Probabilistic Analysis of Power and Temperature Under Process Variation for Electronic System Design

Abstract

Electronic system design based on deterministic techniques for power-temperature analysis is, in the context of current and future technologies, both unreliable and inefficient since the presence of uncertainty, in particular, due to process variation, is disregarded. In this paper, we propose a flexible probabilistic framework targeted at the quantification of the transient power and temperature variations of an electronic system. The framework is capable of modeling diverse probability laws of the underlying uncertain parameters and arbitrary dependencies of the system on such parameters. For the considered system, under a given workload, our technique delivers analytical representations of the corresponding stochastic power and temperature profiles. These representations allow for a computationally efficient estimation of the probability distributions and accompanying quantities of the power and temperature characteristics of the system. The approximation accuracy and computational time of our approach are assessed by a range of comparisons with Monte Carlo simulations, which confirm the efficiency of the proposed technique.Index Terms-Power analysis, process variation, system-level design, temperature analysis, uncertainty quantification.

Probabilistic Analysis of Electronic Systems via Adaptive Hierarchical Interpolation

“…A stochastic collocation [16] approach to static steady-state temperature analysis is given in [10], which relies on global interpolation using Newton polynomials. In [11], transient temperature analysis is considered, and process variation is addressed via PC expansions. The machinery of PC expansions is also utilized in [12] in order to model dynamic steady-state temperature [17] and to enhance reliability models.…”

“…A more realistic assumption is the availability of the marginals and correlation matrix of u. In general, these two pieces are not sufficient to recover the joint of u; however, the joint can be approximated well by accompanying the available marginals by a Gaussian copula constructed based on the available correlation matrix; see [22] and also [11]. Hence, a set of marginals and a Gaussian copula are practical inputs to probabilistic analysis.…”

“…An example of a physical source of uncertainty is process variation [7], which is a side effect of contemporary fabrication processes. Process variation has been central for many lines of research [8], [9], [10], [11], [12]. An example of a digital source of uncertainty (the computer world) is workload.…”

“…In such cases, uncertainty quantification based on polynomial chaos (PC) expansions [16] and other approximation techniques making use of global polynomials generally work well, as in [8], [10], [11], [12]. On the other hand, the variability coming from the computer world has often steep gradients and favors nondifferentiability and even discontinuity.…”

System-Level Analysis and Design under Uncertainty

“…The approach to characterization of process variation developed in [116] is presented in Chapter 4. The techniques for analysis and design under process variation proposed in [111] and [112] are amalgamated in Chapter 5. The approach to analysis under workload variation introduced in [113] is elaborated on in Chapter 6.…”