Managing Vibroacoustic Uncertainty Margins when using
Modeling to define Maximum Expected Environments
Matt Kaplan
ATA Engineering, Inc.
San Diego, CA
(858) 480-2065
19–21 June 2012
© The Aerospace Corporation 2010
© The Aerospace Corporation 2012
Paul Bremner
Sonelite Inc.
Del Mar, CA
(858) 480-2061
Outline
•
•
•
•
•
Maximum expected vs Qual vs Acceptance levels
End-to-end uncertainty margin stack-up
VA modeling issues
Quantifying model uncertainty
Relief from Log-normal assumption
The 2012 Spacecraft & Launch Vehicle
Dynamic Environments Workshop
2
Normal Tolerance Limit
Alan Piersol’s Ch.6 of NASA-HDBK-7005 explains normal tolerance limit (NTL) method for
defining maximum expected environment (MEE)
MEE ( y ) ≡ NTLPβ / γ ( y ) = y + k Pβ / γ s y
Uncertainty Margin
1 n
y = ∑ yi
n i =1
1 n
sy =
∑ ( yi − y )
n − 1 i =1
Log Normal assumption: y = Log(x) of VA quantity x is closer to normal distribution than x
•
•
NASA STD 7001A
– Qualification test level
– Acceptance test level
MIL STD 1540
– Qualification test level
– Acceptance test level
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Dynamic Environments Workshop
P95/50 + 3dB
P95/50 – 3dB
P99/90
P95/50
Typical estimations of P95/50
Flight test data
PA-1 Model & Acoustic test data
Piersol, A. NASA-HDBK-7005
Bremner, Kaplan, et al. ATA Report to NESC 2012
10
10dB
Response PSD (g2/Hz)
1
0.1
CLA-6C Spec - SIGI Box IF In
CCi SIGI Box IF Inplane - 65
Langley SIGI Box Inplane - 44
SIGI Top Left - y, 54.7 g's rms
SIGI Top Left - z, 53.1 g's rms
SIGI Bottom Support Bolt - y,
SIGI Bottom Support Bolt - z,
BEA - SIGI Box IFNode_4155
BEA - SIGI Box IFNode_4156
BEA - SIGI Box IFNode_4155
BEA - SIGI Box IFNode_4154
BEA - SIGI Box IFNode_4154
BEA - SIGI Box IFNode_4153
Minimum Workmanship - 6.8
BEA - SIGI Box IFNode_4156
BEA - SIGI Box IFNode_4155
BEA - SIGI Box IFNode_4155
BEA - SIGI Box IFNode_4154
BEA - SIGI Box IFNode_4154
BEA - SIGI Box IFNode_4153
FEA -SIGI4154868In-Plane A
FEA -SIGI4153987In-Plane A
FEA -SIGI4156067In-Plane A
FEA -SIGI4153987In-Plane T
FEA -SIGI4154868In-Plane T
FEA -SIGI4156067In-Plane T
CLA-6B Spec - SIGI Box IF In
0.01
0.001
0.0001
0.00001
10
The 2012 Spacecraft & Launch Vehicle
Dynamic Environments Workshop
100
Frequency (Hz)
1000
NASA Community Practice – Maximum Expected Environment (MEE)
VA Uncertainty TIM, Huntsville, Feb 2010
Loads task
Owner
MEE Practice
Compliance
ARES 1 Lift-off
Acoustics
MSFC
MEE = Max (Scaled flight data, Model 1, Model 2) + 2dB Flight-flt dispersion
Scaled flight data = Max(P95/50, Max sample)
Excess margin ?
Lift-off Acoustics
Aerospace
Corp
MEE = Max Predicted SPL + 5dB
Excess margin ?
Ground Acoustics
KSC
MEE = Max(Scaled flight data, Models) + Flight-flt dispersion
P97.5/50 = μ + 2σ
Excess margin ?
ARES I Aeroacoustic Loads
MSFC
MEE = Max(Zone FPL, AoA, Mach in range) + 2dB
Excess margin ?
ORION Aeroacoustic Loads
Lockheed
For SEA: MEE = Max(Space Avg(Zone FPL), AoA, Mach in Range) + Flightflt dispersion
For FEM/BEM: MEE = Max(Space Avg(Zone FPL), AoA, Mach in Range) +
RSS(Zone spatial uncertainty, Flight-flt dispersion)
Mostly complies
ARES I VA
Environments
MSFC
VA Analyst Judgment (Scaled flight data, Test data, Models)
Unclear ??
NOTE: Not necessarily Max( ) or P95/50.
Orion VA
Environments
Lockheed
The 2012 Spacecraft & Launch Vehicle
Dynamic Environments Workshop
Max (SEA, FE/BEM, ACRESP)
Excess margin ?
Outline
•
•
•
•
•
Maximum expected vs Qual vs Acceptance levels
End-to-end uncertainty margin stack-up
VA modeling issues
Quantifying model uncertainty
Relief from Log-normal assumption
The 2012 Spacecraft & Launch Vehicle
Dynamic Environments Workshop
6
End-to-end uncertainty margins
2) Zonal
Vibration
Model
Uncertainty
1) Load
Uncertainty
• Spatial
• Flight-to-flight
• Spatial
• Model
3) Local
Component
Loading
Uncertainty
• Model
Acceptance
level
4) Margin(s)
in Test
Specification
Qualification
level
• Enveloping
GOOD NEWS: Uncorrelated sources of uncertainty RSS
sy →
The 2012 Spacecraft & Launch Vehicle
Dynamic Environments Workshop
(σ
2
Flt − flt
2
2
2
2
+ σ Spatial
+ σ VA
mod el + σ GMA mod el + σ Test
)
Recommendations
End-to-end Uncertainty Margins
•
•
Study Recommendation #1
– NASA vibro-acoustics community standard practice should be to define maximum
expected vibro-acoustic environments (MEE) using normal tolerance limit (NTL) process,
and P95/50 unless otherwise directed or approved by the program manager.
Study Recommendation #2
– The NTL estimation of MEE should always be done at the end of the process, being sure
to correctly combine the standard deviations from each source of uncertainty.
The 2012 Spacecraft & Launch Vehicle
Dynamic Environments Workshop
Outline
•
•
•
•
•
Maximum expected vs Qual vs Acceptance levels
End-to-end uncertainty margin stack-up
VA modeling issues
Quantifying model uncertainty
Relief from Log-normal assumption
The 2012 Spacecraft & Launch Vehicle
Dynamic Environments Workshop
9
VA Model versus VA Scaling
•
•
Scaling P95/50 data is OK
Modeling should not use P95/50 or Maximax data as input
2
2
2
σ = σ Flt
− flt + σ Spatial + σ mod el
Load
Data
P95/50,
Maximax
?
OR
Average
?
VA
Model
+ Spatial
Variance
+ Model
Uncertainty
?
+ Flightto-flight
Variance
The 2012 Spacecraft & Launch Vehicle
Dynamic Environments Workshop
RSS
Maximum
Expected
Random
Vibn Level
Maximax load vs Load statistics
Monte Carlo evaluation
( )
NTLP 95 / 50 LGv = L H 2 + LG f + k σ L2H + σ L2 f
2
2
2
= L H 2 + LG f + k σ Flt
− flt + σ mod el + σ spatial
= L H 2 + LG f + (12 ....14) dB
for k = {1.67 ... 1.94}
( )
i max
NTLP 95 / 50 LGv = L H 2 + kσ LH + Lmax
Gf
2
2
≅ L H 2 + k σ mod
el + σ spatial + LG f + 3σ LF
≅ L H 2 + LG f + (20 .... 22) dB
Variation
Model parameters
Load (flight-to-flight)
Spatial response
Model, Flight-to-flight and Spatial
The 2012 Spacecraft & Launch Vehicle
Dynamic Environments Workshop
for k = {1.67 ... 1.94}
Standard Deviation
(dB)
0.77
2.90
3.65
4.71
7dB excess margin
Example: Aero-acoustic Loads
FPL load auto spectra
+
FPL spatial correlation
v
2
p , Δω
G pp (ω )
J r2 (ω )
=
dω Re ∑ )
)
η p m p Δ∫ω
r mr Yr (ω )
J r2 (ω ) =
Transonic M=0.95
The 2012 Spacecraft & Launch Vehicle
Dynamic Environments Workshop
Random Vibration
environments
FE, SEA
Physics-based model
1
A2G pp
∫∫ψ
A
r
( x) G p ( x, x' ; ω )ψ r ( x' ) d xd x'
Norm. Response – TBL Input
Comparison of Input and Response Distribution for TBL Input at 157.49 Hz
9
8
Percent of Samples
7
6
5
4
3
2
1
0
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
3
3.5
Normalized Variable
Comparison of Input and Response Distribution for TBL Input at 1498.31 Hz
9
8
Percent of Samples
7
6
5
4
3
2
1
0
-1.5
-1
-0.5
0
0.5
1
1.5
Normalized Variable
The 2012 Spacecraft & Launch Vehicle
Dynamic Environments Workshop
2
2.5
3
3.5
Recommendations
Statistical quantification of aeroacoustic loads
•
Study Recommendation #3
– When aero-acoustic loads are published in a Loads Data Book, the
levels should be provided as:
i) statistical mean, and
ii) standard deviation (associated with each source of uncertainty), and
iii) maximum expected environment (MEE) levels.
The 2012 Spacecraft & Launch Vehicle
Dynamic Environments Workshop
Outline
•
•
•
•
•
Maximum expected vs Qual vs Acceptance levels
End-to-end uncertainty margin stack-up
VA modeling issues
Quantifying model uncertainty
Relief from Log-normal assumption
The 2012 Spacecraft & Launch Vehicle
Dynamic Environments Workshop
15
Model uncertainty
16
Universality (Langley & Cotoni, JASA 2004)
random masses (20%)
random edge springs
200 samples
random masses (5%)
Mean
The mean and relative variance are independent of the details of the way in which the system is randomised
– a very surprising result which is an illustration of “Universality”
-30
-50
Ensemble mean response
Variance of Energy (dB ref 1 J2)
Mean of Energy (dB ref. 1 J)
-35
-40
-45
-50
-55
-60
Ensemble variance
-100
-65
-70
-150
0
The 2012 Spacecraft & Launch Vehicle
Dynamic Environments Workshop
500
1000
1500
2000
Frequency (Hz)
2500
3000
0
500
1000
1500
2000
Frequency (Hz)
2500
3000
SEA can predict both Mean and Variance due to model uncertainty
Var( E j ) = ∑ ( D0,−1jk ) 2 Var( Pran,k ) + ∑∑ [(D0,−1jk − D0,−1js ) Eˆ s ]2 Var( Dran,ks )
k
k
s ≠k
Inverse of SEA model matrix
Energy predicted by SEA
[Ref: Langley & Cotoni, JASA 2004]
The 2012 Spacecraft & Launch Vehicle
Dynamic Environments Workshop
SEA model variance (uncertainty)
Test validation by Cotoni, Langley & Kidner, Jnl.S&V 2005
of energies
SEAMean
vs Test
- MEAN
-20
Cylinder
Plate 1 (driven)
Plate 2
Plate 3
-30
1
10
-50
Var[T] / E[T]2
E[T] (dB ref. 1 J)
-40
Relative
of energies
SEA
vs variance
Test - VARIANCE
2
10
-60
-70
-80
Ϭm=3dB
0
10
-1
10
-90
-100
-110
-2
0
1000
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Dynamic Environments Workshop
2000
3000
Frequency (Hz)
4000
5000
10
0
1000
2000
3000
Frequency (Hz)
4000
5000
FE Model Uncertainty
Monte Carlo evaluation σmodel < 3dB
Mean Response
-2
10
10% added mass
15% added mass
Mean Response (ensemble of perturbed models)
20% added mass
-3
– 100 lumped masses, uniformly distributed at
random locations over 1151 possible nodes.
– Response statistics were calculated for:
• 10% mass uncertainty (each random
mass is 0.10% of total mass)
• 15% mass uncertainty (each random
mass is 0.15% of total mass)
• 20% mass uncertainty (each random
mass is 0.20% of total mass)
– The mean vibration response across all nodes
on the model, averaged over an ensemble of
50 Monte Carlo simulations
Acceleration (m/s 2)
10
-4
10
-5
10
10% random mass
15% random mass
20% random mass
-6
10
-7
10
0
200
400
600
800
1000
1200
1400
1600
1800
Frequency (Hz)
Response ϭx/μx (ensemble models)
10% random mass
15% random mass
20% random mass
The 2012 Spacecraft & Launch Vehicle
Dynamic Environments Workshop
2000
Recommendations
Model uncertainty
•
•
Study Recommendation #5
– Deterministic (FE, BE) VA model uncertainty should be estimated using Monte
Carlo analysis (or equivalent) with statistical analysis to quantify relative
standard deviation.
– For model parameters which cannot be varied explicitly, the randomized mass
distribution method (or equivalent) should be used.
Study Recommendation #6
– Model uncertainty for statistical energy analysis (SEA) and related high
frequency vibro-acoustic models should use available methods (asymptotic
statistics theory, Monte Carlo analysis or equivalent) to quantify model
variance.
The 2012 Spacecraft & Launch Vehicle
Dynamic Environments Workshop
Outline
•
•
•
•
•
Maximum expected vs Qual vs Acceptance levels
End-to-end uncertainty margin stack-up
VA modeling issues
Quantifying model uncertainty
Relief from Log-normal assumption
The 2012 Spacecraft & Launch Vehicle
Dynamic Environments Workshop
21
Log Normal distribution (?)
Probability Density Fn of Log Plate Vibration (Lv)
LogNormal
• Typically biased estimate of the spread
of the data at the higher end
• Results in overly conservative estimates
of the MEE, especially for the P99/90
level
Alternative PDF models
• Empirical distribution
• Other (Piersol, NASA-HDBK-7005)
The 2012 Spacecraft & Launch Vehicle
Dynamic Environments Workshop
Empirical distribution
Can provide 3-5 dB relief from NTL environments
Flight data evaluation
Model-based Monte Carlo evaluation
Piersol, A. NASA-HDBK-7005
Bremner, Kaplan, et al. ATA Report to NESC 2012
Mean
The 2012 Spacecraft & Launch Vehicle
Dynamic Environments Workshop
Recommendations
PDF for Tolerance Limit Analysis
•
Study Recommendation #7
– Empirical tolerance limit analysis (and other non-normal distributions)
can be used to get relief from conservative NTL prediction of MEE, in
critical equipment qualification cases
The 2012 Spacecraft & Launch Vehicle
Dynamic Environments Workshop
Migrating Lessons Learned
•
Update NASA-HDBK-7005:
– Ch4 Prediction of Dynamic Excitations
• Deliver load data as Mean, Std Dev & Maximax
– Ch5 Prediction of Dynamic Responses
• Use Mean of load(s) as inputs – NOT maximax
• Use mean of model(s)
• Estimate model uncertainty
– Ch6 Maximum Expected Environment
• Combine all uncertainties in MEE response (incl model)
• RSS standard deviations of multiple sources of uncertainty
The 2012 Spacecraft & Launch Vehicle
Dynamic Environments Workshop
Acknowledgement
•
This work was funded by NASA Engineering and Safety Center (NESC)
under program TI-09-00595 - Reducing Risk Associated with
Vibroacoustic Environments
The 2012 Spacecraft & Launch Vehicle
Dynamic Environments Workshop