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Physics-Informed Radial Basis Function Networks: Solving Inverse Problems for Partial Differential Equations Read chapter Read first chapter

2023 | OriginalPaper | Chapter

Method of Expansion of Mathematical Tools of the Reliability Theory Due to the Properties of Stochastic Theory of Similarity

Authors : Sergei Efimenko, Anatolii Smetankin, Aleksandr Liashenko, Melania Arutiunian, Igor Chernorutsky, Sergei Kolesnichenko

Published in: Cyber-Physical Systems and Control II

Publisher: Springer International Publishing

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Abstract

An original approach to the development of mathematical tools of the reliability theory and expanding the range of its capabilities by using the properties of the stochastic theory of similarity are proposed and justified in the article. Such an approach to creating mathematical “symbiosis” of two large theories is aimed at improving the efficiency of solving the problem of identification of the quality indicators (reliability) of complex technical systems during its life cycles: from creation, active usage, and to subsequent disposal. The stochastic similarity is based on the elementary lemma and a metric in the form of a ratio of distribution functions of a random variable. The elementary lemma is also the basis of the probability integral transformation, which is used in the modeling of random variables. Useful properties of the lemma and the integral transformation are given in the study dedicated to the capabilities of the stochastic theory of similarity. In the course of assessing the applicability of the stochastic theory of similarity to the problems of comparing reliability indicators, two alternative methods of solution are presented: the first method is based on the construction of models using the principle of maximum entropy, and the second method is using stochastic similarity.

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Metadata
Title
Method of Expansion of Mathematical Tools of the Reliability Theory Due to the Properties of Stochastic Theory of Similarity
Authors
Sergei Efimenko
Anatolii Smetankin
Aleksandr Liashenko
Melania Arutiunian
Igor Chernorutsky
Sergei Kolesnichenko
Copyright Year
2023
Book
Cyber-Physical Systems and Control II

Print ISBN: 978-3-031-20874-4

Electronic ISBN: 978-3-031-20875-1

Copyright Year: 2023

DOI
https://doi.org/10.1007/978-3-031-20875-1_4

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