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.

利用马尔可夫链蒙特卡洛（MCMC）随机抽样，基于期望最大化（EM）算法的参数优化，提出了冲击波超压的高斯混合模型（GMM），以提高采样的准确性。从瓦斯爆炸事故的统计数据中可以得出不同条件下瓦斯累积引起爆炸的概率。通过使用现场气体数据估算爆炸当量和冲击波超压。建立了不同类型瓦斯爆炸的数据集及其对应的密度分布函数。EM算法用于迭代计算，并获得每个瓦斯爆炸数据集的最佳分布。根据后验优化建立参数。使用状态转换矩阵来实现MCMC气体爆炸冲击波超压的数值反演。反演结果基于矿山的实际情况。在提高随机模拟精度的前提下，冲击波的超压值更符合灾害变化规律，为灾害时的安全防护提供了理论依据。