Multi-data fracturing process knowledge learning method based on NURBS and KAN architecture

Abstract

The invention discloses a multivariate data fracturing process knowledge learning method based on NURBS and KAN architectures. The multivariate data fracturing process knowledge learning method comprises the following steps: 1) collecting parameter data of a rock mass fracturing process; 2) establishing a knowledge learning set function library; 3) carrying out data processing on the collected data to obtain k-step learning data; 4) carrying out data initialization processing on the collected data; the initialization processing comprises residual error amplification and normalization processing in deep learning; (5) the processed data physical parameters and the corresponding spatial position coordinate vectors are input into the fracturing process knowledge learning model; 6) performing correlation test; 7) learning rock mass fracturing knowledge; and 8) circulating the steps 3) to 7) until the physical parameter data of the rock mass fracturing process output by the fracturing process knowledge learning model is no longer increased or reaches a set cycle index, and completing knowledge learning. The KAN architecture is used, and the correlation test is combined, so that the generalization ability of the model can be effectively improved, and the problem of data imbalance can be effectively solved.

Description

Technical Field

[0001] The present invention relates to rock and soil underground engineering technology, and in particular to a multi-dimensional data fracturing process knowledge learning method based on NURBS and KAN architecture. Background Art

[0002] The construction of underground structures, such as vertical shaft development, shale gas extraction, and in-situ leaching of sandstone uranium deposits, involves highly coupled multi-physics fields and highly nonlinear problems, for which theoretical analysis and understanding are extremely limited. With the rapid development of deep learning, deep learning-based knowledge acquisition may surpass researchers' understanding of complex coupled physics fields. Understanding and modeling complex coupled physics fields is crucial for the accuracy and effectiveness of numerical simulations of deep underground uranium in-situ leaching and oil and gas fracturing. Therefore, multi-dimensional data acquisition of rock mass fracturing behavior during construction is a fundamental and challenging issue in rock mechanics.

[0003] Knowledge learning and deep learning models typically require large amounts of labeled data for training, and have high requirements for data quality and diversity. However, in practical applications, obtaining high-quality, large-scale labeled data is often a time-consuming and labor-intensive task. In addition, data bias and imbalance may also affect the performance of deep learning models. Deep learning models perform well on training sets, but may have poor generalization capabilities on unseen data and are prone to overfitting. This limits the robustness and adaptability of deep learning models in practical applications. Training deep learning models typically requires a large amount of computing resources and time. Especially on complex network structures and large-scale datasets, the training process can be very time-consuming and requires high-performance computing equipment. Therefore, there is an urgent need to provide a knowledge learning deep learning model with high computational efficiency and low computational complexity to improve generalization capabilities and address data imbalance. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a multi-data cracking process knowledge learning method based on NURBS and KAN architecture to address the defects in the existing technology.

[0005] The technical solution adopted by the present invention to solve its technical problem is: A multi-dimensional data cracking process knowledge learning method based on NURBS and KAN architecture includes the following steps: 1) Collect parameter data of rock fracturing process, Collect parameter data of the rock mass fracturing process, and record the time t of collecting the parameter data and the corresponding spatial position coordinates as the data to be learned from the rock mass fracturing process test; 2) Establish a knowledge learning set function library; 3) Process the collected data to obtain thek step learning data; the data conversion process is a function conversion process in the function library; 4) Performing data initialization processing on the collected data; the initialization processing includes residual amplification and normalization processing in deep learning; 5) The processed data physical parameters ,as well as The corresponding spatial position coordinate vector Input into the fracture process knowledge learning model to obtain the learned data physical parameters; The fracture process knowledge learning model adopts the KAN architecture and uses non-uniform node NURBS spline interpolation as its basis function; The activation function of the KAN architecture is expressed as:

[0006] Where, is the spline function, is the basis function, w is the weight function; 6) Correlation test: If k The final output of the learning data and The calculated result is less than the set threshold r , r∈R , then remove the parameter data; go to step 3), adjust the knowledge learning set function used for each collected data, and re-start deep learning; if and The calculation results are all greater than the threshold r Then proceed to the next step; 7) The residual is calculated using the following formula:

[0007]

[0008] judge Is it established, among which, 、 is the set value; If so, the rock fracturing knowledge learning is completed, and the physical parameter data of the rock fracturing process are output; otherwise, go to step 3) to continue learning; 8) Repeat steps 3) to 7) until the physical parameter data of the rock mass fracturing process output by the fracturing process knowledge learning model no longer increases or reaches the set number of cycles, and the knowledge learning is completed.

[0009] According to the above scheme, in step 1), The parameter data include: stress, strain, elastic modulus, Poisson's ratio, osmotic pressure, temperature, permeability, crack density, displacement, uniaxial compression strength of rock mass, tensile strength, rock mass cohesion, friction angle, and rock mass fracture toughness.

[0010] According to the above scheme, step 1) also includes data preprocessing, which includes data denoising, desensitization, missing data processing, duplicate checking and deletion of erroneous data.

[0011] According to the above solution, in step 2), the functions in the function library include: exponential functions, logarithmic functions, derivative-related functions, and trigonometric functions.

[0012] According to the above scheme, in step 4), the residual amplification and normalization processing in deep learning adopts the following formula:

[0013]

[0014] in, 、 For the k Step learning data, For the k The average residual of the network of deep learning step; 、 is the normalized value of the k-th step learning data after residual amplification, and the data standardization interval is [-1, 1]. According to the above scheme, in step 5), the model is as follows:

[0015]

[0016]

[0017]

[0018] in, is a function of variables, and For the k The output of step learning data, is a learnable external function in the KAN architecture, is a learnable internal function in the KAN architecture. According to the above scheme, in step 5), ; According to the above scheme, in step 5),

[0019] Where, , is the Nurbs spline interpolation basis function, is the b-spline interpolation basis function, is the Nurbs spline interpolation weight function, n is the number of interpolation control points; are the coordinates of the control points.

[0020] The beneficial effects produced by the present invention are: The present invention combines the isogeometric analysis non-uniform node NURBS spline interpolation method with the KAN deep learning framework, introduces the non-uniform node NURBS spline interpolation into the KAN deep learning framework, forms a deep learning model suitable for rock fracturing process parameters, and implements deep learning of random node distribution with non-uniform distribution of node spacing and node number. Through the method of the present invention, high-quality multivariate data of rock fracturing process can be obtained; The method of the present invention uses the KAN architecture with a small number of computing nodes. It combines correlation testing to improve its generalization ability and solve the data imbalance problem. In theory, it can reduce the residual to machine precision, providing a basis for subsequent multi-physics field coupling model knowledge learning and calculation, and is also conducive to the next step of simulation calculation and understanding of fracturing mechanism. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] The present invention will be further described below with reference to the accompanying drawings and embodiments, in which: Figure 1 It is a flow chart of a method according to an embodiment of the present invention. DETAILED DESCRIPTION

[0022] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0023] like Figure 1 As shown, a multi-dimensional data cracking process knowledge learning method based on NURBS and KAN architecture includes the following steps: 1) Collect parameter data of rock fracturing process test, including stress at any position ,strain , elastic modulus , Poisson's ratio , osmotic pressure ,temperature , permeability , crack density , displacement at any position , uniaxial compression strength of rock mass , tensile strength , rock mass cohesion , friction angle , rock fracture toughness ; Simultaneously record the time t of parameter data acquisition and the corresponding spatial position coordinates; Select one or more parameter data to obtain the data combination to be learned in the rock fracturing process test, and record the combination as X=( x 1 ，…，x m );in, x 1 ，…，x m Indicates the selected m parameter data; 2) Establish a knowledge learning set function library, which includes functions such as exponential functions, logarithmic functions, derivative-related functions, and trigonometric functions; 3) Process the collected data to obtain the k Step 1: learning data; data conversion processing is processed by the function conversion processing in the function library; the details are as follows: (1) (2) in, 、 For the k Step learning data, 、 Learning data for initial knowledge, 、 is the first k -1 step learning data, which is parameter data x i ,time t relevant learning data; 4) Initialize the collected data; (3) (4) (5) (6) in, 、 For the k Step learning data, 、 For the k The average residual of the network of deep learning step; 、 Data physical parameters The normalized value of the k-th step learning data after residual amplification; 、 Data physical parameters The corresponding spatial position coordinate vector The normalized value of the k-th step learning data after residual amplification; 5) The processed data physical parameters ,as well as The corresponding spatial position coordinate vector Input the data into the fracture process knowledge learning model to obtain the learned data physical parameters; the fracture process knowledge learning model adopts the KAN architecture and uses non-uniform node NURBS spline interpolation as its basis function; (7) (8) (9) (10) in, A physical quantity grid prediction function related to the physical parameters of the input data, including parameters of the rock mass fracturing process test; A prediction function for a physical quantity grid related to an input spatial position coordinate vector; is a learnable external function in the KAN architecture, It is a learnable internal function in the KAN architecture; The activation function of the KAN architecture is expressed as: (11) Where, is the spline function, is the basis function, w is the weight function; ; (12) Where, , is the Nurbs spline interpolation basis function, is the b-spline interpolation basis function, is the Nurbs spline interpolation weight function, n is the number of interpolation control points; are the coordinates of the control points; 6) Correlation test: If the result of the variables in formula (9) and (10) is less than the threshold r ( r∈R ), then remove the parameter data; go to step 3), adjust the knowledge learning set function used for each collected data, and re-start deep learning; if all variables calculated by formulas (9) and (10) are greater than the threshold r Then proceed to the next step; 7) The residual is calculated using the following formula: (13) (14) Determine whether the expression of formula (15) is valid. If it is valid, the rock fracturing knowledge learning is completed, and the physical parameter data of the rock fracturing process is output; otherwise, go to step 3) to continue learning; (15) in, 、 is the set value; 8) Repeat steps 3) to 7) until the physical parameter data of the rock mass fracturing process output by the fracturing process knowledge learning model based on multivariate data drive and deep learning no longer increases or reaches the set number of cycles, and the knowledge learning is completed.

[0024] In this way, we obtained a large amount of physical parameter data from a small batch of data, and eliminated the data that did not meet the requirements through correlation testing to obtain high-quality multivariate data of the rock fracturing process.

[0025] The learning data selected in the following embodiments are field-measured displacement and stress data containing certain noise; 1) Collect parameter data of the rock fracturing process test and record the time t of parameter data collection and the corresponding spatial position coordinates; 2) Establish a knowledge learning set function library, which includes functions such as exponential functions, logarithmic functions, derivative-related functions, and trigonometric functions; like: 、 、 、 、 、 、 、 、 、 ; 3) Perform data conversion on the collected data to obtain the k Step by step learning data; take the displacement and stress data measured on site as an example; (2-1) (2-2) 、 For the k Step learning data, 、 Learning data for initial knowledge; 、 is the data obtained by performing (k-1) data conversion on the collected data, and is the parameter data collection time t Related learning data; data conversion is performed using functions in the function library; The learning data selected in this embodiment are field-measured displacement and stress data containing certain noise; 4) Performing data initialization processing on the collected data; the initialization processing includes residual amplification and normalization processing in deep learning; (2-3) (2-4) (2-5) (2-6) in, 、 For the k Step learning data, 、 For the k The average residual of each independent network in the deep learning step is respectively and Related; For the kth step and input and displacement data The normalized value of the correlation, is the kth step and input and displacement data The relevant normalized value; For the kth step and input and stress data The relevant normalized value; For the kth step and input and stress data The relevant normalized value; 5) Adopting the KAN architecture and using the non-uniform node NURBS spline function as its basis function; (2-7) (2-8) Use explicit expressions to express , which can be expressed as: (2-9) Among them, the base function is the function in the function library set in step 2), and the function The first subscript is the number of network architecture layers, the second one is the output, and the third one is the input.

[0026] (2-10) (2-11) in, For input Related physical quantity grid prediction functions, physical quantities include stress, displacement, etc. For input Related physical quantity grid prediction functions, physical quantities include stress, displacement, etc. is the input vector, including the spatial position coordinates; is the activation function of the qth output, see formula (2-12); is the activation function of output q and input p, is the corresponding input; The activation function of the KAN architecture is expressed as: (2-12) Where, is the spline function, is the basis function, w is the weight function; (2-13) Where, , is the Nurbs spline interpolation basis function, is the b-spline interpolation basis function, is the Nurbs spline interpolation weight function, n is the number of interpolation control points; are the coordinates of the control points; 6) If the result of the variables in formulas (2-10) and (2-11) is less than the threshold r ( r∈R ), then remove the variable data; go to step 3), adjust the knowledge learning set function used for each collected data, and re-start deep learning; if all variables calculated by formulas (2-10) and (2-11) are greater than the threshold r Go to step 9); 7) The residual is calculated using the following formula: (2-14) (2-15) Determine whether the expression of formula (2-16) is valid. If so, the rock fracturing knowledge learning is complete; otherwise, proceed to step 3) to continue deep learning; (2-16) 8) Repeat steps 3) to 7) until the data of the rock fracturing process based on multivariate data drive and deep learning no longer increases or reaches the set number of cycles, and the knowledge learning is completed.

[0027] After the knowledge learning is completed, technical personnel in this field can obtain high-quality data based on the multivariate data of the dense rock fracturing process obtained through learning, and can obtain a large amount of data as needed, ensuring the diversity of the data. Based on the above data, it is convenient to carry out the next simulation calculation. Technical personnel in this field can establish a multi-step adaptive fusion deep learning framework to accurately identify the entire process of dense rock fracturing to form a fracture network, including crack initiation, expansion, etc., as well as the intersection of multiple cracks, convergence and penetration, until the formation of a complex crack network, and establish a complex nonlinear coupling relationship based on this.

[0028] It should be understood that those skilled in the art can make improvements or changes based on the above description, and all such improvements and changes should fall within the scope of protection of the appended claims of the present invention.

Claims

1. A multi-dimensional data fracturing process knowledge learning method based on NURBS and KAN architecture, comprising the following steps: 1) Collect parameter data of rock fracturing process; Obtaining data to be learned from a rock mass fracturing process test based on collected parameter data of the rock mass fracturing process, and recording a time t at which the parameter data was collected and a corresponding spatial position coordinate; 2) Establish a knowledge learning set function library; 3) Process the collected data to obtain the k step learning data; the data conversion process is a function conversion process in the function library; 4) Performing data initialization processing on the collected data; the initialization processing includes residual amplification and normalization processing in deep learning; 5) The processed data physical parameters ,as well as The corresponding spatial position coordinate vector Input into the fracture process knowledge learning model to obtain the learned data physical parameters; The fracture process knowledge learning model adopts the KAN architecture and uses non-uniform node NURBS spline interpolation as its basis function; The activation function of the KAN architecture is expressed as: ； Where, is the spline function, is the basis function, w is the weight function; 6) Correlation test: If k The final output of the learning data and The calculated result is less than the set threshold r , r∈R , then remove the parameter data; go to step 3), adjust the knowledge learning set function used for each collected data, and re-carry out deep learning; like and The calculation results are all greater than the threshold r Then proceed to the next step; 7) The residual is calculated using the following formula: judge Is it established, among which, 、 is the set value; if it is established, the rock fracturing knowledge learning is completed, and the physical parameter data of the rock fracturing process is output; otherwise, go to step 3) to continue learning; 8) Repeat steps 3) to 7) until the physical parameter data of the rock mass fracturing process output by the fracturing process knowledge learning model no longer increases or reaches the set number of cycles, and the knowledge learning is completed.

2. The multivariate data fracturing process knowledge learning method based on NURBS and KAN architecture according to claim 1 is characterized in that: In the step 1), The parameter data include: stress, strain, elastic modulus, Poisson's ratio, osmotic pressure, temperature, permeability, crack density, displacement, uniaxial compression strength of rock mass, tensile strength, rock mass cohesion, friction angle, and rock mass fracture toughness at a set position.

3. The multivariate data fracturing process knowledge learning method based on NURBS and KAN architecture according to claim 1 is characterized in that: The step 1) also includes data preprocessing, which includes data denoising, desensitization, missing data processing, duplicate checking and deletion of erroneous data.

4. The multivariate data fracturing process knowledge learning method based on NURBS and KAN architecture according to claim 1 is characterized in that: In step 2), the functions in the function library include: exponential functions, logarithmic functions, derivative-related functions, and trigonometric functions.

5. The multivariate data fracturing process knowledge learning method based on NURBS and KAN architecture according to claim 1 is characterized in that: In step 4), the residual amplification and normalization processing in deep learning adopts the following formula: in, 、 For the k Step learning data, For the k The average residual of the network of step deep learning; 、 is the normalized value of the k-th step learning data after residual amplification, and the data standardization interval is [-1, 1].

6. The multi-data fracturing process knowledge learning method based on NURBS and KAN architecture according to claim 1 is characterized in that: In step 5), the model is as follows: in, is a function of variables, and For the k The output of step learning data, is a learnable external function in the KAN architecture, is a learnable internal function in the KAN architecture.

7. The multi-data fracturing process knowledge learning method based on NURBS and KAN architecture according to claim 1 is characterized in that: In the step 5), Basis functions .

8. The multi-dimensional data fracturing process knowledge learning method based on NURBS and KAN architecture according to claim 1 is characterized in that: In the step 5), Where, , is the Nurbs spline interpolation basis function, is the b-spline interpolation basis function, is the Nurbs spline interpolation weight function, n is the number of interpolation control points; are the coordinates of the control points.

9. An electronic device, characterized in that: include: one or more processors; as well as a storage device for storing one or more programs, When the one or more programs are executed by the one or more processors, the one or more processors are enabled to perform the method according to any one of claims 1 to 8.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method according to any one of claims 1 to 8 is implemented.

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