© united technologies corporation (2012) this document contains no technical data subject to the...
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© United Technologies Corporation (2012)This document contains no technical data subject to the EAR or the ITAR.Reinman, Rev Date 6/19/2012 Slide 1 of 26
Design For Variation
UCM 2012
Sheffield, UK July 2-4, 2012Grant Reinman, Senior Fellow, Statistics and Design For Variation
Pratt & Whitney, East Hartford, CT
Design of Experiments – Gaussian Process Emulation
Monte Carlo Simulation – Bayesian Model Calibration
Un
certainty Q
uan
tification
Sen
siti
vity
An
alys
isIncrease Life
Improve Quality
Improve Producibility
© United Technologies Corporation (2012)This document contains no technical data subject to the EAR or the ITAR.Reinman, Rev Date 6/19/2012 Slide 2 of 26
Pratt & Whitney EngineeringA Passion for Innovation
PurePower® PW1000G Engine
© United Technologies Corporation (2012)This document contains no technical data subject to the EAR or the ITAR.Reinman, Rev Date 6/19/2012 Slide 3 of 26
Deterministic Design, Uncertain WorldTraditional Approach: Empirical Design Margins, Factors of Safety
▲ Manufacturing
Hole Diameter Value
Leading Edge Hole Diameter
▲ Usage
▲ Materials
X
Primary Creep
Secondary Tertiary
Time t
Str
ain
RuptureX
Primary Creep
Secondary Tertiary
Time t
Str
ain
Rupture
543210Hours per Flight
LCOLPR
MXANWARAMSIATCV
TWAUALUPS
AAL
UZBVIMA
AMTAMXCFGCSHDALETHFEAFIN
OPPW2000 Hours per Flight, by Operator
Stress
Tim
e to
Ruptu
re
Time To Creep/ Rupture
▲ Computational Models
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14
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Concentrated Load, lbs
Dis
cre
pa
ncy
, in
.
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14
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-0.2
-0.1
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0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14
-0.3
-0.2
-0.1
0.0
0.1
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0.4
(x)
(x) Discrepancy (bias) function
© United Technologies Corporation (2012)This document contains no technical data subject to the EAR or the ITAR.Reinman, Rev Date 6/19/2012
To Help Prevent Design Iterations due to a Model’s Meanline Miss, by using Bayesian model calibration
process Margin Miss, by replacing legacy margins with a
probabilistic model of uncertainty and variability
To Reduce Cost Focus on important features Relax requirements on unimportant features Use Robust Design to reduce sensitivity
To Maximize Stage Life (Time on Wing) Rotor life depends on max distress / min life airfoil Weakest-link structure pervasive in gas turbines Reducing variation increases rotor life
Probabilistic Design, Uncertain WorldWhy?
Total Effect of Leading Edge Parameters on Oxidation Life(Total effect is how much variation in life would be left if you knew precisely the values of all other
parameters.)
0
5
10
15
20
25
30
35
40
45
Parameter Name
To
tal E
ffect
(%)
Remove cost from low-impact features
Model Inputs
Age
Part-Part
Die/Config/Batch
Supplier
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14
-0.3
-0.2
-0.1
0.0
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0.2
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0.4
Concentrated Load, lbs
Dis
cre
pa
ncy, in
.
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14
-0.3
-0.2
-0.1
0.0
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0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14
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-0.1
0.0
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0.3
0.4
Discrepancy (bias) function
Concentrated Load, lbs
Bia
s, in
.
CYCLES
DIS
TR
ES
S
Slide 4 of 26
© United Technologies Corporation (2012)This document contains no technical data subject to the EAR or the ITAR.Reinman, Rev Date 6/19/2012
To increase the speed of design parametric studies and optimization using engineering model emulators
iSight-FD, etcComputer Model
• Structural FEM• CFD model• Matlab code• Fortran code• Other models
Inputs Design Space
• Geometric dimensions• Loads• Temperatures• Material properties• Heat transfer
coefficients• Etc.
• Drive the DOE through the model
• Emulator• Sensitivit
y
Output in Design Space
• Stress• Deflection• Temperatur
e• Life• Performanc
e• Etc.
Maximin Latin Hypercube DOE
GEMSA, GPMSA, etc
Hours / Run
Seconds / Run
Probabilistic Design, Uncertain WorldWhy?
Slide 5 of 26
© United Technologies Corporation (2012)This document contains no technical data subject to the EAR or the ITAR.Reinman, Rev Date 6/19/2012
DFV Estimated Benefits
▲ Component-level Design For Variation has yielded an estimated 64%-88% return on internal investment. The savings resulted from:
Optimized inspection procedures and tolerances Reduced quality-related analysis and investigation time Reduced design iterations Improved reliability Improved on-time engine deliveries Improved root cause investigation process
▲ Based on Six Sigma history and internal trends, the return is expected to increase rapidly in subsequent years
▲ System-level Design For Variation is predicted to yield 40x return on investment due to
Achieving system-level performance and reliability goals earlier in the development cycle
Shorter development programs
Slide 6 of 26
© United Technologies Corporation (2012)This document contains no technical data subject to the EAR or the ITAR.Reinman, Rev Date 6/19/2012 Slide 7 of 26
Design For Variation (DFV) Strategic Plan
▲ Strategy☑ Identify Key Processes ☑ Define elements of a DFV-enabled modeling process☑ Provide Resources under Strategic Initiative
Fan & CompressorHFB ProducibilityParametric Airfoil
Compressor Aero DesignCompressor Tip Clearances
StructuresProbabilistic Rotor Lifing
Probabilistic Fracture MechanicsProbabilistic HCF
Parametric Geometry Simulation ModelEngine Dynamics and Loads
Combustor and AugmentorCombustor pattern factor
Combustor Liner TMFAugmentor Ignition Margin Audit
Mid Turbine Frame Robust Design
Mechanical Systems and ExternalsCarbon Seal Performance
Ball & Roller Bearing DesignFDGS Durability
Externals: Forced Response Analysis
TurbineTurbine Blade Durability
Turbine Vanes and BOAS DurabilityRotor Thermal Model
Airfoil LCF LifingHSE Combustor / Turbine DFV
Air SystemsThermal Management Model
Internal Air System ModelEngine Data Matching
Performance AnalysisPerformance Monte Carlo Risk Assessment
Engine Test Confidence, UncertaintyUncertainty in Engine System Predictions
Production Test Data Trending and AnalysisStatistical Data-match
System-Level Risk Communication and Decision Making
Validation TestingEngine Validation Planning
DFV Infrastructure (Statistics & Partners)
Emulation, Calibration SoftwareHigh Intensity Computing
Parametric ModelingOptimization
TrainingESW
CommunicationsInput Data
Tech Support
Vehicle SystemsProbabilistic Ambient
Temp Distribution
Vision: All Key Modeling Processes will be DFV-enabled
© United Technologies Corporation (2012)This document contains no technical data subject to the EAR or the ITAR.Reinman, Rev Date 6/19/2012
10 Elements of a DFV-Enabled Modeling Process Physics-Based Models
Model Preparation
1. A robust parametric physics-based model Model Input Variability and Uncertainty Quantification
2. Process for retrieving data needed to quantify variability and uncertainty in model inputs
3. Process for performing statistical analysis/developing statistical model of input dataa. Preserve correlations
Model Sensitivity Analysis
4. Process for generating a matrix of space-filling computer experiments (model runs) for emulator development
5. Process for running the computer code at the space-filling design points
6. Process for a. Building and validating the model emulator
b. Performing a variance-based sensitivity analysis
Model Calibration
7. Process for determining what experimental/field data are required for model calibration and measurement uncertainty (amount, characteristics to be measured, ..)
8. Process for performing Bayesian model calibration: calibrate and bias correct (if needed) and assess residual variation Uncertainty Analysis
9. Process for generating a Monte-Carlo sample and driving it through • Parametric model (if fast enough),• Model emulator, or • Bias corrected and calibrated model
Enable Practice
10. Update local ESW and local training. Put in place a process to ensure the model is capable over time.
Slide 8 of 26
ONE-TIM
E PROCESS
© United Technologies Corporation (2012)This document contains no technical data subject to the EAR or the ITAR.Reinman, Rev Date 6/19/2012
Design For Variation
DEFINE Customer requirements (probabilistic)
ANALYZE Quantify model input variation / uncertainty, emulate
and calibrate model, perform sensitivity and uncertainty analyses
SOLVE Identify ‘optimum’ design that satisfies requirements
VERIFY/VALIDATE Variability/Uncertainty model
SUSTAIN Stable system of causes of performance variation
ANALYZE
SOLVE
VERIFYVALIDATE
DEFINE
SUSTAIN
Five Steps for Executing a DFV-Enabled Process
-3 -2 -1 0 1 2 3
0.0
0.1
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0.4
y
Slide 9 of 26
© United Technologies Corporation (2012)This document contains no technical data subject to the EAR or the ITAR.Reinman, Rev Date 6/19/2012
▲ How do we define the allowable risk of not meeting a requirement?
-3 -2 -1 0 1 2 3
0.0
0.1
0.2
0.3
0.4
y
Requirement
Risk
DEFINE
Design For Variation (DFV): Five StepsDefine Customer Requirements
Slide 10 of 26
Explicit customer requirement Explicit customer requirement
Safety Impact: Follow Regulatory Requirements
Safety Impact: Follow Regulatory Requirements
System-Level Job Ticket Metric Impact: Follow flow-down or roll-up process
System-Level Job Ticket Metric Impact: Follow flow-down or roll-up process
Engine Certification Test ImpactEngine Certification Test Impact
None of the above• Previous acceptable experience or other business considerations• 6 Sigma Criteria • Solve for the probability or rate that minimizes expected total cost
None of the above• Previous acceptable experience or other business considerations• 6 Sigma Criteria • Solve for the probability or rate that minimizes expected total cost
© United Technologies Corporation (2012)This document contains no technical data subject to the EAR or the ITAR.Reinman, Rev Date 6/19/2012
Develop Model Emulator,
Sensitivity Analysis
Refine Distributions of Important Model Inputs
Run Real World Uncertainty
Analysis
Perform Bayesian
Model Calibration
Design Space Filling Experiment Over
Model Input Space
ANALYZE Quantify model input variation & uncertainty, emulate & calibrate model, perform sensitivity and uncertainty analyses
Design For Variation
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0.49 0.48 0.02 0.72 0.53 0.68 0.48 0.970.76 0.18 0.79 0.38 0.75 0.33 0.18 0.54 0.53 0.08 0.12 0.61 0.86 0.18 0.68 0.78 0.70 0.20 0.09 0.570.06 0.77 0.24 0.54 0.05 0.99 0.69 0.29 0.24 0.04 0.86 0.80 0.55 0.22 0.96 0.37 0.63 0.76 0.58 0.060.20 0.71 0.88 0.40 0.47 0.25 0.35 0.76 0.11 0.00 0.84 0.72 0.32 0.25 0.10 0.83 0.36 0.51 0.18 0.320.82 0.83 0.21 0.25 0.82 0.97 0.73 0.05 0.94 0.71 0.43 0.62 0.64 0.20 0.64 0.79 0.49 0.01 0.51 0.040.57 0.87 0.35 0.03 0.37 0.31 0.33 0.02 0.17 0.53 0.22 0.27 0.81 0.82 0.32 0.52 0.83 0.69 1.00 0.920.02 0.58 0.87 0.42 0.16 0.76 0.86 0.91 0.69 0.06 0.88 0.93 0.92 0.74 0.72 0.73 0.14 0.49 0.59 0.510.34 0.07 0.00 0.68 0.88 0.22 0.03 0.18 0.95 0.31 0.76 0.49 0.90 0.10 0.79 0.09 0.02 0.93 0.87 0.190.86 0.45 0.28 0.53 0.12 0.48 0.62 0.41 0.99 0.72 0.95 0.89 0.61 0.86 0.37 0.25 0.65 0.77 0.00 0.200.45 0.66 0.25 0.49 0.76 0.47 0.97 0.32 0.90 0.59 0.63 0.81 0.35 0.41 1.00 1.00 0.92 0.54 0.19 0.650.48 0.44 0.64 0.31 0.60 0.68 0.72 0.98 0.31 0.43 0.06 0.65 0.29 0.83 0.71 0.26 0.03 0.11 0.66 0.980.91 0.79 0.97 0.00 0.85 0.13 0.16 0.67 0.87 0.93 0.36 0.01 0.69 0.85 0.42 0.67 0.69 0.41 0.81 0.290.59 0.36 0.56 0.33 0.91 0.39 0.11 0.51 0.12 0.58 0.27 0.71 0.40 0.96 0.08 0.42 0.90 0.08 0.93 0.440.56 0.05 0.58 0.47 0.89 0.37 0.29 0.99 1.00 0.79 0.05 0.92 0.15 0.71 0.31 0.45 0.66 0.67 0.57 0.240.33 0.00 0.95 0.76 0.07 0.57 0.07 0.57 0.43 0.88 0.55 0.99 0.09 0.05 0.48 0.11 0.29 0.27 0.44 0.840.23 0.69 0.55 0.77 0.03 0.14 0.21 0.07 0.35 0.83 0.01 0.97 0.66 0.45 0.11 0.34 0.62 0.88 0.69 0.280.70 0.14 0.89 0.91 0.64 0.06 0.58 0.96 0.80 0.16 0.52 0.48 0.36 1.00 0.78 0.00 0.78 0.12 0.64 0.800.65 0.26 0.19 0.81 0.20 0.42 0.06 0.15 0.05 0.26 0.73 0.26 0.27 0.88 0.62 0.13 0.00 0.35 0.33 0.760.99 0.90 0.26 0.71 0.84 0.71 0.49 0.43 0.19 0.65 0.34 0.05 0.28 0.65 0.69 0.84 0.76 0.99 0.38 0.180.95 0.31 0.57 0.95 0.93 0.85 0.61 0.94 0.91 0.45 0.64 0.51 0.70 0.15 0.40 0.99 0.91 0.55 0.03 0.710.58 0.48 0.67 0.69 0.87 0.60 0.24 1.00 0.34 0.24 0.02 0.94 0.97 0.52 0.52 0.64 0.21 0.94 0.49 0.030.93 0.56 0.34 0.61 0.28 0.96 0.87 0.01 0.01 0.76 0.25 0.44 0.85 0.30 0.45 0.10 0.39 0.19 0.63 0.380.44 0.76 0.01 0.82 0.24 0.15 0.32 0.44 0.55 0.34 0.58 0.90 0.94 0.42 0.06 0.53 0.15 0.14 0.71 0.860.63 0.81 0.39 0.32 0.43 0.72 0.70 0.90 0.04 0.95 0.85 0.25 0.10 0.07 0.77 0.60 0.87 0.28 0.88 0.050.12 0.24 0.45 0.11 0.81 0.24 0.04 0.64 0.44 0.03 0.78 0.95 0.14 0.93 0.27 0.21 0.54 0.57 0.07 0.110.53 0.13 0.99 0.29 0.48 0.10 0.95 0.93 0.85 0.61 0.92 0.07 0.77 0.63 0.28 0.35 0.30 0.29 0.24 0.580.74 0.20 0.17 0.18 0.14 0.88 0.91 0.84 0.92 0.56 0.39 0.18 0.07 0.08 0.67 0.32 0.38 0.44 0.37 0.740.92 0.82 0.75 0.87 0.90 0.26 0.85 0.14 0.76 0.49 0.18 0.47 0.24 0.92 0.29 0.29 1.00 0.84 0.95 0.090.54 0.63 0.33 0.52 0.45 0.69 0.23 0.78 0.77 0.57 0.93 0.29 0.16 0.60 0.82 0.77 0.34 0.13 0.83 0.560.88 0.34 0.08 0.44 0.72 0.73 0.84 0.49 0.74 0.28 0.65 0.03 0.98 0.58 0.03 0.96 0.17 0.32 0.54 0.450.36 0.32 0.05 0.21 0.30 0.29 0.52 0.80 0.72 0.35 0.41 0.54 0.68 0.29 0.97 0.05 0.97 0.87 0.12 0.630.21 0.62 0.62 0.57 0.56 0.17 0.82 0.42 0.70 0.75 0.46 0.45 0.72 0.27 0.12 0.85 0.72 0.26 0.08 0.120.68 0.91 0.11 0.60 0.92 0.82 0.56 0.31 0.58 0.01 0.79 0.63 0.87 0.11 0.19 0.28 0.58 0.39 0.80 0.470.61 0.95 0.06 0.97 0.66 0.04 0.37 0.60 0.07 0.11 0.10 0.83 0.31 0.70 0.65 0.66 0.55 0.91 0.82 0.540.78 0.52 0.32 0.39 0.61 0.02 0.98 0.70 0.16 0.60 0.15 0.56 0.57 0.53 0.07 0.44 0.18 0.52 0.98 0.480.35 0.94 0.73 0.09 0.51 0.75 0.74 0.04 0.86 0.21 0.48 0.60 0.20 0.32 0.13 0.97 0.43 0.62 0.25 0.820.79 0.60 0.84 0.62 0.59 0.58 0.27 0.03 0.51 0.70 0.04 0.00 0.45 0.47 0.00 0.01 0.74 0.46 0.70 0.640.27 0.84 0.82 0.26 0.55 0.19 0.46 0.00 0.37 0.40 0.87 0.64 0.44 0.34 0.83 0.39 0.16 0.79 0.41 0.950.05 0.96 0.68 0.80 0.29 0.55 0.34 0.11 0.10 0.91 0.90 0.70 0.99 0.43 0.63 0.06 0.40 0.21 0.68 0.660.14 0.41 0.63 0.93 0.70 0.94 0.93 0.38 0.29 0.48 0.98 0.30 0.59 0.39 0.51 0.15 0.27 0.59 0.02 0.59
-1
0
1
2
3
4
5
6
7
8
9
0 1 2 3 4 5 6 7 8 9 10
x
y
Total Effect of Leading Edge Parameters on Oxidation Life(Total effect is how much variation in life would be left if you knew precisely the values of all other
parameters.)
0
5
10
15
20
25
30
35
40
45
Parameter Name
To
tal E
ffect
(%)
Model Inputs
Total Effect of Leading Edge Parameters on Oxidation Life(Total effect is how much variation in life would be left if you knew precisely the values of all other
parameters.)
0
5
10
15
20
25
30
35
40
45
Parameter Name
To
tal E
ffect
(%)
Model Inputs
Bayesian Model
Calibration
Real-World Validation Data
Bayesian Model
Calibration
Real-World Validation Data
EngineeringModel
• Parameter uncertainty update• Bias correction• Residual variation
0.00 0.20 0.40 0.60 0.80 1.00
0.00 0.20 0.40 0.60 0.80 1.00
0.00 0.20 0.40 0.60 0.80 1.00
Model Output
Run Experiment Through
Engineering Model
Accounting for uncertainty in • Model
input• Model
itself
Slide 11 of 26
© United Technologies Corporation (2012)This document contains no technical data subject to the EAR or the ITAR.Reinman, Rev Date 6/19/2012
1. Latin Hypercube Experimental Designs
3. Variance-Based Sensitivity Analysis
2. Gaussian Process Emulators
4. Bayesian Model Calibration
ANALYZE : Key Technologies
-1
0
1
2
3
4
5
6
7
8
9
0 1 2 3 4 5 6 7 8 9 10
x
y
-1
0
1
2
3
4
5
6
7
8
9
0 1 2 3 4 5 6 7 8 9 10
x
y
-1
0
1
2
3
4
5
6
7
8
9
0 1 2 3 4 5 6 7 8 9 10
x
y
Simple function
f(x) = x + 3sin(x/2)
-1
0
1
2
3
4
5
6
7
8
9
0 1 2 3 4 5 6 7 8 9 10
x
y
-1
0
1
2
3
4
5
6
7
8
9
0 1 2 3 4 5 6 7 8 9 10
x
y
-1
0
1
2
3
4
5
6
7
8
9
0 1 2 3 4 5 6 7 8 9 10
x
y
Simple function
f(x) = x + 3sin(x/2)
Total Effect of Leading Edge Parameters on Oxidation Life(Total effect is how much variation in life would be left if you knew precisely the values of all other
parameters.)
0
5
10
15
20
25
30
35
40
45
Parameter Name
To
tal
Eff
ec
t (%
)
Model Inputs
Total Effect of Leading Edge Parameters on Oxidation Life(Total effect is how much variation in life would be left if you knew precisely the values of all other
parameters.)
0
5
10
15
20
25
30
35
40
45
Parameter Name
To
tal
Eff
ec
t (%
)
Model Inputs
Design For Variation
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.4 0.6 0.8 1.0
Slide 12 of 26
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.140
24
68
10
12
14
Concentrated Load, lbs
De
fle
ctio
n, in
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.140
24
68
10
12
14
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.140
24
68
10
12
14
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.140
24
68
10
12
14
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.140
24
68
10
12
14
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.140
24
68
10
12
14
E (psi) x 10^7
2 3 4
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14
02
46
810
12
Concentrated Load, lbs
Def
lect
ion,
in.
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14
02
46
810
12
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14
02
46
810
12
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14
02
46
810
12
2.0 2.5 3.0 3.5 4.0
Modulus E (psix10^7)
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
Concentrated Load, lbs
Dis
cre
pa
ncy, in
.
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
(x) Discrepancy (bias) function
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
Concentrated Load, lbs
Dis
cre
pa
ncy, in
.
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
(x) Discrepancy (bias) function
w
y
F
Y
Xw
© United Technologies Corporation (2012)This document contains no technical data subject to the EAR or the ITAR.Reinman, Rev Date 6/19/2012
▲ Performance characteristic y = f (x1, x2, …, xp) depends on p inputs
▲ The variance of y can be approximated by
22
22
22
22211 pp xx
fxx
fxx
fy
SOLVE Identify optimum design that satisfies requirements
Design For Variation
SOLVE
▲ We can reduce by
1. Reducing : the variance in the inputs x1, x2, …, xp
2. Reducing : the sensitivity of y to variation in x1, x2, ... , xp
2ix
ixf
2y
Slide 13 of 26
© United Technologies Corporation (2012)This document contains no technical data subject to the EAR or the ITAR.Reinman, Rev Date 6/19/2012
Design for Variation SOLVE: Robust Design Strategies
Noise Factors• Filter• Isolate• Reduce at source• Inoculate (anneal, heat treat)
Input Signal• Alter/smooth• Selectively block
Control Factors• Robust optimization• Material change• Create multiple operating modes
Output Response• Calibrate• Average
System
SOLVE
Slide 14 of 26
Adapted from: Jugulum, R. and Frey, D. (2007). Toward a taxonomy of concept designs for improved robustness, Journal of Engineering Design, 18:2, 139 - 156
© United Technologies Corporation (2012)This document contains no technical data subject to the EAR or the ITAR.Reinman, Rev Date 6/19/2012
▲ VERIFY/VALIDATE includes
– Data collection and analysis to validate model input probability distributions
Manufacturing process data
Material property data
Temperatures, pressures, rotor speeds, airflows
Flight characteristics (e.g. length, T2 at takeoff, taxi time, ..)
– Additional calibration of physics-based models
– Trending in-service parts (wear, performance, etc) where feasible to validate models and their inputs
VERIFY/VALIDATE Assumptions made in variability and uncertainty modeling
Design For Variation
VAL/VER
Slide 15 of 26
© United Technologies Corporation (2012)This document contains no technical data subject to the EAR or the ITAR.Reinman, Rev Date 6/19/2012
▲ The SUSTAIN phase requires process control to ensure stable and consistent distributions over time
– Manufacturing
– Assembly
– Acceptance Testing
▲ Process Certification is vitally important– Sustaining capabilities to meet design requirements
– Identifying production & design improvement opportunities
▲ Design Sensitivity and Uncertainty Analyses indicate where process control resources should be focused
SUSTAIN Stable system of causes of performance variation
Design For Variation
Date
Indiv
idual V
alu
e
1/31/20061/28/20061/25/20061/22/20061/19/20061/16/20061/13/20061/10/20061/7/20061/4/2006
35
30
25
20
15
_X=25.49
UCL=34.19
LCL=16.79
Date
Movin
g R
ange
1/31/20061/28/20061/25/20061/22/20061/19/20061/16/20061/13/20061/10/20061/7/20061/4/2006
10.0
7.5
5.0
2.5
0.0
__MR=3.27
UCL=10.69
LCL=0
I-MR Chart of Measured Value of a Key Characteristic
4036322824201612
LSL USLProcess Data
Sample N 30StDev(Within) 2.89922StDev(Overall) 3.30970
LSL 10.00000Target *USL 40.00000Sample Mean 25.48909
Potential (Within) Capability
CCpk 1.72
Overall Capability
Pp 1.51PPL 1.56PPU 1.46Ppk
Cp
1.46Cpm *
1.72CPL 1.78CPU 1.67Cpk 1.67
WithinOverall
Process Capability of Measured Value of a Key Characteristic
SUSTAIN
Slide 16 of 26
© United Technologies Corporation (2012)This document contains no technical data subject to the EAR or the ITAR.Reinman, Rev Date 6/19/2012
Design For Variation
▲ Establish probabilistic design requirements
▲ Emulate, calibrate engineering models
▲ Solve for design that meets probabilistic requirements– Look for opportunities for making design less sensitive to variation
▲ Validate and sustain model
▲ Write Engineering Standard Work, develop local training
Systematic Process for Designing for and Managing Uncertainty and Variability
Slide 17 of 26
© United Technologies Corporation (2012)This document contains no technical data subject to the EAR or the ITAR.Reinman, Rev Date 6/19/2012
Design For Variation
▲ Additional Training Courses Developed
▲ Automated Multi-physics Workflow
▲ System-Level Design
What’s New in 2012?
Slide 18 of 26
© United Technologies Corporation (2012)This document contains no technical data subject to the EAR or the ITAR.Reinman, Rev Date 6/19/2012
▲ Software– Emulation, Sensitivity Analysis, Model Calibration
– Statistical Analysis, Monte Carlo Simulation, Optimization
▲ High Performance Computing Resources
▲ Training– INTRODUCTION
– PRACTITIONERS I: SENSITIVITY ANALYSIS, EMULATION, AND DOE
– PRACTITIONERS II: ISIGHT-FD FOR SENSITIVITY AND UNCERTAINTY ANALYSIS
– PRACTITIONERS III: MODEL CALIBRATION AND UNCERTAINTY ANALYSIS
– MANAGERS: INTRODUCTION, REVIEW CHECKLIST
▲ Communication– Wiki, Website, Meetings
▲ Input Data Quality and Availability– Process Capability, Material Properties
– Systems Performance, Mission Analysis
▲ Engineering Standard Work
Infrastructure: Enabling Design For Variation
Design For Variation – What’s New?
Slide 19 of 26
© United Technologies Corporation (2012)This document contains no technical data subject to the EAR or the ITAR.Reinman, Rev Date 6/19/2012
Design For Variation - What’s New?
Multi-discipline Automated Workflows• Link disciplines: Aero, Thermal, Structures, Materials,
Design• Link components• Enable probabilistic analyses, optimization
20
Slide 20 of 26
© United Technologies Corporation (2012)This document contains no technical data subject to the EAR or the ITAR.Reinman, Rev Date 6/19/2012
What’s New - PADME ProgramSystem Level Probabilistic Design & Validation of Engines
• PADME is a System-Level Extension of Design For Variation
• Quantify uncertainty/risk in system-level metrics
• Determine design drivers
• Determine optimum path to reduce risk
Design changes
Test changes
• PADME Goals
• Improve Mature vs. EIS Performance Gap by 33%
• Improve Mature vs. EIS Reliability Gap by 33%
• Reduce EVP Time by up to 50%
PADME: Probabilistic Analysis and Design of Materials and Engines
Page 12
Strategy☑ Identify Key Processes ☑Define elements of a DFV-enabled modeling process☑Provide Resources under Strategic Initiative
Leveraged Technologies: Design For Variation
Fan & CompressorHFB ProducibilityParametric Airfoil
Compressor Aero Design StructuresProbabilistic HCF
Parametric Geometry Simulation ModelEngine Dynamics and Loads
Combustor and AugmentorCombustor pattern factor
Combustor Liner TMFAugmentor Ignition Margin Audit
Mid Turbine Frame Robust Design
Mechanical Systems and ExternalsCarbon Seal Performance
Ball & Roller Bearing DesignFDGSDurability
Externals: Forced Response Analysis
TurbineTurbine Blade Durability
Turbine Vanes and BOAS DurabilityRotor Thermal Model
Airfoil LCF Lifing
Air SystemsThermal Management Model
Internal Air System ModelEngine Data Matching
Performance AnalysisPerformance Monte Carlo Risk Assessment
Engine Test Confidence, UncertaintyUncertainty in Engine System Predictions
Production Test Data Trending and Analysis
Validation TestingEngine Validation Planning
DFV Infrastructure (Statistics & Partners)
Sens / Uncert / Opt SoftwareHigh Perf Computing
TrainingESW
CommunicationsInput Data
Tech Support
Vehicle SystemsProbabilistic Ambient
Temp Distribution
EAR Export Classification: ECCN: EAR 99
21Slide 21 of 26
DesignValidation Service
Pro
bab
ility
Dis
trib
utio
n (
)
ConceptCustomer Use
PerformanceRequirement
Pro
bab
ility
Dis
trib
utio
n (
)
Design Prototype Production Maintenance &
PerformanceRequirement
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Nominal Design
Performance
UncertaintyBounds on Design:Risk & Confidence
DesignValidation Service
Pro
bab
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Dis
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)
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Pro
bab
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PerformanceRequirement
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Go
od
Ba
d
Concept Design Test Service
Job
Tic
ket
Met
ric
Nominal/ExpectedConfidence bound
Requirement
Uncertainty bound
© United Technologies Corporation (2012)This document contains no technical data subject to the EAR or the ITAR.Reinman, Rev Date 6/19/2012
PADME VisionEntire Engine Life Cycle Governed By Uncertainty Quantification and Management
Rigorously Manage Uncertainty Throughout Life Cycle, Target Validation Testing to Address Largest Sources of Uncertainty
22Slide 22 of 26
Concept Design Test Service
Job
Tic
ket
Met
ric
Nominal/ExpectedConfidence bound
Requirement
Uncertainty boundDesignValidation Service
Pro
bab
ility
Dis
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)
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PerformanceRequirement
Pro
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DesignValidation Service
Pro
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PerformanceRequirement
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Nominal Design
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Go
od
Ba
d
Fuel ConsumptionDelay/Cancellation Rate
WeightCost
© United Technologies Corporation (2012)This document contains no technical data subject to the EAR or the ITAR.Reinman, Rev Date 6/19/2012
PADME: Manage Uncertainty Throughout Engine Life CycleQuantification of Uncertainty Enables Optimized Trades on System Level Metrics
23
= Needs DARPA Support = Supported by P&W or Prior Programs
EVP Optimizer Test
Sensitivity Analysis, Bayesian Model Calibration
Concept (CI/CO) Design (PD/DD) Validation (V&V) Service
Methods
Component & Sub-System Models
System Reliability Bayes Network
System Performance
Bayes Network
Re-optimize EVP
Bayesian Network Development and Updating
Large Scale Optimization Under Uncertainty
Robust Design, Real Options, Quantitative TRLs
PD/DD Emulators
Parametric Rel. Network
Parametric Perf. Network
EVP Optimizer Test
DFV-Enabled Design Models
Parametric Rel. Network
Parametric Perf. Network
EVP Optimizer Test
DFV-Enabled Design Models
Parametric Rel. Network
Parametric Perf. Network
DFV-Enabled Design Models
Parametric Rel. Network
Parametric Perf. Network
UBL / Prognosis
Bayesian Uncertainty Update
Bayesian Uncertainty Update
Bayesian Uncertainty Update
Bayesian Uncertainty Update
Pro
ba
bili
ty D
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tion
(p
df)
Concept Design Prototype Production Maintenance &Customer Use
PerformanceRequirement
UncertaintyBounds on Design:Risk & Confidence
Surprises;New Test Data
Nominal DesignPerformanceP
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Nominal DesignPerformance
Redesign Redesign Redesign Redesign
PADME Governed By System-Level NetworksPopulated By Calibrated Component-Level Emulators
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© United Technologies Corporation (2012)This document contains no technical data subject to the EAR or the ITAR.Reinman, Rev Date 6/19/2012
▲ Uncertainty-Based Design Approach Relies on Calibration of Multivariate Aero-Thermal-Structural Models Using Highly Instrumented Engine
Deterministic Design
Engine Test Deterministic Redesign
Engine Test Deterministic Redesign
Engine Test
ProbabilisticDesign
R&D Rig/Engine Test Engine Endurance Test
crack
oxidation
RobustDesign
LegacyApproach
DFV-PADME Approach
EAR Export Classification: EAR 99
1st
Vane2nd Vane
1st
Blade2nd Blade
Exit Vane
Combustor
Gas Temps Gas Temps Gas TempsBlade Temps Blade Temps
PADME Strategy
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© United Technologies Corporation (2012)This document contains no technical data subject to the EAR or the ITAR.Reinman, Rev Date 6/19/2012
Design For Variation – For More Information
▲ Statistical Engineering Issue
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© United Technologies Corporation (2012)This document contains no technical data subject to the EAR or the ITAR.Reinman, Rev Date 6/19/2012
▲ Goal: quantify, understand, and control the risk of not meeting design criteria or exceeding thresholds
▲ “The revolutionary idea that defines the boundary between modern times and the past is the mastery of risk: the notion that the future is more than a whim of the gods and that men and women are not passive before nature.”– Peter Bernstein, “Against the Gods: The remarkable story of risk”
ModelPrediction
DesignCriteria
True Process Value
Design For Variation
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