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 30332-0405rajat.ghosh@gatech.edu

yogendra.joshi@me.gatech.edu

Levente Klein, Hendrik HamannIBM TJ Watson Research Center

1101 Kitchawan RoadYorktown Heights, NY 10598

kleinl@us.ibm.comhendrikh@us.ibm.com

SEMI-THERM 29March 21, 2013

2

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

3

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

4

Outline

• Problem Statement.• Methodology.• Case Study.• Conclusion.

5

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

6

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.

7

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.

8

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.

9

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.

10

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.

1

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.

12

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

13

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.

14

Data

h 0 1800 3600 540025

25.5

26

26.5

27

27.5

28

28.5

29

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

29

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

33

34

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

34

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

33

34

Time (s)

Te

mp

era

ture

(0 C)

h=3.33 ft.

h

In-phase with blocking/ unblocking

0 1800 3600 540022

23

24

25

26

27

28

29

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

26

26.5

27

Time (s)

Te

mp

era

ture

(0 C)

h=5.83 ft.

h

Boundary Effect Appears

0 1800 3600 540022.5

23

23.5

24

24.5

25

25.5

26

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

21

22

23

24

25

26

27

Time (s)

Te

mp

era

ture

(0 C)

h=7.5 ft.

15

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

20

22

24

26

28

30

32

34

36

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

16

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

17

• Interrogation Point: 3.3 ft. (1006 mm).

POD-based Modeling

• Ensemble Sensor: (5,7).

0 1800 3600 540024

25

26

27

28

29

30

31

Time (s)

Te

mp

era

ture

(0 C)

h=4.16 ft.

0 1800 3600 540027

28

29

30

31

32

33

34

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.

18

Comparison

0 1000 2000 3000 4000 5000 6000 7000

26

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)

19

Error Distribution

Time Sample Size=4425.

Large error due boundary effect

20

Space-time Mapping

Increase in Temperature

due to Blocking

Decrease in Temperature

due to Unblocking

Large Error at h=0 due the

Boundary Effect

21

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.

22

Thank You!!