0
SPECIAL SECTION PAPERS

Inverse Conduction Heat Transfer and Kriging Interpolation Applied to Temperature Sensor Location in Microchips

[+] Author and Article Information
David Gonzalez Cuadrado

Mem. ASME
School of Mechanical Engineering,
Purdue University,
500 Allison Road,
West Lafayette, IN 47906
e-mails: dgcuadrado@purdue.edu;
david.gonzalez.cuadrado@gmail.com

Amy Marconnet

Mem. ASME
School of Mechanical Engineering,
Purdue University,
585 Purdue Mall,
West Lafayette, IN 47907
e-mail: amarconn@purdue.edu

Guillermo Paniagua

Mem. ASME
School of Mechanical Engineering,
Purdue University, 500 Allison Road,
West Lafayette, IN 47906
e-mail: gpaniagua@me.com

1Corresponding author.

Contributed by the Electronic and Photonic Packaging Division of ASME for publication in the JOURNAL OF ELECTRONIC PACKAGING. Manuscript received September 27, 2017; final manuscript received December 28, 2017; published online March 2, 2018. Assoc. Editor: Sreekant Narumanchi.

J. Electron. Packag 140(1), 010905 (Mar 02, 2018) (8 pages) Paper No: EP-17-1099; doi: 10.1115/1.4039026 History: Received September 27, 2017; Revised December 28, 2017

Large thermal gradients represent major operational hazards in microprocessors; hence, there is a critical need to monitor possible hot spots both accurately and in real time. Thermal monitoring in microprocessors is typically performed using temperature sensors embedded in the electronic board. The location of the temperature sensors is primarily determined by the sensor space claim rather than the ideal location for thermal management. This paper presents an optimization methodology to determine the most beneficial locations for the temperature sensors inside of the microprocessors, based on input from high-resolution surface infrared thermography combined with inverse heat transfer solvers to predict hot spot locations. Specifically, the infrared image is used to obtain the temperature map over the processor surface, and subsequently delivers the input to a three-dimensional (3D) inverse heat conduction methodology, used to determine the temperature field within the processor. In this paper, simulated thermal maps are utilized to assess the accuracy of this method. The inverse methodology is based on a function specification method combined with a sequential regularization in order to increase accuracy in the results. Together with the number of sensors, the temperature field within the processor is then used to determine the optimal location of the temperature sensors using a genetic algorithm optimization combined with a Kriging interpolation. This combination of methodologies was validated against the finite element analysis of a chip incorporating heaters and temperature sensors. An uncertainty analysis of the inverse methodology and the Kriging interpolation was performed separately to assess the reliability of the procedure.

FIGURES IN THIS ARTICLE
<>
Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.

References

Arabi, K. , and Bozena, K. , 1997, “ Built-In Temperature Sensors for On-Line Thermal Monitoring of Microelectronic Structures,” IEEE International Conference on Computer Design: VLSI in Computers and Processors (ICCD), Austin, TX, Oct. 12–15, pp. 462–467.
Huang, Y. , Shen, X. , Li, J. , Li, B. , Duan, R. , Lin, C.-H. , Liu, J. , and Chen, Q. , 2015, “ A Method to Optimize Sampling Locations for Measuring Indoor Air Distributions,” Atmos. Environ., 102, pp. 355–365. [CrossRef]
Brooks, D. , and Margaret, M. , 2001, “ Dynamic Thermal Management for High-Performance Microprocessors,” The Seventh International Symposium on High-Performance Computer Architecture (HPCA), Monterrey, Mexico, Jan. 19–24, pp. 171–182.
Skadron, K. , Tarek, A. , and Stan, M. R. , 2002, “ Control-Theoretic Techniques and Thermal-RC Modeling for Accurate and Localized Dynamic Thermal Management,” IEEE Eighth International Symposium on High-Performance Computer Architecture, Cambridge, MA, Feb. 2–6, pp. 17–28.
Coskun, A. K. , Ayala, J. L. , Atienza, D. , Rosing, T. S. , and Leblebici, Y. , 2009, “ Dynamic Thermal Management in 3D Multicore Architectures,” Design, Automation and Test in Europe Conference Exhibition (DATE), Nice, France, Apr. 20–24, pp. 1410–1415.
Ranjan, R. , Matthew R, P. , and Shashank, K. , 2016, “ Thermoelectric Package Design for High Ambient Temperature Electronics Cooling,” 15th IEEE Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems (ITherm), Las Vegas, NV, May 31–June 3, pp. 857–861.
Choi, J. , Kim, Y. , Sivasubramaniam, A. , Srebric, J. , Wang, Q. , and Lee, J. , 2007, “ Modeling and Managing Thermal Profiles of Rack-Mounted Servers With Thermostat,” IEEE 13th International Symposium on High Performance Computer Architecture (HPCA), Scottsdale, AZ, Feb. 10–14, pp. 205–215.
Stanley, T. J. , and Mudge, T. , 1995, “ A Parallel Genetic Algorithm for Multiobjective Microprocessor Design,” International Conference on Genetic Algorithms (ICGA), Pittsburgh, PA, July 15–19, pp. 597–604.
Breen, T. J. , Walsh, Ed. J. , Punch, J. , Shah, A. J. , and Bash, C. E. , 2010, “ From Chip to Cooling Tower Data Center Modeling: Part I Influence of Server Inlet Temperature and Temperature Rise Across Cabinet,” 12th IEEE Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems (ITherm), Las Vegas, NV, June 2–5, pp. 1–10.
Walsh , Ed. J. , Breen, T. J. , Punch, J. , Shah, A. J. , and Bash, C. E. , 2010, “ From Chip to Cooling Tower Data Center Modeling: Part II Influence of Chip Temperature Control Philosophy,” 12th IEEE Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems (ITherm), Las Vegas, NV, June 2–5, pp. 1–7.
Patel, C. D. , Sharma, R. , Bash, C. E. , and Beitelmal, A. , 2002, “ Thermal Considerations in Cooling Large Scale High Compute Density Data Centers,” The Eighth Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems (ITHERM), San Diego, CA, May 30–June 1, pp. 767–776.
Sharma, R. K. , Bash, C. E. , Patel, C. D. , Friedrich, R. J. , and Chase, J. S. , 2005, “ Balance of Power: Dynamic Thermal Management for Internet Data Centers,” IEEE Internet Comput., 9(1), pp. 42–49. [CrossRef]
Beck, J. V. , Blackwell, B. , and St. Clair, C. R. , 1985, Inverse Heat Conduction: Ill-Posed Problems, Wiley, New York.
Alifanov, O. M. , 1994, Inverse Heat Transfer Problems, Springer-Verlag, New York. [CrossRef]
Colaço, M. J. , Orlande, H. R. B. , and Dulikravich, G. S. , 2006, “ Inverse and Optimization Problems in Heat Transfer,” J. Braz. Soc. Mech. Sci. Eng., 28(1), pp. 1–24. [CrossRef]
Jarny, Y. , Ozisik, M. N. , and Bardon, J. P. , 1991, “ A General Optimization Method Using Adjoint Equation for Solving Multidimensional Inverse Heat Conduction,” Int. J. Heat Mass Transfer, 34(11), pp. 2911–919. [CrossRef]
Sousa, J. F. L. , Lavagnoli, S. , Paniagua, G. , and Villafañe, L. , 2012, “ Three-Dimensional (3D) Inverse Heat Flux Evaluation Based on Infrared Thermography,” Quant. InfraRed Thermogr. J., 9(2), pp. 177–191. [CrossRef]
Sousa, J. , Villafañe, L. , and Paniagua, G. , 2014, “ Thermal Analysis and Modeling of Surface Heat Exchangers Operating in the Transonic Regime,” Energy, 64, pp. 961–969.
Huang, C.-H. , and Wang, S.-P. , 1999, “ A Three-Dimensional Inverse Heat Conduction Problem in Estimating Surface Heat Flux by Conjugate Gradient Method,” Int. J. Heat Mass Transfer, 42(18), pp. 3387–3403. [CrossRef]
Najafi, H. , Woodbury, K. A. , and Beck, J. V. , 2015, “ Real Time Solution for Inverse Heat Conduction Problems in a Two-Dimensional Plate With Multiple Heat Fluxes at the Surface,” Int. J. Heat Mass Transfer, 91, pp. 1148–1156. [CrossRef]
Najafi, H. , Woodbury, K. A. , and Beck, J. V. , April 2015, “ A Filter Based Solution for Inverse Heat Conduction Problems in Multi-Layer Mediums,” Int. J. Heat Mass Transfer, 83, pp. 710–720. [CrossRef]
Fernandes, A. P. , dos Santos, M. B. , and Guimarães, G. , 2015, “ An Analytical Transfer Function Method to Solve Inverse Heat Conduction Problems,” Appl. Math. Modell., 39(22), pp. 6897–6914. [CrossRef]
Kleijnen, J. P. C. , 2009, “ Kriging Metamodeling in Simulation: A Review,” Eur. J. Oper. Res., 192(3), pp. 707–716. [CrossRef]
Jalali, H. , Van Nieuwenhuyse, I. , and Picheny, V. , 2017, “ Comparison of Kriging-Based Algorithms for Simulation Optimization With Heterogeneous Noise,” Eur. J. Oper. Res., 261(1), pp. 279–301. [CrossRef]
Clark, I. , 1977, “ Practical Kriging in Three Dimensions,” Comput. Geosci., 3(1), pp. 173–180. [CrossRef]
Venturelli, G. , Ernesto, B. , and Łukasz, Ł.-W. , 2017, “ A Kriging-Assisted Multiobjective Evolutionary Algorithm,” Appl. Soft Comput., 58, pp. 155–175.
Khademi, G. , and Karimaghaee, P. , 2016, “ Hybrid FDG Optimization Method and Kriging Interpolator to Optimize Well Locations,” J. Pet. Explor. Prod. Technol., 6(2), pp. 191–200. [CrossRef]
Chiles, J.-P. , and Pierre, D. , 2009, Geostatistics: Modeling Spatial Uncertainty, Vol. 497, Wiley, Hoboken, NJ.

Figures

Grahic Jump Location
Fig. 2

Sketch of the simulated microchip with the sources of heat flux and the temperature reading location

Grahic Jump Location
Fig. 1

Schematic of the inverse 3D conduction methodology coupled with Kriging method optimization to obtain the optimal sensor location

Grahic Jump Location
Fig. 4

Sketch of the reduced chip structure including the geometry of the real microchip with 100 heaters

Grahic Jump Location
Fig. 5

Temperature distribution within the chip for the reduced chip and the simplified reduced chip model at t = 1.5 s and t = 5 s

Grahic Jump Location
Fig. 6

(a) Imposed heat flux in the numerical experiment for the corner and center heaters and (b) temperature increase over time at the top surface in the corner and center locations of the microchip

Grahic Jump Location
Fig. 7

Comparison between the imposed heat flux and the heat flux estimated with the inverse 3D methodology

Grahic Jump Location
Fig. 8

Temperature maps in the plane where the temperature sensors should be located at t = 1.5 s and t = 2.7 s

Grahic Jump Location
Fig. 9

Location of the optimal points inside of the microchip envelope for the case run with eight sensors

Grahic Jump Location
Fig. 3

(top) Schematic of the complete experimental test fixture and (bottom) the comsol model used for the inverse method and Kriging model. (bottom inset) Approximate verification model to prove the simplified geometry.

Grahic Jump Location
Fig. 10

Kriging interpolation results for the temperature maps using the optimal location for the sensors

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In