| Abstrakt: |
Abstract: The paper presents the considerations devoted to homomorphism analysis of processes: displacement and medium (rock) vibration, generating physical risk for the area of topological transformations. The aim of the study was to a ssociate interactions: mining induced vibrations and displacement and their temporal relations. The basis for the analysis were both: sets of observed displacements - measured with GPS technology and recordings of acceleration process by using 3D vibration sensors, as well as mathematical modelling of these processes. It has been indicated, that the carrier of a formal process will be the probability space - which implies the stochastic nature of the phenomenon. Measures of the destruction occurrence - a critical process - there are the probability meas ures. In the estimated moment of timet, the results of observations of both processes - which are sets of real numbers - indicate that objects that are at risk of event are subjected to danger or failure. Fundamental here are mappings, used for modelling of concurrent processes, those comm unicate with each other. Features of timing relationships are: the structure and dynamics of processes. The emergence of the conflict - the occurrence of a critical event - has been estimated on the basis of the lemma for reaching of the outer extremes, in terms of equivalence relations in a fixed set of circumstances. The structural similarity between the two processes, their predictability and determination of characteristic frequencies was performed with using the relevant statistics, including the so-called Hurst exponent. An important element of proceeding the threats is the relationship in the domain of extreme events as a decisive influence - the difference compared to traditional analysis. The application layer contains specific examples of estimating the risk of a critical event arising. |
