Received 03.01.2021
Revised 08.05.2021
Accepted 18.06.2021
Retrieved from Iss. 109, 2021
Pages 79 -87
Abstract
The life cycle of a construction (or its element) is considered as markovian process with discrete states and continuous time. Five operational states have been accepted, in which the construction may be. The corresponding system of differential equations is obtained for the case of a homogeneous markovian process with a constant conversion rate (Kolmogorov system). The method of uncertain coefficients is applied to solve the system of equations in analytical form. The obtained solutions make it possible to determine the probability of finding the construction in a particular state as well as the most likely transition time from one operational state to another. Security function defined as the probability of not finding the construction in its last (inoperable) state and the failure rate function. The graphs of the probability of finding a construction in each of the five states, reliability and failure rate functions are presented and investigated. The obtained ana lytical dependences make it possible to determine the longevity and residual life of the work both individual elements and structures as a whole and optimize scheduling for ongoing maintenance work, significantly im prove the performance of the structure, reduce the cost of repair work and extend the life of the structure.
Keywords:
reliability function, Kolmogorov equations, markovian model, failure rate, durability, residual lifeDSTU-N B V.2.3-23: 2009. Guidelines for estimating and forecasting the technical condition of road bridges: - K .: Minregionstroi Ukraine, 2009. - 49 p.
Bogdanof J. Probabilistic models of damage accumulation / Kozin F. - Moscow: Mir, 1989. - 344 p.
Bolotin V.V. Resource machines and structures. / V.V. Bolotin. - M: Mechanical Engineering, 1990. - 446 p.
Wentzel, E.S. Theory of random processes an d its engineering applications / E. S. Wentzel, L. A. Ovcharov - Moscow: Higher. School, 2000. - 383 p.
Gmurman, V.E. Probability theory and mathematical statistics / V.E. Gmurman. - Moscow: High School. - 1972. - 367 s.
Gnedenko V.V., Belyaev Yu.K., Soloviev A.D. Mathematical methods in the theory of reliability / V.V. Gnedenko, Yu.K. Belyaev, A.D. Soloviev. Gnedenko V.V., Belyaev Yu.K., Soloviev A.D. - Moscow: Science. - 1965. - 361 s.
Yevseychik Yu.B., Medvediev K.V. Algorithm for determining the reliability of an element of a design with a function of the function of the intensity of the failures // Prob. Motor roads and road construction. - 2017, vp. 99 - p.210 - 217.
Lantuh-Lyashchenko A.І. A probabilistic model for assessing the technical condition and forecasting the residual life of road bridge elements / Lantukh-Lyashchenko A.I. - M .: Roads and bridges. Russian Road Research Institute. 2007. - p. 103–111
Lantuch-Lyashenko A.I. Estimation of the reliability of the construction on the model of a random Markov process with discrete states. // Sb. Motor roads and road construction. - 1999, issue 57 - pp. 183-188.
Lantuch-Lyashenko A.I. Estimation of technical condition of transport structures in operation. Bulletin of the Transport Academy of Ukraine, №3, Kyiv: 1999.-с. 59-63.
Lantuch-Lyashenko AI, Kirian V.I., Koval P.M. etc. Guidelines for determining the technical condition of bridges. - TAO Kind. "Logos", K.: 2002. 117 p.
Petrovsky I.G. Lectures on the theory of ordinary differential equations. M .: Science, 1970.
Rzhanitsyin A.R. Teoriya rascheta stroitelnyih konstruktsiy na nadezhnost. M.: Stroyizdat, 1978.