PARAMETRIC MATHEMATICAL MODEL OF SEISMOACOUSTIC MONITORING OF A SINGLE MORTAR EXPLOSION

DOI: 10.31673/2412-4338.2024.019903

Abstract

The article is devoted to constructing a mathematical model of a single mortar explosion signal for automated seismoacoustic monitoring systems to identify mortar weapons for remote reconnaissance. Structural analysis and identification of the dynamic parameters of such objects is an extremely important topic when monitoring them to classify the weapons used for remote reconnaissance. A new mathematical model for identifying a mortar explosion is proposed, which reflects the most significant aspects of the monitoring process, which includes both the process itself and the interference and background noise accompanying this process imposed on a natural research. The article presents a technique for identifying the main structural parameters, such as the leading natural frequencies and the quality factor of the structure at these frequencies. The work proposed a new, previously unused method for assessing the identification of a mortar explosion, within the framework of which an original mathematical model was proposed that solves these problems.
The proposed model is a nonlinear regression problem. To find an approximate solution to such a problem, the authors use non-convex optimization methods, for example, to find local minima - Livenberg-Marquardt gradient methods, and to find a global minimum, the Monte Carlo method using specific sequences is effective. In some cases, it is possible to search for local extrema in the vicinity of given vectors of values of all parameters when, for nonlinearly entering parameters, there is only one root closest to the given value of the corresponding parameter.
As a signal model, a superposition of solutions of a second-order differential equation was chosen, which describes a superposition of oscillators that entered at different times, having their eigenfrequency and corresponding amplitudes.
The optimal estimation of the signal parameters consists in determining the vector of free parameters that minimize the value of the criterion of agreement between the model and the observed data. Such a model is supported by the fact that it gives good agreement in the case of modeling a linear system of oscillating objects and, thus, takes into account the oscillating nature of the observed data and its simplicity. Thus, the presented model displays each type of mortar firing shots into its n-dimensional vector of informative parameters, making classifying small arms possible. To evaluate the informative parameters of the proposed model of the automated seismo-acoustic monitoring system, the article solves the problem of nonlinear regression, considering them as the point of the criterion optimum in the n-dimensional space.

Key words: mathematical model, sesmoacoustic monitoring, Monte Carlo method, nonlinear regression, vector of informative parameters, Livenberg-Marquardt method, explosion identification.

References
1. Mostovyy V. Models of geophysical fields of monitoring systems, dissertation for the academic degree “Doctor of Physical and Mathematical Sciences”, Kyiv, 2013, 233 pages.
2. R. Bellman. Dynamic Programming. Princeton University Press, 1957 -339 р.
3. Plessix R.-E. A review of the adjoint-state method for computing the gradient of a functional with geophysical applications - Geophys. J. Int. (2006) 167, 495
4. Sobol’ I. Monte Carlo numerical methods. M. Nauka , 1973. 311 p.
5. http://mathworld.wolfram.com/HeavisideStepFunction.html
6. Plessix R.-E. A review of the adjoint-state method for computing the gradient of a functional with geophysical applications - Geophys. J. Int. (2006) 167, 495-503.
7. K. Levenberg. A method for the solution of certain non-linear problems in least squares. Quart. Appl. Math., 2:164–168, 1944.
8. D. Marquardt. An algorithm for least-squares estimation of nonlinear parameters. J. Soc. Indust. Appl. Math., 11:431–441, 1963.
9. Mostovyy S., Mostovyy V., Osadchuk A. A mathematical model of prediction of seismic events. Proceedings of the second workshop “Application of artificial intelligence techniques in seismologic and engineering seismology” Consel de l’Europe Cahiers Europeen de Geodinamiqueet de seismologie, Luxembourg. 1996, Vol. 12, pp. 163-164.
10. Mostovyy S., Mostovyy V., Osadchuk A. Processing of seismic signals under coastal background noise. Application of artificial intelligence techniques in seismologic and engineering seismology Consel de l’Europe Cahiers Europeen de Geodinamiqueet de seismologie, Luxembourg, 1996, Vol. 12, p. 297-299.
11. Mostovyy V., Mostovyy S., Osadchuk A, Gay A.. On-line systems of monitoring of ecologically hazardous objects. Transactions of KDS-97, Yalta 1997, Vol. 1, pp. 456-465.
12. Mostovyy V., Mostovyy S. Estimation of parameters of seismic waves. Transactions of NAS of Ukraine.2014, Vol. 2, pp. 118-123.
13. V. S. Mostovoy, S. V, Mostovyi Mathematical model of seismic signal, as a flow of physically non realizable single seismic waves // Geophysical journal 2016, Vol. 38, № 5, p. 166-169.