Study on the features of coal rock failure potential signal based on multiscale multifractal analysis method
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摘要: 煤岩变形破坏诱发的表面电位信号包含损伤演化的关键信息，在煤岩动力灾害监测领域得到广泛研究，但大多是在单一时间维度对电位时序信号的波动特征进行研究，对时序信号的非线性、多尺度特征变化规律缺乏深入研究。针对该问题，搭建了煤岩破坏电位监测系统，同步测试了原煤和辉长岩2种试样的电位时序信号，并通过多尺度多重分形（MMA）法，深入研究了多尺度下的电位信号非线性特征，得到了电位时序信号的奇异性指数、奇异维数、局部赫斯特指数等参数，并采用L2范数对赫斯特曲面予以量化。实验结果表明：原煤和辉长岩的总体电位信号都呈现出多尺度多重分形特征，且裂纹萌生前后的电位多重分形图谱呈现一定差异性；相较于辉长岩，煤样在加载前后阶段不同位置处电位信号的奇异性指数差异Δα正负趋势呈现不同特征，表明了煤样具有更强的非线性演化特征；多尺度下局部赫斯特指数的L2范数更好地体现出试样不同通道电位信号间的长程相关性，并能够量化试样电位时序信号的非线性演化特征，进而实现煤岩失稳破坏预测。Abstract: The surface potential signals induced by the deformation and failure of coal and rock contain key information on damage evolution. It has been widely studied in the field of coal and rock dynamic disaster monitoring. However, most of these studies focus on the fluctuation features of potential time series signals in a single time dimension. There is a lack of in-depth research on the nonlinear and multiscale feature changes of the time series signals. To solve this problem, a monitoring system for the potential of coal and rock failure is built, and the potential time series signals of raw coal and gabbro samples are synchronously tested. Through the multiscale multifractal analysis (MMA) method, the nonlinear features of potential signals at multiple scales are studied in depth. The singularity index, singularity dimension, local Hurst index and other parameters of the potential time series signals are obtained. The Hurst surface is quantified by the L2 norm. The experimental results show that the overall potential signals of raw coal and gabbro show multiscale multifractal features, and the potential multifractal maps before and after crack initiation show some differences. Compared with gabbro, the positive and negative trends of the singularity index difference Δα of the potential signals of the coal samples at different positions in the pre-loading and post-loading phases show different features. It indicates a stronger non-linear evolution of the coal samples. The L2 norm of the local Hurst index at multiple scales better reflects the long-range correlation between different channel potential signals of the sample. It can quantify the nonlinear evolution features of the sample time series signals, thereby achieving the prediction of coal rock instability and failure.
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图 5 原煤通道1前后期及总体赫斯特曲面
Figure 5. Hurst surface of early, late and overall stage of raw coal's channel 1
图 6 原煤通道2前后期及总体赫斯特曲面
Figure 6. Hurst surface of early, late and overall stage of raw coal's channel 2
图 7 辉长岩通道1前后期及总体赫斯特曲面
Figure 7. Hurst surface of early, late and overall stage of gabbro's channel 1
图 8 辉长岩通道2前后期及总体赫斯特曲面
Figure 8. Hurst surface of early, late and overall stage of gabbro's channel 2
表 1 原煤与辉长岩物理力学特性
Table 1. Physical and mechanical properties of row coal and gabbro
试样 密度/ (g·cm−3) 弹性模量/GPa 峰值强度/MPa 原煤 1.19 2.00 14.55 辉长岩 2.92 14.84 75.22 
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表 2 不同通道各时期L2范数
Table 2. L2 norms of different periods in different channels
通道 d1 d2 d0 L2范数比值/% d1/d0 d2/d0 原煤通道1 16.16 15.28 14.96 108.02 102.14 原煤通道2 16.32 13.87 14.77 110.49 93.91 辉长岩通道1 15.35 18.02 16.56 92.69 108.82 辉长岩通道2 15.46 17.80 16.03 96.44 110.04
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