Mathematical Modelling of the Stochastic Nonlinear Thermal Processes in Electronic Systems by the Method of Pseudoinverse Matrix
Thermal processes in electronic systems are stochastic and nonlinear. The stochasticity of thermal processes in electronic systems can be caused by both external stochastic environmental factors and internal stochastic factors of the electronic systems. Methods existing in the literature allow modeling thermal processes caused only by external stochastic factors. At the same time, there are no methods that would have the ability to simulate thermal processes, taking into account both nonlinearities and stochasticities of external and internal factors. In this study is developed a method that allows us to simulate stationary stochastic thermal processes in electronic systems taking into account the stochasticity of both external and internal factors and nonlinearity too. The method is based on the concept of a pseudoinverse matrix as well as on the decomposition of a stochastic temperature-dependent matrix of thermal conductivities into a product of two matrices. One of this matrix depends only on temperature and the other matrix depends only on stochastic factors. The application of the proposed method to the design of real electronic systems has shown its adequacy and efficiency sufficient for engineering practice.