This paper presents an inverse problem protocol designed to estimate the explosive mass involved in accidental explosions by analyzing the observed effects on structures and individuals. Theoretical equations for calculating overpressure and momentum—which, although less accurate than finite element simulations, do not require significant computational resources—and the Probit methodology for damage quantification are widely employed. By applying both techniques, this study identifies the most suitable effects for applying the inverse problem, considering their distribution relative to distance and explosive mass. Mortality-related effects are considered unreliable due to their extremely narrow range, introducing significant uncertainty. However, eardrum rupture offers a broader distribution, although its practical application is complex due to the difficulties in determining both the distance to the population and the percentage of affected individuals. Conversely, structural damage to buildings proves to be the most accurate and reliable indicator, facilitated by GIS-based distance measurements and the clear categorization of damage levels. Finally, the use of a confidence interval in the inverse problem protocol allows for the filtering of highly biased data, ensuring that unreliable observations do not compromise the accuracy of the result. Furthermore, analysis demonstrates that a 90% confidence level minimizes relative error and improves robustness. In conclusion, a protocol is presented that allows the determination of the mass of the unstable substance involved in accidental explosions, specifying both the appropriate statistical indicators and the effects that are suitable for use in the inverse problem.
Citation: Juan Francisco Sánchez-Pérez, Manuel Conesa, José Jodar, Enrique Castro, Martina Fernández-García. Inverse protocol for determining the explosive mass of unstable substances in real accidental explosions[J]. AIMS Mathematics, 2026, 11(4): 9612-9632. doi: 10.3934/math.2026398
This paper presents an inverse problem protocol designed to estimate the explosive mass involved in accidental explosions by analyzing the observed effects on structures and individuals. Theoretical equations for calculating overpressure and momentum—which, although less accurate than finite element simulations, do not require significant computational resources—and the Probit methodology for damage quantification are widely employed. By applying both techniques, this study identifies the most suitable effects for applying the inverse problem, considering their distribution relative to distance and explosive mass. Mortality-related effects are considered unreliable due to their extremely narrow range, introducing significant uncertainty. However, eardrum rupture offers a broader distribution, although its practical application is complex due to the difficulties in determining both the distance to the population and the percentage of affected individuals. Conversely, structural damage to buildings proves to be the most accurate and reliable indicator, facilitated by GIS-based distance measurements and the clear categorization of damage levels. Finally, the use of a confidence interval in the inverse problem protocol allows for the filtering of highly biased data, ensuring that unreliable observations do not compromise the accuracy of the result. Furthermore, analysis demonstrates that a 90% confidence level minimizes relative error and improves robustness. In conclusion, a protocol is presented that allows the determination of the mass of the unstable substance involved in accidental explosions, specifying both the appropriate statistical indicators and the effects that are suitable for use in the inverse problem.
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Juan Francisco Sánchez-Pérez, Manuel Conesa, José Jodar, Enrique Castro, Martina Fernández-García. Inverse protocol for determining the explosive mass of unstable substances in real accidental explosions[J]. AIMS Mathematics, 2026, 11(4): 9612-9632. doi: 10.3934/math.2026398
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