Reduced-order Modeling Framework for Improving Spatial Resolution

1. Reduced-order Modeling Framework for Improving Spatial Resolution of Data Center Transient Air Temperatures Levente Klein, Hendrik Hamann IBM TJ Watson Research Center 1101 Kitchawan Road Yorktown Heights, NY 10598 kleinl@us.ibm.com hendrikh@us.ibm.com Rajat Ghosh, Yogendra Joshi Georgia Institute of Technology 801 Ferst Drive Atlanta, GA 30332-0405 rajat.ghosh@gatech.edu yogendra.joshi@me.gatech.edu SEMI-THERM 29 March 21, 2013

2. Dynamic Events in Data Centers • Fluctuating IT load • Power Outage Liu et al., Phil. Trans. R. Soc. A 2012 370 Microsoft Live Messenger Courtesy Junwei Li, CERCS, GT

3. Dynamic Resource Allocation Over-Provisioning Loss of cooling resources ( Lower CRAC set points than required) Need for real-time datacenter thermal characterization for better capacity planning Armbrust et al., 2009, Report UCB/EECS-2009-28

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 rack 800 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 Problem A 2 ft. x 2 ft. x 6ft. 10 kW Rack • Computational simulation • 1.4 grid points. • 8 hr. (Quad-core processor and 12 GB RAM) for convergence. • Experiment • 6” resolution. • Difficulty in sensor deployment in largely space-constraint facility. • Measurement-based Modeling • A 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.

11. Experimental Facility 2013 W 2 ft. X2 ft. X 6 ft. 1 3 2 5.85 m3/s (12400 cfm) 5.85 m3/s (12400 cfm) 2075 W 2 ft. X1.8 ft. X 6 ft. 2753 W 2 ft. X2.5 ft. X 6 ft. Grey blocks: IT rack. Blue blocks: ACUs. Yellow blocks: PDU. Red block: Storage.

12. Temperature Measurement x • 10 K-type thermocouples placed on a pole, located at the server outlets. • Measurement period: 1.5 s. • Measurement uncertainty:

13. Experimental Condition Photograph Courtesy to Dr. Levente Klein, IBM For this case study, the block/ unblocking period is 30 min. Simulated dynamic temperature field: Periodic blocking and unblocking of rack airflow intake.

14. Data h h h h h h h h h Significant phase shift due to boundary effect (cold air mixing) In-phase with blocking/ unblocking In-phase with blocking/ unblocking In-phase with blocking/ unblocking In-phase with blocking/ unblocking Boundary Effect Appears Boundary Effect Appears In-phase with blocking/ unblocking Boundary effect dominant

15. Data Comparison • No particular temperature trend is observed • Maximum at 3.3 ft. • Minimum at 7.5 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: Interrogation Point Class-2 Ensemble sensor data Class-1 Ensemble sensor data Interrogation Point

17. POD-based Modeling • Eigen Space • Prediction • Interrogation Point: 3.3 ft. (1006 mm). • Ensemble Sensor: (5,7). Data Matrix: 4425 x 2 • Computational prediction time for a new temperature data ~ 1 s • (2.66 GHz Core2Duo processor, 4 GB RAM). • k=1: only 2 interpolations required. 1st POD mode captures dominant characteristics.

18. Comparison

19. Error Distribution Large error due boundary effect Time Sample Size=4425.

20. Space-time Mapping Large Error at h=0 due the Boundary Effect Increase in Temperature due to Blocking Decrease in Temperature due to Unblocking

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!!