MATHEMATICAL MODEL OF THE SIGNAL EMISSION DYNAMICS IN SEISMIC-ACOUSTIC MONITORING SYSTEMS OF BUILDING STRUCTURES

Abstract

B a c k g r o u n d . The paper presents a mathematical model of automated systems of seismoacoustic monitoring of building structures to assess the dynamics of crack formation in building structures to prevent the destruction of the objects under investigation. The seismoacoustic field generated by the research objects is reflected in the matrix of informative parameters, the dynamics of which characterize the dynamics of the object's state. To assess the dynamics of high-frequency signals generated by cracks that occur during the operation of the structure, it is advisable to use the dynamics of emissions that generate these signals. For this, from the point of view of physical practicality, it makes sense to choose a model that characterizes the dynamics of the high-frequency range of the spectrum. Namely, the work presents an algorithm based on a theorem for stationary processes in a broad sense.

M e t h o d s . The aging process can be reflected in the feature space, which can be reduced to parameters characterizing the elastic properties of the materials that form the objects under study. Since the propagation velocities and the shape of longitudinal and transverse waves in the material depend on the elastic parameters of these materials (Poisson's ratio and Young's modulus), the change in these parameters leads to changes in the spectral characteristics of the emission signals that occur in the aging material. Any redistribution of energy in the material is accompanied by the appearance of signals that generate emission. The dynamics of the parameters of the emission signal reflect the change in the elastic properties of the object under study. Possible reasons for changes in the internal structure are the appearance and growth of cracks, phase transitions in monolithic materials, and loosening of components. This means that changes in the dynamic parameters of emission signals are related to the dynamic characteristics of this object.

R e s u l t s . A mathematical model of building structure aging is proposed. This model of aging of the object must consider the nature of external influences on the object and the nature of its reaction to external disturbances. Given stochastic background noise during monitoring, only the statistical nature of this dependence should be accepted in the model. This model is implemented in building № 3 (cell) of the Kyiv Pechersk Lavra.

C o n c l u s i o n s . Two stages of the study of the emission dynamics of building № 3 of the Kyiv Pechersk Lavra showed that during the given time interval, the change in the emission characteristics of this object is within the measurement error. Thus, for an adequate assessment of the emission dynamics generated by cracks that arise during the KPL hull No. 3 operation, it is necessary to collect statistics over a time interval of several decades. To solve this problem, it is essential to carry out permanent seismoacoustic monitoring of the building structure.