STATISTICAL ANALYSIS OF RANDOM EXPLOSION PARAMETERS AT VARIOUS LEVELS OF DAMAGE TO STRUCTURES AND BUILDINGS

Аннотация

This article examines the issue of determining the resource capacity of structures and buildings using statistical methods. Based on experimental data, mathematical modeling was used to study the durability of objects and their condition under the influence of internal and external forces. The assessment of the degree of damage to buildings and structures under the impact of explosive substances was carried out using the Gaussian normal distribution. Statistical parameters such as the coefficient of variation, arithmetic mean, variance, and standard deviation were determined. The calculation results showed that the mathematical and statistical analysis of random explosion processes corresponds to theexperimentaldata. Keywords: statistical analysis, mathematical modeling, structural durability, Gaussian normal distribution, coefficient of variation, arithmetic mean, variance, standard deviation, explosive processes, building damage. Using statistical methods, any experimental results can be mathematically modeled. The essence of mathematical statistics lies in determining all parameters of the probability distribution functions of random processes (phenomena). To find these parameters and their values, integral calculus and the solution of differential equations are usually required. Such problems are addressed within the field ofmathematical analysis. When determining the resource capacity of structures based on experimental data, the mathematical expectation , the arithmetic mean , and the behavior of structures and buildings under the influence of external and internal forces (earthquakes, explosions, loads, pressure, etc.) are analyzed. In particular , t(h e)ir oscillations or damag es of varying degrees are considered, expressed through deviations from thecenter ofgravity varianceand thestandard deviation ( ). The resource is an indicator that det er(m )ines how long a structure (building) can be operated and how long it can continue functioning without interruption. The resource diagnosis is expressed through the function . The condition of structures damaged as a result of a random explosion has been proven to de−p e nd on the parameters of the explosive material. However, the degree of correlation between th e constituent components of explosives and their statistical parameters ( , , z coefficients of variation) is not always precisely determinable. The coefficient of variation ( ) , expressed as a percentage, represents the ratio of the standard deviation to the arithmetic mean хa nd i 6 sdetermined bytheformula: 6 19 INTERNATIONAL MULTIDISCIPLINARY JOURNAL FOR RESEARCH & DEVELOPMENT SJIF2019:5.2222020:5.5522021:5.6372022:5.4792023:6.5632024:7,805 eISSN:2394-6334 https://www.ijmrd.in/index.php/imjrd Volume12,issue03(2025) . ( ) If the mass of the explosive substance increases and the distance between the charge and the = object becomes relatively smaller (closer), then thepressure variation coefficient will behigher. In all statistical distributions (Gauss ian , Rayleigh, Student's t-distribution, Fisher-Snedecor, Weibul l-Gnedenko, etc.), three main parameters must be determined: the mathematical expectation , the variance of the random variable , and the standard deviation ( ). Among them, the Gaussian normal distribution stands out due to its high accuracy in diagnosing the degree of( d)am=ag e to structures and buildings, as well a s( in) scientific research of their physical and mechanical properties [1-3]. In a series of studies, experiments were conducted in which pressure was recorded at various distances from the explosion epicenter. The impact of the explosion was analyzed using a numerical model and subjected to statistical analysis [4]. For random TNT (trinitrotoluene) charges with a mass of kg, the correspondence of building damage points to the Gaussian normal distribution is scientifically analyzed. During the calculations, the coefficient of variation was assumed to be = 10,..3a0nd was considered constant for aseries ofrandom explosions. The density (differential)function ofthenormal distributionc a n=be0e,x2pressed in thefollowing form: (1) 2 1 ( − ) Here: 2 = ( ) 2 ⋅exp− 2 ( ) ( ) —differential (density) function oftheGaussian distribution bymass; —standard deviation; —unknown mathematical expectation, = 2 .71=... — baseofthe natural logarithm. T able 1 20 forebmuN ) ( segrahc )гк( ssam egrahC ytilibaborp modnaR 61+ 4 = 2 2 ( ) ( ) ( ) ( ) ( ) 1. 1 20 0.05 1 1 08.3 01.61 02.12 65.62 2.5 2. 2 24 0.10 2 4 3. 6 28 0.30 3 9 4. 3 32 0.15 4 16 5. 7 26 0.35 5 25 6. 1 40 0.05 6 36 If this statistical distribution is close to the mean value, the approximate equality holds. More precise criteria corresponding to empirical and theoretical distribution laws will be proposed in the future. ℎ ( ) Table 2 1 2 3 4 5 6 0,05 0,10 0,30 0,15 0,35 0,05 1 4 9 16 25 36 2 INTERNATIONAL MULTIDISCIPLINARY JOURNAL FOR RESEARCH & DEVELOPMENT SJIF