Rock mechanical property prediction method and system based on PINN-XGBoost model

Abstract

The invention provides a rock mechanical property prediction method and system based on a PINN-XGBoost model, and relates to the technical field of rock engineering, and the method comprises the following steps: obtaining experiment data of rock mechanical parameters, and generating simulation data according to the experiment data; processing the simulation data to obtain a to-be-predicted data set; constructing a prediction model, inputting the to-be-predicted data set into the trained prediction model, and outputting a final prediction value; wherein the prediction model comprises a physical constraint model and an XGBoost model; the prediction model comprises a physical constraint model and an XGBoost model. According to the method, the physical constraint neural network (PINN) is used as a basic prediction model, it is ensured that the prediction result conforms to the rock mechanics law, on the basis of the PINN, the XGBoost model is superimposed for integrated prediction, and the rock mechanics characteristic prediction precision is further improved.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of rock engineering, and particularly relates to a rock mechanics property prediction method and system based on a PINN-XGBoost model. BACKGROUND

[0002] The statements in this section merely provide background information related to the application and do not necessarily constitute prior art.

[0003] The acquisition of rock mechanics parameters and mechanics properties is a prerequisite for engineering safety and stability analysis, and directly affects structural safety, construction efficiency, cost control, and geological disaster prevention.

[0004] Currently, the methods for acquiring rock mechanics properties mainly include laboratory experiments and field tests. In terms of laboratory experiments, uniaxial compression tests, triaxial compression tests, etc. are often used to acquire parameters such as rock compressive strength and elastic modulus, so as to more comprehensively study the deformation and failure characteristics of rocks under complex stress conditions. In terms of field tests, in-situ triaxial compression tests can directly measure parameters such as rock cohesion and elastic modulus under actual geological conditions; rock mass shear tests can acquire parameters such as rock shear strength; and rock mass deformation tests can acquire parameters such as rock deformation modulus. However, the above methods require a large amount of manpower, material resources and time. Laboratory tests face problems such as insufficient sample representativeness and inconsistent test conditions with field conditions; field tests face problems such as long test period and high test cost. By introducing numerical simulation technology, these problems can be effectively solved, and the test efficiency and parameter accuracy can be improved, providing more reliable support for engineering design, construction and monitoring.

[0005] However, due to limitations of testing equipment and technology, domestic and foreign scholars sometimes have difficulty in accurately measuring certain key parameters in current numerical simulation research. For example, in jointed and fractured rock mass, the distribution, morphology and mechanics properties of fractures have important influence on rock mechanics parameters, but these properties vary greatly in space, making it difficult to efficiently and accurately conduct numerical simulation prediction research. SUMMARY

[0006] In view of the problems existing in the prior art, the application provides a rock mechanics parameter prediction method and system based on a PINN-XGBoost model, which uses a physically constrained neural network (PINN) as a basic prediction model, and superimposes an XGBoost model on the basis of the PINN for integrated prediction, so as to more accurately simulate and predict various mechanics properties of rocks.

[0007] To achieve the above purpose, the application adopts the following technical solutions: The application provides a rock mechanics parameter prediction method based on a PINN-XGBoost model, which comprises the following steps: obtain experimental data of rock mechanics parameters, and generate simulation data according to the experimental data; process the simulation data to obtain a to-be-predicted data set; construct a prediction model, input the to-be-predicted data set into the trained prediction model, and output a final prediction value; The prediction model comprises a physical constraint model and an XGBoost model. The first prediction value is obtained by inputting the to-be-predicted data set into the physical constraint model. The second prediction value is obtained by inputting the first prediction value into the XGBoost model. The final prediction value is obtained by weighted sum of the first prediction value and the second prediction value.

[0008] Further, the rock sample of the experimental data of rock mechanics parameters comprises: obtaining particle size distribution data by sieving method, measuring particle density of fillers by drainage method, and calculating fractal dimension data statistical characteristics. The particle size distribution data, the particle density data of the fillers, and the fractal dimension data are the experimental data.

[0009] Further, the experimental data is input into a rock mechanics numerical model to simulate the same loading conditions as the indoor test, a series of virtual triaxial compression tests are performed, and simulation data is generated.

[0010] Further, the preprocessing of the simulation data comprises: removing noise and outliers in the experimental data, and performing interpolation processing on the simulation data to ensure uniform distribution of data points; using a generative adversarial network to expand data, and screening data conforming to statistical rules as a to-be-predicted data set.

[0011] Further, in the XGBoost model construction stage, a target function is constructed based on mean square error, and the model capacity is optimized by initializing tree structure parameters and regularization terms.

[0012] Further, the first predicted cohesion and the first predicted internal friction angle are obtained by inputting the to-be-predicted data set into the PINN model. The second predicted cohesion and the second predicted internal friction angle are obtained by inputting the first predicted cohesion and the first predicted internal friction angle into the XGBoost model. The final predicted cohesion is obtained by adding the product of the weight of the PINN model and the first predicted cohesion to the product of the weight of the XGBoost model and the second predicted cohesion. The final predicted internal friction angle is obtained by adding the product of the weight of the PINN model and the first predicted internal friction angle to the product of the weight of the XGBoost model and the second predicted internal friction angle.

[0013] The second aspect of the present application provides a rock mechanics parameter prediction system based on a PINN-XGBoost model, based on a rock mechanics parameter prediction method based on a PINN-XGBoost model as described in the first aspect, comprising: A simulation data generation module configured to obtain experimental data of rock mechanics parameters and generate simulation data according to the experimental data; A data processing module configured to process the simulation data to obtain a to-be-predicted data set; A model construction module configured to construct a prediction model and input the to-be-predicted data set into the prediction model; A prediction result output module configured to output the final prediction value of the rock mechanics parameters by the prediction model.

[0014] The third aspect of the present application provides a computer program product, wherein the computer program is executed by a processor to realize the steps of the rock mechanics parameter prediction method based on the PINN-XGBoost model as described in the first aspect of the present application.

[0015] The fourth aspect of the present application provides a computer readable storage medium, which stores a program, and the program is executed by a processor to realize the steps of the rock mechanics parameter prediction method based on the PINN-XGBoost model as described in the first aspect of the present application.

[0016] The fifth aspect of the present application provides an electronic device, which includes a memory, a processor, and a program stored in the memory and executable on the processor, and the processor executes the program to realize the steps of the rock mechanics parameter prediction method based on the PINN-XGBoost model as described in the first aspect of the present application.

[0017] The technical scheme of the present application has the following beneficial effects: 1. The present application constructs a prediction model, uses a physically constrained neural network (PINN) as a basic prediction model to ensure that the prediction result conforms to the rock mechanics law, and further improves the prediction accuracy of the rock mechanics characteristics by stacking an XGBoost model for integrated prediction based on the PINN.

[0018] 2. The rock mechanics experiment data collection is carried out, the particle density, particle size distribution, cohesion and internal friction angle and other parameters of the rock are obtained through the indoor test, and the fractal dimension and other statistical characteristics are calculated; the discrete element or finite element numerical simulation software is used to construct the rock numerical model, the mechanical response of the rock under different working conditions is simulated, and part of the experimental database is expanded; the indoor test and numerical simulation data are used as experimental data to train the generative adversarial network (GAN), so that it has preliminary learning ability, then the test and simulation data are input, and more high-quality synthetic data are generated; the rock mechanics property acquisition method of fusing the generative adversarial network (GAN), numerical simulation and indoor test is used to expand the database of rock mechanics test, so that the various mechanical properties of the rock can be simulated more accurately.

[0019] 3. The model is trained by using transfer learning, the model is pre-trained on simulation data, and then fine-tuned on experimental data, the regression task index, classification task index and the like are used to evaluate the model performance, and the generalization ability of the model is verified on an independent data set.

[0020] The advantages of the additional aspects of the application will be partially given in the following description, partially become obvious from the following description, or be known by the practice of the application. BRIEF DESCRIPTION OF DRAWINGS

[0021] The drawings accompanying the specification of this application form a part thereof, serve to provide further understanding of the application, and together with the description of the exemplary embodiments of the application and the explanation thereof serve to explain the application, and do not constitute an improper limitation of the application.

[0022] Figure 1 The method flowchart of the first embodiment.

[0023] Figure 2 The calculation flowchart of the generative adversarial network of the first embodiment.

[0024] Figure 3 The system structure diagram of the second embodiment. DETAILED DESCRIPTION

[0025] It should be noted that the following detailed description is exemplary, and is intended to provide further explanation of the application. Unless otherwise indicated, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which the application belongs.

[0026] It should be noted that the terms used herein are only for the purpose of describing the specific embodiments, and are not intended to limit the exemplary embodiments according to the application.

[0027] The embodiments in the application and the features in the embodiments can be combined with each other without conflict.

[0028] Embodiment one The embodiment provides a rock mechanical property prediction method based on a PINN-XGBoost model, as shown in the following steps: Figure 1 Step 1: Obtain experimental data of rock mechanical parameters, and generate simulation data according to the experimental data; Step 2: Process the simulation data to obtain a to-be-predicted data set; Step 3: Construct a prediction model, input the to-be-predicted data set into the trained prediction model, and output a final prediction value; Preferably, the prediction model comprises a physical constraint model and an XGBoost model; The to-be-predicted data set is input into the physical constraint model to obtain a first prediction value; The first prediction value is input into the XGBoost model to obtain a second prediction value; The first prediction value and the second prediction value are weighted and summed to obtain the final prediction value.

[0029] Preferably, step 1 is specifically as follows: Step 1.1: Obtain experimental data of rock mechanical parameters through indoor tests.

[0030] Representative rock samples are selected, and particle size distribution (PSD) data are obtained through a screening method. Next, corresponding cohesion and internal friction angle are determined through a direct shear test, and particle density of fillers is determined by using a drainage method and the like. Fractal dimension data and other statistical characteristics are calculated. The particle size distribution (PSD) data, the particle density data of the fillers, and the fractal dimension data are the experimental data.

[0031] Step 1.2: Generate simulation data.

[0032] In the embodiment, a discrete element or finite element numerical simulation software is used to construct a rock numerical model, simulate mechanical responses of the rock under different working conditions, and expand part of an experimental database.

[0033] Different particle size distribution data, fractal dimension and other statistical characteristics, and particle density are input into a rock mechanical numerical model, a series of virtual triaxial compression tests are performed under the same loading conditions as the indoor tests, and simulation data of simulation cohesion and simulation internal friction angle are generated.

[0034] Step 2: Process the simulation data to obtain a to-be-predicted data set, specifically including: Step 2.1: Preprocessing of the simulation data. ​

[0035] To remove noise and outliers from the experimental data and interpolate the simulation data to ensure uniform distribution of data points. Then, standardize the experimental and simulation data using the following formula: (1) where is the mean, is the standard deviation, and x is a single experimental or simulation data point. Align the experimental and simulation data to ensure consistent data formats.

[0036] As shown in Figure 2 , step 2.2: Data augmentation using a generative adversarial network (GAN).

[0037] Step 2.21: Designing the generator of the generative adversarial network (GAN)First, establish the generator of the generative adversarial network. The network structure of the generator is a fully connected network, which is divided into an input layer, a hidden layer, and an output layer. The loss function of the generator uses the Wasserstein distance (WGAN). In general, in GAN, the 1-Wasserstein distance (i.e. ) is commonly used, and its formula is: (2) where: is the distance in the metric space ; is the set of all joint distributions with and as marginal distributions; is the differential form of , and is the joint probability distribution.

[0038] Step 2.22: Designing the discriminator of the generative adversarial network (GAN).

[0039] Similarly, the network structure of the discriminator can also be a fully connected network. Unlike the generator, the output layer activation function of the discriminator is Sigmoid. This is because the discriminator is used to judge whether the input data comes from the real data distribution or the fake data generated by the generator. The Sigmoid function is commonly used in binary classification problems, as it can map the output value to the range of [0, 1], directly representing the probability value.

[0040] Step 2.23: Availability judgment of generated data.

[0041] The availability judgment of the data can use a sample overlap rate index, which is the ratio of the generated data falling within the range of the original data values, used to measure the distribution similarity of the original data and the generated data. If the sample overlap rate is high, it is considered that the distribution of the generated data and the original data has similarity. The processed experimental data and the simulation data are taken as the original data, and the sample overlap rate (denoted as SOR) is shown in the following formula: (3) (4) wherein, is an activation function, is a discriminator function, is a generator function, is an input noise vector of the generator, is a sample size of the generated data, is a sample number.

[0042] The threshold value can be set to 95% to ensure that the generated data has strong similarity with the original data.

[0043] Step 2.24: Training of the generative adversarial network (GAN) model.

[0044] Rock mechanics data such as stress-strain curves are obtained from triaxial compression tests and simulation data. The data are standardized to ensure consistent input ranges. The weights of the generator and discriminator are initialized using Xavier. Next, the generator and discriminator are alternately trained. A batch of data is randomly sampled from the standardized stress-strain curves and other rock mechanics data, input into the discriminator, and the loss of the real data is calculated. A batch of synthetic data is generated from the generator and input into the discriminator to calculate the loss of the synthetic data. The parameters of the discriminator are updated to minimize the total loss.

[0045] When the network converges, if the GAN-generated data highly overlaps the value range of the standardized stress-strain curves and other rock mechanics data, the overlapping data is selected and combined with the two sets of data. After the standardized stress-strain curves and other rock mechanics data are randomly inserted, an enhanced data set of the standardized stress-strain curves and other rock mechanics data is obtained. Next, the enhanced data set is verified. The Z-score method can be used to select data that conforms to the statistical law as the predicted data set for the prediction model, which includes particle density and particle size distribution parameters.

[0046] Step 3 specifically includes: Step 3.1: Construction of a physically constrained model: The network structure of the PINN includes an input layer, a hidden layer, and an output layer. The input layer inputs the predicted data set, and the output layer outputs the first predicted cohesion and the first predicted internal friction angle .

[0047] The Mohr-Coulomb failure criterion in rock mechanics is embedded in the training loss function of PINN as a physical constraint term to ensure the physical rationality of the prediction. The Mohr-Coulomb failure criterion is expressed as: (5) in, is the shear strength, is the first predicted cohesion, is the first predicted internal friction angle, is the normal stress.

[0048] Next, the mathematical expression of the Mohr-Coulomb criterion is converted into an additional term in the loss function, which directly penalizes the prediction results that do not conform to the laws of physics. The total loss function can be expressed as: (6) in, is the error between the model prediction value and the preprocessed data, To punish the part of the model prediction results that violates the laws of physics, is the regularization weight coefficient.

[0049] Step 3.2: Build the XGBoost model: Before building the XGBoost model, a multidimensional feature set is first constructed based on generated data, simulation data, and experimental data, and PINN is introduced to calculate the first predicted cohesion after physical constraints. and the first predicted internal friction angle As the input feature of the XGBoost model, it is integrated with physical knowledge and outputs the second predicted cohesion and the second predicted internal friction angle After data cleaning, the XGBoost output data is normalized into a two-dimensional table structure dataset, and the dataset is split into training set, validation set, and test set in a ratio of 7:2:1. The test set is retained only for the final evaluation.

[0050] During the XGBoost model construction phase, the objective function was constructed based on the mean squared error (MSE). The model capacity was optimized by initializing the tree structure parameters (maximum depth ≥ 5, learning rate 0.05–0.3) and the regularization term. Statistical features such as particle density and fractal dimension were standardized to form a structured feature matrix, which served as the input for XGBoost. The model was fitted using the training set data, and overfitting was prevented by early stopping. The root mean square error (RMSE) and the coefficient of determination ( ) to evaluate the model performance and calculate and To ensure the accuracy of the prediction results.

[0051] Step 3.3: Model fusion prediction and output of final prediction value: The results of PINN and XGBoost are weighted averaged, and the root mean square error (RMSE) and the coefficient of determination ( ) etc. to evaluate the accuracy of the two models’ predictions. If the two models perform similarly, the weights can be set to 0.5. The product of the weight of the PINN model and the first predicted cohesion is added to the product of the weight of the XGBoost model and the second predicted cohesion to obtain the final predicted cohesion. The final predicted internal friction angle is obtained by adding the product of the PINN model weight and the first predicted internal friction angle to the product of the XGBoost model weight and the second predicted internal friction angle. Specifically, the final predicted internal friction angle is and the final predicted cohesion This is the final predicted value, which is also Figure 1 The output rock mechanical parameters in the formula can be calculated as follows: (7) (8) in, is the weight of the PINN model, is the weight of the XGBoost model, is the first predicted cohesion, is the first predicted internal friction angle, is the second predicted cohesion, is the second predicted internal friction angle.

[0052] Step 3.4: Data Verification: The input data (statistical features such as particle density and fractal dimension) are constructed into a two-dimensional structured table, where each row represents a sample and each column is used as a feature. The feature is input into the prediction model and the final prediction results of rock mechanical parameters are output ( and The final prediction results are compared with the experimental data (cohesion and internal friction angle ) comparison to verify the predicted and The model then verifies whether the rock mechanics constitutive relations are satisfied, calculating the mean square error (MSE) and other methods for data validation. If the predicted data violates the rock constitutive relations, feedback is provided to the PINN to adjust its physical loss function. This allows the model to predict rock mechanics parameters from raw loading data while maintaining compliance with physical laws.

[0053] Embodiment Two The embodiment discloses a rock mechanics parameter prediction system based on a PINN-XGBoost model, and is based on a rock mechanics parameter prediction method based on a PINN-XGBoost model as described in Embodiment 1, as shown in the accompanying drawings, and comprises: Figure 3 a simulation data generation module configured to obtain experimental data of rock mechanics parameters and generate simulation data according to the experimental data; a data processing module configured to process the simulation data to obtain a to-be-predicted data set; a model construction module configured to construct a prediction model and input the to-be-predicted data set into the prediction model; a prediction result output module configured to output a final prediction value of the rock mechanics parameters by the prediction model.

[0054] Embodiment Three The purpose of the embodiment is to provide a computer program product, which, when executed by a processor, implements the steps in the rock mechanics characteristic prediction method based on a PINN-XGBoost model as described in Embodiment One of the present disclosure.

[0055] Embodiment Four The purpose of the embodiment is to provide a computer-readable storage medium. A computer-readable storage medium has a computer program stored thereon, and the program, when executed by a processor, implements the steps in the rock mechanics parameter prediction method based on a PINN-XGBoost model as described in Embodiment One of the present disclosure.

[0056] Embodiment Five The purpose of the embodiment is to provide an electronic device. An electronic device includes a memory, a processor, and a program stored on the memory and executable on the processor, and the processor executes the program to implement the steps in the rock mechanics parameter prediction method based on a PINN-XGBoost model as described in Embodiment One of the present disclosure.

[0057] The steps involved in the devices of Embodiments Two, Three, Four, and Five above correspond to the method of Embodiment One, and the specific embodiments can be referred to the relevant description part of Embodiment One. The term "computer-readable storage medium" should be understood to include a single medium or multiple media of one or more instruction sets; it should also be understood to include any medium that can store, encode, or carry instruction sets for execution by a processor and cause the processor to perform any of the methods in the present disclosure.

[0058] ​Those skilled in the art should understand that the modules or steps of the present application described above can be realized by general computer devices, or alternatively, they can be realized by program codes executable by the computer devices, so that they can be stored in the storage devices and executed by the computer devices, or they can be respectively manufactured into individual integrated circuit modules, or a plurality of modules or steps among them can be manufactured into a single integrated circuit module. The present application is not limited to any specific combination of hardware and software.

[0059] The specific embodiments of the present application described above with reference to the accompanying drawings are not intended to limit the protection scope of the present application, and those skilled in the art should understand that various modifications or changes made on the basis of the technical solutions of the present application without creative labor are still within the protection scope of the present application.

Claims

1. A rock mechanics parameter prediction method based on the PINN-XGBoost model, characterized in that: The steps include: Obtain experimental data of rock mechanics parameters and generate simulation data based on the experimental data; Processing the simulation data to obtain a data set to be predicted; Build a prediction model, input the data set to be predicted into the trained prediction model, and output the final prediction value; Wherein, the prediction model includes a physical constraint model and an XGBoost model; Inputting the to-be-predicted data set into the physical constraint model to obtain a first prediction value; Inputting the first predicted value into the XGBoost model to obtain a second predicted value; The first predicted value and the second predicted value are weightedly summed to obtain a final predicted value.

2. A rock mechanics parameter prediction method based on the PINN-XGBoost model according to claim 1, characterized in that: The rock sample of experimental data for obtaining rock mechanical parameters specifically includes: obtaining particle size distribution data by sieving method, measuring the particle density of the filling material by using water displacement method; and calculating the statistical characteristics of fractal dimension data; The particle size distribution data, filler particle density data and fractal dimension data are the experimental data.

3. The rock mechanics parameter prediction method based on the PINN-XGBoost model according to claim 1, characterized in that: The experimental data are input into a rock mechanics numerical model to simulate the same loading conditions as the indoor test, and a series of virtual triaxial compression tests are carried out to generate simulation data.

4. A rock mechanics parameter prediction method based on the PINN-XGBoost model according to claim 1, characterized in that: The preprocessing of the simulation data specifically includes: removing noise and outliers in the experimental data, and interpolating the simulation data to ensure that the data points are evenly distributed; using a generative adversarial network to expand the data and screen data that conforms to statistical laws as the data set to be predicted.

5. The rock mechanics parameter prediction method based on the PINN-XGBoost model according to claim 1, characterized in that: During the XGBoost model construction phase, an objective function is constructed based on the mean square error, and the model capacity is optimized by initializing tree structure parameters and regularization terms.

6. A rock mechanics parameter prediction method based on the PINN-XGBoost model according to claim 1, characterized in that: The final predicted value is obtained by inputting the data set to be predicted into the PINN model to obtain a first predicted cohesion and a first predicted internal friction angle; Inputting the first predicted cohesion and the first predicted internal friction angle into the XGBoost model to obtain a second predicted cohesion and a second predicted internal friction angle; The product of the PINN model weight and the first predicted cohesion is added to the product of the XGBoost model weight and the second predicted cohesion to obtain the final predicted cohesion; The product of the weight of the PINN model and the first predicted internal friction angle is added to the product of the weight of the XGBoost model and the second predicted internal friction angle to obtain the final predicted internal friction angle.

7. A rock mechanics parameter prediction system based on the PINN-XGBoost model, based on the rock mechanics parameter prediction method based on the PINN-XGBoost model according to any one of claims 1 to 6, characterized in that: include: The simulation data generation module is configured to: obtain experimental data of rock mechanics parameters and generate simulation data based on the experimental data; A data processing module is configured to: process the simulation data to obtain a data set to be predicted; The model building module is configured to: build a prediction model and input the data set to be predicted into the prediction model; The prediction result output module is configured to: the prediction model outputs the final predicted value of the rock mechanical parameters.

8. A computer program product comprising a computer program, characterized in that When the computer program is executed by a processor, the steps of the rock mechanics parameter prediction method based on the PINN-XGBoost model described in any one of claims 1 to 6 are implemented.

9. A computer-readable storage medium having a program stored thereon, characterized in that: When the program is executed by a processor, the steps of the rock mechanics parameter prediction method based on the PINN-XGBoost model as described in any one of claims 1 to 6 are implemented.

10. An electronic device comprising a memory, a processor, and a program stored in the memory and executable on the processor, wherein: When the processor executes the program, the steps in the rock mechanics parameter prediction method based on the PINN-XGBoost model as described in any one of claims 1 to 6 are implemented.

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