Numerical inversion of Gaussian mixture model for gas explosion shock wave based on a Markov chain Monte Carlo algorithm

Abstract

Using Markov chain Monte Carlo (MCMC) random sampling, a Gaussian mixture model (GMM) of the overpressure of a blast shock wave based on parameter optimization of an expectation-maximization (EM) algorithm is proposed to improve the accuracy of sampling. The probability of an explosion caused by gas accumulation under different conditions is obtained from statistics of gas explosion accidents. The explosion equivalent and shock wave overpressure are estimated by using field gas data. The data sets of different types of gas explosions and their corresponding density distribution functions are established. The EM algorithm is used for iterative calculation, and the optimal distribution of each gas explosion data set is obtained. The parameters are built according to a posteriori optimization. A state transition matrix is used to achieve numerical inversion of the overpressure of an MCMC gas explosion shock wave. The inversion results are based on the actual conditions of the mine. On the premise of improving the accuracy of the random simulation, the overpressure value of shock wave is more in line with the law of disaster change, which provides theoretical support for safety protection during a disaster.