Probabilistic analysis of reliability for structural elements in case of incomplete statistical information with data recovery

DOI: 10.37153/2618-9283-2025-5-121-132

Authors:  
Rubric:     Theoretical and experimental studies   
Key words: reliability, failure probability, incomplete information, data sampling, nonparametric statistics, structures, risk, A/R sampling, probabilistic design
Annotation:

Introduction. Structural reliability is one of the key parameters of a building at all stages of its life cycle. An effective approach to reliability analysis is the use of probabilistic methods of structural mechanics. The actual problem of their application in practice is incomplete statistical information about the design parameters.

Aim. The research is aimed at developing a probabilistic approach to analyzing the reliability of structural elements in conditions of incomplete statistical information on random variables using methods for probability distribution function recovery.

Materials and methods. Nonparametric methods are used to recover an unknown probability distribution density of random variables based on data from a sample. Due to the fact that the reconstructed probability densities function has a complex analytical form for generating data using the N.V. Smirnov’s inverse transform sampling, the study uses the method of acceptance-rejection sampling (A/R sampling) for further use of the Monte Carlo Simulation (MCS) in the problem of probabilistic reliability analysis.

Results. The proposed algorithm is demonstrated by the example of a probabilistic calculation of the reliability of an element of a rod system. In case of incomplete statistical information, individual design parameters are estimated as confidence intervals, which leads to an interval estimate of the failure probability for a structural element. The estimated reliability is taken at the upper limit of the failure probability interval within the safety level.

Conclusions. The numerical approach to assessing the reliability of a structural object or its individual element is presented for cases of incomplete statistical information, in which reliability is expressed as an interval of failure probability. If the failure probability interval turns out to be too wide to make a decision on the reliability level, it can be narrowed by additional collection of statistical data on random parameters, or the cross-section can be increased (at the design stage) or reinforcement (at the operational stage) of the structural element can be performed.  Used Books:

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