Coal rock fracture evolution mechanism construction method and system based on interpretable neural operator

Abstract

The invention discloses a coal rock fracture evolution mechanism construction method and system based on an interpretable neural operator. The exploration method comprises the following steps: obtaining staged time CT detection and full space-time acoustic emission monitoring data in a coal rock sample loading process; cT detection and acoustic emission monitoring data are subjected to correspondence according to moments, and a fracture parameter data set is obtained; performing multi-source information construction and feature extraction on fracture and acoustic emission parameter data of a training set and a verification set in the fracture parameter data set based on a neural network model of an interpretable neural operator to obtain an acoustic emission parameter weight factor; inputting the acoustic emission parameter weight factor, the fracture of the test set and the acoustic emission parameter data into a mechanism equation parameter multi-objective optimization model to obtain a fracture evolution mechanism equation; and solving through a mechanism equation to obtain a three-dimensional coal rock sample fracture field evolution result, and performing deviation calculation through the fracture evolution result and test set CT detection data to adjust neural operator network parameters.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of coal rock monitoring, and particularly relates to a coal rock fracture evolution mechanism construction method and system based on an interpretable neural operator. BACKGROUND

[0002] In the process of coal mining, mining activities and other weight factors will destroy the original stress balance state of the coal rock mass. This process usually involves rapid and unstable expansion of fractures, which is the root cause of inducing dynamic disasters such as rock burst, coal and gas outburst, etc. Therefore, in order to deeply understand the mechanism of coal rock dynamic disasters and realize early warning of the disasters, it is necessary to carry out in-depth research on the evolution mechanism of the fracture field and other aspects.

[0003] Although existing rock mechanics theories and methods attempt to explain the evolution of the fracture field of the coal rock mass caused by mining activities, this complex process is still considered as a "black box" that is difficult to measure and reveal. In exploring the formation mechanism of the fracture field and revealing its development and evolution process, there are still many challenges. At present, industrial CT detection and numerical simulation methods have made certain progress, and these technologies can be used to reconstruct the internal structure of the coal rock mass, and especially show potential in constructing three-dimensional digital models of non-continuous structures and fracture fields. For example, patent CN118275656A discloses a method for determining the damage degree of surrounding rock in a predetermined area, patent CN118506104A discloses a rock fracture identification and expansion prediction method and system, and patent CN110146525A discloses a coal body porosity and permeability parameter prediction method based on fractal theory and CT scanning. However, these methods still have some limitations. They usually rely on high-specification laboratory conditions and cumbersome model reconstruction methods, which limits their wide application in actual engineering. In addition, these methods cannot realize the analysis of the evolution mechanism of the fracture field, which may cause certain limitations in actual production processes.

[0004] In recent years, some experimental methods combining exploration-monitoring technology with numerical simulation have been applied in the laboratory. However, the current utilization of these exploration-monitoring data still mainly focuses on manually analyzing the temporal variation law. In addition, the calculation of fracture field evolution completely relying on numerical simulation requires extremely high computational cost, and even a slight modification in the model may cause a large negative weight in the model calculation process. Therefore, how to utilize the exploration-monitoring data to realize the full spatio-temporal fracture field evolution and overcome the limitations of traditional methods still needs further research. With the continuous progress and development of science and technology, the breakthrough progress of neural operator network and multi-objective optimization method has attracted people's attention in the construction of fracture field evolution mechanism. Especially the neural operator network based on selective state space architecture and the weight extraction method based on SHAP can effectively extract the characteristics of different types of data, significantly improve the computational efficiency and reduce the demand for computing resources compared with the traditional neural network architecture. In addition, the multi-objective optimization method has a significant advantage in exploring equation parameters, which can consider multiple conflicting objective functions at the same time, so as to find a balanced solution in a complex parameter space.

[0005] This provides the possibility for realizing the exploration and optimization of the fracture evolution mechanism equation by using the above method, but there is still a lack of specific feasible ideas and implementation methods. Therefore, it is urgent to carry out the actual measurement of the detection and monitoring signals in the loading process of coal rock samples, propose a coal rock fracture evolution mechanism construction method and system based on an interpretable neural operator, realize the exploration and optimization of the fracture evolution mechanism equation based on full spatio-temporal acoustic emission monitoring data, and have a significant promoting effect on revealing the "black box" evolution process of coal rock mass dynamic disaster and realizing the monitoring and early warning of coal rock dynamic disaster. SUMMARY

[0006] The present scheme proposes a coal rock fracture evolution mechanism construction method and system based on an interpretable neural operator, which can realize the above technical purposes and bring other technical effects due to the adoption of the following technical features.

[0007] One object of the present application is to propose a coal rock fracture evolution mechanism construction method based on an interpretable neural operator, which comprises the following steps:

[0008] S10: arranging CT detection sensors and acoustic emission monitoring sensors on the coal rock sample, and placing the coal rock sample in a testing machine for loading test, and acquiring the CT detection data and full spatio-temporal acoustic emission monitoring data of the coal rock sample at the stage time through the CT detection sensors and acoustic emission monitoring sensors; wherein the CT detection data is the full spatio-temporal fracture parameter data at the stage time, and the acoustic emission monitoring data is the full spatio-temporal acoustic emission parameter data;

[0009] S20: corresponding the CT detection data and the full-time and space acoustic emission monitoring data in the staged time of the coal rock sample loading process according to the time, obtaining a crack parameter data set, and dividing the crack parameter data set into a training set, a verification set and a test set;

[0010] S30: establishing an interpretable neural operator network model, performing feature extraction on the spatial crack parameter data and the corresponding time acoustic emission parameter data in the training set and the verification set in the crack parameter data set based on the interpretable neural operator network model, and obtaining an acoustic emission parameter weight factor;

[0011] S40: inputting the acoustic emission parameter weight factor, the crack parameter and the acoustic emission parameter data of the test set into a multi-objective optimization module to obtain equation parameters, and the equation parameters, the crack parameter and the acoustic emission parameter constitute a crack evolution mechanism equation;

[0012] S50: obtaining a three-dimensional coal rock sample crack field evolution result through the mechanism equation, judging whether the precision of the coal rock three-dimensional crack field imaging result meets the requirements, and when the precision of the coal rock three-dimensional crack field imaging result cannot meet the requirements, performing deviation calculation through the test set CT detection data and adjusting the neural network parameters until the precision of the coal rock three-dimensional crack field imaging result meets the requirements.

[0013] In addition, the coal rock crack evolution mechanism construction method based on the interpretable neural operator according to the present application can also have the following technical features:

[0014] In an example of the present application, in the step S30, the neural network model based on the interpretable neural operator performs feature extraction on the full-space crack parameter data and the corresponding time acoustic emission parameter data in the training set in the crack parameter data set, including the following steps:

[0015] S31: extracting the acoustic emission parameter through the data coding layer to obtain the parameter-enhanced acoustic emission feature AEf se ;

[0016] S32: the coded data are spliced into the features AE b obtained by the feature extraction layer B through the residual connection layer;

[0017] S33: performing regularization on the parameter-enhanced acoustic emission feature AEf se through the first Normalization function to obtain the feature AE n ;

[0018] S34: performing feature extraction on the regularized feature AE n through the residual connection composed of the second linear feature extraction layer A and the second activation function layer to obtain AE a+s spliced into the features AEsssm AE is obtained in the middle SSSM ;

[0019] S35: the feature AE output by the first linear feature extraction layer A a The feature AE of higher dimension is obtained by the convolution layer and the first activation function layer conv+s ;

[0020] S36: the high-dimensional feature is calculated by the selective state space architecture, and the features extracted by the convolution layer and the first activation function layer are spliced to obtain the feature AE SSSM ;

[0021] S37: the linear feature extraction layer B extracts the features obtained by splicing, and splices the extracted features with the features of the encoded data obtained by the residual connection layer to obtain the feature AEf b+se ;

[0022] S38: the spliced features are regularized by the second normalization function to obtain the feature AEf n ;

[0023] S39: the extracted features are calculated by the full connection layer, and the multi-source information construction result MI is calculated f .

[0024] In one example of the application, in the step S36, the selective state space architecture is implemented as follows:

[0025] First, the state space architecture is built by a continuous state space equation, wherein the expression of the continuous state space equation is as follows:

[0026] h t = Ah t-1 +Bx t

[0027] y t = Ch t

[0028] Where h t-1 represents the system state; h t represents the updated system state; matrix A represents the state transition matrix; B represents the input gating matrix; C represents the output mapping matrix; x t represents the data of the current state input architecture;

[0029] Second, the state space architecture is adapted to discrete data by a discrete state space equation; wherein the equation expression of the state transition matrix A is as follows:

[0030]

[0031] wherein n is a row index related to an orthogonal basis function in a polynomial space, and k is a column index related to an orthogonal basis function in a polynomial space.

[0032] In one example of the present application, the state transition matrix A is randomly initialized, and a low-rank matrix after matrix decomposition is used, and the low-rank matrix equation is as follows:

[0033]

[0034] wherein P and Q are both vectors with a length of N; V represents an eigenvector matrix; V * represents a transposed matrix; A represents an eigenmatrix; and * represents a projection operation.

[0035] In one example of the present application, the expression of the discrete state space equation is as follows:

[0036]

[0037] wherein h k and y k respectively represent a memory control unit and an output control unit for selecting a current state in a state space architecture; h k-1 represents a memory control unit for selecting a previous state in the state space architecture; h0 represents an initialized state of the memory control unit; x k represents data of a current state input architecture; and x0 represents data of an initial state input architecture. are all matrices after A, B and C are discretely adapted.

[0038] In one example of the present application, the matrix is obtained by the following derivation formula:

[0039]

[0040] wherein A represents a discretization nonlinear function for discretizing a continuous state; and I represents a unit matrix.

[0041] In one example of the present application, in the step S30, the expression formula of the acoustic emission parameter weight factor S i is as follows:

[0042]

[0043] wherein M represents the number of input acoustic emission parameters; and represents a set composed of all permutation combinations of M features, X x represents the set of all feature combinations preceding feature k in the ranking R, f s S represents the conditional expectation given the feature subset S; i represents the weight factor serial number.

[0044] In one example of the present application, in the step S40, the acoustic emission parameter weight factor, the fracture parameter and the acoustic emission parameter data of the test set are input into the mechanism equation parameter multi-objective optimization model to obtain the fracture evolution mechanism equation, specifically including the following steps:

[0045] S41: the acoustic emission parameter data is extracted as a feature vector X f by a data coding layer;

[0046] S42: the weight factor of each acoustic emission parameter is extracted as a global weight factor S m by a data coding layer;

[0047] S43: the feature vector X f and the fracture parameter F M are normalized;

[0048] S44: the basic form of the equation is constructed, and the mechanism equation is selected as a linear equation or a nonlinear equation;

[0049] S45: the minimum mean square error objective function of the multi-objective optimization method is set, and the minimum mean square error objective function formula is as follows:

[0050]

[0051] In the formula, represents the predicted fracture parameter based on the equation parameter ; F Mn represents the real fracture parameter; and N represents the total number of samples.

[0052] S46: the maximum weight factor penalty item objective function of the multi-objective optimization method is set, and the maximum weight factor penalty item objective function expression is as follows:

[0053]

[0054] In the formula, represents the equation parameter; n represents the total number of acoustic emission parameters; and S mj represents the average value of the weight factor of the jth feature on all samples;

[0055] ​S47: set the final objective function of the multi-objective optimization method, maximize the weight factor penalty objective function; wherein the formula of the weight factor penalty objective function is as follows:

[0056] Object=[MSE, Penalty]

[0057] Wherein, [ ] represents that the multi-objective optimization method finds a balance point between MSE and Penalty.

[0058] S48: mechanism equation parameter multi-objective optimization model executes optimization: first, initialize the population Then, the equation parameter optimization is carried out through the final objective function Object; finally, the crack evolution mechanism equation is output.

[0059] In one example of the present application, in the step S50, the deviation is calculated through the test set CT detection data, and the specific implementation process is as follows:

[0060] The crack evolution mechanism equation is input into the equation solver to obtain the crack parameter F pred , the crack parameter F pred and the full space-time crack parameter F M obtained by CT detection are input into the root mean square error equation to calculate the deviation, and the root mean square error formula is as follows:

[0061]

[0062] Wherein, N represents the total number of samples.

[0063] Another object of the present application is to provide a coal rock crack evolution mechanism construction system based on an interpretable neural operator, comprising:

[0064] The information acquisition module is configured to arrange CT detection sensors and acoustic emission monitoring sensors on the coal rock sample, and place the coal rock sample in a testing machine for loading test, and acquire CT detection data and full space-time acoustic emission monitoring data at periodic time points in the loading process of the coal rock sample through the CT detection sensors and the acoustic emission monitoring sensors; wherein the CT detection data is full space crack parameter data at periodic time points, and the acoustic emission monitoring data is full space-time acoustic emission parameter data;

[0065] The data division module is configured to correspond the CT detection data and the full space-time acoustic emission monitoring data at periodic time points in the loading process of the coal rock sample according to time points, obtain a crack parameter data set, and divide the crack parameter data set into a training set, a validation set and a test set;

[0066] a weight factor extraction module configured to establish an interpretable neural operator network model, and to extract features of spatial fracture parameter data and corresponding acoustic emission parameter data of a training set and a validation set in a fracture parameter data set based on a neural network model of an interpretable neural operator, to obtain acoustic emission parameter weight factors;

[0067] a fracture evolution mechanism equation module configured to input the acoustic emission parameter weight factors, fracture parameters and acoustic emission parameter data of a test set into a multi-objective optimization module to obtain equation parameters, and to construct a fracture evolution mechanism equation with the equation parameters, fracture parameters and acoustic emission parameters;

[0068] a mechanism equation optimization module configured to obtain a three-dimensional coal rock sample fracture field evolution result by solving the mechanism equation, to determine whether the accuracy of the coal rock three-dimensional fracture field imaging result meets the requirements, and to perform deviation calculation on the test set CT detection data and adjust the neural network parameters until the accuracy of the coal rock three-dimensional fracture field imaging result meets the requirements when the accuracy of the coal rock three-dimensional fracture field imaging result cannot meet the requirements.

[0069] Compared with the prior art, the present application has the following beneficial effects:

[0070] 1. The present application focuses on the discovery of a fracture evolution mechanism equation in the loading test process of a coal rock sample by combining a neural operator network, SHAP and multi-objective optimization, and reveals the fracture parameter evolution mechanism in the loading test process of a coal rock sample. Compared with traditional numerical simulation and neural network methods, this coal rock fracture evolution mechanism equation discovery method based on interpretable deep learning and multi-objective optimization has automatic equation discovery capability, high-precision feature extraction capability and low dependence on computing resources, and has strong interpretability and good generalization ability, providing a new technical path for intelligent research and engineering application of coal rock fracture evolution mechanism.

[0071] 2. The neural operator network in the present application is obtained by performing spatio-temporal feature extraction on the data in the fracture parameter data set based on a selective state space architecture, and a feature extraction method for fracture parameter data and acoustic emission data in the loading process of a coal rock sample is proposed. Based on the proposed spatio-temporal feature extraction method, multi-source information construction of full spatio-temporal acoustic emission data and fracture parameter data can be realized, and storage and computing power costs can be significantly saved.

[0072] 3、The acoustic emission parameter weight factor in the application is obtained by feature extraction of the multi-source information construction result of the full space-time acoustic emission scalar parameter and the crack parameter data through the SHAP weight extraction module. The SHAP weight extraction module can obtain the acoustic emission parameter weight factor in the loading process of the coal rock sample through the multi-source information construction result, and input the multi-objective optimization module to adjust the proportion weight of each equation parameter in the mechanism equation, so as to realize the exploration of the crack evolution mechanism equation and reveal the black box process of the crack parameter inversion of the coal rock sample in the loading process.

[0073] The most preferred embodiments of the application will be described in more detail below with reference to the accompanying drawings, so that the features and advantages of the application can be easily understood. BRIEF DESCRIPTION OF DRAWINGS

[0074] In order to more clearly illustrate the technical solutions of the embodiments of the application, the drawings of the embodiments of the application will be briefly introduced below. The drawings are only used to show some embodiments of the application, and the application is not limited to the drawings.

[0075] Figure 1 A flow chart of the coal rock crack evolution mechanism construction method based on the interpretable neural operator according to the embodiments of the application;

[0076] Figure 2 A neural network model structure diagram of the interpretable neural operator according to the embodiments of the application;

[0077] Figure 3 A schematic diagram of the arrangement structure of the coal rock sample in the testing machine according to the embodiments of the application;

[0078] LIST OF REFERENCE NUMERALS

[0079] Testing machine 100;

[0080] Loading device 110;

[0081] Acoustic emission sensor 120;

[0082] Coupler 130;

[0083] Pre-amplifier 140;

[0084] X-ray detector 150;

[0085] X-ray source 160;

[0086] Coal rock sample 200;

[0087] Transverse direction X;

[0088] Longitudinal direction Y. DETAILED DESCRIPTION

[0089] In order to make the purpose, technical solutions and advantages of the technical solutions of the present application clearer, the technical solutions of the embodiments of the present application will be described clearly and completely below in conjunction with the drawings of specific embodiments of the present application. The same reference signs in the drawings represent the same parts. It should be noted that the described embodiments are part of the embodiments of the present application, not all of the embodiments. Based on the described embodiments of the present application, all other embodiments obtained by those of ordinary skill in the art without creative labor fall within the scope of protection of the present application.

[0090] Unless otherwise defined, technical terms or scientific terms used herein should be understood as having the common meaning in the field of the present application to which they pertain. The terms "first", "second", and similar terms used in the description and the claims of the present patent application do not denote any order, quantity, or importance, but are used to distinguish different components. Similarly, the terms "one" or "a" or similar terms do not necessarily denote the quantity of the components. The terms "comprising" or "including" or similar terms mean that the elements or objects before the term encompass the elements or objects listed after the term and their equivalents, without excluding other elements or objects. The terms "connected" or "connected" or similar terms do not necessarily mean physical or mechanical connections, but can include electrical connections, whether direct or indirect. The terms "up", "down", "left", "right", and the like are used only to indicate relative positional relationships, and when the absolute positions of the described objects change, the relative positional relationships may also change accordingly.

[0091] According to the coal rock fracture evolution mechanism construction method based on the interpretable neural operator, as shown in Figure 1 The method comprises the following steps:

[0092] S10: CT detection sensors and acoustic emission monitoring sensors are arranged on the coal rock sample, and the coal rock sample is placed in a testing machine for loading test. CT detection data and full-time and space acoustic emission monitoring data of the coal rock sample at the stage time during loading are collected by the CT detection sensors and the acoustic emission monitoring sensors. The CT detection data are full-space fracture parameter data at the stage time, and the acoustic emission monitoring data are full-time and space acoustic emission parameter data. The acoustic emission monitoring data are full-time and space acoustic emission parameter data, and the CT detection data are full-space fracture parameter data at the stage time. The sample is, for example, Figure 3As shown, the testing machine 100 comprises a loading device 110, an acoustic emission sensor 120, a coupler 130, a preamplifier 140, an X-ray detector 150, an X-ray source 160 and a box sample 170; wherein the loading device 110, the acoustic emission sensor 120, the coupler 130, the preamplifier 140, the X-ray detector 150 and the X-ray source 160 are all installed in the box sample 170, a coal rock sample 200 is arranged in the loading device 110, acoustic emission sensors 120 are arranged on both sides of the coal rock sample 200 in the transverse direction X, wherein the acoustic emission sensors 120 are electrically connected with the coupler 130 and are electrically connected with the preamplifier 140, and the X-ray detector 150 and the X-ray source 160 are arranged on both sides of the coal rock sample 200 in the longitudinal direction Y, wherein the transverse direction X and the longitudinal direction Y are perpendicular to each other. The working process is as follows: the coal rock sample 200 is loaded by the loading device 110, in this process, X-rays are emitted by the X-ray source 160 and received by the X-ray detector 150, thereby obtaining CT detection data of the coal rock sample 200 in the breaking process, at the same time, full-time and space acoustic emission monitoring data are obtained by the acoustic emission sensor 120.

[0093] S20: corresponding the stage time CT detection data and the full-time and space acoustic emission monitoring data in the loading process of the coal rock sample according to time, obtaining a crack parameter data set, and dividing the crack parameter data set into a training set, a validation set and a test set;

[0094] S30: establishing an interpretable neural operator network model, performing feature extraction on the spatial crack parameter data and the corresponding acoustic emission parameter data in the training set and the validation set in the crack parameter data set based on the interpretable neural operator network model, and obtaining an acoustic emission parameter weight factor;

[0095] S40: inputting the acoustic emission parameter weight factor, the crack parameter and the acoustic emission parameter data of the test set into a multi-objective optimization module to obtain equation parameters, and the equation parameters, the crack parameter and the acoustic emission parameter constitute a crack evolution mechanism equation;

[0096] S50: obtaining a three-dimensional coal rock sample crack field evolution result by solving the mechanism equation, judging whether the precision of the coal rock three-dimensional crack field imaging result meets the requirements, when the precision of the coal rock three-dimensional crack field imaging result meets the requirements, ending the operation; when the precision of the coal rock three-dimensional crack field imaging result cannot meet the requirements, performing deviation calculation through the test set CT detection data and adjusting the neural network parameters until the precision of the coal rock three-dimensional crack field imaging result meets the requirements.

[0097] The exploration method focuses on the discovery of the crack evolution mechanism equation in the loading test process of the coal rock sample by combining the neural operator network, SHAP and multi-objective optimization, and reveals the crack parameter evolution mechanism in the loading test process of the coal rock sample. Compared with the traditional numerical simulation and neural network method, the crack evolution mechanism equation exploration and discovery method based on the interpretable deep learning and multi-objective optimization method has the characteristics of automatic equation discovery, high precision feature extraction and low dependence on computing resources, and has strong interpretability and good generalization ability, which provides a new technical path for the intelligent research and engineering application of the coal rock crack evolution mechanism.

[0098] The neural operator network in the exploration method is obtained by performing spatiotemporal feature extraction on the data in the crack parameter data set based on the neural network with a selective state space architecture, and a feature extraction method for the crack parameter data and acoustic emission data in the loading process of the coal rock sample is proposed. Based on the proposed spatiotemporal feature extraction method, multi-source information construction of the full spatiotemporal acoustic emission data and crack parameter data can be realized, and the storage and computing cost can be significantly saved.

[0099] The acoustic emission parameter weight factor in the exploration method is obtained by performing feature extraction on the multi-source information construction results of the full spatiotemporal acoustic emission scalar parameter and crack parameter data through the SHAP weight extraction module. The SHAP weight extraction module can obtain the acoustic emission parameter weight factor in the loading process of the coal rock sample through the multi-source information construction results, and input the multi-objective optimization module to adjust the proportion weight of each equation parameter in the mechanism equation, so as to realize the exploration of the crack evolution mechanism equation and reveal the black box process of the crack parameter inversion in the loading process of the coal rock sample.

[0100] In one example of the present application, as shown in Figure 2 In the step S30, the neural network model based on the interpretable neural operator extracts the full spatial crack parameter data and the corresponding acoustic emission parameter data of the training set in the crack parameter data set, including the following steps:

[0101] S31: The acoustic emission parameter is extracted to obtain the parameter enhanced acoustic emission feature AEf se ;

[0102] S32: The encoded data is spliced into the feature AE b obtained by the feature extraction layer B through the residual connection layer;

[0103] S33: The parameter enhanced acoustic emission feature AEf se is normalized by the first Normalization function to obtain the feature AE n ;

[0104] S34: the regularized feature AE n The feature AE is extracted by the residual connection composed of the second linear feature extraction layer A and the second activation function layer a+s The feature AE is spliced to the output of the selective state space architecture sssm The AE is obtained in the middle SSSM ;

[0105] S35: the feature AE output by the first linear feature extraction layer A a The feature AE of higher dimension is extracted by the convolution layer and the first activation function layer conv+s ;

[0106] S36: the feature AE is obtained by the selective state space architecture for the gate calculation of the high-dimensional feature and splicing the feature extracted by the convolution layer and the first activation function layer SSSM ;

[0107] S37: the feature is extracted by the linear feature extraction layer B, and the extracted feature is spliced with the feature of the encoded data by the residual connection layer, to obtain the feature AEf b+se ;

[0108] S38: the feature is regularized by the second normalization function, to obtain the feature AEf n ;

[0109] S39: the feature is extracted by the full connection layer, and the multi-source information construction result MI is calculated f .

[0110] In one example of the present application, in the step S36, the selective state space architecture is implemented as follows:

[0111] First, the state space architecture is built by the continuous state space equation, wherein the expression of the continuous state space equation is as follows:

[0112] h t =Ah t-1 +Bx t

[0113] y t =Ch t

[0114] Wherein, h t-1 represents the system state; h t represents the updated system state; matrix A represents the state transition matrix; B represents the input gating matrix; C represents the output mapping matrix; x t represents the data of the current state input architecture;

[0115] Secondly, the state space architecture is discretely adapted by a discrete state space equation; wherein, the equation expression of the state transition matrix A is as follows:

[0116]

[0117] In the formula, n is the row index related to the orthogonal basis function in the polynomial space, and k is the column index related to the orthogonal basis function in the polynomial space.

[0118] In an example of the present application, the state transition matrix A is randomly initialized, and a low-rank matrix after matrix decomposition is adopted, and the equation formula of the low-rank matrix is as follows:

[0119]

[0120] Wherein, P and Q are both vectors with a length of N; V represents an eigenvector matrix; V * represents a transposed matrix; Lambda represents an eigenmatrix; and * represents a projection operation.

[0121] In an example of the present application, the expression of the discrete state space equation is as follows:

[0122]

[0123] In the formula, h k and y k respectively represent a memory control unit and an output control unit for selecting a current state in the state space architecture; h k-1 represents a memory control unit for selecting a previous state in the state space architecture; h0 represents an initialized state of the memory control unit; x k represents data of a current state input architecture; and x0 represents data of an initial state input architecture. A, B and C are all matrices after discrete adaptation.

[0124] In an example of the present application, the matrix is obtained by the following derivation formula:

[0125]

[0126] In the formula, Delta represents a discretization nonlinear function for discretizing continuous states; and I represents a unit matrix.

[0127] In an example of the present application, in the step S30, the expression formula of the acoustic emission parameter weight factor S i is as follows:

[0128]

[0129] wherein M represents the number of input acoustic emission parameters; denotes a set of all permutations of M features, denotes a set of all features before feature k in permutation R, f x (S) = E(f(X) | X s = x S denotes the conditional expectation given the feature subset S; i represents the weight factor serial number.

[0130] In one example of the present application, in the step S40, the acoustic emission parameter weight factor, the fracture parameter and the acoustic emission parameter data of the test set are input into the mechanism equation parameter multi-objective optimization model to obtain the fracture evolution mechanism equation, specifically including the following steps:

[0131] S41: the acoustic emission parameter data is extracted as a feature vector X f by a data coding layer;

[0132] S42: the weight factor of each acoustic emission parameter is extracted as a global weight factor S m by a data coding layer;

[0133] S43: the feature vector X f and the fracture parameter F M are normalized;

[0134] S44: the basic form of the equation is constructed, and the mechanism equation is selected as a linear equation or a nonlinear equation;

[0135] S45: a minimum mean square error objective function of a multi-objective optimization method is set, and the minimum mean square error objective function formula is as follows:

[0136]

[0137] In the formula, represents the predicted fracture parameter based on the equation parameter ; F Mn represents the real fracture parameter; and N represents the total number of samples;

[0138] S46: a maximum weight factor penalty item objective function of a multi-objective optimization method is set, and the maximum weight factor penalty item objective function expression is as follows:

[0139]

[0140] In the formula, represents the equation parameter; n represents the total number of acoustic emission parameters; and S mj represents the average value of the weight factor of the jth feature on all samples;

[0141] S47: Set the final objective function of the multi-objective optimization method, maximize the weight factor penalty objective function; wherein the formula of the weight factor penalty objective function is as follows:

[0142] Object=[MSE,Penalty]

[0143] Wherein, [ ] represents the balance point between MSE and Penalty found by the multi-objective optimization method;

[0144] S48: Mechanism equation parameter multi-objective optimization model executes optimization: first initialize the population Then, the equation parameter optimization is performed through the final objective function Object; and finally, the crack evolution mechanism equation is output.

[0145] In one example of the present application, in the step S50, the deviation is calculated through the test set CT detection data, and the specific implementation process is as follows:

[0146] The crack evolution mechanism equation is input into the equation solver to obtain the crack parameter F pred The crack parameter F pred And the full space-time crack parameter F M Inputted by the CT detection, the root mean square error equation is calculated to calculate the deviation, and the root mean square error formula is as follows:

[0147]

[0148] Wherein, N represents the total number of samples.

[0149] That is, the crack evolution mechanism equation is input into the mechanism equation solving and precision verification model to obtain the crack evolution result, and the deviation is calculated through the crack evolution result and the test set CT detection data to adjust the neural network model parameters.

[0150] According to the coal rock crack evolution mechanism construction system based on the interpretable neural operator, the system comprises:

[0151] The information acquisition module is configured to arrange CT detection sensors and acoustic emission monitoring sensors on the coal rock sample, and place the coal rock sample in a testing machine for loading test, and acquire CT detection data and full space-time acoustic emission monitoring data at stage time in the loading process of the coal rock sample through the CT detection sensors and the acoustic emission monitoring sensors; wherein the CT detection data is stage time full space crack parameter data, and the acoustic emission monitoring data is full space-time acoustic emission parameter data.

[0152] a data division module configured to correspond CT detection data and full-time and space acoustic emission monitoring data at a time point during a coal rock sample loading process according to the time point, to obtain a fracture parameter data set, and to divide the fracture parameter data set into a training set, a verification set, and a test set;

[0153] a weight factor extraction module configured to establish an interpretable neural operator network model, to perform feature extraction on spatial fracture parameter data and corresponding time point acoustic emission parameter data in the training set and the verification set in the fracture parameter data set based on the neural network model of the interpretable neural operator, and to obtain acoustic emission parameter weight factors;

[0154] a fracture evolution mechanism equation module configured to input the acoustic emission parameter weight factors, the fracture parameters of the test set, and the acoustic emission parameter data into a multi-objective optimization module to obtain equation parameters, and to construct a fracture evolution mechanism equation from the equation parameters, the fracture parameters, and the acoustic emission parameters;

[0155] a mechanism equation optimization module configured to obtain a three-dimensional coal rock sample fracture field evolution result by solving the mechanism equation, to determine whether the precision of a coal rock three-dimensional fracture field imaging result meets a requirement, to end the operation when the precision of the coal rock three-dimensional fracture field imaging result meets the requirement, and to perform deviation calculation on the test set CT detection data and adjust neural network parameters until the precision of the coal rock three-dimensional fracture field imaging result meets the requirement when the precision of the coal rock three-dimensional fracture field imaging result cannot meet the requirement.

[0156] The exploration system focuses on discovering a fracture evolution mechanism equation in a coal rock sample loading test process by combining a neural operator network, SHAP, and multi-objective optimization, and reveals the fracture parameter evolution mechanism in the coal rock sample loading test process. Compared with traditional numerical simulation and neural network methods, this coal rock fracture evolution mechanism equation discovery method based on interpretable deep learning and multi-objective optimization has automatic equation discovery capability, high-precision feature extraction capability, and low dependence on computing resources, and has strong interpretability and good generalization ability, providing a new technical path for intelligent research and engineering application of coal rock fracture evolution mechanisms.

[0157] The neural operator network in the exploration system is obtained by performing spatio-temporal feature extraction on data in the fracture parameter data set based on a selective state space architecture, and a feature extraction method for fracture parameter data and acoustic emission data in a coal rock sample loading process is proposed. Based on the proposed spatio-temporal feature extraction method, multi-source information construction of full-time and space acoustic emission data and fracture parameter data can be realized, and storage and computing costs can be significantly saved.

[0158] The acoustic emission parameter weight factor in the exploration system is obtained by feature extraction on the multi-source information construction result of the full space-time acoustic emission scalar parameter and the fracture parameter data through the SHAP weight extraction module. The SHAP weight extraction module can obtain the acoustic emission parameter weight factor in the loading process of the coal rock sample through the multi-source information construction result, and input the multi-objective optimization module to adjust the proportion weight of each equation parameter in the mechanism equation, so as to realize the exploration of the fracture evolution mechanism equation and reveal the black box process of the fracture parameter inversion of the coal rock sample in the loading process.

[0159] It should be noted that the coal rock fracture evolution mechanism construction system based on the interpretable neural operator of the present application can also perform any processing in the coal rock fracture evolution mechanism construction method based on the interpretable neural operator as previously described, and specific details will not be repeated here.

[0160] The exemplary embodiments of the coal rock fracture evolution mechanism construction method and system based on the interpretable neural operator proposed by the present application are described in detail above with reference to the preferred embodiments, however, those skilled in the art can understand that various modifications and modifications can be made to the above specific embodiments without departing from the concept of the present application, and various technical features and structures proposed by the present application can be combined without exceeding the protection scope of the present application, and the protection scope of the present application is determined by the appended claims.

Claims

1. A method for constructing a coal rock fracture evolution mechanism based on an interpretable neural operator, characterized in that, The method comprises the following steps: S10: arranging CT detection sensors and acoustic emission monitoring sensors on the coal rock sample, and placing the coal rock sample in a testing machine for loading test, and collecting CT detection data and full-time and space acoustic emission monitoring data of the coal rock sample at periodic time points during the loading process through the CT detection sensors and the acoustic emission monitoring sensors; wherein the CT detection data are full-space crack parameter data at periodic time points, and the acoustic emission monitoring data are full-time and space acoustic emission parameter data; S20: corresponding the CT detection data and the full-time and space acoustic emission monitoring data at periodic time points during the loading process of the coal rock sample according to time points, obtaining a crack parameter data set, and dividing the crack parameter data set into a training set, a verification set and a test set; S30: establishing an interpretable neural operator network model, and performing feature extraction on the spatial crack parameter data and the corresponding time acoustic emission parameter data in the training set and the verification set in the crack parameter data set based on the interpretable neural operator network model, realizing multi-source information construction of the crack parameter data and the acoustic emission parameter data, and obtaining a multi-source information construction result; S40: a SHAP weight extraction module performs feature extraction on the neural operator model and the multi-source information construction result, and obtains an acoustic emission parameter weight factor; S50: inputting the acoustic emission parameter weight factor, the crack parameter and the acoustic emission parameter data of the test set into a multi-objective optimization module to obtain equation parameters, and the equation parameters, the crack parameter and the acoustic emission parameter constitute a crack evolution mechanism equation; S60: solving the three-dimensional coal rock sample crack field evolution result through the crack evolution mechanism equation, judging whether the precision of the coal rock three-dimensional crack field imaging result meets the requirements, and when the precision of the coal rock three-dimensional crack field imaging result cannot meet the requirements, performing deviation calculation through the test set CT detection data and adjusting the neural network parameters until the precision of the coal rock three-dimensional crack field imaging result meets the requirements.

2. The coal rock crack evolution mechanism construction method based on an interpretable neural operator according to claim 1, wherein in the step S30, the neural network model based on the interpretable neural operator performs feature extraction on the full-space crack parameter data and the corresponding time acoustic emission parameter data in the training set in the crack parameter data set, realizes multi-source information construction of the crack parameter data and the acoustic emission parameter data, and obtains a multi-source information construction result; and the step S30 comprises the following steps:

3. The coal rock crack evolution mechanism construction method based on an interpretable neural operator according to claim 2, wherein in the step S36, the selective state space architecture is specifically implemented as follows: S31 : extracting the parameter-enhanced acoustic emission feature AEf by parameterizing the acoustic emission parameters through the data encoding layer se ; S32: The encoded data is spliced to the feature AE obtained by the feature extraction layer B through a residual connection layer b In the present application; S33: enhancing the parameter acoustic emission feature AEf by a first Normalization function se obtaining the feature AE by regularization n ; S34: regularized feature AE n Feature extraction by residual connection of a second linear feature extraction layer A and a second activation function layer to obtain AE a+s Feature AE spliced to the output of the selective state space architecture sssm AE obtained in SSSM ; S35: the feature AE output by the first linear feature extraction layer A a The feature AE with higher dimension is obtained through the convolution layer and the first activation function layer conv+s ; S36: Gating computation on high-dimensional features by a selective state space architecture, and concatenating the extracted features with the features extracted by the convolutional layer and the first activation function layer to obtain feature AE SSSM ; S37: The linear feature extraction layer B performs feature extraction on the spliced features, and splices the extracted features with the features of the encoded data spliced by the residual connection layer to obtain features AFf b+se ; S38: Regularize the spliced features by a second Normalization function to obtain features AEf n ; S39: The extracted features are input into a fully connected layer to calculate a multi-source information construction result MI f . First, a state space architecture is built through a continuous state space equation, wherein an expression of the continuous state space equation is as follows: Second, the state space architecture is adapted to discrete data by a discrete state space equation; wherein an equation expression of a state transition matrix A is as follows: In the formula, n is a row index related to an orthogonal basis function in a polynomial space, and k is a column index related to an orthogonal basis function in the polynomial space. h t = Ah t-1 +Bx t y t = Ch t where h t-1 represents the system state; h t represents the updated system state; matrix A represents a state transition matrix; B represents an input gate matrix; C represents an output mapping matrix; x t represents data of the current state input architecture; 4. The coal rock crack evolution mechanism construction method based on an interpretable neural operator according to claim 3, wherein ​ ​ Further comprising: randomly initializing the state transition matrix A, and using the low-rank matrix after matrix decomposition, the low-rank matrix equation is as follows: where P and Q are both vectors of length N; V represents the eigenvector matrix; V * represents the transpose matrix; A represents the eigenmatrix; and * represents the projection operation.

5. The coal rock fracture evolution mechanism construction method based on an interpretable neural operator according to claim 3, characterized in that, The expression of the discrete state space equation is as follows: wherein h k and y k represent the memory control unit and the output control unit of the current state in the selected state space architecture, respectively; h k-1 represents the memory control unit of the previous state in the selected state space architecture; h0 represents the initial state of the memory control unit; x k represents the data of the current state input architecture; x0 represents the data of the initial state input architecture; are all matrices after the discrete adaptation of A, B and C.

6. The coal rock fracture evolution mechanism construction method based on an interpretable neural operator according to claim 5, characterized in that, matrix is derived from the following equation: In the formula, Δ represents a discretized nonlinear function for discretizing continuous states; and I represents a unit matrix.

7. The coal rock fracture evolution mechanism construction method based on an interpretable neural operator according to claim 1, characterized in that, In the step S30, the acoustic emission parameter weight factor S i The expression formula is: where M represents the number of input acoustic emission parameters; denotes the set of all permutations of M features, denotes the set of all combinations of features preceding feature k in permutation R, f x (S) = E(f(X) | X s = x S denotes the conditional expectation given the feature subset S; i represents the weight factor index number.

8. The coal rock fracture evolution mechanism construction method based on an interpretable neural operator according to claim 1, characterized in that, In the step S40, the acoustic emission parameter weight factor, the fracture parameter and the acoustic emission parameter data of the test set are input into the mechanism equation parameter multi-objective optimization model to obtain the fracture evolution mechanism equation, and the step S40 specifically includes the following steps: S41: Extract the acoustic emission parameter data as a feature vector X through the data encoding layer f ; S42: extracting the weight factor of each acoustic emission parameter as a global weight factor S by the data encoding layer m ; S43: Normalization of the feature vector X f and the fracture parameter F M Normalization; S44: constructing an equation basic form, and selecting the mechanism equation as a linear equation or a nonlinear equation; S45: setting a minimum mean square error objective function of the multi-objective optimization method, and the minimum mean square error objective function is as follows: wherein represent the predicted fracture parameters based on the equation parameters predicted fracture parameters; F Mn represent the true fracture parameters; N represents the total number of samples; S46: setting a maximum weight factor penalty item objective function of the multi-objective optimization method, and the expression of the maximum weight factor penalty item objective function is as follows: wherein, represents the equation parameters; n represents the total number of acoustic emission parameters; S mj represents the average value of the weight factor of the jth feature over all samples; S47: setting a final objective function of the multi-objective optimization method, and the maximum weight factor penalty item objective function; and the formula of the weight factor penalty item objective function is as follows: Object=[MSE,Penalty] Wherein, [,] represents a balance point searched by the multi-objective optimization method between MSE and Penalty; S48: Mechanism equation parameter multi-objective optimization model executes optimization: first initialize population Then optimize the equation parameters through the final target function Object; finally output the fracture evolution mechanism equation.

9. The coal rock fracture evolution mechanism construction method based on an interpretable neural operator according to claim 1, characterized in that, In the step S50, deviation calculation is performed through the test set CT detection data, and the specific implementation process is as follows: The fracture evolution mechanism equation is input into the equation solver to obtain the fracture parameter F pred The fracture parameter F pred and the full-time-space fracture parameter F M obtained by CT detection is input into the root mean square error equation to calculate the deviation, wherein the root mean square error formula is as follows: Wherein, N represents the total number of samples.

10. A coal rock fracture evolution mechanism construction system based on an interpretable neural operator, characterized in that, It includes: An information acquisition module configured to arrange a CT detection sensor and an acoustic emission monitoring sensor on a coal rock sample, place the coal rock sample in a testing machine for a loading test, and acquire CT detection data and full-time-space acoustic emission monitoring data at a stage time during the loading process of the coal rock sample through the CT detection sensor and the acoustic emission monitoring sensor; wherein the CT detection data are stage-time full-space fracture parameter data, and the acoustic emission monitoring data are full-time-space acoustic emission parameter data; A data division module configured to correspond the CT detection data and the full-time-space acoustic emission monitoring data at the stage time during the loading process of the coal rock sample according to time, obtain a fracture parameter data set, and divide the fracture parameter data set into a training set, a validation set and a test set; A weight factor extraction module configured to establish an interpretable neural operator network model, and perform feature extraction on the spatial fracture parameter data and the corresponding time acoustic emission parameter data in the training set and the validation set in the fracture parameter data set based on the neural network model of the interpretable neural operator to obtain an acoustic emission parameter weight factor; The fracture evolution mechanism equation module is configured to input the acoustic emission parameter weight factor, the fracture parameter and the acoustic emission parameter data of the test set into the multi-objective optimization module to obtain equation parameters, and the equation parameters, the fracture parameters and the acoustic emission parameters constitute a fracture evolution mechanism equation. The mechanism equation optimization module is configured to obtain a three-dimensional coal rock sample fracture field evolution result by solving the mechanism equation, judge whether the precision of the coal rock three-dimensional fracture field imaging result meets the requirements, and when the precision of the coal rock three-dimensional fracture field imaging result cannot meet the requirements, perform deviation calculation through the CT detection data of the test set and adjust the neural network parameters until the precision of the coal rock three-dimensional fracture field imaging result meets the requirements.

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