation! Moderate, in-library damage case! Performing low-stress LT, PU, RT maneuvers! Estimating capability for LT, PU, RT!
Maneuver Capability Estimates with Conjunctive Filtering 0.08
0.08 True µ 1st estimate st 1 update nd 2 update
0.07
Density!
0.06
0.07 0.06
0.08 True µ 1st estimate st 1 update nd 2 update
0.06
0.05
0.05
0.05
0.04
0.04
0.04
0.03
0.03
0.03
0.02
0.02
0.02
0.01
0.01
0.01
0 400
450
500
550
600
650
Minimum Turn Radius – Left Turn!
0 400
450
500
True µ 1st estimate st 1 update nd 2 update
0.07
550
600
650
Minimum Turn Radius – Pull Up!
0 400
450
500
550
600
650
Minimum Turn Radius – Right Turn!
35
Demonstration Comparison! Maneuver Capability Estimates ‘
0.08
0.08 True µ Left Turn Pull Up Right Turn
Density!
0.07 0.06
0.07 0.06
0.08 True µ Left Turn Pull Up Right Turn
0.06
0.05
0.05
0.05
0.04
0.04
0.04
0.03
0.03
0.03
0.02
0.02
0.02
0.01
0.01
0.01
0 400
450
500
550
600
650
Minimum Turn Radius – Left Turn!
0 400
450
500
True µ Left Turn Pull Up Right Turn
0.07
550
600
650
Minimum Turn Radius – Pull Up!
0 400
450
500
550
600
650
Minimum Turn Radius – Right Turn!
Maneuver Capability Estimates with Conjunctive Filtering 0.08
0.08 True µ st 1 estimate 1st update nd 2 update
0.07
Density!
0.06
0.07 0.06
0.08 True µ st 1 estimate 1st update nd 2 update
0.06
0.05
0.05
0.05
0.04
0.04
0.04
0.03
0.03
0.03
0.02
0.02
0.02
0.01
0.01
0.01
0 400
450
500
550
600
650
Minimum Turn Radius – Left Turn!
0 400
450
500
True µ st 1 estimate 1st update nd 2 update
0.07
550
600
650
0 400
450
500
550
600
650
Minimum Turn Radius – Pull Up! Minimum Turn Radius – Right Turn!36
Conclusions & Future Work! • Extended the offline/online DDDAS paradigm for enabling self-aware UAVs to incorporate multiple maneuvers! • Implemented and defined enhancements to online capability estimation approach! • Using information from multiple tasks has the potential to mitigate misclassification in online stage! Future Work! • Study the conjunctive filter and implement robustness features! • Incorporate online reduced-order models as another source of information! • Heterogeneous sensing capabilities! • Online sensor “placement”! • Out-of-library classification confidence metrics! 37
38
References! • • •
• •
•
•
•
• •
Dynamic Data Driven Application Systems community website: http://www.dddas.org! Drela, M. (1999). Integrated Simulation Model for Preliminary Aerodynamic , Structural , and Control-Law Design of Aircraft. In 40th AIAA SDM Conference (pp. 1–13).! Greitzer, E., M.; Bonnefoy, P., A.; Blanco, E., De la Rosa; Dorbian, C., S.; Drela, M.; Hall, D., K.; Hansman, R., J.; Hileman, J., I.; Liebeck, R., H.; Lovegren, J.; Mody, P.; Pertuze, J., A.; Sato, S.; Spakovszky, Z., S.; Tan, C., S.; Hollman, J., S.; Duda, J., E.; Fitzgerald, N.; Houghton, J.; Kerrebrock, J., L.; Kiwada, G., F.; Kordonowy, D.; Parrish, J., C.; Tylko, J.; Wen, E., A.; Lord, W., K. (2010). N + 3 Aircraft Concept Designs and Trade Studies , Final Report Volume 1 (Vol. 1, pp. 1–187).! Willis, S. (2009). OLM : A HANDS-ON APPROACH. In 25th ICAF Symposium (pp. 1199–1214). Rotterdam.! Fox, J. J., & Glass, B. J. (n.d.). Impact of integrated vehicle health management (IVHM) technologies on ground operations for reusable launch vehicles (RLVs) and spacecraft. In 2000 IEEE Aerospace Conference. Proceedings (Vol. 2, pp. 179–186). IEEE. doi:10.1109/AERO.2000.878223! Mehr, A. F., Tumer, I., & Barszcz, E. (2005). Optimal Design of Integrated Systems Health Management ( ISHM ) for Improving the Safety of NASA ’ s Exploration Missions : A Multidisciplinary Design Approach. In 6th World Congresses on Structural and Multidisciplinary Optimization. Rio de Janeiro.! Glaessgen, E. H., & Stargel, D. S. (2012). The Digital Twin Paradigm for Future NASA and U.S. Air Force Vehicles. In the 53rd American Institute of Aeronautics and Astronautics Structures, Structural Dynamics, and Materials Conference.! Saxena, A., Celaya, J., Balaban, E., Goebel, K., Saha, B., Saha, S., & Schwabacher, M. (2008). Metrics for evaluating performance of prognostic techniques. In 2008 International Conference on Prognostics and Health Management (pp. 1–17). Ieee. doi:10.1109/PHM.2008.4711436! Palacios, R., & Cesnik, C. E. S. (2005). Cross-sectional analysis of nonhomogeneous anisotropic active slender structures. AIAA journal, 43(12), 2624–2638.! Lecerf, M., Allaire, D., and Willcox, K., “Methodology for Dynamic Data-Driven Online Flight Capability Estimation,” AIAA Journal, Vol. 53, No. 10, 2015, pp. 3073-3087.!
39
References! • • • • • • • • • • • • • •
Cacuci, D., “Sensitivity and Uncertainty Analysis: Theory, Sensitivity and Uncertainty Analysis”, Chapman & Hall/CRC, 2003.! McDonald, R. A., “Error Propagation and Metamodeling for a Fidelity Tradeoff Capability in Complex Systems Design”, Ph.D. thesis, Georgia Institute of Technology, 2006.! Martin, J. D., “A methodology for evaluating system-level uncertainty in the conceptual design of complex multidisciplinary systems”, Ph.D. thesis, Dept. of Mechanical Engineering, The Pennsylvania State University, May 2005.! Liu, H., Chen, W., Kokkolaras, M., Papalambros, P. Y., and Kim, H. M., “Probabilistic Analytical Target Cascading: A Moment Matching Formulation for Multilevel Optimization Under Uncertainty," Journal of Mechanical Design, Vol. 128, No. 4, 2006, pp. 991-1000. ! Du, X. and Chen, W., “Collaborative Reliability Analysis for Multidisciplinary Systems Design," 2002.! Rubin, D. B., “Using the SIR algorithm to simulate posterior distributions,“ Bayesian Statistics 3 , edited by M. H. Bernardo, K. M. Degroot, D. V. Lindley, and A. F. M. Smith, Oxford University Press, 1988.! Scott, D., “Multivariate Density Estimation: Theory, Practice, and Visualization”. John Wiley & Sons, Inc. 1992.! Grimmett, G.R., Strizaker, D., “Probability and Random Process”, Texts from Oxford University Press, 2001.! Weibach, R. and Wied, D., “Consistency of the kernel density estimator-a survey”, HT014602036 , 2009.! Peherstorfer, B., Pflüger D., Bungartz H.J.: “Clustering Based on Density Estimation with Sparse Grids”, Proceedings of German Conference on Artificial Intelligence (KI 2012), (2012). ! MacKay, D., Information theory, inference and learning algorithms, Cambridge University Press, 2003, p 370.! March, A. and Willcox, K., “A Provably Convergent Multifidelity Optimization Algorithm not Requiring HighFidelity Derivatives,” Proceedings of the 3rd MDO Specialists Conference, Orlando, FL, AIAA-2010-2912.! James, W. and Stein, C., “Estimation with Quadratic Loss,” Proceedings of the 4th Berkeley Symposium on Mathematical Statistics and Probability, Vol. 1, 1961, pp. 361-379.! Allaire, D., Kordonowy, D., Cowlagi, R., Chambers, J., Mainini, L., Ulker, F., Lecerf, M., and Willcox, K., “An Offline/Online Dynamic Data-Driven Capability for Self-Aware Aerospace Vehicles," Procedia Computer Science, 18:1959-1968, 2013.!
40
Fusing Information from Multiple Maneuvers! 5. Online Estimation Enhancement! 1. Bayesian approach with two information sources!
µupdated =
2 2 µ1 2 1
+ +
2 1 µ2 2 2
2 updated
=
2 2 1 2 2 1
+
2 2
2. Graphically! Combine Similar Trust Sources with Combine Similar Trust Sources Combine Similar Trust Sources with Combine Similar Trust Sources withwith Combine Similar Trust Sources with Sources! Lower Variance! Sources! Lower Variance! Sources! Lower Variance! Sources! Lower Variance! Sources! Lower Variance!
(Adapted from March and Willcox, 2010)!
Estimate! Updated Estimate! Source Source 1! Source 2!2!Updated Updated Estimate! Estimate! Updated Estimate! Source 1! 1! 2! 2! Source 1! Source Source 2! Updated Source 1! Source
41
Demonstration with Bayesian Fusion ! Online Simulation Explanation! Moderate, in-library damage case! Performing low-stress LT, PU, RT maneuvers! Estimating capability for LT, PU, RT!
Maneuver Capability Estimates with Bayesian Fusion 0.08
0.08 True µ 1st estimate 1st update 2nd update
0.07
Density!
0.06
0.07 0.06
0.08 True µ 1st estimate 1st update 2nd update
0.07 0.06
0.05
0.05
0.05
0.04
0.04
0.04
0.03
0.03
0.03
0.02
0.02
0.02
0.01
0.01
0.01
0 400
450
500
550
600
650
Minimum Turn Radius – Left Turn!
0 400
450
500
True µ 1st estimate 1st update 2nd update
550
600
650
Minimum Turn Radius – Pull Up!
0 400
450
500
550
600
650
Minimum Turn Radius – Right Turn!
42
Demonstration Comparison! Maneuver Capability Estimates with Bayesian Fusion 0.08
0.08 True µ 1st estimate 1st update 2nd update
0.07
Density!
0.06
0.07 0.06
0.08 True µ 1st estimate 1st update 2nd update
0.06
0.05
0.05
0.05
0.04
0.04
0.04
0.03
0.03
0.03
0.02
0.02
0.02
0.01
0.01
0.01
0 400
450
500
550
600
650
Minimum Turn Radius – Left Turn!
0 400
450
500
True µ 1st estimate 1st update 2nd update
0.07
550
600
650
Minimum Turn Radius – Pull Up!
0 400
450
500
550
600
650
Minimum Turn Radius – Right Turn!
Maneuver Capability Estimates with Conjunctive Filtering 0.08
0.08 True µ st 1 estimate 1st update nd 2 update
0.07
Density!
0.06
0.07 0.06
0.08 True µ st 1 estimate 1st update nd 2 update
0.06
0.05
0.05
0.05
0.04
0.04
0.04
0.03
0.03
0.03
0.02
0.02
0.02
0.01
0.01
0.01
0 400
450
500
550
600
650
Minimum Turn Radius – Left Turn!
0 400
450
500
True µ st 1 estimate 1st update nd 2 update
0.07
550
600
650
0 400
450
500
550
600
650
Minimum Turn Radius – Pull Up! Minimum Turn Radius – Right Turn!43
Literature Review! Operation Loads Monitoring (OLM), [Willis, 2009]! • •
On-board aircraft sensors gather structural loading! Identify damage and fatigue (post-flight)!
Prognostics Health Management (PHM), [NASA Ames ISD Saxena et al, 2008]!
• •
System Characterization
System Health Monitoring
Integrated System/Vehicle Health Monitoring (ISHM/ISVM), [Fox and Glass, System 2000 and NASA Ames, Mehr et al, 2005] :! Diagnosis of possible problems, Health automatic detection and correction! Increase safety, Increase reliability and Reduce cost!
Monitoring
“Digital Twin” [Glaessgen and Stargel, 2012]!
Machine
• •
Physics-physics-based models of aircraft with operational data! Integrates multi-level Operational Based data: On-board ISVHM, maintenance Learning history and /historical data!
•
machine learning in the physics-based modeling sense to capture failure modes (SVMs), reliability-based MDO !
Statistical Modeling Learning Response Surface Methods for reliability analysis [Hurtado, 2004] • Unified statistical framework for System all regression, classification and probability density estimation in system reliability analysis! Reliability Reliability Based Multi Disciplinary Optimization and Design Space Analysis Decomposition [Basudhar and Missoum, 2010]!
Dynamic Data-Driven Application Systems (DDDAS)! • Real-time modeling of Composite Damage [Prudencio & Oden et al., 2013]! • Dynamic Data Driven Methods for Self-aware Aerospace Vehicles, [Allaire et al. 2012]! • Surrogate Modeling Approach for Real-time Structural Assessment [Mainini, Willcox, 2015]!
Physics Based Modeling
Incorporates probabilistic uncertainty estimates from prognostic algorithms Machine Learning \ Statistical Learning
•
44
