基于混沌理论的岩石声发射性能研究
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摘要
声发射技术作为对岩土工程进行安全监测的有效手段之一,近年来越来越得到广泛应用,然而在声发射技术的实际监测预报应用中却还存在一些问题。究其原因是岩体系统是高度非线性复杂大系统,并处于动态不可逆演化之中,人们尚未完全掌握岩石破坏的特征。要对岩石(体)的力学行为进行预测和控制,应该借助当代非线性科学,建立适合于岩石力学与工程特点的岩石非线性静力和动力系统理论。而混沌是非线性数学、力学研究的一个热点,它也是非线性系统的根本特征之一。岩体系统中存在大量的非稳定数据和离散的非均匀数据,如位移、声发射、地震的时序记录数据等,均有可能用混沌模型予以很好的描述,并能揭示出更深刻的岩体力学机制与规律。基于以上思想,本文主要研究工作为:
①本文采用AG-I液压伺服材料试验机以及PCI-2声发射仪等仪器设备,对钙质泥岩、砂岩、细砂岩、高丽山砂岩四种不同的岩石,进行单轴压缩破坏试验和声发射试验,运用声发射仪器监测岩石损伤破坏过程中的声发射现象,记录下声发射事件数时序、声发射能量时序、位移(应变)时序及应力时序,运用非线性动力学原理建立岩石在失稳破坏过程中的非线性动力学数学模型。
②对声发射事件数时序,进行了小波降噪处理,并进行了降噪后的混沌特征量的计算,与原始数据序列的结果做了对比,研究噪声对计算结果的影响。
③针对试验记录的声发射事件数时序,分别计算了声发射时间序列的嵌入维数和延迟时间,延迟时间的选取采用互信息量法,嵌入维数的选取采用Cao方法和饱和关联维数法。
④计算了声发射时间序列的特征量,分维数和Lyapunov指数(主要是最大Lyapunov指数)。分维数的不同定义和估计有不同结果,关联维数是最常用的分维数估计值,因此本文只采用了G-P关联积分法计算关联维数。对于最大Lyapunov指数的计算,则采用了小数据量法。从定性、定量两个方面对岩石声发射时间序列的混沌性质进行了判别,采用的定性方法为:主分量分析(PCA)方法;采用的定量分析方法为:饱和关联维数法和最大Lyapunov指数法。
⑤对岩石破坏声发射信号前兆特征进行了探讨,对应用声发射基本参数判断岩石破坏进行了讨论,运用混沌分形理论建立声发射时间序列分维模型,通过讨论岩石破坏各阶段分形维数的变化,对岩石破坏的声发射前兆特征进行研究,寻找岩石破坏的判据。
Recently AE technology widely used is one of the effective means of the safety monitoring to geotechnical engineering. However some problems are met when AE technique is applied to monitoring and forecasting. The reason is that rock system is a highly nonlinear complex system during a dynamic and irreversible evolution, and the characteristics of rock damage are not fully understood. In order to predict the mechanical behavior of rock, the rock nonlinear static and dynamic systems should be established by using nonlinear sciences, which are suitable for describing the characteristics of rock mechanics and engineering. Chaos is suitable for researching non-linear mathematics and mechanics, which is also one of the fundamental characteristics of non-linear system. There is a large number of non-stable dispersion of data and non-uniform data in rock system, such as displacement, AE series, seismic data and other records of time series, which reveal failure mechanism of rock by using chaos.
The main points in this thesis are summarized as follows:
①Uniaxial compression damage tests and Acoustic emission test of Calcareous mudstone, sandstone, fine sandstone, Korea sandstone are carried with AG-I Full-digitally Servo-controlled testing machine and PCI-2 emissions equipment. Acoustic emission events time series, AE energy time series, displacement (strain) and stress time series are recorded in the process of rock test. On the basis of the theory of nonlinear kinetic principle, nonlinear dynamics model of rock failure process are discussed.
②Acoustic emission events time series is treated by using the wavelet noise reduction method. The chaotic characteristics are determined after the noise reduction. Comparing between the noise reduction data and the original data is done. The effect of noise on the chaotic characteristics was studied.
③AE time series embedding dimension and the delay time are calculated from the recorded acoustic emission time series. Delay time was chosen by using mutual information method. Embedding dimension was obtained by using Cao method and saturation correlation dimension law.
④Chaotic characteristics, i.e. fractal dimension and Lyapunov exponents (mainly the largest Lyapunov exponents), were given out. Fractal dimension from different definitions and estimates have different results, the correlation dimension is the most commonly used estimate of fractal dimension. The G-P saturation correlation dimension method is applied to compute the correlation dimension. The small data set method is applied to calculate the largest Lyapunov exponents of the time series. The chaotic feature of the rock AE time series is determined from the qualitative and quantitative aspects. The qualitative method is PCA (Principal Components Analysis) method, and the quantitative analysis methods are based on saturated correlation dimension law and the largest Lyapunov exponents method.
⑤The application of characteristics of the rock failure AE signal and the AE basic parameters to analyze the rock damage are discussed. The fractal model of acoustic emission time series is established based on the chaos fractal theory. By means of the changes of fractal dimension and the AE characteristics of rock damage during the various stages of rock damage, the criterion of rock damage is found.
①本文采用AG-I液压伺服材料试验机以及PCI-2声发射仪等仪器设备,对钙质泥岩、砂岩、细砂岩、高丽山砂岩四种不同的岩石,进行单轴压缩破坏试验和声发射试验,运用声发射仪器监测岩石损伤破坏过程中的声发射现象,记录下声发射事件数时序、声发射能量时序、位移(应变)时序及应力时序,运用非线性动力学原理建立岩石在失稳破坏过程中的非线性动力学数学模型。
②对声发射事件数时序,进行了小波降噪处理,并进行了降噪后的混沌特征量的计算,与原始数据序列的结果做了对比,研究噪声对计算结果的影响。
③针对试验记录的声发射事件数时序,分别计算了声发射时间序列的嵌入维数和延迟时间,延迟时间的选取采用互信息量法,嵌入维数的选取采用Cao方法和饱和关联维数法。
④计算了声发射时间序列的特征量,分维数和Lyapunov指数(主要是最大Lyapunov指数)。分维数的不同定义和估计有不同结果,关联维数是最常用的分维数估计值,因此本文只采用了G-P关联积分法计算关联维数。对于最大Lyapunov指数的计算,则采用了小数据量法。从定性、定量两个方面对岩石声发射时间序列的混沌性质进行了判别,采用的定性方法为:主分量分析(PCA)方法;采用的定量分析方法为:饱和关联维数法和最大Lyapunov指数法。
⑤对岩石破坏声发射信号前兆特征进行了探讨,对应用声发射基本参数判断岩石破坏进行了讨论,运用混沌分形理论建立声发射时间序列分维模型,通过讨论岩石破坏各阶段分形维数的变化,对岩石破坏的声发射前兆特征进行研究,寻找岩石破坏的判据。
Recently AE technology widely used is one of the effective means of the safety monitoring to geotechnical engineering. However some problems are met when AE technique is applied to monitoring and forecasting. The reason is that rock system is a highly nonlinear complex system during a dynamic and irreversible evolution, and the characteristics of rock damage are not fully understood. In order to predict the mechanical behavior of rock, the rock nonlinear static and dynamic systems should be established by using nonlinear sciences, which are suitable for describing the characteristics of rock mechanics and engineering. Chaos is suitable for researching non-linear mathematics and mechanics, which is also one of the fundamental characteristics of non-linear system. There is a large number of non-stable dispersion of data and non-uniform data in rock system, such as displacement, AE series, seismic data and other records of time series, which reveal failure mechanism of rock by using chaos.
The main points in this thesis are summarized as follows:
①Uniaxial compression damage tests and Acoustic emission test of Calcareous mudstone, sandstone, fine sandstone, Korea sandstone are carried with AG-I Full-digitally Servo-controlled testing machine and PCI-2 emissions equipment. Acoustic emission events time series, AE energy time series, displacement (strain) and stress time series are recorded in the process of rock test. On the basis of the theory of nonlinear kinetic principle, nonlinear dynamics model of rock failure process are discussed.
②Acoustic emission events time series is treated by using the wavelet noise reduction method. The chaotic characteristics are determined after the noise reduction. Comparing between the noise reduction data and the original data is done. The effect of noise on the chaotic characteristics was studied.
③AE time series embedding dimension and the delay time are calculated from the recorded acoustic emission time series. Delay time was chosen by using mutual information method. Embedding dimension was obtained by using Cao method and saturation correlation dimension law.
④Chaotic characteristics, i.e. fractal dimension and Lyapunov exponents (mainly the largest Lyapunov exponents), were given out. Fractal dimension from different definitions and estimates have different results, the correlation dimension is the most commonly used estimate of fractal dimension. The G-P saturation correlation dimension method is applied to compute the correlation dimension. The small data set method is applied to calculate the largest Lyapunov exponents of the time series. The chaotic feature of the rock AE time series is determined from the qualitative and quantitative aspects. The qualitative method is PCA (Principal Components Analysis) method, and the quantitative analysis methods are based on saturated correlation dimension law and the largest Lyapunov exponents method.
⑤The application of characteristics of the rock failure AE signal and the AE basic parameters to analyze the rock damage are discussed. The fractal model of acoustic emission time series is established based on the chaos fractal theory. By means of the changes of fractal dimension and the AE characteristics of rock damage during the various stages of rock damage, the criterion of rock damage is found.
引文
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