矿山微震时间序列的相空间构建与混沌吸引子维数确立

为了进一步挖掘矿山微震信号内蕴藏的信息，初步研究了微震信号的混沌特性。针对矿山微震信号非平稳、非线性的特点开展了以下研究:建立了一维时间序列的相空间重构模型，分析了一维和多维微震时间序列的空间相型；选取了矿山现场监测一维微震时间序列（N=2 000），利用自相关函数求取了时间序列的延迟时间τ；建立了微震时间序列关联分维数的循环计算模型；最终确立了相应临界距离r（r=250）和相空间维数m（m=50）的值，计算求得分维数D的值为1.088 5。研究结果表明，微震一维时间序列的吸引子维数存在，同时也证明了微震时间序列具有混沌特性。该研究结果为利用混沌理论处理矿山微震数据，如初始到时精确拾取、信号特征分析与提取以及波形降噪等提供理论依据。

Construction of phase space and determination of chaotic attractor dimension for time series of mine microseismic

The chaotic characteristics of microseismic signals were studied to investigate the underlying information of mine microseismic signals, and the following research was conducted aiming at the non-stationary and nonlinear characteristics of mine microseismic signals. A phase space reconstruction model of one-dimensional time series was established, and the spatial phase types of one-dimensional and multi-dimensional microseismic time series were analyzed. The delay time τ of time series was determined by using the autocorrelation function for the one-dimensional microseismic time series obtained by field monitoring in mine (N=2 000). The circulation calculation model on correlation fractal dimension of microseism time series was established. Finally, the values of corresponding critical distance r(r=250) and phase space dimension m(m=50) were determined, and the value of fractal dimension D was determined to be 1.088 5. The results showed that the attractor dimension of microseismic one-dimensional time series was existent, and the microseismic time series has the chaotic characteristics. It lays a foundation for the processing of mine microseismic data by using chaos theory, such as the precise picking of initial arriving time, the analysis and extraction of signal features, the waveforms denoising and so on.