(untitled) (MODERN CONSTRUCTION AND ARCHITECTURE, 2023)
It is established that in terms of the discrete Markov process, the problem is reduced to the search for unconditional probabilities of the system S at an arbitrary step k in state Si, that is, obtaining a transition probabilities matrix. In this formulation, the model is used for assessing the technical condition of the element; assessing the level of safety of operation of structural elements; ranking elements according to the need for repairs, reconstruction or replacement; in strategic planning of repair or reconstruction costs in conditions of limited funding and forecasting the remaining resource of elements. It is established that the theoretical basis of the study, which aims to predict the resource of hydraulic structures in operation, is the Markov theory of random processes. For a mathematical description of the process of element degradation, the most successful is the mathematical apparatus of the Markov random processes. Determination of the failure intensity parameter is the dominant feature of the Markov phenomenological model of damage accumulation to hydraulic structures’ elements. The only parameter of lifecycle management is the failure rate l. In the model under consideration, the parameterl is determined based on the initial conditions for an individual element obtained from the survey results. Because the parameter λ is determined for an individual element and must be specified each time after the next survey, the accuracy of the model will increase. The proposed model is integral. It does not contain an explicit theoretical apparatus for a material-sensitive element, its static scheme, construction technology, environmental conditions, etc. On the other hand, all these factors and many other secondary ones are taken into account in the model at the moment the state of the element is determined using classification tables containing physical and mechanical signs of degradation. In the theory of structures, the statistical approach to formulating the transition matrix is widespread and is based on historical data from the structure operation system. It is believed that the transition matrix based on the data of the operating system is a more realistic basis for predicting the processes of structures degradation. A large number of foreign studies are devoted to the practical application of the transition matrix based on statistical data, which consider the features of transition matrices related to the bridge operation system in different countries. In this formulation, each element of the transition probability matrix P is the probability that the system in the state will move to state j in one step (i.e., in one year). At the same time, it is considered that there are no operational interventions, so the sub-diagonal elements are zero. As before, the sum of elements of the same line is 1 and the element pjj = 1 because state j is absorbing. For the implementation algorithm of the Markov chain model for forecasting the technical condition of hydraulic structures in general, the initial data are: statistical data of the distribution of structures by the state at the time of the forecast, the rating assessment of the structure is calculated by an expert according to the scale and the forecast time in years. It is established that the degradation properties of structural designs are described by two parameters: the degradation criterion and the failure rate. Any factor of the stress-strain state can be taken as a degradation criterion: reliability, internal forces, or deformations. The degradation criterion can be an arbitrary rating assessment. In our case, the reliability of the element is taken as the degradation criterion, as the most general factor of the stress-strain state.