Modeling of complex thermal processes in electronic systems by the method of generalized pseudosolution


Аuthors

Madera A. G.

Federal State Institution “Federal Scientific Center Scientific Research Institute for System Analysis of the Russian Academy of Sciences”, Nachimovskiy prosp., Moscow, 117218, Russia

e-mail: agmprof@mail.ru

Abstract

To increase the adequacy of modeling of thermal processes in electronic systems it is necessary that the developed methods and models take into account both the nonlinear and stochastic nature of real thermal processes in electronic systems. The nonlinear nature of thermal processes in the electronic systems is due to the non-linearity of temperature dependences of heat transfer factors and the power consumption of electronic components of the electronic systems as a result of the effect of thermal feedback. The stochastic character of thermal processes in such systems is determined by both internal system factors and external factors arising from the functioning of the electronic systems and its interaction with the environment. The stochasticity of the internal factors of the electronic systems arises due to their statistical technological variation in production and installation, and the stochasticity of external factors is due to the random nature of the environmental parameters. In this article proposed is a method to simulate thermal processes that are both nonlinear and stochastic, and which are influenced by external and internal stochastic factors. The modeling method is based on the generalized normal pseudosolution in the form of a pseudo- inverse matrix method, on the method of analyzing stochastic fields by statistical measures fields, and also on decomposing a stochastic nonlinear thermal conductivity matrix into a product of two matrices, one of which depends only on temperature and the other only on stochastic factors. The method developed in the article makes it possible to find the equations that determine the statistical measures of the stochastic temperature distributions in the electronic systems. Computation by this method requires significantly less computer time and computer RAM compared to the Monte Carlo method. The application of the method to the design of real electronic systems showed its adequacy and efficiency for engineering practice.

Keywords:

generalized solution, pseudoinverse matrix, thermal processes, electronic system, nonlinear, stochastic, mathematical model.

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