thermal analysis of spacecraft using data assimilation · 2019. 12. 18. · node no. content 1...
TRANSCRIPT
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Presented By
Hiroto TANAKA
Thermal & Fluids Analysis Workshop
TFAWS 2019
August 26-30, 2019
NASA Langley Research Center
Hampton, VA
TFAWS Interdisciplinary Paper Session
Thermal Analysis of Spacecraft
using Data Assimilation
Hiroto TANAKA1, Hiroki NAGAI1
and Takashi Misaka2
1Tohoku University, Japan2AIST, Japan
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Table of Contents
1. Research Background
2. Objective
3. Methodology
4. Experiment
5. Result and Discussion
6. Conclusion / Future Work
TFAWS 2019 – August 26-30, 2019 2
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Research Background
Thermal analysis of the Spacecraft
TFAWS 2019 – August 26-30, 2019 3
Temperature Prediction
✓ Temperature prediction of TMM has uncertainty due to
“model incompleteness” and “disturbance of boundary condition”
✓ In deep space missions, estimating thermal state of entire system is difficult
due to limited temperature data
Uncertainty of TMM
Maximum case
T [
K]
t [sec.]
Minimum case
Prediction
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Research Background
Temperature Estimation using “Data Assimilation”
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➣ By using flight temperature datasets, estimate the thermal
state in higher accuracy than conventional TMM analysis
Thermal Analysis by TMM Flight Data
Temperature
monitoring
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Research Background
Data assimilation technique
TFAWS 2019 – August 26-30, 2019 5
✓ Statistic approach to combine observed data and simulated data
Data Assimilation
Simulation
Estimation of System State
Observation
Observed data
Simulated data
Data assimilation
T [
K]
t [sec.]
True Value
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Objective
TFAWS 2019 – August 26-30, 2019 6
✓ Apply the data assimilation technique to the TMM in order to
improve the temperature estimation accuracy
✓ Confirm the availability of data assimilation assisted TMM and
compare its performance with conventional thermal analysis
Thermal Mathematical Model
Limited Temperature Datasets
Better Temperature Estimation?
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Methodology
1. Thermal Mathematical Model (TMM)
2. Ensemble Kalman Filter (EnKF)
3. Data Assimilation / Ensenble Kalman Filter
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Methodology
1. Thermal Mathematical Model (TMM)
8
…
4 4
1 1
( 1) ( ) ( ) ( ) ( ) ( ) ( )n n
i i i ij i j ij i j
j ji
tT t T t Q t C T t T t R T t T t
C
Governing equation
Heat balance between nodes
1 2 3
Node
Conductance : Cij
Prediction
STEP : 1 STEP : 2Update
Initial StateUpdate
STEP : 0
Prediction
TMM consists of…
✓Node : heat generation / temperature / heat capacity
✓Path : thermal conductance
Temperature distribution
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Methodology
2. Ensemble Kalman Filter (EnKF)
9
Kalman Filtering
Xest = Xsimu + K × ( Xsimu – Y )
Xest : Estimated data
Xsimu : Simulated data
Y : Observed data
K : Kalman gain
Xest : Estimated data Xsimu : Simulated data Y : Observed data
✓ Simulated data is modified by difference between simulation and observation
✓ Kalman gain “K” is calculated from Variance of Xsimu
Estimation variance σ2 : System Noise σ2 : Observation Noise
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Methodology
2. Ensemble Kalman Filter (EnKF)
10
Prediction
Observation
Estimation
Filtering
STEP : 1 STEP : 2
・・・
PDF : Probability Density Function
Update
σ2 : System Noise
σ2 : Observation Noise
Minimum Variance Estimation
Prediction
Observation
Estimation
Filtering
σ2 : Noise
σ2 : Noise
Update
STEP : 0
Initial State
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Methodology
2. Ensemble Kalman Filter (EnKF)
11
Initial State Prediction
Observation
Estimation
Update
Filtering
・・・
PDF : Probability Density Function
Update
σ2 : Noise
σ2 : Noise
Prediction
Observation
Estimation
Filtering
σ2 : Noise
σ2 : NoiseDiscretization of PDF
: Particle
STEP : 1 STEP : 2STEP : 0
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Experiment
1. Overview
2. Building a TMM
3. Thermal Test Setup
4. Correlation and Uncertainty Analysis of TMM
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Experiment
13
Compare the Accuracy of Temperature Estimation
Thermal Test A (Ground Test Data)
Build a Simple Thermal Mathematical Model
Model - Test Correlation
Thermal Test B (Flight Data)
Conventional
TMM Analysis
EnKF Assisted TMM
Analysis
1. Overview
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Experiment
2. Building a TMM
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1
2
4
C12
C23
3
C34
C45
Qin
Qout
✓ 1-Dimensional thermal mathematical model
✓ Each conductance Cij has different uncertainty
✓ Heat input and output Q have uncertainty
➣ Built a simple and high uncertain thermal model
Governing Equation
4 4
1 1
(T T ) (T T )N N
ii i ij i j ij i j
j j
dTC Q C R
dt
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Experiment
3. Thermal Test
TFAWS 2019 – August 26-30, 2019 15
Heater
Heatsink
Aluminum
Acrylic resin
Temperature Sensor
Node No. Content
1 Heater
2 Aluminum
3 Acrylic resin / upper part
4 Acrylic resin / lower part
- Heatsink
Test Model
1
2
4
C12
C23
3
C34
C45
Qin
Qout
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Experiment
3. Thermal Test
TFAWS 2019 – August 26-30, 2019 16
1
2
4
C12
C23
3
C34
C45
Qin
Qout
Heater
Heatsink
Aluminum
Acrylic
resin
Parameter Factor ± 3σ
Qin Heat generation : Qheater ± 15 %
Qout Heatsink temperature : Theatsink ± 0.45 K
C12 Contact conductance : h12 ± 50 %
C23 Contact conductance : h23 ± 50 %
C34 Thermal conductivity : kresin ± 0.04 W/(m・K)
C45 Contact conductance : h45 ± 50 %
Model Uncertainty
Uncertainty of the Thermal Test
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Experiment
4. Correlation and Uncertainty Analysis of TMM
① Test A (Ground Test Simulation)
Test Condition Value
Qheater 2.0 W
Theatsink 383.2 K
Measurement Error (3σ) ± 1.0 K
Thermal Test Result
③ Test B (Flight Data Simulation)
Test Condition Value
Qheater 2.4 W
Theatsink 383.2 K
Measurement Error (3σ) ± 1.0 K
④ Thermal Analysis② Model-Test Correlation result
Content Value
h12 300 W/(m2・K)
h23 500 W/(m2・K)
kresin 0.26 W/(m・K)
h45 10000 W/(m2・K)
1
2
4
h12
h23
3kresin
h45
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Result and Discussion
1. Conventional TMM Analysis
2. EnKF Assisted TMM Analysis
3. Comparison of Two Methods
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Result and Discussion
1. Conventional TMM Analysis
19
T1 Transition
T3 Transition
T2 Transition
T4 Transition
Thermal Analysis by TMM
1
2
4
T1
3
T2
T3
T4
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Result and Discussion
2. EnKF Assisted TMM Analysis
20
T1 Transition / observing T1
T3 Transition / observing T1
T2 Transition / observing T1
T4 Transition / observing T1
1
2
4
T1
3
T2
T3
T4
Thermal Analysis by EnKF applied TMM / Observation Node : Node 1
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Result and Discussion
21
➣ The data assimilation result agrees with measured data very well
➣ The uncertainty of the temperature estimation decrease drastically
comparing with conventional TMM analysis
T1 Transition / observing T1 T3 Transition / observing T1
1
2
4
T1
3
T2
T3
T4
Comparison with “Conventional TMM” & “EnKF assisted TMM”
3. Comparison of Two Methods
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Result and Discussion
3. Comparison of Two Methods
22
Standard Deviation of Analysis Result
TMMEnKF assisted TMM
(T1 Observation)
T1 2.13 K 0.00 K
T2 1.96 K 0.08 K
T3 2.07 K 0.37 K
T4 - 0.41 K -0.43 K
Difference from Measured Temperature
TMMEnKF assisted TMM
(T1 Observation)
T1 2.91 K 0.27 K
T2 2.74 K 0.68 K
T3 2.28 K 0.75 K
T4 0.43 K 0.55 K
➣ Difference from measured data is decreased by data assimilation
➣ The uncertainty of the analysis is decreased by data assimilation
➣ T4 result was not improved very well due to observation position
and dominant effect of heatsink
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Conclusion
23
➣ The data assimilation result agreed with measured data
➣ The uncertainty of the temperature estimation decreased drastically
comparing with conventional TMM analysis
➣We confirmed an availability of data assimilation on thermal analysis
by simple model and thermal test
✓ Data assimilation technique was introduced
✓ Data assimilation was applied to TMM and node temperature was
estimated using partial measured data
✓ Performance of conventional TMM and data assimilation assisted
TMM were compared
Content of the presentation
Result