A parameter optimization heuristic for a temperature estimation model

Abstract

We present a heuristic technique for solving a parameter estimation problem that arises in modeling the thermal behavior of electronic chip packages. Compact Thermal Models (CTMs) are network models of steady state thermal behavior, which show promise in augmenting the use of more detailed and computationally expensive models. The CTM parameter optimization problem that we examine is a nonconvex optimization problem in which we seek a set of CTM parameters that best predicts, under general conditions, the thermal response of a particular chip package geometry that has been tested under a small number of conditions. We begin by developing a nonlinear programming formulation for this parameter optimization problem, and then develop an algorithm that uses special characteristics of the optimization problem to quickly generate heuristic solutions. Our algorithm descends along a series of solutions to one-dimensional nonconvex optimization problems, obtaining a locally optimal set of model parameters at modest computational cost. Finally, we provide some experimental results and recommendations for extending this research.

An exact reformulation-linearisation technique algorithm for solving a parameter extraction problem arising in compact thermal models

“…However, the feasible region given by Equations (2b) and (2c) is non-convex because of the terms dividing T -variables by R-variables. As noted in [26], our model is general enough to allow different weights according to node and boundary conditions, in case certain conditions are more likely to occur in nature, and/or the accurate prediction of certain nodes is more important than others. As a default for the weights, we adopt the following weighting scheme proposed by [18] and employed in [11,26]:…”

“…In [26] we showed that general-purpose non-linear techniques are ill-suited to solving this problem and presented a heuristic algorithm for quickly finding locally optimal solutions. While the solutions obtained in that paper are an improvement over the previous state-of-the-art, their quality relative to optimality is still unknown.…”

“…In order to improve our ability to fathom nodes by bound, we employ the heuristic technique developed in [26] to obtain upper bounds for the parameter extraction problem. This heuristic is a coordinate-descent approach, in which each coordinate search is (virtually always) solved to optimality despite the non-convexity of the line searches.…”

“…This heuristic is a coordinate-descent approach, in which each coordinate search is (virtually always) solved to optimality despite the non-convexity of the line searches. The coordinate searches are done quickly because of the closed-form characterisation of line search functions and their properties (see [26] for a full description of the heuristic).…”

“…At each branch-and-bound node we have a candidate vector of resistance variable values that can be used as a starting point for the heuristic algorithm given in [26]. This heuristic can be executed from nodes having small optimal objective function values, with the promise of quickly identifying a near-optimal solution.…”