A method of solving problems in statistical dynamics for the reliability assessment of complex technical systems with limited internal parameters of the system
Journal Title: Вісник Одеської державної академії будівництва та архітектури - Year 2017, Vol 1, Issue 66
Abstract
This work was further develops the method of solving problems in statistical dynamics within the reliability assessment of complex technical systems. In applying the method of statistical tests (Monte Carlo) to assess the reliability of a complex technical system, it is necessary to perform a significant number of statistical tests. This implies determination of internal parameters of the system during each statistical test. This is what causes some technical difficulties while solving problems in statistical dynamics. This work aims at improving the methods of probabilistic reliability assessment of complex technical systems with a limited number of its internal parameters. It offers approaches to determine internal parameters of a complex technical system, when their number is limited, and to further assess the system’s reliability by the method of statistical tests. The suggested approaches may consider certain correlations that exist between the natural factors that are crucial in the assessment of their reliability using the method of statistical tests. As an example, a concrete gravity dam at the Dnieper hydropower scheme is discussed. The initial data are random variables: a water level in the headrace, as well as a tangent of the angle of internal friction in the rock base. In the first method, fixed values of external parameters Xi, Yi, (i = 1 ... n) are assigned, for example, when n = 3, as well as fixed values of internal parameters of the system Ki, j (i = 1 ... n, j = 1 ... n), which depend on external parameters Xi, Yi; then, one by one, three systems of equations with three unknowns coefficients xj, yj, zj (j = 1 ... n) are solved. The presented method makes it possible to obtain, in a closed form, the necessary number of values of the internal random parameter of the system K*, depending on fixed values of external parameters X, Y to use the method of statistical tests (Monte Carlo). Another method of solving this problem is to use a module of interpolation functions built-in in the software package Mathcad. This module allows building functional relationships using empirical data. After obtaining, by the two methods, appropriate dependencies of criteria of stability against the displacement for a concrete dam from the water level in the headrace and the tangent of the angle of internal friction in the rock base by using the method of statistical tests, probability assessment of stability loss against displacement of a concrete gravity dam at the Dnieper hydropower scheme was performed. The results can be used in the probabilistic reliability analyses of hydraulic structures and cascades of hydropower projects.
Authors and Affiliations
A. O. , Mozgovuy
Keywords
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