With the characteristic size reducing as well as the power densities exponentially increasing, elevated
chip temperatures are true limiters to the performance and reliability of integrated circuits. To address these
thermal issues, it is essential to use a set of on-chip thermal sensors to monitor temperatures during operation.
These temperature sampling results are then used by thermal management techniques to appropriately manage
chip performance. In this paper, we propose a surface spline interpolation method to reconstruct the full thermal
characterization of integrated circuits with non-uniform thermal sensor placements. We construct the thermal
surface function using the mathematical tool of surface spline with the matrix calculation of the non-uniform
sample data. Then, we take the coordinates of the points at grid locations into the surface function to get its
temperature value so that we can reconstruct the full thermal signals. To evaluate the effectiveness of our method,
we develop an experiment for reconstructing full thermal status of a 16-core processor. Experimental results show
that our method outperforms the inverse distance weighting method based on dynamic Voronoi diagram and
spectral analysis techniques both in the average absolute error metric and the hot spot absolute error metric with
short enough runtime to meet the real-time process demand. Besides, our method still has the advantages such
as its mathematical simplicity with no need of pre-process.
WANG Ruo-lin (王若琳), LI Xin (李 鑫), LIU Wen-jiang (刘文江), LIU Tao* (刘 涛), RONG Meng-tian (戎蒙恬), ZHOU Liang (周 亮)
. Surface Spline Interpolation Method for Thermal Reconstruction with Limited Sensor Data of Non-Uniform Placements[J]. Journal of Shanghai Jiaotong University(Science), 2014
, 19(1)
: 65
-71
.
DOI: 10.1007/s12204-013-1469-z
[1] Jayaseelan R, Mitra T. Dynamic thermal management via architectural adaptation [C]//Proceedings of the 46th Annual Design Automation Conference. Singapore:IEEE, 2009: 484-489.
[2] Coskun A K, Rosing T S, Gross K C.Proactive temperature management in MPSoCs[C]//International Symposium on Low Power Electronics and Design. Bangalore, India: ACM, 2008:213-218.
[3] Memik S O, Mukherjee R, Ni M, et al. Optimizing thermal sensor allocation for microprocessors [J]. IEEE Transactions on Computer-Aided Design of Integrated Circuits, 2008, 27(3): 516-527.
[4] Cochran R, Reda S. Spectral techniques for highresolution thermal characterization with limited sensor data [C]//Proceedings of the 46th Annual Design Automation Conference. San Francisco, USA: ACM,2009: 478-483.
[5] Li X, Rong M T, Liu T, et al. Inverse distance weighting method based on a dynamic Voronoi diagram for thermal reconstruction with limited sensor data on multiprocessors [J]. IEICE Transactions on Electronics, 2011, E94-C(8): 1295-1301.
[6] Long J, Memik S O, Memik G, et al. Thermal monitoring mechanisms for chip multiprocessors [J]. ACM Transactions on Architecture and Code Optimization,2008, 5(2): 2008-9.
[7] Shepard D. A two-dimensional function for irregularly-spaced data [C]// Proceedings of the 1968 23rd ACM National Conference. [s.l.]: ACM, 1968: 517-524.
[8] Harder R L, Desmarais R N. Interpolation using surface splines [J]. Journal of Aircraft, 1972, 9(2): 189-191.
[9] Yu Z W. Surface interpolation from irregularly distributed points using surface splines, with Fortran program[J]. Computers & Geosciences, 2001, 27(7): 877-882.
[10] Franke R. Scattered data interpolation: Tests of some methods [J]. Mathematics of Computation, 1982,38(157): 181-200.
[11] Franz A. Voronoi diagrams: A survey of a fundamental geometric data structure [J]. ACM Computing Surveys, 1991, 23(3): 345-405.
[12] Zhang Y, Ankur S. Accurate temperature estimation using noisy thermal sensors [C]//Proceedings of the 46th Annual Design Automation Conference. San Francisco, USA: ACM, 2009: 472-477.
[13] Nowroz A N, Cochran R, Reda S. Thermal monitoring of real processors: Techniques for sensor allocation and full characterization [C]// Proceedings of the 47th Design Automation Conference. Anaheim, USA:ACM, 2010: 56-61.
