A method for evaluating the dynamic characteristics of rock damage based on phase space reconstruction and sample entropy

Abstract

This invention provides a method for evaluating the dynamic characteristics of rock damage based on phase space reconstruction and sample entropy, belonging to the fields of rock mechanics and geotechnical engineering. The specific method is as follows: First, real-time acoustic emission monitoring of the rock failure process under external force is performed to acquire waveform data of acoustic emission events; second, phase space reconstruction is performed on the waveform data, using the autocorrelation function method to select the delay time, and using the information dimension method and sample entropy to select the embedding dimension, thus establishing the phase space; third, the dynamic evolution index of the acoustic emission event is calculated; finally, as failure progresses, the above steps are repeated for the next acoustic emission event, calculating the dynamic evolution index throughout the entire rock failure process, and providing a clear and real-time evaluation of the dynamic characteristics of rock damage. The advantage of this invention is that it achieves dynamic characteristic evaluation of damage during rock deformation and failure, with efficient methods and clear results, and has significant application value.

Description

Technical Field

[0001] This invention relates to a method for evaluating the dynamic characteristics of rock damage under external forces, and particularly to a dynamic evolution index suitable for measuring the microscopic damage of rocks under external forces, belonging to the fields of rock mechanics and geotechnical engineering. Background Technology

[0002] Rock damage is a widespread problem in engineering projects such as mining, tunneling, and water conservancy. Under external forces, rocks often undergo complex deformation and failure, affecting the safety and stability of engineering projects. Rock failure is characterized by its suddenness, spatiotemporal uncertainty, and nonlinearity, making it difficult for traditional damage assessment methods to accurately predict the failure process. Therefore, how to monitor and assess the dynamic characteristics of rock damage in real time has become a core issue in the field of rock mechanics.

[0003] Currently, rock damage assessment methods largely rely on stress-strain testing and microstructure analysis, primarily focusing on macroscopic assessments after failure, and failing to reveal the microscopic damage evolution during the failure process. Acoustic emission (AE) technology, as an important monitoring method, is widely used in rock failure processes, capable of obtaining damage status information by detecting signals released during rock fracturing. However, existing AE techniques mostly focus on signal amplitude and frequency analysis, lacking microscopic analysis of complex failure processes. Especially in high-frequency complex signal processing, existing methods struggle to accurately identify microscopic damage at different stages.

[0004] To overcome the shortcomings of existing technologies, the AE entropy parameter based on Shannon information entropy has been proposed in recent years. AE entropy, by quantifying the uncertainty of amplitude distribution, is independent of thresholds and other time-domain parameters, effectively reflecting the microstructural deformation process, distinguishing different damage stages, and reliably identifying critical damage. However, in the complex damage processes of rock materials, this method still has limitations in accurately locating the timing of micro-damage occurrence and assessing the severity of micro-damage.

[0005] Therefore, there is an urgent need for a new method to overcome the shortcomings of existing technologies and provide more accurate real-time damage monitoring and assessment tools. 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] To achieve the above objectives, 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 is disclosed. The method first involves real-time monitoring of acoustic emission during the rock failure process, acquiring waveform data of acoustic emission events, and reconstructing their phase space. Second, the delay time is selected using the autocorrelation function method, and the embedding dimension is selected using the information dimension method and sample entropy. Third, based on the phase space reconstruction, dynamic evolution indices of acoustic emission events are calculated to reflect the dynamic characteristics of rock damage. Finally, during the rock failure 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 method includes the following steps:

[0009] S1. Real-time acoustic emission monitoring of rock failure process under external force, and acquisition of waveform data of all acoustic emission events;

[0010] S2. Reconstruct the phase space of the waveform data of a single acoustic emission event;

[0011] For the waveform data of a single acoustic emission event obtained by S1, the voltage at each sampling point in the waveform data is recorded in chronological order as x1, x2, ..., x n This constitutes a one-dimensional time series {x1,x2,...,x} n}, where n is the total number of samples for 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 time order. Each phase space vector X(t) consists of m points in the time series that are τ apart.

[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 constructed phase space vector 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] Phase space reconstruction is performed on the waveform data of a single acoustic emission event, constructing a 1-dimensional time series into numerous m-dimensional phase space vectors, and then combining these numerous phase space vectors into an m-dimensional phase space.

[0017] S21. Use the autocorrelation function method to select the delay time;

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

[0019]

[0020] Where, x t and x t+τ These represent the voltage values ​​at sequence number t and sequence number t+τ, respectively, after the waveform data is recorded in chronological order. The voltage mean of the waveform data is represented by τ; n is the total number of sampling points of the waveform data; τ is the delay time, representing the time interval between 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 of the autocorrelation function as the delay time τ for phase space reconstruction.

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

[0023] S22. Use the information dimension method and sample entropy to select the embedding dimension;

[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 measure that overcomes the sensitivity of approximate entropy to the same pattern and is more computationally accurate.

[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, numerous phase space vectors X(t) are constructed from the waveform data of a single acoustic emission event obtained by S1.

[0027] For each pair of phase space vectors, the 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) between the interior vectors. i ),X(t j If d(X(t) i ),X(t j If the tolerance value is less than or equal to the set tolerance value γ, the vector pair is considered similar; if it is greater than the set tolerance value, the vector pair is considered dissimilar.

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

[0029] Furthermore, the Euclidean distance d(X(t) between the interior vectors i ),X(t j The formula for calculating )) is:

[0030]

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

[0032] S222. For a tentative embedding dimension m, calculate the proportion K of similar vector pairs to the total number of vector pairs. m Then calculate the sample entropy E(m) for the nearest neighbor dimension pairs m and m+1. The formula for calculating the sample entropy is:

[0033]

[0034] Among them, K m and K m+1 These represent the proportions of similar vector pairs to the total number of vector pairs under tentative dimensions m and m+1, respectively.

[0035] 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, and use it as the embedding dimension m for phase space reconstruction.

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

[0037] Using the delay time determined in S21 and the embedding dimension determined in S22, phase space reconstruction is performed on the waveform data of a single acoustic emission event obtained in S1. The change in the average adjacent phase space vectors within 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 its calculation formula is as follows:

[0038] DI=avg(‖X(t)-X(t-1)‖)(5)

[0039] Where, ||X(t)-X(t-1)|| is the vector change between adjacent time indices in the phase space formed by reconstructing the waveform data of the acoustic emission event;

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

[0041] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0042] The rock failure process can only be simply reflected by changes in 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. To accurately reveal the microscopic changes during rock failure, this invention proposes a novel evaluation index for the dynamic characteristics of rock damage—the Dynamic Evolution Index (DI). Specifically:

[0043] (1) This invention first reconstructs the phase space of the acoustic emission waveform data, transforming the one-dimensional time series into a phase space vector in a high-dimensional phase space. As the external force continues to act and the damage continues, the phase space vector changes continuously in the high-dimensional space. The changes between adjacent phase space vectors can accurately reflect the microscopic damage evolution of rock materials during deformation and failure. By calculating the changes between adjacent phase space vectors and taking their average value, the dynamic evolution index DI is obtained. This index 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) Dynamic evolution indicators have significant application value. They can intuitively and clearly present the damage evolution process of rocks under external forces, especially the evolution process of micro-damage, which helps to assess the health status and failure risk of rock materials and provides an important basis for the design and safety control of rock materials. Attached Figure Description

[0045] Figure 1 This is a flowchart illustrating the rock damage dynamic characteristic evaluation method based on phase space reconstruction and sample entropy provided by the present invention.

[0046] Figure 2 The graph shows the waveform data of an acoustic emission event and its autocorrelation function at different time delays: Figure 2 (a) Site plan; Figure 2 (b) Enlarged view of a section.

[0047] Figure 3 It is a curve showing the change of sample entropy of an acoustic emission event with respect to the smaller dimension among neighboring dimension pairs.

[0048] Figure 4 It is a curve showing the change of dynamic evolution indicators with respect to time during the process of rock integrity failure; Figure 4 (a) Site plan; Figure 4 (b) Figure 4 (a) A magnified view of point A. Detailed Implementation

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

[0050] like Figure 1 As shown, this invention provides a method for evaluating the dynamic damage characteristics of rocks under external forces, the specific steps of which are as follows:

[0051] S1. Acoustic emission monitoring and data acquisition for rock failure. First, real-time acoustic emission monitoring is performed on the deformation and failure process of the rock under external force to acquire waveform data of acoustic emission events. In this embodiment, the Brazilian splitting test of marble was used to monitor the entire deformation and failure process in real time, and waveform data of acoustic emission events were acquired, including sampling time and sampling voltage.

[0052] S2. Phase space reconstruction for a single acoustic emission event. Based on the waveform data of the acoustic emission event collected in S1, the total number of samples n is counted, and an appropriate delay time τ and embedding dimension m are selected. 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 1D waveform data to mD phase space.

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

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

[0055] S3. Calculate the dynamic evolution index of a single acoustic emission event. The change in the average adjacent vector in phase space is defined 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 two to three 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, thereby intuitively and clearly evaluating the dynamic characteristics of rock damage.

[0057] The above-described embodiments are merely one specific practice of the present invention and do not constitute a limitation on the scope of patent protection of the present invention. It should be emphasized that those skilled in the art, while maintaining the core concept of the present invention, have the right to make various adjustments and optimizations, all of which are considered to fall within the scope of protection of the present invention.

Claims

1. A method for evaluating the dynamic characteristics of rock damage based on phase space reconstruction and sample entropy, characterized in that, The method for evaluating the dynamic characteristics of rock damage includes the following steps: S1. Real-time acoustic emission monitoring of rock failure process under external force, and acquisition of waveform data of all acoustic emission events; S2. Reconstruct the phase space of the waveform data of the acoustic emission event and select the delay time using the autocorrelation function method; 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: Use a defined delay time and the embedding dimension of the temporary assumption Numerous phase space vectors are constructed from the waveform data of a single acoustic emission event obtained from S1. ; For each pair of phase space vectors, the vectors are combined into vector pairs. and Calculate the Euclidean distance between interior vectors. ;if Less than or equal to the set tolerance If the tolerance is greater than the set tolerance, then the pair of vectors is considered similar; if it is greater than the set tolerance, then the pair of vectors is considered dissimilar. S222, regarding the provisional embedding dimension Calculate the proportion of similar vector pairs to the total number of vector pairs. Then calculate the nearest neighbor dimension pairs. and Sample entropy The formula for calculating the sample entropy is: （4）； in, and They represent the provisional dimensions, respectively. and The proportion of similar vector pairs to the total number of vector pairs; S223, Sample entropy obtained from S222 The embedding dimension at which the sample entropy tends to plateau or no longer decreases significantly is selected as the embedding dimension for phase space reconstruction. ; S3. Based on phase space reconstruction, calculate the dynamic entropy evolution index of acoustic emission events to reflect the dynamic characteristics of rock damage; The S3 mentioned above includes the following steps: Using a defined delay time and a defined embedding dimension, the waveform data of a single acoustic emission event obtained from S1 are reconstructed in phase space. The change in the average adjacent phase space vectors within the phase space reveals the dynamic characteristics of rock failure corresponding to the acoustic emission event, and is defined as a dynamic evolution index. The calculation formula is: （5）； in, It is the vector change between adjacent time indices in the phase space formed by reconstructing acoustic emission event waveform data; S4. During the rock failure process, repeat the above process for the waveform data of each acoustic emission event to obtain the dynamic evolution index of the entire rock failure process and evaluate the dynamic characteristics of rock damage in real time.

2. The method for evaluating the dynamic characteristics of rock damage based on phase space reconstruction and sample entropy according to claim 1, characterized in that, In step 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 chronological order. ,constitute dimensional time series , The total number of samples for a single acoustic emission event; Select an appropriate delay time for the waveform data of a single acoustic emission event. and embedding dimension Construct phase space vectors in chronological order Each phase space vector From the time series Time Composed of points: （1）； Assuming a delay time for the selection of a certain acoustic emission waveform data and embedding dimension If the values ​​are 2 and 3 respectively, then the phase space vectors they construct are as follows: ； Phase space reconstruction is performed on the waveform data of a single acoustic emission event. Time series in multiple dimensions are constructed into numerous A 3D phase space vector is formed by combining numerous phase space vectors. A phase space of dimensionality.

3. The method for evaluating the dynamic characteristics of rock damage based on phase space reconstruction and sample entropy according to claim 2, characterized in that, In step S2, the autocorrelation function method is used to select the delay time, which includes the following steps: S211. Select the delay time using the autocorrelation function method for the waveform data of a single acoustic emission event obtained in S1, and define the autocorrelation function. It is the waveform data and itself at different delay times. The autocorrelation function, as a correlation metric, is calculated using the following formula: （2）； in, and These represent the sequence numbers of the waveform data after being recorded in chronological order. and serial number The voltage value; This represents the average voltage value of the waveform data. This is the total number of sampling points for the waveform data; It is the delay time, representing the phase space vector during phase space reconstruction. The time interval between interior points; S212, the autocorrelation function obtained from S211 The first integer zero of the autocorrelation function is selected as the delay time for phase space reconstruction. .

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

5. The method for evaluating the dynamic characteristics of rock damage based on phase space reconstruction and sample entropy according to claim 1, characterized in that, The tolerance It is 5% to 10% of the maximum absolute voltage in the waveform data.

6. The method for evaluating the dynamic characteristics of rock damage based on phase space reconstruction and sample entropy according to claim 1, characterized in that, The Euclidean distance between the interior vectors The calculation formula is: （3）； in, Represents phase space vectors interior point A multiple of the time interval.

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