A research into the development of models of random variables as part of the structural reliability analysis performed in the absence of some statistical information

Abstract

Introduction. The scientific review article addresses the approaches to the modeling of random variables performed as part of the structural reliability analysis of elements provided that some statistical information missing (limited). The objectives of the research include the statement of the problem of the probabilistic structural reliability analysis subject to incomplete statistical data, the study of the development of approaches to the generation of models of random variables within the framework of this problem, as well as the assessment of the current state of affairs in this field and some development prospects for the coming years.
 Materials and methods. The principal model of a random variable, considered in the article, represents a p-box (pro­bability box) model. A p-box is an area of possible functions of distributed probabilities of a random variable generated by the two boundary functions of the probability distribution. The article addresses p-boxes generated using the fuzzy set theory, the probability theory, Kolmogorov–Smirnov boundaries, etc.
 Results. The approaches, considered in the article, are illustrated by the numerical examples of p-boxes that use the same statistical data. P-boxes, based on the probability theory, allow to accurately simulate a random variable; however, a priori information about the type of the distribution function is needed. P-boxes, based on the possibility theory, can be used even if an extremely small amount of statistical data is available, and it is also necessary to carefully address the issue of assigning the cutoff (risk) level. P-boxes based on the Chebyshev inequality and the Kolmogorov–Smirnov statistics allow to effectively simulate random variables regardless of the type of the probability distribution. However, these approaches may generate an assessment that is too uninformative for decisions to be made in a number of tasks.
 Conclusions. The choice of a probabilistic model of a random variable for the further reliability analysis of structural elements will depend on the amount and type of statistical data obtained about the random variable. In particular cases, if the statistical information represents a subset of intervals, special approaches based on the Dempster–Shafer theory can be used. A promising and relevant method that underlies both the development of probabilistic models of random variables and the analysis of structural reliability in case of missing statistical information encompasses the employment of numerical modeling methods that employ surrogate models (kriging, Bayesian networks, interval predictors, etc.) and neural network algorithms.

Evaluation of a reliability index for steel trusses to the deflection criterion with interval uncertainty of data

“…Как только статистическая гипотеза о распределении вероятностей не выполняется, анализ надежности становится недостоверным и бессмысленным». Для восполнения этого недостатка разработаны новые модели случайных величин -р-блоки [5], позволяющие использовать интервальные оценки параметров функций распределения, интервальные модели [6], которые представляют случайные величины в виде границ их изменчивости, и др.…”