Interval-Stochastic Thermal Processes in ElectronicSystems: Modeling in Practice

Journal of Engineering Thermophysics. 2017. Vol. 26. No. 1. P. 29–38.

Madera A. G.

Mathematical and computer modeling of thermal processes, applied presently in thermal design of electronic systems, is based on the assumption that the factors determining the thermal processes are completely known and uniquely determined, that is, they are deterministic. Meanwhile, practice shows that the determining factors are of indeterminate interval-stochastic character. Moreover, thermal processes in electronic systems are nonstationary and nonlinearly depend on both the stochastic determining factors and the temperatures of electronics elements and environment. At present, the literature does not present methods of mathematical modeling of nonstationary, stochastic, nonlinear, interval-stochastic thermal processes in electronic systems to model thermal processes, which satisfy all the above-listed requirements to modeling adequacy. The present paper develops a method of mathematical and computer modeling of the nonstationary interval-stochastic nonlinear thermal processes in electronic systems. The method is based on obtaining equations describing the dynamics of time variation of statistical measures (expectations, variances,covariances)oftemperatureofelectronicsystemelementswithgivenstatisticalmeasures of the initial interval-stochastic determining factors. A practical example of applying the developed approach to a the real electronic system is given.

Keywords: mathematical modeling, thermal processes, expectations, electronic systems, interval stochastic, variances, covariances