Rock damage dynamic characteristic evaluation method based on phase-space reconstruction and sample entropy

Abstract

The invention provides a rock damage dynamic characteristic evaluation method based on phase-space reconstruction and sample entropy, and belongs to the field of rock mechanics and geotechnical engineering. The method specifically comprises the following steps: firstly, carrying out real-time acoustic emission monitoring on the rock in the damage process under the action of external force, and obtaining waveform data of an acoustic emission event; secondly, performing phase space reconstruction on the waveform data, selecting delay time by using an autocorrelation function method, selecting an embedded dimension by using an information dimension method and a sample entropy, and establishing a phase space; thirdly, calculating a dynamic evolution index of the acoustic emission event; and finally, repeating the steps for the next acoustic emission event along with the breaking, calculating the dynamic evolution index in the whole rock breaking process, and clearly evaluating the rock damage dynamic characteristics in real time. The method has the advantages that the dynamic characteristic evaluation of the damage in the rock deformation and damage process is realized, the method is efficient, the result is clear, and the method has a remarkable application value.

Description

Technical Field

[0001] The invention relates to an evaluation method for dynamic characteristics of rock damage under external force, and in particular to a dynamic evolution index suitable for measuring microscopic damage of rock under external force, and belongs to the field of rock mechanics and geotechnical engineering. Background Art

[0002] Rock damage problems are widely seen in mining, tunneling, water conservancy and other projects. Under the action of external forces, rocks often undergo complex deformation and damage, affecting the safety and stability of the project. Rock failure has the characteristics of suddenness, spatiotemporal uncertainty and nonlinearity. Traditional damage assessment methods are difficult to accurately predict the failure process. Therefore, how to monitor and evaluate the dynamic characteristics of rock damage in real time has become a core issue in the field of rock mechanics.

[0003] At present, rock damage assessment methods mostly rely on stress-strain testing and microstructure analysis, focusing mainly on macroscopic assessment after damage, and it is difficult to reveal the evolution of microscopic damage during the damage process. Acoustic emission technology, as an important monitoring method, has been widely used in the process of rock damage, and can obtain damage status information by detecting the signals released when the rock breaks. However, existing acoustic emission technology mostly focuses on the amplitude and frequency analysis of the signal, lacks microscopic analysis of the complex damage process, especially in high-frequency complex signal processing, and existing methods are difficult to accurately identify microscopic damage at different stages.

[0004] In order to overcome the shortcomings of existing technologies, the AE entropy parameter based on Shannon information entropy has been proposed in recent years. AE entropy can effectively reflect the deformation process of microstructures by quantifying the uncertainty of amplitude distribution, independently of thresholds and other time domain parameters, and can distinguish different damage stages and reliably identify critical damage. However, in the complex damage process of rock materials, this method still has the limitation of being unable to accurately locate the time of occurrence of microdamage and assess the severity of microdamage.

[0005] Therefore, a new method is urgently needed to overcome the shortcomings of existing technologies and provide more accurate real-time damage monitoring and assessment methods. Summary of the invention

[0006] In view of this, the present invention provides a method for evaluating the dynamic characteristics of rock damage based on phase space reconstruction and sample entropy. The results of this method are intuitive and clear, and can quantitatively evaluate the dynamic characteristics of rock damage under external forces.

[0007] In order to achieve the above object, the technical solution adopted by the present invention is as follows:

[0008] A method for evaluating the dynamic characteristics of rock damage based on phase space reconstruction and sample entropy. The method first performs real-time acoustic emission monitoring of the rock destruction process, obtains waveform data of acoustic emission events, and reconstructs the phase space. Secondly, the autocorrelation function method is used to select the delay time, and the information dimension method and sample entropy are used to select the embedding dimension. Thirdly, based on the phase space reconstruction, the dynamic evolution index of the acoustic emission event is calculated to reflect the dynamic characteristics of rock damage. Finally, during the rock destruction process, the above process is repeated for the waveform data of each acoustic emission event to evaluate the dynamic characteristics of rock damage in real time. The following steps are included:

[0009] S1. Real-time acoustic emission monitoring of the rock destruction process under external force is performed to obtain waveform data of all acoustic emission events;

[0010] S2, reconstructing the waveform data of a single acoustic emission event in phase space;

[0011] For the waveform data of a single acoustic emission event obtained by S1, the voltage of each sampling point in the waveform data is recorded in time sequence as x1, x2, ..., x n , forming a 1-dimensional time series {x1,x2,...,x n}, n is the total sampling number of a single acoustic emission event;

[0012] For the waveform data of a single acoustic emission event, a suitable delay time τ and embedding dimension m are selected, and a phase space vector X(t) is constructed in chronological order. Each phase space vector X(t) consists of m points separated by τ in the time series:

[0013] X(t)=(x(t),x(t+τ),x(t+2τ),...,x(t+(m-1)τ))(1)

[0014] Assuming that the delay time τ and embedding dimension m of a certain acoustic emission waveform data are 2 and 3 respectively, the phase space vector constructed is as follows:

[0015] X(1)=(x(1),x(3),x(5)),X(2)=(x(2),x(4),x(6)),X(3)=(x(3),x(5),x(7)),…

[0016] The waveform data of a single acoustic emission event is reconstructed in phase space, the 1-dimensional time series is constructed into a number of m-dimensional phase space vectors, and the many phase space vectors are combined into an m-dimensional phase space;

[0017] S21, selecting a delay time using an autocorrelation function method;

[0018] S211, using the autocorrelation function method to select the delay time for the waveform data of the single acoustic emission event obtained in S1, defining the autocorrelation function R(τ) as a correlation measure between the waveform data and itself at different delay times τ, and the calculation formula of the autocorrelation function is:

[0019]

[0020] Among them, x t and x t+τ They respectively represent the voltage values ​​of sequence number t and sequence number t+τ after the waveform data is recorded in time sequence; represents the voltage mean of the waveform data; n is the total number of sampling points of the waveform data; τ is the delay time, which represents the time interval of the points in the phase space vector X(t) during phase space reconstruction;

[0021] S212, for the autocorrelation function R(τ) obtained in S211, select the first integer zero point of the autocorrelation function as the delay time τ for phase space reconstruction;

[0022] Furthermore, the first integer zero point of the autocorrelation function may not exist. In order to meet the requirement that the time interval is an integer, a non-integer zero point needs to be selected for rounding.

[0023] S22, select the embedding dimension using the information dimension method and sample entropy;

[0024] In the information dimension method, the entropy of waveform data can be used to evaluate the complexity of phase space reconstruction under different embedding dimensions and help select the optimal embedding dimension; sample entropy is a commonly used nonlinear complexity measurement method, which overcomes the sensitivity of approximate entropy to the same pattern and is more accurate in calculation;

[0025] S221. The specific calculation steps for selecting the embedding dimension using sample entropy are as follows:

[0026] Using the delay time τ determined by S21 and the temporarily assumed embedding dimension m, a number of phase space vectors X(t) are constructed for the waveform data of a single acoustic emission event obtained by S1;

[0027] Many phase space vectors are combined into vector pairs. For each pair of phase space vectors X(t i ) and X(t j ), calculate the Euclidean distance d(X(t i ),X(t j )). If d(X(t i ),X(t j )) is less than or equal to the set tolerance γ, the pair of vectors is considered to be similar; if it is greater than the set tolerance, the pair of vectors is considered to be dissimilar;

[0028] Furthermore, the tolerance γ is 5% to 10% of the maximum absolute value voltage in the waveform data;

[0029] Furthermore, the Euclidean distance d(X(t i ),X(t j )) is calculated as:

[0030]

[0031] Where z represents the point x in the phase space vector X(t) t A multiple of the time interval;

[0032] S222. For the temporarily assumed embedding dimension m, calculate the ratio K of similar vector pairs to the total vector pairs m , and then calculate the sample entropy E(m) under the adjacent dimension pair m and m+1. The calculation formula of the sample entropy is:

[0033]

[0034] Among them, K m and K m+1 They represent the proportion of similar vector pairs to the total vector pairs under the temporary dimension m and m+1 respectively;

[0035] S223, for the sample entropy E(m) obtained in S222, select the embedding dimension when the sample entropy will tend to be stable or no longer decrease significantly, as the embedding dimension m for phase space reconstruction;

[0036] S3, calculating the dynamic entropy evolution index of a single acoustic emission event;

[0037] The delay time determined by S21 and the embedding dimension determined by S22 are used to reconstruct the waveform data of a single acoustic emission event obtained by S1 in phase space. The change in the average adjacent phase space vector in the phase space reveals the dynamic characteristics of rock failure corresponding to the acoustic emission event, which is defined as the dynamic evolution index DI, and the calculation formula is:

[0038] DI=avg(‖X(t)-X(t-1)‖)(5)

[0039] Among them, ‖X(t)-X(t-1)‖ is the vector variation between adjacent time numbers in the phase space formed by the reconstruction of the acoustic emission event waveform data;

[0040] S4. As the destruction proceeds, the operations from S2 to S3 are repeated for the waveform data of the next acoustic emission event, thereby obtaining the dynamic evolution index of the entire rock destruction process, and evaluating the dynamic characteristics of rock damage in real time and clearly.

[0041] Compared with the prior art, the present invention has the following beneficial effects:

[0042] The rock destruction process can only be simply reflected by the changes in the acoustic emission waveform data, while the complex dynamic changes hidden in the acoustic emission signal are usually difficult to extract directly from the waveform data. In order to accurately reveal the microscopic changes in the rock destruction process, this paper proposes a new type of rock damage dynamic characteristic evaluation index - dynamic evolution index DI. Specifically:

[0043] (1) The present invention first reconstructs the acoustic emission waveform data in phase space, converting the one-dimensional time series into a phase space vector in a high-dimensional phase space. With the continuous action of external forces and the continuous destruction, the phase space vector changes continuously in the high-dimensional space, and the change between adjacent phase space vectors can accurately reflect the evolution of microscopic damage of rock materials during deformation and destruction. By calculating the change of adjacent phase space vectors and taking their average value, the dynamic evolution index DI is obtained, which can reveal the dynamic change characteristics in the acoustic emission signal, especially the subtle changes related to the microscopic damage of the rock.

[0044] (2) The dynamic evolution index has significant application value. It can intuitively and clearly present the damage evolution process of rock under external forces, especially the evolution process of microscopic damage, which helps to assess the health status and damage risk of rock materials and provide an important basis for the design and safety control of rock materials. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 A schematic flow chart of the method for evaluating dynamic characteristics of rock damage based on phase space reconstruction and sample entropy provided by the present invention.

[0046] Figure 2 This is the autocorrelation function diagram of the waveform data of an acoustic emission event and itself at different time delays: Figure 2 (a) General plan; Figure 2 (b) Partial magnification.

[0047] Figure 3 It is a curve of the sample entropy of an acoustic emission event changing with respect to the smaller dimension in a pair of adjacent dimensions.

[0048] Figure 4 It is the curve of the dynamic evolution index changing with time during the complete destruction of rock; Figure 4 (a) General plan; Figure 4 (b) Figure 4 (a) A local enlarged view of point A. DETAILED DESCRIPTION

[0049] In order to further explain the technical solution of the present invention, the present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0050] like Figure 1 As shown, the present invention provides a method for evaluating the dynamic characteristics of rock damage under external force, and the specific steps are as follows:

[0051] S1. Acoustic emission monitoring and data collection for rock damage. First, real-time acoustic emission monitoring is performed on the deformation and damage process of the rock under the action of external force to obtain waveform data of the acoustic emission event. This embodiment adopts the Brazilian splitting test of marble, performs real-time acoustic emission monitoring on the entire deformation and damage process, and collects waveform data of the acoustic emission event, including sampling time and sampling voltage.

[0052] S2, reconstruct the phase space of a single acoustic emission event. According to the waveform data of the acoustic emission event collected by S1, the total number of samples n is counted, the appropriate delay time τ and embedding dimension m are selected, and the phase space vector X(t) is constructed using formula (1). Each phase space vector consists of m sampling points separated by τ in the waveform data. This process maps the 1-dimensional waveform data to the m-dimensional phase space.

[0053] S21, select the delay time using the autocorrelation function method. For the waveform data obtained in S1, use formula (2) to calculate its autocorrelation function. Select the integer zero point or non-integer zero point of the autocorrelation function as the delay time τ for phase space reconstruction. Figure 2 As shown, in this embodiment, the non-integer zero point of the autocorrelation function of an acoustic emission event is 8.15, which is rounded to 8.

[0054] S22. Use the information dimension method and sample entropy to select the embedding dimension. Use the delay time τ determined by S21 and the temporarily assumed embedding dimension m to construct the phase space vector X(t) for the acoustic emission waveform data collected by S1. Pair the phase space vectors, and for each pair of phase space vectors, use formula (3) to calculate the Euclidean distance d between the vectors within the pair. If the Euclidean distance d is less than or equal to the set tolerance γ, the pair of vectors is considered to be similar; if it is greater than the tolerance, they are considered to be dissimilar. The tolerance γ of this embodiment is 5% of the maximum absolute value voltage in the waveform data. The sample entropy E for each adjacent dimension pair is calculated using the similarity vector comparison ratio K and formula (4). Select the embedding dimension when the sample entropy will tend to be stable as the embedding dimension m for phase space reconstruction. Figure 3 As shown, in this embodiment, when the sample entropy of an acoustic emission event tends to be stable, the corresponding embedding dimension is 15 and the entropy value is 0.020788.

[0055] S3. Calculate the dynamic evolution index of a single acoustic emission event. Define the change in the average adjacent vector in the phase space as the dynamic evolution index DI, which is calculated using formula (5). Figure 4As shown, the dynamic evolution index of an acoustic emission event in this embodiment is 0.0627318.

[0056] S4. Repeat steps 2 to 3 to calculate the sample entropy E and dynamic evolution index DI of all acoustic emission events in the entire rock deformation and failure process of this embodiment, so as to intuitively and clearly evaluate the dynamic characteristics of rock damage.

[0057] The above implementation case is only a specific practice of the present invention and does not constitute a limitation on the scope of patent protection of the present invention. It should be emphasized that technical experts in this field have the right to make various adjustments and optimizations on the basis of maintaining the core concept of the present invention unchanged, which are deemed to fall within the scope of protection of the present invention.

Claims

1. A method for evaluating dynamic characteristics of rock damage based on phase space reconstruction and sample entropy, characterized in that: The rock damage dynamic characteristics evaluation method comprises the following steps: S1. Real-time acoustic emission monitoring of the rock destruction process under external force is performed to obtain waveform data of all acoustic emission events; S2, reconstructing the waveform data of the acoustic emission event in phase space; S3. Based on phase space reconstruction, the dynamic entropy evolution index of acoustic emission events is calculated to reflect the dynamic characteristics of rock damage; S4. During the rock destruction process, the above process is repeated for the waveform data of each acoustic emission event to obtain the dynamic evolution index of the entire rock destruction process and evaluate the dynamic characteristics of rock damage in real time.

2. According to claim 1, a method for evaluating dynamic characteristics of rock damage based on phase space reconstruction and sample entropy is characterized in that: In S2, the phase space reconstruction of the waveform data of a single acoustic emission event includes the following steps: For the waveform data of a single acoustic emission event obtained by S1, the voltage of each sampling point in the waveform data is recorded in time sequence as x1, x2, ..., x n , forming a 1-dimensional time series {x1,x2,...,x n }, n is the total sampling number of a single acoustic emission event; For the waveform data of a single acoustic emission event, a suitable delay time τ and embedding dimension m are selected, and a phase space vector X(t) is constructed in chronological order. Each phase space vector X(t) consists of m points separated by τ in the time series: X(t)=(x(t),x(t+τ),x(t+2τ),...,x(t+(m-1)τ))(1) Assuming that the delay time τ and embedding dimension m of a certain acoustic emission waveform data are 2 and 3 respectively, the phase space vector constructed is as follows: X(1)=(x(1),x(3),x(5)),X(2)=(x(2),x(4),x(6)),X(3)=(x(3),x(5),x(7)),… The waveform data of a single acoustic emission event is reconstructed in phase space, the 1-dimensional time series is constructed into a number of m-dimensional phase space vectors, and the many phase space vectors are combined into an m-dimensional phase space.

3. The method for evaluating dynamic characteristics of rock damage based on phase space reconstruction and sample entropy according to claim 2 is characterized in that: In the above-mentioned S2, the delay time is selected using the autocorrelation function method, which includes the following steps: S211, using the autocorrelation function method to select the delay time for the waveform data of the single acoustic emission event obtained in S1, defining the autocorrelation function R(τ) as a correlation measure between the waveform data and itself at different delay times τ, and the calculation formula of the autocorrelation function is: Among them, x t and x t+τ They respectively represent the voltage values ​​of sequence number t and sequence number t+τ after the waveform data is recorded in time sequence; represents the voltage mean of the waveform data; n is the total number of sampling points of the waveform data; τ is the delay time, which represents the time interval of the points in the phase space vector X(t) during phase space reconstruction; S212. For the autocorrelation function R(τ) obtained in S211, select the first integer zero point of the autocorrelation function as the delay time τ for phase space reconstruction.

4. The method for evaluating dynamic characteristics of rock damage based on phase space reconstruction and sample entropy according to claim 3 is characterized in that: The first integer zero point of the autocorrelation function may not exist. In order to meet the requirement that the time interval is an integer, a non-integer zero point needs to be selected for rounding.

5. The method for evaluating dynamic characteristics of rock damage based on phase space reconstruction and sample entropy according to claim 3 is characterized in that: In S2, the embedding dimension is selected using the information dimension method and sample entropy, including the following steps: S221. The specific calculation steps for selecting the embedding dimension using sample entropy are as follows: Using the delay time τ determined by S21 and the temporarily assumed embedding dimension m, a number of phase space vectors X(t) are constructed for the waveform data of a single acoustic emission event obtained by S1; Many phase space vectors are combined into vector pairs. For each pair of phase space vectors X(t i ) and X(t j ), calculate the Euclidean distance d(X(t i ),X(t j )); if d(X(t i ),X(t j )) is less than or equal to the set tolerance γ, the pair of vectors is considered to be similar; if it is greater than the set tolerance, the pair of vectors is considered to be dissimilar; S222. For the temporarily assumed embedding dimension m, calculate the ratio K of similar vector pairs to the total vector pairs m , and then calculate the sample entropy E(m) under the adjacent dimension pair m and m+1. The calculation formula of the sample entropy is: Among them, K m and K m+1 They represent the proportion of similar vector pairs to the total vector pairs under the temporary dimension m and m+1 respectively; S223. For the sample entropy E(m) obtained in S222, select the embedding dimension when the sample entropy tends to be stable or no longer decreases significantly, as the embedding dimension m for phase space reconstruction.

6. The method for evaluating dynamic characteristics of rock damage based on phase space reconstruction and sample entropy according to claim 5 is characterized in that: The tolerance γ is 5% to 10% of the maximum absolute value voltage in the waveform data.

7. The method for evaluating dynamic characteristics of rock damage based on phase space reconstruction and sample entropy according to claim 5 is characterized in that: The Euclidean distance d(X(t i ),X(t j )) is calculated as: Where z represents the point x in the phase space vector X(t) t A multiple of the time interval.

8. The method for evaluating dynamic characteristics of rock damage based on phase space reconstruction and sample entropy according to claim 5 is characterized in that: The S3 comprises the following steps: The delay time determined by S21 and the embedding dimension determined by S22 are used to reconstruct the waveform data of a single acoustic emission event obtained by S1 in phase space. The change in the average adjacent phase space vector in the phase space reveals the dynamic characteristics of the rock failure corresponding to the acoustic emission event, which is defined as the dynamic evolution index DI, and the calculation formula is: DI=avg(‖X(t)-X(t-1)‖)(5) Among them, ‖X(t)-X(t-1)‖ is the vector change between adjacent time numbers in the phase space formed by reconstructing the acoustic emission event waveform data.

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