Метод вероятностного анализа надежности элементов конструкций на основе граничных функций распределения

Abstract

Introduction. The research is aimed at the development of methods for assessing and analyzing the structural reliability of elements of building structures in practical tasks when statistical data about random variables may be incomplete or limited. In such cases, it is difficult to identify the specific type of the exact cumulative distribution function of a random variable or to give an accurate estimate of the distribution parameter, because there is a need to take into account epistemic uncertainty in addition to aleatory uncertainty. Materials and methods. For effective modelling of two types of uncertainties, it is proposed to use boundary distribution functions of a random variable that form a p-box (probability box). P-boxes take into account both types of uncertainty: caused by natural variability of random parameters and uncertainty caused by lack of knowledge about the random variable (number of control samples, accuracy of measuring instruments, etc.). Results. The paper proposes a new type of p-box based on the Dvoretzky – Kiefer – Wolfowitz inequality and Chebyshev’s inequality, which form two boundary distribution functions based on the sample population data. The numerical example shows the approach to arithmetic operations with p-boxes, which make it possible to bring complex mathematical models to simpler ones and estimate the failure probability in an interval form. The difference between the analytical and numerical solution for the example is 0.9 %. Conclusions. Boundary distribution functions form a more cautious and reliable approach to the structural reliability analysis. The result of reliability assessment using p-boxes is presented in an interval form. If the interval turns out to be too wide and uninformative, then it is necessary to increase the quantity or quality of statistical data or to increase the cross-sections of structural elements to achieve the lower limit of the interval of the required reliability level.