Method of structural reliability analysis based on boundary distribution functions
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 spe...
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Moscow State University of Civil Engineering (MGSU)
2023-10-01
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| Online Access: | https://www.vestnikmgsu.ru/jour/article/view/81 |
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| author | S. A. Solovev A. A. Soloveva |
| author_facet | S. A. Solovev A. A. Soloveva |
| author_sort | S. A. Solovev |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-c4e0213a88064b078c8f46bcafbf9278 |
| institution | Kabale University |
| issn | 1997-0935 2304-6600 |
| language | English |
| publishDate | 2023-10-01 |
| publisher | Moscow State University of Civil Engineering (MGSU) |
| record_format | Article |
| series | Vestnik MGSU |
| spelling | doaj-art-c4e0213a88064b078c8f46bcafbf92782025-01-09T08:22:49ZengMoscow State University of Civil Engineering (MGSU)Vestnik MGSU1997-09352304-66002023-10-0118101545155510.22227/1997-0935.2023.10.1545-155529Method of structural reliability analysis based on boundary distribution functionsS. A. Solovev0A. A. Soloveva1Vologda State University (VSU)Vologda State University (VSU)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.https://www.vestnikmgsu.ru/jour/article/view/81reliabilityprobabilistic designp-boxesfailure probabilitykolmogorov – smirnov criterionuncertaintysafety |
| spellingShingle | S. A. Solovev A. A. Soloveva Method of structural reliability analysis based on boundary distribution functions Vestnik MGSU reliability probabilistic design p-boxes failure probability kolmogorov – smirnov criterion uncertainty safety |
| title | Method of structural reliability analysis based on boundary distribution functions |
| title_full | Method of structural reliability analysis based on boundary distribution functions |
| title_fullStr | Method of structural reliability analysis based on boundary distribution functions |
| title_full_unstemmed | Method of structural reliability analysis based on boundary distribution functions |
| title_short | Method of structural reliability analysis based on boundary distribution functions |
| title_sort | method of structural reliability analysis based on boundary distribution functions |
| topic | reliability probabilistic design p-boxes failure probability kolmogorov – smirnov criterion uncertainty safety |
| url | https://www.vestnikmgsu.ru/jour/article/view/81 |
| work_keys_str_mv | AT sasolovev methodofstructuralreliabilityanalysisbasedonboundarydistributionfunctions AT aasoloveva methodofstructuralreliabilityanalysisbasedonboundarydistributionfunctions |