Temperature-to-power mapping

Abstract

Abstract-Accurate power maps are useful for power model validation, process variation characterization, leakage estimation, and power optimization, but are hard to measure directly. Deriving power maps from measured thermal maps is the inverse problem of the power-to-temperature mapping, extensively studied through thermal simulation. Until recently this inverse heat conduction problem has received little attention in the microarchitecture research community. This paper first identifies the source of difficulties for the problem. The inverse mapping is then performed by applying constraints from microarchitecture-level observations. The inherent large sensitivity of the resultant power map is minimized through thermal map-filtering and constrained least-squares optimization. Choices of filter parameters and optimization constraints are investigated and their effects are evaluated. Furthermore, the paper highlights the differences between the grid and block modeling in the inverse mapping which were often ignored by previous schemes. The proposed methods reduce the mapping error by more than 10× compared to unoptimized solutions. To our best knowledge this is the first work to quantitatively evaluate and minimize the noise effect in the temperature to power mapping problem at the microarchitecture level for both grid and block mode, and for the steady and transient case. I. MOTIVATION FOR POST-SILICON POWER MAPSThe "power wall" has become a critical performance limiter for integrated circuit design. Excessive power consumption leads to short battery life, higher utility costs, large currents in interconnect, and elevated temperatures. Moreover, the very power models which are intended to enable poweraware analysis and optimization are often inaccurate-in part because of changes in leakage power due to parameter variation-and need to be validated against silicon measurement. If they could be reliably derived, accurate power maps (the temporal and spatial power distribution) would provide an avenue not only to perform post-silicon power model validation, but also to characterize process variation over large regions, complementary to timing based methods like maximum frequency or critical path delay monitoring [1]. Per unit power consumption could also be used to inform power/energy-aware task scheduling or reconfiguration, and to capture long term wearout mechanisms and proactively eliminate potential reliability and thermal hazards.Unfortunately, direct fine grain power measurement is expensive and difficult, and event-counter based power proxies cannot capture workload induced power variation [2]. However, accurate and high resolution thermal maps (temporal and spatial temperature distribution) can be measured using infra-red (IR) cameras or thermal sensors. While the direct heat conduction problem (DHCP) of solving thermal maps from power maps is essential for thermal simulation [3], [4], the inverse heat conduction problem (IHCP) of solving power maps from thermal maps is a possible approach to obtaining power ...

Temperature Sensitive Microprocessor Design to Reduce Heat Generation and Improve Performance

“…Skadron proposed most of the temperature control mechanisms in literature [3,11,15,19]. His several publications show many different improvements for heat control.…”

Temperature Sensitive Microarchitecture Design Circuit Design

“…Skadron proposed most of the temperature control mechanisms in literature [3,11,15]. His several publications show many different improvements for heat control.…”

Inverse Thermal Modeling to Determine Power Losses in Induction Motor

“…While the inverse of this relationship generates the losses accurately with noise-free input, with noisy temperature measurements the results are erratic. In the latter case, solution is obtained in a similar fashion as [3] by overdetermining the system and obtaining the loss vector which is the least square (LS) optimal solution satisfying the linear constraints imposed on the system. This approach is tested also with a different set of measurements, from the motor's numerical finite element (FE) thermal solution.…”

“…Usually this is overcome with stabilization techniques [5] that approximate the inverse problem to a well-posed function which is solved instead. [3] addresses the inverse heat conduction problem at microarchitecture level with constrained least squares optimisation quite effectively.…”

“…There exists a large body of work dealing with inverse heat problems; 2D conduction [2], source mapping in micro electromechanical systems [3], and also 3D spatial source reconstruction [4] with thermal camera input. Overall, the systems studied and solution methodologies adopted have been mostly restricted to structurally simple and homogeneous systems.…”