A mathematical representation of an automated system designed to monitor critical infrastructure objects using seismic and acoustic signals

DOI: 10.31673/2786-8362.2024.011111

Abstract

The article considers the mathematical model of the automated system of seismoacoustic monitoring of critical infrastructure objects. In the monitoring approach, the object is identified with a point in the multidimensional space of free model parameters. Thus, the forecast about the state of the object is a forecast of a significant shift in the position of the parameter vector in the parameters space. When choosing a mathematical model, it is necessary to select a space of informative parameters to reduce the probability of errors of two types. First of all, it is necessary to build a mathematical model of the dynamics of the OKI, which reflects the most significant moments of the monitoring process, including both the process itself and the disturbances accompanying this process and the noise background superimposed on the process of the dynamics of the state of the OKI. A priori knowledge of the interference of an arbitrary process will significantly weaken its influence on obtaining estimates of the parameters of the process, which is perceived as a useful signal. This attenuation is achieved by optimizing processing procedures that take into account the a priori statistics of the random interference process. A new mathematical model in the form of a superposition of Berlasi pulses in the seismoacoustic frequency range and constructive algorithms for its implementation are proposed. The mathematical properties of the model were studied. Thus, the state of OKI is reflected in the vector of free parameters of the above model. To evaluate the informative parameters of the proposed model of the automated seismo-acoustic monitoring system, the work solves the problem of nonlinear regression, considering them as the point of the criterion optimum in the n-dimensional space. In the situation that has developed in our country, related to the conduct of military operations on its territory and missile attacks, the creation of automated seismo-acoustic monitoring systems of critical infrastructure objects is a necessary task.

Keywords: monitoring, critical infrastructure, acoustic signal, information parameters, automated system.

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