2026, Vol. 13, No. 1. - go to content...

Permanent address of this page - https://t-s.today/en/30sats126.html

Метаданные этой статьи так же доступны на русском языке

DOI: 10.15862/30SATS126 (https://doi.org/10.15862/30SATS126)

Full article in PDF format (file size: 1.7 MB)

For citation:

Khairullin V.A., Terekhov I.G. Theory and method of thresholds in construction and various engineering tasks. Russian Journal of Transport Engineering. 2026; 13(1). Available at: https://t-s.today/PDF/30SATS126.pdf (in Russian). DOI: 10.15862/30SATS126

Theory and method of thresholds in construction and various engineering tasks

Khairullin Vitaly Agzamovich
Ufa State Petroleum Technical University, Ufa, Russia
Scientific Research Design Institute of Architecture and Construction
E-mail: Vitalik000@yandex.ru
ORCID: https://orcid.org/0000-0002-3854-2193
RSCI: https://elibrary.ru/author_profile.asp?id=671334
ResearchGate: https://www.researchgate.net/profile/Vitaliy-Khayrullin?ev=hdr_xprf

Terekhov Ivan Gennadievich
Ufa State Petroleum Technological University, Ufa, Russia
Institute of Architecture and Civil Engineering
E-mail: iv_98_04@mail.ru
RSCI: https://elibrary.ru/author_profile.asp?id=528528

Abstract. This study logically continues the previous work of the authors devoted to the Theory of extreme values in assessing the durability of building structures. The object of research is the theory of extreme values. The subject of the research is the theory of threshold values. The purpose of the study is to present the applied application of Threshold Theory in construction and in various engineering tasks. In this study, we will look at the key works of the subject area. We will also answer the question about the admissibility of the minimum sample size of n = 30 in the previous study. This is an important applied point, which some researchers interpreted as a calculation error. We have answered this question in detail. The key methodological differences between extreme values (the block maxima method) and threshold values (all exceedances of a given level) are formulated. A step-by-step threshold method procedure adapted for engineering tasks (primarily in construction) is proposed, including threshold selection, estimation of parameters of the generalized Pareto distribution, model adequacy verification and calculation of probabilistic forecasts with return levels. The practical approbation of the method was performed on real data of vertical movements of the nodes of the draining and filling overpass. The authors have demonstrated that even with a limited amount of initial information (123 observations), the Threshold Value method allows: (1) it is reasonable to choose the threshold u = 2.0 mm according to the graph of the average excess; (2) obtain relevant estimates of the GPD parameters (ξ = 0,58, σ = 2,94 mm), indicating a heavy tail of the distribution; (3) confirm the adequacy of the model using the QQ graph and the Kolmogorov distance (d = 0,069); (4) calculate the annual probabilities excess of the standard deflection (30 mm) and cumulative risks of deflections above the standard value for 5 and 10 years (61 % and 85 %, respectively), as well as return levels for repeatability periods of 5, 10 and 20 years. We also once again considered an important applied difficulty — the interpretation of the time scale, which plays a key role for effective probabilistic forecasts of the technical condition of an engineering structure.

Keywords: theory of threshold values; generalized Pareto distribution; theory of extreme values; method of threshold exceedances; return levels; Gnedenko’s theorem; Pickands-Balkema-de Haan theorem; Karamata theory

Download article in PDF format