Reduced-order Modeling Framework for Improving Spatial Resolution
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Transcript of Reduced-order Modeling Framework for Improving Spatial Resolution
Reduced-order Modeling Framework for Improving Spatial Resolution of Data Center Transient Air
Temperatures
Rajat Ghosh, Yogendra JoshiGeorgia Institute of Technology
801 Ferst DriveAtlanta, GA [email protected]
Levente Klein, Hendrik HamannIBM TJ Watson Research Center
1101 Kitchawan RoadYorktown Heights, NY 10598
[email protected]@us.ibm.com
SEMI-THERM 29March 21, 2013
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Dynamic Events in Data Centers
• Fluctuating IT load
0 5 10 15 20 25 30760
780
800
820
VM Power Profile
Time (min)
Po
we
r (W
)
Courtesy Junwei Li, CERCS, GT
Liu et al., Phil. Trans. R. Soc. A 2012 370
Microsoft Live Messenger
• Power Outage
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Dynamic Resource Allocation
Armbrust et al., 2009, Report UCB/EECS-2009-28
Loss of cooling resources ( Lower CRAC set points than required)
Over-Provisioning
Need for real-time datacenter thermal characterization for better capacity planning
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Outline
• Problem Statement.• Methodology.• Case Study.• Conclusion.
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Optimization Problem• Efficient CRAC control system
Return/ supply air temperature control based on air temperature field.
• Requirement Rapid dynamic characterization of DC air temperature field. Highly-resolved air temperature prediction in time and space.
Time scale:10 s
10 kW IT rack800 W/ ft3 heat load
Length scale: 1” / 2.5 cm
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Potential Solution
Computational Modeling• CFD/ HT-based solution.• Discretization of the domain into grid points.• Iterative solution of discretized conservation equations.
Experiment• Deployment of sensor network.• Data acquisition.
Measurement-based Modeling• Using sensor data as input to statistical modeling framework.• Data compression techniques:
• Proper orthogonal decomposition (POD).• Multivariate interpolation.
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Example ProblemA 2 ft. x 2 ft. x 6ft. 10 kW Rack
Computational simulation1.4 grid points.8 hr. (Quad-core processor and 12 GB RAM) for convergence.
Experiment6” resolution.Difficulty in sensor deployment in largely space-constraint facility.
Measurement-based ModelingA platform for improving granularity of sensor data.2 decades of length scale faster than CFD modeling.
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Interpolation Vs. POD• Data Matrix: m x n
• Interpolation:– Computation ~ O(m)
• POD:– Computation ~ log(k) : k<m.
• POD Coefficient determination:– Column wise interpolation with a k x n base matrix.– Base matrix elements smaller than data
• Smaller error due to interpolation.
• Advantages of POD:– Computationally more efficient.– Better accuracy.
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Modeling Algorithm Independent Variable• Time. • Row-wise compilation in ensemble .
Parameter• Spatial location.• Column-wise compilation in ensemble.
POD Modes• Optimal basis.
POD Coefficients• Spatial dependency of interrogation.
Principal Component• Cut-off Criteria.
Useful tool for analyzing time signals of high dimensionality.
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Ensemble Compilation
Interrogation Points • Two-point method– Two transient temperature
data (vector) constitutes the ensemble.
– Least data acquisition cost.– Two near most sensors are
reasonable choice.– 1-D spatial prediction.
Class-1:- Two nearest sensors lying in opposite direction.
Class-2: - Two nearest sensors lying in same direction.
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2 3
Experimental Facility
Grey blocks: IT rack. Blue blocks: ACUs. Yellow blocks: PDU. Red block: Storage.
5.85 m3/s (12400 cfm)
5.85 m3/s (12400 cfm)
2075 W2 ft. X1.8 ft. X 6 ft.
2013 W2 ft. X2 ft. X 6 ft.
2753 W2 ft. X2.5 ft. X 6 ft.
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Temperature MeasurementSensor # Height
mm. (ft.)
1 2286 (7.5)
2 2012 (6.6)
3 1768 (5.8)
4 1524 (5)
5 1280 (4.2)
6 1006 (3.3)
7 762 (2.5)
8 488 (1.6)
9 244 (0.8)
10 0(0) 10 K-type thermocouples placed on
a pole, located at the server outlets. Measurement period: 1.5 s. Measurement uncertainty: 00.1 .C
x
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Experimental Condition
Simulated dynamic temperature field: Periodic blocking and unblocking of rack airflow intake.
Photograph Courtesy to Dr. Levente Klein, IBM
For this case study, the block/ unblocking period is 30 min.
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Data
h 0 1800 3600 540025
25.5
26
26.5
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27.5
28
28.5
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Time (s)
Te
mp
era
ture
(0 C)
h=0 ft.
Boundary effect dominant
h
In-phase with blocking/ unblocking
0 1800 3600 540028
28.5
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29.5
30
30.5
31
31.5
32
32.5
Time (s)
Te
mp
era
ture
(0 C)
h=0.83 ft.
h
In-phase with blocking/ unblocking
0 1800 3600 540027
28
29
30
31
32
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Time (s)
Te
mp
era
ture
(0 C)
h=1.66 ft.
h
In-phase with blocking/ unblocking
0 1800 3600 540027
28
29
30
31
32
33
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Time (s)
Te
mp
era
ture
(0 C)
h=2.5 ft.
h
In-phase with blocking/ unblocking
0 1800 3600 540027
28
29
30
31
32
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Time (s)
Te
mp
era
ture
(0 C)
h=3.33 ft.
h
In-phase with blocking/ unblocking
0 1800 3600 540022
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24
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Time (s)
Te
mp
era
ture
(0 C)
h=5 ft.
h
Boundary Effect Appears
0 1800 3600 540022.5
23
23.5
24
24.5
25
25.5
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26.5
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Time (s)
Te
mp
era
ture
(0 C)
h=5.83 ft.
h
Boundary Effect Appears
0 1800 3600 540022.5
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23.5
24
24.5
25
25.5
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Time (s)
Te
mp
era
ture
(0 C)
h=6.66 ft.
h
Significant phase shift due to boundary effect (cold air mixing)
0 1800 3600 540020
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Time (s)
Te
mp
era
ture
(0 C)
h=7.5 ft.
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Data Comparison
• No particular temperature trend is observed• Maximum at 3.3 ft.• Minimum at 7.5 ft.
0 1000 2000 3000 4000 5000 6000 700018
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Time (s)
Te
mp
era
ture
(0 C)
7.5 ft6.6 ft
5.8 ft
5 ft
4.2 ft3.3 ft
2.5 ft
1.6 ft
0.8 ft0 ft
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POD-based Prediction• For Validation purpose, POD-based predictions are computed
at points coincident with the sensors.
• Two point ensemble compilation method used: Ensemble Sensor # Height
mm. (ft.)
(2, 3) 2286 (7.5)
(1,3) 2012 (6.6)
(2,4) 1768 (5.8)
(3,5) 1524 (5)
(4,6) 1280 (4.2)
(5,7) 1006 (3.3)
(6,8) 762 (2.5)
(7,9) 488 (1.6)
(8,10) 244 (0.8)
(8,9) 0(0)
Interrogation Point
Ensemble sensor data
Class-2
Ensemble sensor dataInterrogation
Point
Class-1
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• Interrogation Point: 3.3 ft. (1006 mm).
POD-based Modeling
• Ensemble Sensor: (5,7).
0 1800 3600 540024
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26
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28
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30
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Time (s)
Te
mp
era
ture
(0 C)
h=4.16 ft.
0 1800 3600 540027
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29
30
31
32
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Time (s)T
em
pe
ratu
re (0 C
)
h=2.5 ft.
Data Matrix: 4425 x 2
• Eigen Space
1st POD mode captures dominant characteristics.
• Prediction
• Computational prediction time for a new temperature data ~ 1 s • (2.66 GHz Core2Duo processor, 4 GB RAM).• k=1: only 2 interpolations required.
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Comparison
0 1000 2000 3000 4000 5000 6000 7000
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28
30Data at h=0 ft.
0 1000 2000 3000 4000 5000 6000 700025
30
35Prediction at h=0 ft.
Te
mp
era
ture
(0 C)
0 1000 2000 3000 4000 5000 6000 7000-10
-5
0Error at h=0 ft.
Time (s)
0 1000 2000 3000 4000 5000 6000 700025
30
35Data at h=0.83 ft.
0 1000 2000 3000 4000 5000 6000 700025
30
35Prediction at h=0.83 ft.
Te
mp
era
ture
(0 C)
0 1000 2000 3000 4000 5000 6000 7000-5
0
5Error at h=0.83 ft.
Time (s)
0 1000 2000 3000 4000 5000 6000 700025
30
35Data at h=1.66 ft.
0 1000 2000 3000 4000 5000 6000 700025
30
35Prediction at h=1.66 ft.
Te
mp
era
ture
(0 C)
0 1000 2000 3000 4000 5000 6000 7000-0.5
0
0.5Error at h=1.66 ft.
Time (s)
0 1000 2000 3000 4000 5000 6000 700025
30
35Data at h=2.5 ft.
0 1000 2000 3000 4000 5000 6000 700025
30
35Prediction at h=2.5 ft.
Te
mp
era
ture
(0 C)
0 1000 2000 3000 4000 5000 6000 7000-2
0
2Error at h=2.5 ft.
Time (s)
0 1000 2000 3000 4000 5000 6000 700025
30
35Data at h=3.33 ft.
0 1000 2000 3000 4000 5000 6000 700020
30
40Prediction at h=3.33 ft.
Te
mp
era
ture
(0 C)
0 1000 2000 3000 4000 5000 6000 70000
5Error at h=3.33 ft.
Time (s)
0 1000 2000 3000 4000 5000 6000 700020
30
40Data at h=4.16 ft.
0 1000 2000 3000 4000 5000 6000 700020
30
40Prediction at h=4.16 ft.
Te
mp
era
ture
(0 C)
0 1000 2000 3000 4000 5000 6000 7000-5
0
5Error at h=4.16 ft.
Time (s)
0 1000 2000 3000 4000 5000 6000 700020
25
30Data at h=5 ft.
0 1000 2000 3000 4000 5000 6000 700020
25
30Prediction at h=5 ft.
Te
mp
era
ture
(0 C)
0 1000 2000 3000 4000 5000 6000 7000-2
0
2Error at h=5 ft.
Time (s)
0 1000 2000 3000 4000 5000 6000 700020
25
30Data at h=5.83 ft.
0 1000 2000 3000 4000 5000 6000 700020
25
30Prediction at h=5.83 ft.
Te
mp
era
ture
(0 C)
0 1000 2000 3000 4000 5000 6000 7000-5
0
5Error at h=5.83 ft.
Time (s)
0 1000 2000 3000 4000 5000 6000 700022
24
26Data at h=6.66 ft.
0 1000 2000 3000 4000 5000 6000 700020
25
30Prediction at h=6.66 ft.
Te
mp
era
ture
(0 C)
0 1000 2000 3000 4000 5000 6000 7000-5
0
5Error at h=6.66 ft.
Time (s)
0 1000 2000 3000 4000 5000 6000 700020
25
30Data at h=7.5 ft.
0 1000 2000 3000 4000 5000 6000 700010
20
30Prediction at h=7.5 ft.
Te
mp
era
ture
(0 C)
0 1000 2000 3000 4000 5000 6000 7000-5
0
5Error at h=7.5 ft.
Time (s)
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Error Distribution
Time Sample Size=4425.
Large error due boundary effect
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Space-time Mapping
Increase in Temperature
due to Blocking
Decrease in Temperature
due to Unblocking
Large Error at h=0 due the
Boundary Effect
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Conclusion
• A modeling framework is developed for improving the spatial resolution of experimentally-acquired transient temperature data.
• The framework is applied on a representative case study with dynamic temperature evolution.
The framework predicts the temperature evolution with reasonable accuracy.
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Thank You!!