Application of variational principles in problems of development and testing of complex technical systems
Abstract
Application of variational principles in problems of development and testing of complex technical systems
Incoming article date: 22.12.2024The technology of applying the variational principle in problems of development and testing of complex technical systems is described. Let there be a certain set of restrictions imposed on random variables in the form of given statistical moments and/or in the form of a restriction by some estimates from above and below the range of possible values of these random variables. The task is set: without knowing anything except these restrictions, to construct for further research, ultimately, for assessing the efficiency of the complex technical system being developed, the probability distribution function of its determining parameter. By varying the functional, including Shannon entropy and typical restrictions on the distribution density function of the determining parameter of a complex technical system, the main stages of constructing the distribution density function are described. It is shown that, depending on the type of restriction, the constructed distribution density function can have an analytical form, be expressed through special mathematical functions, or be calculated numerically. Examples of applying the variational principle to find the distribution density function are given. It is demonstrated that the variational principle allows obtaining both the distribution laws widely used in probability theory and mathematical statistics, and specific distributions characteristic of the problems of developing and testing complex technical systems. The technology of applying the variational principle presented in the article can be used in the model of managing the self-diagnostics process of intelligent control systems with machine consciousness.
Keywords: variational principle, distribution density function, Shannon entropy, complex technical system