Sandstone nanoindentation discrete element contact mechanics parameter calibration method and system

Abstract

This application provides a method and system for calibrating discrete element contact mechanics parameters of sandstone using nanoindentation, relating to the field of oil and gas resource development technology. The method includes: selecting a predetermined number of sample data points from a target dataset to form an optimization starting point set. The target dataset is used to train a target prediction model. The sample data includes the values ​​of discrete element contact mechanics parameters as input features of the model, and the values ​​of sandstone mechanical property parameters as standard output results of the model. Using each sample data point in the optimization starting point set as a search starting point, an optimization solver iteratively solves the problem by minimizing the objective function to obtain the optimal data point. The values ​​of the discrete element contact mechanics parameters of the optimal data point are determined as the calibration results of the discrete element contact mechanics parameters required for nanoindentation simulation experiments on the sandstone to be calibrated. This aims to improve the calibration efficiency and accuracy of nanoindentation discrete element contact mechanics parameters.

Description

Technical Field

[0001] This application relates to the field of oil and gas resource development technology, specifically to a method and system for calibrating discrete element contact mechanical parameters of sandstone nanoindentation. Background Technology

[0002] As a high-resolution mechanical testing method, nanoindentation testing is a modern micromechanical experimental technique capable of characterizing the mechanical properties of materials in situ at the microscale. It provides important support for analyzing the influence of reservoir heterogeneity on rock mechanical behavior. Meanwhile, with the development of computer technology, numerical simulation technology is becoming increasingly prevalent in the study of material mechanical behavior, gradually becoming an important tool for studying the mechanical behavior of complex materials and finding wide application in scientific research.

[0003] Sandstone and other rock materials are essentially granular materials composed of discrete cemented particles, exhibiting significant granularity and heterogeneity, making them more consistent with discontinuous characteristics. With the improvement of computing power and the continuous refinement of contact constitutive models between particles, the Discrete Element Method (DEM) has gradually developed into an important tool for studying the complex mechanical behavior of materials at multiple scales.

[0004] In recent years, Discrete Element Methods (DEMs) have gained increasing popularity due to their unique advantages in handling discrete media problems. Despite their growing application, research on using DEMs to simulate nanoindentation testing of rock materials such as sandstone remains relatively scarce. This is mainly because the calibration of discrete element contact mechanics parameters in traditional DEMs relies heavily on manual trial and error and repeated adjustments until the simulation results match the experimental results; this inversion method is known as the trial-and-error method. However, this type of method exhibits significant shortcomings in practical applications, including low computational efficiency, difficulty in covering complex parameter spaces, strong subjectivity in parameter selection which easily introduces non-negligible errors, and high sensitivity of calibration results to operator experience, reducing the reproducibility of research conclusions. Summary of the Invention

[0005] In view of this, this application provides a method and system for calibrating discrete element contact mechanical parameters of sandstone nanoindentation. It aims to solve or partially solve the problems existing in the prior art.

[0006] The first aspect of this application provides a method for calibrating discrete element contact mechanical parameters of sandstone using nanoindentation, the method comprising: A predetermined number of sample data are selected in the target dataset to form an optimization starting point set. The target dataset is a dataset used to train the target prediction model. The sample data in the target dataset includes the values ​​of each discrete element contact mechanics parameter as the input feature of the model, and the values ​​of each sandstone mechanical property parameter as the standard output result of the model. Using each sample data in the set of optimization starting points as the search starting point, the optimization solver iteratively solves the problem with the objective function as the goal, and obtains the optimal data point. The values ​​of the discrete element contact mechanical parameters of each of the optimal data points are determined as the discrete element contact mechanical parameter calibration results required for the nanoindentation simulation experiment of the sandstone to be calibrated. Specifically, taking each sample data in the set of optimization starting points as the search starting point, the optimization solver iteratively solves the problem with the objective function as the goal, to obtain the optimal data point, including: Using each sample data in the set of optimization starting points as the search starting point, an iterative search is performed through the optimization solver; The values ​​of the discrete element contact mechanics parameters of each candidate data point are input into the target prediction model to obtain the values ​​of the sandstone mechanical property parameters of each candidate data point. By using a predefined objective function, the comprehensive deviation between the values ​​of each sandstone mechanical property parameter of the candidate data point and the values ​​of each sandstone mechanical property parameter of the sandstone to be calibrated is calculated, and the mechanical characteristic deviation value of the candidate data point is obtained. From all the candidate data points obtained from the search, the candidate data point with the smallest mechanical characteristic deviation value is determined as the optimal data point.

[0007] A second aspect of this application provides a sandstone nanoindentation discrete element contact mechanical parameter calibration system, the system comprising: The optimization starting point set construction module is used to select a preset number of sample data in the target dataset to form an optimization starting point set. The target dataset is a dataset used to train the target prediction model. The sample data in the target dataset includes the values ​​of each discrete element contact mechanics parameter as the input feature of the model, and the values ​​of each sandstone mechanical property parameter as the standard output result of the model. The optimal data point determination module is used to take each sample data in the optimization starting point set as the search starting point, and iteratively solve the problem through an optimization solver with the goal of minimizing the objective function to obtain the optimal data point; The calibration result determination module is used to determine the values ​​of each discrete element contact mechanical parameter of the optimal data point as the discrete element contact mechanical parameter calibration result required for the nanoindentation simulation experiment of the sandstone to be calibrated. The optimal data point determination module includes: The iterative search module is used to perform iterative search through the optimization solver, taking each sample data in the set of optimization starting points as the search starting point. The sandstone mechanical property parameter determination module is used to input the values ​​of the discrete element contact mechanical parameters of each candidate data point into the target prediction model to obtain the values ​​of the sandstone mechanical property parameters of each candidate data point. The mechanical characteristic deviation value determination module is used to calculate the comprehensive deviation between the values ​​of each sandstone mechanical property parameter of the candidate data point and the values ​​of each sandstone mechanical property parameter of the sandstone to be calibrated through a predefined objective function, so as to obtain the mechanical characteristic deviation value of the candidate data point. The optimal data point determination submodule is used to determine the candidate data point with the smallest mechanical characteristic deviation value from all the candidate data points obtained by the search as the optimal data point.

[0008] The discrete element method for calibrating contact mechanical parameters of sandstone using nanoindentation provided in this application has the following advantages: The discrete element contact mechanics parameter calibration method for sandstone nanoindentation provided in this application selects a preset number of sample data in the target dataset to form an optimization starting point set. This target dataset is used to train the target prediction model. The sample data in this target dataset includes the values ​​of each discrete element contact mechanics parameter as the model input features, and the values ​​of each sandstone mechanical property parameter as the model's standard output. Using each sample data in the optimization starting point set as the search starting point, an iterative search is performed through an optimization solver. The values ​​of each discrete element contact mechanics parameter of the searched candidate data points are input into the target prediction model to obtain the values ​​of each sandstone mechanical property parameter of the candidate data points. This is achieved through a predefined... The objective function calculates the deviation between the values ​​of each mechanical property parameter of the candidate data point and the values ​​of each mechanical property parameter of the sandstone to be calibrated, thus obtaining the mechanical characteristic deviation value of the candidate data point. From all the searched candidate data points, the candidate data point with the smallest mechanical characteristic deviation value is determined as the optimal data point. Finally, the values ​​of each discrete element contact mechanical parameter of the optimal data point are determined as the calibration results of the discrete element contact mechanical parameters required for the nanoindentation discrete element numerical simulation experiment of the sandstone to be calibrated. That is, when conducting the nanoindentation discrete element numerical simulation experiment on the sandstone to be calibrated, the calibration results are used to set the discrete element contact mechanical parameters of the constructed nanoindentation discrete element model corresponding to the sandstone to be calibrated. The sandstone to be calibrated is the actual sandstone collected for the nanoindentation discrete element numerical simulation experiment, and the values ​​of its various sandstone mechanical property parameters are obtained through laboratory nanoindentation testing. The method described in this application allows for the calibration of various sandstones by performing laboratory nanoindentation tests to obtain their mechanical property parameters. Then, the nanoindentation discrete element contact mechanical parameters of each sandstone can be calibrated using an automatic optimization solution. This improves the efficiency of discrete element parameter calibration while avoiding the subjectivity of manual calibration, thus preventing potential errors. This enhances the stability and accuracy of the calibration and ensures repeatability. Attached Figure Description

[0009] To more clearly illustrate the technical solutions of the embodiments of this application, the accompanying drawings used in the description of the embodiments of this application will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0010] Figure 1 This is a flowchart illustrating a method for calibrating discrete element contact mechanical parameters of sandstone using nanoindentation, as shown in one embodiment of this application. Figure 2This is a schematic diagram of curves plotted based on nanoindentation indenter load and displacement data in a discrete element contact mechanics parameter calibration method for sandstone nanoindentation, as shown in one embodiment of this application. Figure 3 This is a schematic diagram of a nanoindentation discrete element model in a sandstone nanoindentation discrete element contact mechanical parameter calibration method according to an embodiment of this application; Figure 4 This is a schematic diagram of a sandstone nanoindentation discrete element contact mechanical parameter calibration system according to one embodiment of this application. Detailed Implementation

[0011] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this application. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0012] Before explaining the sandstone nanoindentation discrete element contact mechanical parameter calibration method provided in this application, the specific background of proposing this method in this application will be explained first.

[0013] With the increasing demand for unconventional oil and gas resource development, traditional macroscopic mechanical testing is gradually proving insufficient in characterizing the heterogeneous features of rocks, making multi-scale mechanical characterization a research hotspot. As a high-resolution mechanical testing method, nanoindentation testing is a modern microscopic mechanical experimental technique capable of characterizing the mechanical properties of materials in situ at the microscale. Its core principle is to record the changes in load and indentation displacement applied to the material surface during loading and unloading, and to analyze the instantaneous load and displacement data generated by the material to obtain the material's mechanical response parameters at the microscale, such as Young's modulus, hardness, inelastic properties, and fracture characteristics. Therefore, it provides important support for analyzing the impact of reservoir heterogeneity on rock mechanical behavior.

[0014] With the development of computer technology, numerical simulation technology is becoming increasingly prevalent in the study of the mechanical behavior of materials. Compared with research methods that rely on laboratory experiments, numerical simulation methods have significant advantages in terms of research cost, experimental cycle, and implementation flexibility. By constructing reasonable physical models and numerical solution frameworks, numerical simulation can not only achieve multi-condition and parametric mechanical analysis at a lower cost, but also, to some extent, compensate for the shortcomings of experimental methods in terms of repeatability and controllability. Therefore, numerical simulation has gradually become an important tool for studying the mechanical behavior of complex materials and is widely used in scientific research.

[0015] Sandstone and other rock materials are essentially granular materials composed of discrete cemented particles, exhibiting significant granularity and heterogeneity, making them more consistent with discontinuous characteristics. Unlike continuous medium methods, the Discrete Element Method (DEM) is a numerical simulation method based on the idea of ​​particle discretization. By explicitly describing the contact, interaction, and evolution processes between particles, it directly characterizes the microscopic mechanical behavior of materials. Compared to traditional continuous medium numerical methods, such as the Finite Element Method (FEM), DEM can naturally characterize discontinuous deformation processes such as particle rearrangement, thus demonstrating unique advantages in the study of the mechanical properties of typical discrete medium materials such as rocks and concrete. With the improvement of computing power and the continuous refinement of contact constitutive models between particles, the Discrete Element Method has gradually developed into an important tool for studying the complex mechanical behavior of materials at multiple scales.

[0016] In recent years, the Discrete Element Method (DEM) has gained increasing popularity due to its unique advantages in handling discrete media problems. Despite its growing application, research on using the DEM to simulate nanoindentation testing processes in rock materials such as sandstone remains relatively scarce. There are three main factors limiting the application of the DEM in nanoindentation: (1) Difficulty in obtaining contact mechanical parameters in the discrete element method. The rationality of the contact mechanical parameters in the discrete element model plays a decisive role in the accuracy of numerical simulation. However, the contact mechanical parameters of the discrete element model cannot directly correspond to the physical and mechanical properties of rock samples in laboratory tests. Therefore, in the process of simulating the mechanical behavior of rocks using the discrete element method, the determination of contact mechanical parameters is not only crucial, but also difficult to obtain.

[0017] (2) The inversion method for contact mechanical parameters in the numerical simulation of nanoindentation using the discrete element method is inefficient. For a long time, the calibration of contact mechanical parameters in the traditional discrete element method (DEM) has mainly relied on manual trial and error and repeated adjustment of contact mechanical parameters until the simulation results match the experimental results. This inversion method is called the trial and error method. However, this type of method has revealed obvious shortcomings in practical applications, including low computational efficiency, difficulty in covering complex parameter spaces; strong subjectivity in parameter selection, which easily introduces non-negligible errors; and the calibration results are highly sensitive to the operator's experience, reducing the reproducibility of research conclusions.

[0018] (3) The calibration tests and scales for contact mechanical parameters using the Discrete Element Method (DEM) are relatively limited. In existing research, the calibration methods for the DEM have gradually evolved from traditional manual trial-and-error methods to semi-automated or fully automated calibration methods based on machine learning. However, most researchers using these methods employ uniaxial compression or shear tests. Furthermore, due to considerations of computational efficiency and cost, the sample and particle sizes for these uniaxial and shear calibration tests are mostly in the millimeter to centimeter range, making them difficult to apply to microscopic mechanical tests like nanoindentation, which are highly sensitive to sample surface roughness. Consequently, nanoindentation simulation using the DEM still relies on relatively primitive manual trial-and-error methods for calibrating contact mechanical parameters. Therefore, this limitation in the variety of calibration tests and scales greatly restricts the application of the DEM in nanoindentation.

[0019] Based on the above problems, in order to overcome the limitations of the discrete element method in nanoindentation and the existing technology in the calibration of contact mechanical parameters, this application adopts a new method for calibrating the contact mechanical parameters of sandstone nanoindentation discrete element method. The specific calibration process of the method provided in this application will be described in detail below.

[0020] refer to Figure 1 , Figure 1 This is a flowchart illustrating a method for calibrating discrete element contact mechanical parameters of sandstone using nanoindentation, as shown in one embodiment of this application. Figure 1 As shown, the method includes: Step S01: Select a preset number of sample data in the target dataset to form an optimization starting point set. The target dataset is a dataset used to train the target prediction model. The sample data in the target dataset includes the values ​​of each discrete element contact mechanical parameter as the input feature of the model, and the values ​​of each sandstone mechanical property parameter as the standard output result of the model.

[0021] In this embodiment, the sandstone nanoindentation discrete element contact mechanics parameter calibration method provided in this application pre-trains a target prediction model before calibrating the contact mechanics parameters. Once the target prediction model is trained, any sandstone to be calibrated can be calibrated using this target prediction model, instead of needing to train a corresponding target prediction model for each pair of sandstones to be calibrated.

[0022] Based on the input values ​​of the discrete element contact mechanics parameters, the target prediction model predicts the output as follows: the experimental results obtained after setting the discrete element contact mechanics parameters of the sandstone nanoindentation discrete element model to these values ​​and conducting nanoindentation simulation experiments. These experimental results represent the specific values ​​of each sandstone mechanical property parameter.

[0023] In this embodiment, the dataset used to train the prediction model is the target dataset, which consists of a large number of sample data. Each sample data point in the target dataset comprises two parts: the values ​​of the discrete-time contact mechanics parameters that serve as input features to the model, and the values ​​of the sandstone mechanical property parameters that serve as the model's standard output. The values ​​of the discrete-time contact mechanics parameters that serve as input features to the model are used for training the prediction model, while the values ​​of the sandstone mechanical property parameters that serve as the model's standard output are actually the labels used to evaluate the prediction accuracy of the prediction model.

[0024] The target dataset includes at least five discrete element contact mechanical parameters: parallel bond normal stiffness, the ratio of parallel bond normal stiffness to parallel bond tangential stiffness, linear contact normal stiffness, the ratio of linear contact normal stiffness to linear contact tangential stiffness, and the friction coefficient. The target dataset also includes at least three sandstone mechanical property parameters: reduced modulus, hardness, and maximum indentation depth.

[0025] In this application, constructing the target dataset includes: Step S001: Construct an input dataset, wherein the input data in the input dataset includes the values ​​of each discrete element contact mechanical parameter as a feature of the model input, and the value of each discrete element contact mechanical parameter is obtained by stratified random sampling within its corresponding set value range.

[0026] In this embodiment, the process of constructing the target dataset is described. First, an input dataset is constructed consisting of a predetermined number of input data points (this predetermined number can be set according to the actual scenario, and is not specifically limited here, such as 500, 1000, etc.). Each individual input data point in this dataset consists of the values ​​of various discrete element contact mechanical parameters. For example, if the discrete element contact mechanical parameters in a sample data point in the target dataset are the aforementioned five discrete element contact mechanical parameters, then each individual input data point in this dataset consists of the values ​​of these five discrete element contact mechanical parameters.

[0027] In this embodiment, the values ​​of each discrete element contact mechanical parameter of each input data in the input dataset are obtained through stratified random sampling. Simultaneously, before sampling, this application predefines the value range of each type of discrete element contact mechanical parameter, and each type of discrete element contact mechanical parameter of each input data is obtained through stratified random sampling within its corresponding value range. This application preferably employs the Latin hypercube sampling (LHS) method to perform stratified random sampling within the value range corresponding to each type of discrete element contact mechanical parameter. This sampling technique utilizes the concept of space filling, ensuring that the extracted samples cover the entire parameter space uniformly, reducing redundancy between samples, and improving sampling efficiency and accuracy.

[0028] Step S002: Substitute the i-th input data in the input dataset into the pre-constructed nanoindentation discrete element model for numerical simulation to obtain the nanoindentation indenter load and displacement data corresponding to the i-th input data.

[0029] In this embodiment, a nanoindentation discrete element model of sandstone is pre-constructed. The specific construction of this nanoindentation discrete element model will be described in subsequent implementation methods. Each input data point in the constructed input dataset is sequentially substituted into the pre-constructed nanoindentation discrete element model for numerical simulation to obtain the nanoindentation indenter load and displacement data corresponding to each input data point. Specifically, the i-th input data point in the input dataset is substituted into the pre-constructed nanoindentation discrete element model for numerical simulation to obtain the nanoindentation indenter load and displacement data corresponding to the i-th input data point, where i ranges from 1 to N, and N is the total number of input data points in the input dataset. This application uses the Fish syntax provided by PFC to write the indenter load and displacement detection function to record the displacement and force changes of the indenter in real time throughout the loading and unloading process. Finally, the nanoindentation indenter load and displacement data are plotted based on these recorded data points, as shown below. Figure 2 As shown, Figure 2 An exemplary curve was plotted, consisting of the load and displacement data of the nanoindentation head.

[0030] Step S003: By calculating and analyzing the nano-indentation head load and displacement data of the i-th input data, the values ​​of each sandstone mechanical property parameter corresponding to the i-th input data are obtained.

[0031] In this embodiment, when the sandstone mechanical property parameters in the target dataset include the maximum indentation depth, the displacement data in the obtained nanoindentation indenter load and displacement data already records the maximum indentation depth. Therefore, based on the nanoindentation indenter load and displacement data corresponding to each input data, the maximum indentation depth corresponding to each input data can be directly obtained without further calculation. When the sandstone mechanical property parameters in the target dataset include reduced modulus and hardness, based on the nanoindentation indenter load and displacement data corresponding to any input data, the reduced modulus and hardness corresponding to that input data can be calculated using the classic Oliver-Pharr method. Specifically, by calculating and analyzing the nanoindentation indenter load and displacement data of the i-th input data, the values ​​of each sandstone mechanical property parameter corresponding to the i-th input data are obtained, where i ranges from 1 to N, and N is the total number of input data in the input dataset.

[0032] Step S004: Based on the obtained input dataset and the values ​​of each sandstone mechanical property parameter corresponding to each input data in the input dataset, construct the target dataset.

[0033] In this embodiment, after obtaining the values ​​of each sandstone mechanical property parameter corresponding to each input data in the input dataset, the i-th input data and the values ​​of each sandstone mechanical property parameter corresponding to the i-th input data are used to construct the i-th sample data, where i ranges from 1 to N, and N is the total number of input data in the input dataset. All the obtained sample data constitute the target dataset for training the prediction model and determining the set of optimization starting points.

[0034] In this embodiment, this application selects a preset number of sample data (the preset number can be set according to the actual scenario, and is not specifically limited here, such as 20, 30, etc.) in the target dataset to form an optimization starting point set. The selected sample data is used as a corresponding optimization starting point, and the optimization starting point is the search starting point for subsequent optimization solutions.

[0035] In this application, step S01 may include: Step S01_1: Calculate the mechanical characteristic deviation value between each sample data in the target dataset and the sandstone to be calibrated using a predefined objective function.

[0036] In this embodiment, considering the optimization path and efficiency issues in the optimization algorithm, if the data point is arbitrarily selected as the starting point for the optimization solution, the optimizer is prone to getting trapped in local minima and will find it difficult to find the true global optimum.

[0037] Therefore, this application aims to select some high-quality data points in advance as the starting point for the search. High-quality data points refer to data points with small overall deviations between their own sandstone mechanical property parameters and the values ​​of the sandstone mechanical property parameters to be calibrated. Specifically, when the discrete element contact mechanical parameters include the above five parameters, the coordinates of a data point are represented by the values ​​of these five discrete element contact mechanical parameters.

[0038] To select high-quality data points, the selection process requires determining the values ​​of each sandstone mechanical property parameter for each data point and then comparing them with the values ​​of the sandstone mechanical property parameters to be calibrated, thus determining whether the data point is high-quality. One possible approach is to input the discrete element contact mechanics parameters of each data point into a trained target prediction model, which then predicts the corresponding sandstone mechanical property parameters for that data point. However, this application provides a more efficient method for determining high-quality data points: directly selecting high-quality data points from the target dataset. Since the target dataset is a pre-constructed dataset before training the prediction model, the sample data in this dataset already contains data with existing correspondences between discrete element contact mechanics parameters and sandstone mechanical property parameters. Therefore, directly selecting high-quality data points from the target dataset eliminates the need to determine the sandstone mechanical property parameters for each data point, as these values ​​are readily available, thus further improving calibration efficiency.

[0039] The method for more efficiently identifying high-quality data points provided in this application is as follows: Since the calculation method for the mechanical characteristic deviation between each sample data point in the target dataset and the sandstone to be calibrated is the same, a single sample data point will be used as an example for explanation. Using a predefined objective function, the comprehensive deviation between the values ​​of each sandstone mechanical property parameter in the sample data point and the values ​​of each sandstone mechanical property parameter in the sandstone to be calibrated is calculated, thus obtaining the mechanical characteristic deviation value of the sample data point. Through the same implementation method, the mechanical characteristic deviation value between each sample data point and the sandstone to be calibrated can be obtained.

[0040] Step S01_2: Sort all the obtained mechanical characteristic deviation values ​​from smallest to largest, and select the sample data corresponding to the first number of mechanical characteristic deviation values ​​in the sort as the optimization starting point.

[0041] In this embodiment, after obtaining the mechanical characteristic deviation values ​​between each sample data in the target dataset and the sandstone to be calibrated, all mechanical characteristic deviation values ​​are sorted from smallest to largest. The first number of mechanical characteristic deviation values ​​(this first number can be set according to the actual scenario, and is not specifically limited here, such as 20) are selected, and the sample data to which these selected mechanical characteristic deviation values ​​belong are determined as the optimization starting point. The optimization starting point is actually also a data point, and the coordinates of a data point constitute the values ​​of the discrete element contact mechanical parameters. Therefore, when determining the sample data as the optimization starting point, only the values ​​of the discrete element contact mechanical parameters of that sample data are recorded at that optimization starting point.

[0042] Step S01_3: Randomly select a second number of sample data from the remaining sample data in the target dataset as the optimization starting point, and the sum of the first number and the second number is the preset number.

[0043] In this embodiment, selecting a first number of sample data points as the optimization starting point based on the magnitude of the mechanical characteristic deviation value can improve the convergence efficiency of the search. In addition, this application will also randomly select a second number of sample data points from the remaining sample data in the target dataset as the optimization starting point. The purpose of random selection here is to conduct targeted searches on some regions that perform poorly but may contain hidden optimal solutions.

[0044] Step S01_4: Construct an optimization starting point set using all selected optimization starting points.

[0045] In this embodiment, the first number of optimized starting points and the second number of optimized starting points together constitute the set of optimized starting points.

[0046] Step S02: Using each sample data in the set of optimization starting points as the search starting point, the optimization solver iteratively solves the problem with the objective function as the goal, and obtains the optimal data point.

[0047] In this embodiment, after obtaining the set of optimized starting points, each sample data in the set of optimized starting points (that is, each optimized starting point in the set of optimized starting points) is used as the search starting point. Through the optimization solver, with the goal of minimizing the objective function, the data point is searched and iteratively solved in the discrete element contact mechanics parameter space to obtain the optimal data point.

[0048] The optimal data point is actually the data point with the smallest overall deviation between its own values ​​of various sandstone mechanical property parameters and the values ​​of various sandstone mechanical property parameters of the sandstone to be calibrated, among all the data points searched.

[0049] The values ​​of the sandstone mechanical property parameters for each data point are obtained as follows: the discrete element contact mechanics parameters of each data point are input into the trained target prediction model, which then predicts and outputs the values ​​of the sandstone mechanical property parameters for that data point. Preferably, this application uses the fmincon optimization solver in the Matlab optimization toolbox for optimization, and the SQP algorithm is preferred for parameter optimization within the solver. It should be understood that this is only a preferred implementation method, and other optimization solvers and parameter optimization algorithms can also be selected.

[0050] In this application, the predefined objective function is:

[0051] Where x is an input vector composed of the values ​​of the discrete element contact mechanics parameters of each candidate data point; The value of the i-th sandstone mechanical property parameter corresponding to the candidate data point obtained from the target prediction model; , where is the weighting coefficient for the i-th sandstone mechanical property parameter; Let be the value of the i-th mechanical property parameter of the sandstone to be calibrated.

[0052] In this application, step S02 may include: Step S02_1: Using each sample data in the set of optimization starting points as the search starting point, perform an iterative search through the optimization solver.

[0053] In this embodiment, step S02 of this application is implemented in more detail as follows: Using each sample data in the set of optimization starting points as the search starting point, an iterative search for data points is performed based on the selected optimization solver and parameter optimization algorithm.

[0054] Step S02_2: Input the values ​​of the discrete element contact mechanics parameters of each candidate data point into the target prediction model to obtain the values ​​of the sandstone mechanical property parameters of each candidate data point.

[0055] In this embodiment, each time a candidate data point is searched, the discrete element contact mechanical parameters of the candidate data point are taken and input into the trained target prediction model to predict and output the values ​​of the sandstone mechanical property parameters of the candidate data point.

[0056] Step S02_3: Using a predefined objective function, calculate the comprehensive deviation between the values ​​of each sandstone mechanical property parameter of the candidate data points and the values ​​of each sandstone mechanical property parameter of the sandstone to be calibrated, and obtain the mechanical characteristic deviation value of the candidate data points.

[0057] In this embodiment, for each sandstone mechanical property parameter value of the candidate data point obtained by calculation, the values ​​of each sandstone mechanical property parameter of the candidate data point and the values ​​of each sandstone mechanical property parameter of the sandstone to be calibrated are substituted into a predefined objective function for calculation to obtain the mechanical characteristic deviation value between the candidate data point and the sandstone to be calibrated.

[0058] Step S02_4: From all the candidate data points obtained by the search, determine the candidate data point with the smallest mechanical characteristic deviation value as the optimal data point.

[0059] In this embodiment, among all the candidate data points searched, the candidate data point with the smallest mechanical characteristic deviation value is selected as the optimal data point.

[0060] Step S03: Determine the values ​​of the discrete element contact mechanical parameters of each of the optimal data points as the discrete element contact mechanical parameter calibration results required for the nanoindentation simulation experiment of the sandstone to be calibrated.

[0061] In this embodiment, the values ​​of the discrete element contact mechanical parameters of each optimal data point are finally determined as the discrete element contact mechanical parameter calibration results required for the nanoindentation simulation experiment of the sandstone to be calibrated. When it is necessary to conduct a nanoindentation simulation experiment on the sandstone to be calibrated, the nanoindentation discrete element model corresponding to the sandstone to be calibrated is set according to the discrete element contact mechanical parameter calibration results.

[0062] The discrete element contact mechanics parameter calibration method for sandstone nanoindentation provided in this application selects a preset number of sample data in the target dataset to form an optimization starting point set. This target dataset is used to train the target prediction model. The sample data in this target dataset includes the values ​​of each discrete element contact mechanics parameter as the model input features, and the values ​​of each sandstone mechanical property parameter as the model's standard output. Using each sample data in the optimization starting point set as the search starting point, an iterative search is performed through an optimization solver. The values ​​of each discrete element contact mechanics parameter of the searched candidate data points are input into the target prediction model to obtain the values ​​of each sandstone mechanical property parameter of the candidate data points. This is achieved through a predefined... The objective function calculates the deviation between the values ​​of each mechanical property parameter of the candidate data point and the values ​​of each mechanical property parameter of the sandstone to be calibrated, thus obtaining the mechanical characteristic deviation value of the candidate data point. From all the searched candidate data points, the candidate data point with the smallest mechanical characteristic deviation value is determined as the optimal data point. Finally, the values ​​of each discrete element contact mechanical parameter of the optimal data point are determined as the calibration results of the discrete element contact mechanical parameters required for the nanoindentation discrete element numerical simulation experiment of the sandstone to be calibrated. That is, when conducting the nanoindentation discrete element numerical simulation experiment on the sandstone to be calibrated, the calibration results are used to set the discrete element contact mechanical parameters of the constructed nanoindentation discrete element model corresponding to the sandstone to be calibrated. The sandstone to be calibrated is the actual sandstone collected for the nanoindentation discrete element numerical simulation experiment, and the values ​​of its various sandstone mechanical property parameters are obtained through laboratory nanoindentation testing. The method described in this application allows for the calibration of various sandstones by performing laboratory nanoindentation tests to obtain their mechanical property parameters. Then, the nanoindentation discrete element contact mechanical parameters of each sandstone can be calibrated using an automatic optimization solution. This improves the efficiency of discrete element parameter calibration while avoiding the subjectivity of manual calibration, thus preventing potential errors. This enhances the stability and accuracy of the calibration and ensures repeatability.

[0063] In conjunction with the above embodiments, in one implementation, this application also provides a method for calibrating discrete element contact mechanical parameters of sandstone nanoindentation. In this method, step S02 may include: using each sample data point in the optimized starting point set as a search starting point, iteratively solving the problem using a low-precision optimization solver with the objective function minimization as the goal, to obtain potential optimal data points around each search starting point; selecting a target potential optimal data point from all obtained potential optimal data points; and using the target potential optimal data point as a search starting point, iteratively solving the problem using a high-precision optimization solver with the objective function minimization as the goal, to obtain the optimal data point.

[0064] In the above embodiments of this application, a single optimization solver is used for optimization. In the current embodiment, this application provides another optimization solution method, which employs a hierarchical optimization strategy by sequentially deploying two optimization solvers of different precisions: a low-precision solver and a high-precision solver. This optimization solution method first uses the low-precision solver, employing a more lenient convergence tolerance and fewer iterations, to perform a rapid optimization round on each of all optimization starting points within a specified parameter space, thereby quickly identifying the potential optimal solutions surrounding each optimization starting point.

[0065] Then, among all the potential optimal solutions, the optimal potential optimal solution is selected. A high-precision optimization solver, with a stricter convergence tolerance and more iterations, is used to perform a more detailed optimization solution on this optimal potential optimal solution to ensure that the global optimal solution is found.

[0066] The iteration count in the optimization solver represents the maximum number of data points searched during its optimization process. The search ends when the number of data points searched reaches this maximum. The convergence tolerance represents the criterion for ending the data point search; if this criterion is met during the optimization process, the search also ends. In this application, the convergence tolerance includes: when the mechanical characteristic deviation between a candidate data point and the sandstone to be calibrated is lower than a certain set value, the criterion is satisfied; or, when the mechanical characteristic deviations between multiple consecutively searched candidate data points and the sandstone to be calibrated tend to stabilize, the criterion is satisfied.

[0067] Specifically, each sample data in the set of optimization starting points is used as the search starting point. A low-precision optimization solver is used to iteratively solve the problem with the objective function as the goal, and the potential optimal data points around each search starting point are obtained respectively.

[0068] Then, the best potential optimal data point is selected from all the obtained potential optimal data points as the target potential optimal data point. Using this target potential optimal data point as the starting point, a high-precision optimization solver is used to iteratively solve the problem with the objective function as the goal, and the optimal data point is obtained.

[0069] In conjunction with the above embodiments, in one implementation, this application also provides a method for calibrating discrete element contact mechanical parameters of sandstone nanoindentation. In this method, an initial prediction model is trained based on a target dataset to obtain a trained target prediction model, including: Step S01_a: Train each initial prediction model based on the target dataset to obtain each prediction model after training.

[0070] In this embodiment, in order to improve the accuracy of calibration, this application trains a corresponding target prediction model for each sandstone mechanical property parameter to predict the value of the corresponding sandstone mechanical property parameter.

[0071] Specifically, four types of initial prediction models are selected: Support Vector Machine (SVM), Gaussian Process Regression (GPR), Gradient Boosting Regression Tree (GBDT), and Random Forest (RF). This application preferably uses the MATLAB machine learning toolbox to train these four types of initial prediction models.

[0072] The inputs to these four types of initial prediction models are the same, including the values ​​of each discrete element contact mechanics parameter. For example, if the discrete element contact mechanics parameters include the above five discrete element contact mechanics parameters, then the input parameters of the initial prediction model are these five discrete element contact mechanics parameters.

[0073] This application employs a Bayesian optimization algorithm to automatically tune the model's hyperparameters, with the objective function being the minimization of mean squared error (MSE). The optimization hyperparameters for Support Vector Machines (SVM) include: box constraints, kernel function, and Epsilon value; the optimization functions for Gaussian Process Regression (GPR) include: sigma value, basis function, kernel function, and kernel scale; the optimization hyperparameters for Gradient Boosting Regression Trees (GBDT) include: number of decision trees, learning rate, and minimum leaf size; and the optimization hyperparameters for Random Forests (RF) include: minimum leaf size and number of decision trees.

[0074] In this embodiment, for any sandstone mechanical property parameter, these four types of initial prediction models are used to predict its output, and these four types of initial prediction models are trained. Finally, the prediction model with the best prediction effect is selected from the four trained prediction models to predict the value of the sandstone mechanical property parameter.

[0075] Given that the mechanical properties of sandstone include the three types of sandstone mechanical properties mentioned above, four types of initial prediction models are constructed to predict the value of the reduced modulus. These four types of initial prediction models are then trained, and finally, the prediction model with the best prediction effect is selected from the four trained prediction models to predict the value of the reduced modulus.

[0076] For hardness, a mechanical property parameter of sandstone, four types of initial prediction models were constructed to predict its output. These four types of initial prediction models were trained, and finally, the prediction model with the best prediction effect was selected from the four trained prediction models to predict the value of hardness.

[0077] For the maximum indentation depth, a mechanical property parameter of sandstone, four types of initial prediction models were constructed to predict its output. These four types of initial prediction models were then trained, and finally, the best-performing prediction model was selected from the four trained models to predict the maximum indentation depth. That is, when the sandstone mechanical property parameters include the three mentioned above, there will be 12 initial prediction models. For each sandstone mechanical property parameter, four different types of initial prediction models will be trained to obtain four corresponding target prediction models.

[0078] In this embodiment, the four initial prediction models corresponding to each sandstone mechanical property parameter are trained using a pre-constructed target dataset to obtain four target prediction models corresponding to each sandstone mechanical property parameter after training.

[0079] Step S01_b: Among the various prediction models that have been trained, select the target prediction model for predicting each mechanical property parameter of sandstone.

[0080] In this embodiment, given that the mechanical properties of sandstone include reduced modulus, hardness, and maximum indentation depth, for the reduced modulus, the target prediction model is determined from the four trained target prediction models corresponding to the reduced modulus to be the most accurate in predicting the reduced modulus. This most accurate target prediction model is then selected as the target prediction model for predicting the reduced modulus. The average performance index of 5-fold cross-validation can be used as the evaluation benchmark for the regression model, comprehensively considering the root mean square error (RMSE), mean square error (MSE), mean absolute error (MAE), and coefficient of determination (R²). Through a comparative analysis of multi-dimensional indicators, the target prediction model corresponding to each mechanical property parameter of sandstone is selected from these four target prediction models.

[0081] Meanwhile, for hardness, we determine which of the four target prediction models corresponding to hardness is most accurate in predicting hardness from the trained models, and then select the target prediction model that is most accurate in predicting hardness as the target prediction model for predicting hardness.

[0082] Meanwhile, for the maximum indentation depth, from the four target prediction models that have been trained and correspond to the maximum indentation depth, we determine which target prediction model is the most accurate in predicting the maximum indentation depth, and select the target prediction model that is the most accurate in predicting the maximum indentation depth as the target prediction model for predicting the maximum indentation depth.

[0083] In this application, step S02_2 may include: inputting the values ​​of the discrete element contact mechanical parameters of each candidate data point into a target prediction model for predicting each sandstone mechanical property parameter, thereby obtaining the values ​​of each sandstone mechanical property parameter of the candidate data point, wherein the target prediction model for predicting the i-th sandstone mechanical property parameter is used to obtain the value of the i-th sandstone mechanical property parameter of the candidate data point.

[0084] In this embodiment, instead of using a single overall target prediction model to predict all sandstone mechanical property parameters, the application employs a corresponding target prediction model for each sandstone mechanical property parameter. Step S02_2 will then adopt another implementation method: the values ​​of the discrete element contact mechanical parameters of each candidate data point will be input into the target prediction model corresponding to each sandstone mechanical property parameter for prediction, thereby obtaining the values ​​of each sandstone mechanical property parameter for that candidate data point. Specifically, the target prediction model used to predict the i-th sandstone mechanical property parameter is used to predict the value of the i-th sandstone mechanical property parameter for that candidate data point.

[0085] In conjunction with the above embodiments, in one implementation, this application also provides a method for calibrating discrete element contact mechanical parameters of sandstone nanoindentation. In this method, an initial prediction model is trained based on a target dataset to obtain a trained target prediction model, including: The target dataset is divided into a training dataset and a test dataset according to a preset ratio; The sample data from the training dataset is input into the initial prediction model based on the current hyperparameter combination to obtain the prediction result; The deviation between the prediction result and the model's standard output result in the sample data is calculated using a preset optimization function. Determine whether the deviation meets the preset training completion conditions; If the deviation does not meet the preset training completion conditions, the hyperparameter combination of the initial prediction model is tuned using a Bayesian optimization algorithm to generate a new hyperparameter combination, and then the process is returned to start a new round of training. If the deviation meets the preset training completion conditions, the corresponding training completed prediction model is obtained. The trained prediction model is tested using the test dataset to obtain the corresponding performance test results. Determine whether the performance test results meet the preset stability conditions; If the performance test results meet the preset stability conditions, the corresponding target prediction model is obtained; If the performance test results do not meet the preset stability conditions, the trained prediction model is retrained until the performance test results of the trained prediction model meet the preset stability conditions.

[0086] In this embodiment, the training process for each type of initial prediction model is the same. Here, we will use an initial prediction model as an example to illustrate the training process: First, the target dataset is divided into training dataset and test dataset according to a preset ratio, preferably with the training dataset accounting for 80% and the test dataset accounting for 20%.

[0087] The values ​​of the discrete element contact mechanics parameters of the sample data in the divided training dataset are input into the initial prediction model under the current hyperparameter combination. The initial prediction model will then output the corresponding prediction results. When the sandstone mechanical property parameters include the three types of sandstone mechanical property parameters mentioned above, the prediction results will include the values ​​of these three sandstone mechanical property parameters. The deviation between the measured result of the current input model sample data and the standard output result of the model recorded in the sample data is calculated using a preset optimization function (preferably minimizing mean squared error (MSE)). It is then determined whether this deviation meets the preset training completion conditions; for example, if the minimum mean squared error is lower than a set threshold, the preset training completion conditions are considered met. If the deviation does not meet the preset training completion conditions, the hyperparameter combination of the initial prediction model is tuned using a Bayesian optimization algorithm to generate a new hyperparameter combination. The prediction model with this new hyperparameter combination is then used for a new round of training. If the deviation meets the preset training completion conditions, the corresponding fully trained prediction model is obtained.

[0088] For the trained prediction model, its performance is tested using a divided test dataset to obtain the corresponding performance test results. The results are then used to determine whether the performance meets preset stability conditions. These stability conditions include calculating RMSE, MSE, MAE, and R2 to quantitatively evaluate the performance of the trained prediction model on unseen data. If the values ​​of each of the above-mentioned indicators meet their respective thresholds, the performance on unseen data is deemed to meet the conditions. At this point, the performance on the training dataset (e.g., 5-fold cross-validation results) is further compared with the performance on the test dataset to systematically analyze whether the model is overfitting, thereby verifying the model's stability.

[0089] If the performance test results of the trained prediction model meet the preset stability conditions, the corresponding target prediction model is obtained. If the performance test results of the trained prediction model do not meet the preset stability conditions, the trained prediction model is retrained until the performance test results of the trained prediction model meet the preset stability conditions.

[0090] In conjunction with the above embodiments, in one implementation, this application also provides a method for calibrating the contact mechanical parameters of sandstone using a nanoindentation discrete element method. In this method, a nanoindentation discrete element model is constructed, including: A square computational domain with a set side length and dimensions is defined, and the square computational domain is composed of 4 walls; Within the square computational domain, particles with diameters within a set range are generated based on a set porosity value; All generated particles are allowed to move within the square computational domain. The motion equations of the particles are solved iteratively, and the calculation is continued until the force equilibrium state is reached within the square computational domain, thus obtaining the generated discrete particle system within the square computational domain. By setting an adhesion model between the particles in the discrete particle system, a target discrete particle system with adhesive mechanical properties is obtained. An indenter is established in the model space above the target discrete particle system to obtain a nanoindentation discrete element model.

[0091] In this embodiment, the process of constructing a nanoindentation discrete element model of sandstone is described in detail below: The main method involves using the PFC 2D program to construct a nanoindentation discrete element model of sandstone. By calculating the unbalance rate of the discrete particle system, a target discrete particle system with cohesive mechanical properties is established and loaded. The specific process includes three steps: sample preparation, cementation, and loading.

[0092] Sample formation: Define a square computational domain with a set side length, preferably 10000 nm, and the corresponding size of the square computational domain is 10000 × 10000. The square computational domain consists of four walls. It should be understood that this is a preferred size, and other values ​​can be set according to the actual application scenario.

[0093] Within this square computational domain, particles with diameters within a set range are generated based on a predetermined porosity value, preferably 30 to 50 nanometers. It should be understood that this range is a preferred range and can be set to other values ​​depending on the specific application scenario. During calculation, all particles are allowed to move within the square computational domain, and the calculation program continues to run until a force equilibrium state is reached within the square computational domain. This force equilibrium state can be selected when the ratio of the unbalanced contact force to the particle contact force is less than [a certain value]. This process completes the particle filling, resulting in a discrete particle system within the square computational domain.

[0094] Bonding: A target discrete particle system with adhesive mechanical properties is constructed based on the Linear Parallel Bond Model (LPBM) in the PFC (Particle Flow Code) contact constitutive model library. The linear parallel bond model mainly includes two types of contact interfaces: linear contact interfaces and linear elastic bond interfaces. Linear contact interfaces can only transmit forces (such as tension or friction), while linear elastic bond interfaces can transmit not only forces but also torques, allowing rotation between unit cells. In this application, the contact constitutive models between particles and walls, and between particles and indenters, adopt linear models. This linear model only transmits forces, mainly composed of linear forces and damping forces. This application uses linear parallel bond models between particles in the discrete particle system, and linear models between particles and walls, and between particles and indenters, to construct a target discrete particle system with adhesive mechanical properties. The contact forces and torques in the PFC contact model are updated by force-displacement laws, where the core calculation formulas for force and torque are as follows:

[0095]

[0096] in, To work together, For linear force, For damping force, This refers to the cohesive force (which does not exist in the linear model). For contact torque, This is the torque of the parallel bond (which does not exist in the linear model).

[0097] Loading: An indenter is established in the model space above the target discrete particle system. By performing a two-dimensional model of the Boehringer Indenter, the Berkovich Indenter is modeled three-dimensionally as a two-dimensional inverted triangular indenter with an angle of 65.27° between its centerline and the facet. The indenter is thus established, as shown below. Figure 3 As shown, Figure 3The triangle at the top represents the indenter. The loading mode employs a load-controlled approach, consisting of two stages: loading and unloading. First, the indenter is pressed into the surface of the target discrete particle system with cohesive mechanical properties at a constant downward velocity (e.g., 0.001 m / s). Once the indenter reaches the target load, it is then subjected to an upward velocity equal in absolute value to the loading velocity, completing the unloading operation. This process constructs a nanoindentation discrete element model of sandstone, as shown below. Figure 3 As shown, Figure 3 This is a schematic diagram of a discrete element model of nanoindentation in sandstone.

[0098] In one alternative embodiment, this application can perform numerous nanoindentation tests on the sandstone surface. For each indentation point, a corresponding load-displacement curve is obtained, resulting in a large number of load-displacement curves. For each load-displacement curve, the reduced modulus, hardness, and maximum indentation depth are calculated using the classic Oliver-Pharr method. This forms a clustered dataset containing three features, where each data point in the clustered dataset represents the values ​​of the three features corresponding to a load-displacement curve: reduced modulus, hardness, and maximum indentation depth.

[0099] Then, a Gaussian Mixture Model (GMM) is used to perform three-dimensional clustering analysis on the obtained clustered dataset. The number of clusters can be set according to the actual scenario. After clustering, the corresponding clustering results are obtained. For example, this application preferably sets the number of clusters to 3, and the clustering result is that the clustered dataset is clustered into 3 categories. This application calculates the intensity features of all data in the same cluster category to obtain the mean intensity of that cluster category. Through the same implementation method, the mean intensity of each cluster category can be calculated. Then, the strength mean values ​​of the three clusters were sorted. The cluster with the largest strength mean was determined as the first cluster. Based on the values ​​of sandstone mechanical property parameters recorded in all data in the first cluster, the nanoindentation mechanical properties of high-strength minerals were determined. The cluster with the second largest strength mean was determined as the second cluster. Based on the values ​​of sandstone mechanical property parameters recorded in all data in the second cluster, the nanoindentation mechanical properties of medium-strength minerals were determined. The cluster with the smallest strength mean was determined as the third cluster. Based on the values ​​of sandstone mechanical property parameters recorded in all data in the third cluster, the nanoindentation mechanical properties of low-strength minerals were determined.

[0100] After obtaining the nanoindentation mechanical properties of high, medium, and low strength minerals, the nanoindentation discrete element contact mechanical parameters of high-strength minerals, the nanoindentation discrete element contact mechanical parameters of medium-strength minerals, and the nanoindentation discrete element contact mechanical parameters of low-strength minerals can be calibrated using the same implementation method as described above.

[0101] Based on the same inventive concept, this application provides a sandstone nanoindentation discrete element contact mechanical parameter calibration system, such as... Figure 4 As shown, the system 400 includes: The optimization starting point set construction module 401 is used to select a preset number of sample data in the target dataset to form an optimization starting point set. The target dataset is a dataset used to train the target prediction model. The sample data in the target dataset includes the values ​​of each discrete element contact mechanical parameter as the input feature of the model, and the values ​​of each sandstone mechanical property parameter as the standard output result of the model. The optimal data point determination module 402 is used to take each sample data in the optimization starting point set as the search starting point, and perform iterative solution through the optimization solver with the goal of minimizing the objective function to obtain the optimal data point; The calibration result determination module 403 is used to determine the values ​​of each discrete element contact mechanical parameter of the optimal data point as the discrete element contact mechanical parameter calibration result required for the nanoindentation simulation experiment of the sandstone to be calibrated. The optimal data point determination module 402 includes: The 4021 iterative search module is used to perform iterative search through the optimization solver, with each sample data in the set of optimization starting points as the search starting point. The 4022 Sandstone Mechanical Property Parameter Determination Module is used to input the values ​​of the discrete element contact mechanical parameters of each candidate data point into the target prediction model to obtain the values ​​of the sandstone mechanical property parameters of each candidate data point. The 4023 Mechanical Characteristic Deviation Value Determination Module is used to calculate the comprehensive deviation between the values ​​of each sandstone mechanical property parameter of the candidate data point and the values ​​of each sandstone mechanical property parameter of the sandstone to be calibrated through a predefined objective function, so as to obtain the mechanical characteristic deviation value of the candidate data point. The 4024 optimal data point determination submodule is used to determine the candidate data point with the smallest mechanical characteristic deviation value from all the candidate data points obtained by the search as the optimal data point.

[0102] It should be noted that, for the sake of simplicity, the method embodiments are all described as a series of actions. However, those skilled in the art should understand that the embodiments of this application are not limited to the described order of actions, because according to the embodiments of this application, some steps can be performed in other orders or simultaneously. Secondly, those skilled in the art should also understand that the embodiments described in the specification are all preferred embodiments, and the actions involved are not necessarily necessary for the embodiments of this application.

[0103] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0104] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, embodiments of this application can take the form of entirely hardware embodiments, entirely software embodiments, or embodiments combining software and hardware aspects. Furthermore, embodiments of this application can take the form of computer program products implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0105] This application describes embodiments with reference to flowchart illustrations and / or block diagrams of methods, terminal devices (systems), and computer program products according to embodiments of this application. It should be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing terminal device to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing terminal device, generate instructions for implementing the flowchart illustrations. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0106] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing terminal device to operate in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0107] These computer program instructions can also be loaded onto a computer or other programmable data processing terminal equipment, causing a series of operational steps to be performed on the computer or other programmable terminal equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable terminal equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0108] Although preferred embodiments of the present application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of the embodiments of the present application.

[0109] Finally, it should be noted that in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or terminal device that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or terminal device. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or terminal device that includes said element.

[0110] The above provides a detailed description of the sandstone nanoindentation discrete element contact mechanical parameter calibration method and system provided in this application. Specific examples have been used to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of this application. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this application. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for calibrating contact mechanics parameters of sandstone nanoindentation discrete element, characterized in that, The method includes: A predetermined number of sample data are selected in the target dataset to form an optimization starting point set. The target dataset is a dataset used to train the target prediction model. The sample data in the target dataset includes the values ​​of each discrete element contact mechanics parameter as the input feature of the model, and the values ​​of each sandstone mechanical property parameter as the standard output result of the model. Using each sample data in the set of optimization starting points as the search starting point, the optimization solver iteratively solves the problem with the objective function as the goal, and obtains the optimal data point. The values ​​of the discrete element contact mechanical parameters of each of the optimal data points are determined as the discrete element contact mechanical parameter calibration results required for the nanoindentation simulation experiment of the sandstone to be calibrated. Specifically, taking each sample data in the set of optimization starting points as the search starting point, the optimization solver iteratively solves the problem with the objective function as the goal, to obtain the optimal data point, including: Using each sample data in the set of optimization starting points as the search starting point, an iterative search is performed through the optimization solver; The values ​​of the discrete element contact mechanics parameters of each candidate data point are input into the target prediction model to obtain the values ​​of the sandstone mechanical property parameters of each candidate data point. By using a predefined objective function, the comprehensive deviation between the values ​​of each sandstone mechanical property parameter of the candidate data point and the values ​​of each sandstone mechanical property parameter of the sandstone to be calibrated is calculated, and the mechanical characteristic deviation value of the candidate data point is obtained. From all the candidate data points obtained from the search, the candidate data point with the smallest mechanical characteristic deviation value is determined as the optimal data point.

2. The method according to claim 1, wherein, Using each sample data point in the set of optimization starting points as the search starting point, the optimization solver iteratively solves the problem with the objective function as the goal, to obtain the optimal data point, including: Using each sample data in the set of optimization starting points as the search starting point, an iterative solution is performed using a low-precision optimization solver with the objective function as the goal, to obtain the potential optimal data points around each search starting point; Select the target potential optimal data point from all the obtained potential optimal data points; Starting from the potential optimal data point of the target, the optimal data point is obtained by iteratively solving the problem using a high-precision optimization solver with the goal of minimizing the objective function.

3. The method according to claim 1, wherein, Select a predetermined number of sample data from the target dataset to form the optimization starting point set, including: The mechanical characteristic deviation value between each sample data in the target dataset and the sandstone to be calibrated is calculated using a predefined objective function. All obtained mechanical characteristic deviation values ​​are sorted from smallest to largest, and the sample data corresponding to the first number of mechanical characteristic deviation values ​​in the sort is selected as the optimization starting point. A second number of sample data is randomly selected from the remaining sample data in the target dataset as the optimization starting point, and the sum of the first number and the second number is the preset number; The set of all selected optimization starting points is formed.

4. The method according to claim 1, wherein, The initial prediction model is trained based on the target dataset to obtain the trained target prediction model, including: Each initial prediction model is trained based on the target dataset to obtain each trained prediction model. Among the various prediction models that have been trained, a target prediction model is selected to predict each mechanical property parameter of sandstone. The step of inputting the values ​​of the discrete element contact mechanics parameters of each candidate data point found in the search into the target prediction model to obtain the values ​​of the sandstone mechanical property parameters of each candidate data point includes: The values ​​of the discrete element contact mechanics parameters of each candidate data point are input into the target prediction model for predicting each sandstone mechanical property parameter to obtain the values ​​of each sandstone mechanical property parameter of the candidate data point. The target prediction model for predicting the i-th sandstone mechanical property parameter is used to obtain the value of the i-th sandstone mechanical property parameter of the candidate data point.

5. The method according to claim 1, wherein, The predefined objective function is: wherein x is an input vector composed of values of each discrete element contact mechanics parameter of the candidate data point; is a value of the i th sandstone mechanics characteristic parameter corresponding to the candidate data point obtained by the corresponding target prediction model; is a weight coefficient of the i th sandstone mechanics characteristic parameter; is a value of the i th sandstone mechanics characteristic parameter of the sandstone to be calibrated.

6. The method according to claim 1, wherein, The initial prediction model is trained based on the target dataset to obtain the trained target prediction model, including: The target dataset is divided into a training dataset and a test dataset according to a preset ratio; Input the sample data from the training dataset into the initial prediction model based on the current hyperparameter combination to obtain the prediction result; The deviation between the prediction result and the model's standard output result in the sample data is calculated using a preset optimization function. Determine whether the deviation meets the preset training completion conditions; If the deviation does not meet the preset training completion conditions, the hyperparameter combination of the initial prediction model is tuned using a Bayesian optimization algorithm to generate a new hyperparameter combination, and then the process is returned to start a new round of training. If the deviation meets the preset training completion conditions, the corresponding training completed prediction model is obtained. The trained prediction model is tested using the test dataset to obtain the corresponding performance test results. Determine whether the performance test results meet the preset stability conditions; If the performance test results meet the preset stability conditions, the corresponding target prediction model is obtained; If the performance test results do not meet the preset stability conditions, the trained prediction model is retrained until the performance test results of the trained prediction model meet the preset stability conditions.

7. The method for calibrating discrete element contact mechanical parameters of sandstone through nanoindentation according to claim 1, characterized in that, Constructing the target dataset includes: Construct an input dataset, wherein the input data in the input dataset includes the values ​​of each discrete element contact mechanical parameter as a feature of the model input, and the value of each discrete element contact mechanical parameter is obtained by stratified random sampling within its corresponding set value range; Substitute the i-th input data in the input dataset into the pre-built nanoindentation discrete element model for numerical simulation to obtain the nanoindentation indenter load and displacement data corresponding to the i-th input data. By calculating and analyzing the nano-indentation indenter load and displacement data of the i-th input data, the values ​​of each sandstone mechanical property parameter corresponding to the i-th input data are obtained. Based on the obtained input dataset and the values ​​of each sandstone mechanical property parameter corresponding to each input data in the input dataset, the target dataset is constructed.

8. The method for calibrating discrete element contact mechanical parameters of sandstone through nanoindentation according to claim 7, characterized in that, Constructing a nanoindentation discrete element model, including: A square computational domain with a set side length and dimensions is defined, and the square computational domain is composed of 4 walls; Within the square computational domain, particles with diameters within a set range are generated based on a set porosity value; All generated particles are allowed to move within the square computational domain. The motion equations of the particles are solved iteratively, and the calculation is continued until the force equilibrium state is reached within the square computational domain, thus obtaining the generated discrete particle system within the square computational domain. By setting an adhesion model between the particles in the discrete particle system, a target discrete particle system with adhesive mechanical properties is obtained. An indenter is established in the model space above the target discrete particle system to obtain a nanoindentation discrete element model.

9. The method for calibrating discrete element contact mechanical parameters of sandstone through nanoindentation according to claim 1, characterized in that, Each of the discrete element contact mechanical parameters includes at least: parallel bond normal stiffness, the ratio of parallel bond normal stiffness to parallel bond tangential stiffness, linear contact normal stiffness, the ratio of linear contact normal stiffness to linear contact tangential stiffness, and friction coefficient; Each of the aforementioned sandstone mechanical property parameters includes at least: reduced modulus, hardness, and maximum indentation depth.

10. A discrete element method (DEM) contact mechanical parameter calibration system for sandstone nanoindentation, characterized in that, The system includes: The optimization starting point set construction module is used to select a preset number of sample data in the target dataset to form an optimization starting point set. The target dataset is a dataset used to train the target prediction model. The sample data in the target dataset includes the values ​​of each discrete element contact mechanics parameter as the input feature of the model, and the values ​​of each sandstone mechanical property parameter as the standard output result of the model. The optimal data point determination module is used to take each sample data in the optimization starting point set as the search starting point, and iteratively solve the problem through an optimization solver with the goal of minimizing the objective function to obtain the optimal data point; The calibration result determination module is used to determine the values ​​of each discrete element contact mechanical parameter of the optimal data point as the discrete element contact mechanical parameter calibration result required for the nanoindentation simulation experiment of the sandstone to be calibrated. The optimal data point determination module includes: The iterative search module is used to perform iterative search through the optimization solver, taking each sample data in the set of optimization starting points as the search starting point. The sandstone mechanical property parameter determination module is used to input the values ​​of the discrete element contact mechanical parameters of each candidate data point into the target prediction model to obtain the values ​​of the sandstone mechanical property parameters of each candidate data point. The mechanical characteristic deviation value determination module is used to calculate the comprehensive deviation between the values ​​of each sandstone mechanical property parameter of the candidate data point and the values ​​of each sandstone mechanical property parameter of the sandstone to be calibrated through a predefined objective function, so as to obtain the mechanical characteristic deviation value of the candidate data point. The optimal data point determination submodule is used to determine the candidate data point with the smallest mechanical characteristic deviation value from all the candidate data points obtained by the search as the optimal data point.

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