基于多元正态分布理论的盐岩蠕变参数概率分布

Probability Distribution of Rock Salt Creep Parameters Based on Multivariate Normal Distribution

根据某拟建储气库库址盐岩的蠕变实验数据和蠕变变化规律,基于伯格斯蠕变模型拟合得到该库区盐岩的蠕变参数。将各蠕变参数当作随机变量,考虑盐岩形成过程及蠕变实验过程中多种随机因素对蠕变参数的影响。考虑各蠕变参数之间的相互联系,假设由各蠕变参数变量共同构成的五维总体随机样本服从五元正态分布,求解得到该五元正态分布的联合密度函数,通过协方差阵揭示各蠕变参数之间的联系,并利用χ2统计量的Q Q图检验法对多元正态假设进行检验。结果表明,由各蠕变参数变量共同构成的五维总体随机样本可以很好地服从五元正态分布。研究结果可为盐岩蠕变参数概率分布的研究提供参考。

According to the rock salt creep experimental data at a would-be gas storage site and their variation pattern, based on the Burgers creep model fitting, the rock salt creep parameters of the gas storage are obtained. Taking each of the creep parameters as a random variable, the influence of many random factors on the creep parameters is studied during the rock salt formation and its creep experiment process. Considering the linkages between the creep parameters, assuming a five variable overall random sample constituted by the creep parameter variables in accordance with a five variable normal distribution, the joint density function of the five variable normal distribution is obtained. Then the link between the creep parameters is revealed through the covariance matrix, and the multivariate normal distribution assumption is tested by the Q-Q test method of the X^2 statistics. It is shown that the five variable overall random sample constituted by the creep parameter variables can be very well represented by the five variable normal distribution. The results provide an insight for the probability distribution of rock salt creep parameters.