Mathematical Modelling of Sayano-Shushenskaya Dam Displacement Process after 2009 Accident

Abstract

The research presented in the article is of cutting-edge importance because it proves the necessity to develop prognostic mathematical models with the view to studying the behavior of high-head dams for identifying the regularities of their deformations development process and thus providing quantitative definition for the set criteria values of the diagnostic indices to ensure safe operation of such structures. The paper focuses on the peculiarities of building prognostic mathematical models of the dynamic type on the basis of recurrent equations of the 1stand 2ndorders of different types depending on the order of the mathematical model, number of the principal acting factors and discreteness of the input data, with decorrelation of the input actions and sequence of transport delay introduction. It is shown that the properties of the recurrent equation solution in the form of two first conditional moment generating functions of the displacement process of the observed points in the structure delineate a prognostic model which allows predicting the displacements of the observed points. The paper describes the sequence of estimation stages during the creation of prognostic mathematical models in respect to the character of the predictive problem for various time periods of the structure operation. Different combinations of input actions and discreteness of input data, as well as their decorrelation, have been used. We also applied transport delay in order to correctly consider the inertial delay of the dam under different loads. To account for the residual part of the inertial delay, which is affected by random and unaccounted for factors, we used the autoregression model of the process development regularity. To determine the order of the autoregression model, we calculated asymptotically unbiased ratings of the correlation function for the residual error as a difference between the actual and predicted displacements. Methodological specifics of constructing prognostic models have been established in the context of the factors above. Prognostic mathematical models of different types have been developed for the selected period of the dam operation and the results of prediction have been discussed.

Mathematical Modeling of Landslide Slope Dynamics and Sustainable Development of Territories of Asian Russia

“…Predicted results of mathematical models can become one of the key tools used as a "solver" in spatial expert systems when shaping knowledge about the state of a link of a particular regional or interregional production chain. In this regard, dynamic models are more advantageous since they have flexible structure that matches the physical essence of the developed process and takes into account inertial interaction both landslide process and influencing factors and their temporal changes (Khoroshilov 2018). For instance, a second-order lag input-output model that describes the movement of a randomly selected landslide point caused by two main influencing factors is defined by the following recurrent expression:…”

“…where: µ, η are estimated parameters. Khoroshilov (2018) recommends estimating parameters  , by minimizing the functionality:…”