Bayesian surrogates for integrating numerical, analytical, and experimental data: application to inverse heat transfer in wearable computers

Wearable computers are portable electronics worn on the body. The increasing thermal challenges facing these compact electronics systems have motivated new cooling strategies such as transient thermal management with thermal storage materials. The ability of building models to assess quickly the effect of different design parameters is critical for effectively incorporating innovative thermal strategies into new products. System models that enable design space exploration are built from different information sources such as numerical simulations, physical experiments, analytical solutions and heuristics. These models, called surrogates, are nonlinear, adaptive, and suitable for system responses where limited information is available and few realizations of experiments or numerical simulations are feasible. This paper applies a Bayesian surrogate framework to estimate values for unknown physical parameters of an embedded electronics system. Physical experiments and numerical simulations are performed on an embedded electronics prototype system of a wearable computer. Numerical models for the experimental prototype, which involve five and three unknown parameters, are implemented with and without thermal contact resistances. Through the use of orthogonal arrays and optimal sampling, an efficient exploration of the parameter space is performed to determine thermal conductivities, thermal contact resistances and heat transfer coefficients. Surrogate models are built that combine information obtained from numerical simulations, experimental model measurements and a thermal resistance network. The integration of several information sources reduces the number of large-scale numerical simulations needed to find reliable estimates of the system parameters. For the embedded electronics case, the use of prior information from the thermal resistance network model reduces significantly the computational effort required to investigate the solution space.