岩石声发射b值变化是岩石破坏的重要前兆之一,由于b值大小受到样本数、起算幅值和幅值间隔等人为设定的影响,开展b值误差量化分析意义重大。采用不同的样本数、起算幅值和幅值间隔,使用最大似然法和最小二乘法计算由随机数组成的岩石声发射幅值目录的b值,将结果中分布在误差以内的数据记为有效数据,使用有效数据占比分析了b值误差大小,并使用室内花岗岩三轴压缩的声发射幅值目录对其进行了验证。结果表明:使用最大似然法计算岩石声发射b值时,有效数据占比随着样本数的增加而减少,随着起算幅值的增大而增加。使用最小二乘法估计b值时,随着样本数的增加,有效数据占比先增后减,样本数为2 000个左右时可得到最多的有效数据;幅值间隔一定时,起算幅值越大,有效数据占比越小;随着起算幅值的增加,对应的取得最多有效数据的幅值间隔从22 dB减少到18 dB。研究成果可为岩石破坏声发射b值的合理计算提供参考。
Abstract
The change in b-value of rock acoustic emission is an important precursors of rock fracture. However, b-value is affected by artificial settings such as sample size, start amplitude and amplitude interval. It is of great significance to quantify the error of b-value. In this paper, the maximum likelihood method and the least squares method are employed to calculate the b-value of the rock fracture acoustic emission amplitude catalogues composed of random numbers with different sample sizes, start amplitudes and amplitude intervals. The results distributed within the error are recorded as valid data, and the error of b-value is analyzed according to the proportion of valid data. The result is verified using the acoustic emission amplitude catalog of indoor triaxial compression test data. For maximum likelihood method, the valid data proportion reduces as the sample size increases, while augments as the start amplitude increases. For least squares method, as sample size increases, valid data proportion first increases and then declines. The most valid data is obtained when the sample size is around 2000. Given the same amplitude interval, as the start amplitude increases, the corresponding optimal amplitude interval reduces from 22 dB to 18 dB. This study provides a conducive reference for the reasonable calculation of b-values of rock fracture acoustic emission.
关键词
声发射b值 /
误差分析 /
最小二乘法 /
最大似然法 /
有效数据占比 /
蒙特卡洛方法
Key words
b-value of acoustic emission /
error analysis /
least squares method /
maximum likelihood method /
valid data proportion /
Monte-Carlo method
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基金
国家自然科学基金项目(51774327,51822407); 湖南省杰出青年基金项目(2018JJ1037)
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