Mechanical characterization method and apparatus

Abstract

Disclosed are a mechanical characterization method and apparatus. The method comprises: for any monitoring point among a plurality of monitoring points in a target mining area, acquiring a plurality of initial state pair values corresponding to the monitoring point; constructing a finite element geometric model corresponding to the target mining area; for any monitoring point, performing data preprocessing on the plurality of initial state pair values corresponding to the monitoring point, so as to obtain a plurality of first state pair values corresponding to the monitoring point; and on the basis of the finite element geometric model and the plurality of first state pair values corresponding to each monitoring point, using a data-driven algorithm to determine an optimal state pair value corresponding to each monitoring point. Therefore, data preprocessing is performed in advance on initial state pair values of each monitoring point, so as to improve the data accuracy, thereby effectively enhancing the performance of digital-driven mechanical characterization in actual engineering.

Description

Mechanical characterization method and device

[0001] Cross-reference to related applications

[0002] The present disclosure claims the priority of Chinese Patent Application No. 202410789326.0, filed on June 18, 2024, entitled "Mechanical characterization method and device", by Beijing Technology Research Branch of Tiandi Technology Co., Ltd. and China Coal Technology and Engineering Group Co., Ltd. TECHNICAL FIELD

[0003] The present disclosure relates to the technical field of computers, in particular to a mechanical characterization method and device. BACKGROUND

[0004] Stress monitoring in coal mines has always been a key issue in the prevention and control of coal mine rock burst disasters and deep mining. The stress distribution in coal mines is affected by various factors, such as burial depth, lithology, and geological structure. These factors cause the stress data to have a certain degree of dispersion, increasing the difficulty of monitoring and analysis.

[0005] Currently, although there are various stress measurement methods, such as stress relief method and hydraulic fracturing method, these methods may be limited by the underground environment in practical application, such as narrow space, high temperature and humidity, etc. Therefore, different monitoring methods are often used according to the actual conditions during monitoring, and the returned data formats and accuracies are not the same. Stress monitoring in coal mines requires accurate and real-time data collection and analysis, but the current technology is not mature enough in data processing and analysis, which seriously restricts the development of deep underground resource mining. SUMMARY

[0006] The present disclosure provides a mechanical characterization method and device.

[0007] According to an embodiment of the present disclosure, a mechanical characterization method is provided, comprising:

[0008] For any of the monitoring points in the plurality of monitoring points in the target mining area, a plurality of initial state pair values corresponding to the monitoring point are obtained; wherein the initial state pair values include a first value of a stress state and a second value of a strain state; and

[0009] A finite element geometric model corresponding to the target mining area is constructed; wherein the finite element geometric model includes a plurality of nodes, and each of the monitoring points has a corresponding node in the finite element geometric model; and

[0010] For any of the monitoring points, data preprocessing is performed on the plurality of initial state pair values corresponding to the monitoring point to obtain a plurality of first state pair values corresponding to the monitoring point; and

[0011] Based on the finite element geometric model and the first state pair values corresponding to each monitoring point, a data-driven algorithm is used to determine the optimal state pair values corresponding to each monitoring point.

[0012] According to an embodiment of another aspect of the present disclosure, a mechanical characterization device is provided, comprising:

[0013] The acquisition module is configured to acquire, for any monitoring point in the plurality of monitoring points in the target mining area, a plurality of initial state pair values corresponding to the monitoring point, wherein the initial state pair values include a first value of a stress state and a second value of a strain state; and

[0014] The construction module is configured to construct a finite element geometric model corresponding to the target mining area, wherein the finite element geometric model includes a plurality of nodes, and each monitoring point has a corresponding node in the finite element geometric model; and

[0015] The processing module is configured to, for any monitoring point, perform data preprocessing on the plurality of initial state pair values corresponding to the monitoring point to obtain a plurality of first state pair values corresponding to the monitoring point; and

[0016] The determination module is configured to, based on the finite element geometric model and the first state pair values corresponding to each monitoring point, use a data-driven algorithm to determine the optimal state pair values corresponding to each monitoring point.

[0017] According to an embodiment of another aspect of the present disclosure, an electronic device is provided, comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, wherein when the processor executes the program, the mechanical characterization method according to an embodiment of the present disclosure is implemented.

[0018] According to an embodiment of another aspect of the present disclosure, a non-transitory computer-readable storage medium is provided, which stores a computer program executable by a processor to implement the mechanical characterization method according to an embodiment of the present disclosure.

[0019] According to an embodiment of another aspect of the present disclosure, a computer program product is provided, which, when the instructions in the computer program product are executed by a processor, performs the mechanical characterization method according to an embodiment of the present disclosure.

[0020] The technical solutions provided by the present disclosure at least have the following beneficial effects:

[0021] For any given monitoring point among multiple monitoring points in the target mining area, multiple initial state pairs are obtained. These initial state pairs include a first value for stress and a second value for strain. A finite element geometric model corresponding to the target mining area is constructed, comprising multiple nodes, with each monitoring point having a corresponding node. For any given monitoring point, the multiple initial state pairs are preprocessed to obtain multiple first state pairs. Based on the finite element geometric model and the multiple first state pairs for each monitoring point, a data-driven algorithm is used to determine the optimal state pair for each monitoring point. Therefore, preprocessing the initial state pairs for each monitoring point improves data accuracy and effectively enhances the performance of digitally driven mechanical characterization in practical engineering.

[0022] Additional aspects and advantages of this disclosure will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of this disclosure. Attached Figure Description

[0023] The above and / or additional aspects and advantages of this disclosure will become apparent and readily understood from the following description of the embodiments taken in conjunction with the accompanying drawings, in which:

[0024] Figure 1 is a schematic flowchart of a mechanical characterization method provided in an embodiment of this disclosure;

[0025] Figure 2 is a flowchart illustrating another mechanical characterization method provided in another embodiment of this disclosure;

[0026] Figure 3 is a flowchart illustrating a mechanical characterization method provided in another embodiment of this disclosure;

[0027] Figure 4 is a flowchart illustrating a mechanical characterization method provided in another embodiment of this disclosure;

[0028] Figure 5 is a flowchart illustrating a mechanical characterization method provided in an embodiment of this disclosure;

[0029] Figure 6 is a schematic diagram of the structure of a mechanical characterization method apparatus provided in an embodiment of this disclosure. Detailed Implementation

[0030] Embodiments of this disclosure are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain this disclosure, and should not be construed as limiting this disclosure.

[0031] In related technologies, the steps of a data-driven mechanical characterization method are as follows:

[0032] (1) Specify a stress-strain state pair value for each material point (also known as a monitoring point), where the stress-strain state pair value comes from a pre-specified material dataset and needs to meet compatibility and balance constraints.

[0033] (2) Define the penalty function: evaluate the degree of deviation between the state of each material point (such as stress state, strain state) and the corresponding dataset.

[0034] (3) Define the constraint optimization problem: minimize the global penalty function while satisfying balance and compatibility constraints.

[0035] (4) Problem transformation: The constrained optimization problem is transformed into an equivalent steady-state problem using the Lagrange multiplier method.

[0036] (5) Solve steady-state problems: obtain variables such as displacement and stress.

[0037] (6) Global search: Find the data point in the dataset that is closest to the state of each material point.

[0038] (7) Repeat steps (5) and (6) until convergence.

[0039] As the dataset approaches the true constitutive relation of the material, the data-driven solution will converge to the classical solution.

[0040] However, the above method has the following drawbacks:

[0041] 1. High data requirements. Current technology requires a specified stress-strain state pair value for each material point. However, in actual engineering applications, depending on the monitoring methods used, the values ​​or data corresponding to the stress state and strain state may not be able to be measured simultaneously.

[0042] 2. Sensitive to data noise. In practical engineering, poor data accuracy is very common. However, the above method relies entirely on the collected data. If the collected data is not accurate, it will greatly affect the characterization results, resulting in significant errors.

[0043] To address at least one of the aforementioned problems, this disclosure proposes a mechanical characterization method and apparatus that can preprocess the initial state values ​​of each monitoring point to improve data accuracy and effectively enhance the performance of digitally driven mechanical characterization in practical engineering.

[0044] The mechanical methods and apparatus of embodiments of this disclosure are described below with reference to the accompanying drawings.

[0045] Figure 1 is a schematic flowchart of a mechanical characterization method provided in an embodiment of this disclosure.

[0046] This disclosure illustrates the mechanical characterization method by describing it as being configured in a mechanical characterization method apparatus, which can be applied to any electronic device so that the electronic device can perform the mechanical characterization method function.

[0047] Among them, electronic devices can be any device with computing capabilities, such as PCs (Personal Computers), mobile terminals, servers, etc. Mobile terminals can be hardware devices with various operating systems, touch screens and / or displays, such as mobile phones, tablets, personal digital assistants, wearable devices, etc.

[0048] As shown in Figure 1, this mechanical characterization method includes steps 101-104.

[0049] Step 101: For any one of the multiple monitoring points in the target mining area, obtain multiple initial state pairs corresponding to the monitoring point.

[0050] The initial state value can be a combination of the first value of the stress state and the second value of the strain state.

[0051] In this embodiment of the disclosure, there may be multiple monitoring points in the target mining area, so that multiple monitoring points in the target mining area can be monitored and multiple initial state pairs corresponding to any monitoring point can be obtained.

[0052] It should be noted that the first value in each initial state pair may or may not exist; similarly, the second value in each initial state pair may or may not exist.

[0053] It should also be noted that this disclosure does not impose any restrictions on the noise level of the first value in each initial state pair. For example, the noise level of the first value in the initial state pair may be less than 5%, or the noise level of the first value in the initial state pair may be greater than 5%. Similarly, this disclosure does not impose any restrictions on the noise level of the second value in each initial state pair.

[0054] It should be noted that in practical applications, the number of initial state pairs corresponding to each monitoring point can be multiple, such as 500, 1000, 2000, etc. This disclosure does not limit this.

[0055] Step 102: Construct the finite element geometric model corresponding to the target mining area.

[0056] The finite element geometric model includes multiple nodes, and each monitoring point has a corresponding node in the finite element geometric model.

[0057] As an example, when constructing the finite element geometric model corresponding to the target mining area, the model can define each node, the topological relationship between each node, the shape function between each node, the derivative matrix of the shape function, and the weight of each node. Each monitoring point has a corresponding node in the finite element geometric model.

[0058] Step 103: For any monitoring point, perform data preprocessing on the multiple initial state pairs corresponding to the monitoring point to obtain multiple first state pairs corresponding to the monitoring point.

[0059] Data preprocessing may include missing value handling, data augmentation, etc., and this disclosure does not limit it.

[0060] Step 104: Based on the finite element geometric model and multiple first state pairs corresponding to each monitoring point, a data-driven algorithm is used to determine the optimal state pair corresponding to each monitoring point.

[0061] In this embodiment of the disclosure, based on the finite element geometric model and multiple first state pairs corresponding to each monitoring point, a data-driven algorithm can be used to determine the optimal state pair (also known as the global state pair) corresponding to each monitoring point.

[0062] In this embodiment, for any one of multiple monitoring points in the target mining area, multiple initial state pairs are obtained. These initial state pairs include a first value of the stress state and a second value of the strain state. A finite element geometric model corresponding to the target mining area is constructed. This model includes multiple nodes, and each monitoring point has a corresponding node within the model. For any given monitoring point, the multiple initial state pairs are preprocessed to obtain multiple first state pairs. Based on the finite element geometric model and the multiple first state pairs for each monitoring point, a data-driven algorithm is used to determine the optimal state pair for each monitoring point. Therefore, preprocessing the initial state pairs of each monitoring point improves data accuracy and effectively enhances the performance of digitally driven mechanical characterization in practical engineering.

[0063] To more clearly illustrate how, for any given monitoring point, multiple initial state pairs are preprocessed to obtain multiple first state pairs corresponding to the monitoring point in the above embodiments of this disclosure, another embodiment of this disclosure provides another possible implementation of the mechanical characterization method. Figure 2 is a flowchart illustrating another mechanical characterization method provided by another embodiment of this disclosure.

[0064] As shown in Figure 2, the mechanical characterization method includes steps 201-205.

[0065] Step 201: For any one of the multiple monitoring points in the target mining area, obtain multiple initial state pairs corresponding to the monitoring point.

[0066] Step 202: Construct the finite element geometric model corresponding to the target mining area.

[0067] The execution process of steps 201 to 202 can be referred to the execution process of any embodiment of this disclosure, and will not be repeated here.

[0068] Step 203: For any monitoring point, divide the multiple initial state pairs corresponding to the monitoring point according to the data category to which each initial state pair belongs, so as to obtain at least one subset corresponding to the monitoring point.

[0069] In one possible implementation of this disclosure, the data category may include at least one of a first category, a second category, a third category, and a fourth category, wherein:

[0070] The first category can indicate that both the first and second values ​​exist in the corresponding initial state pair, and the noise levels of both the first and second values ​​in the corresponding initial state pair are less than a set threshold.

[0071] The second category can indicate that the first or second value is missing in the corresponding initial state pair, and the noise level of the first or second value present in the corresponding initial state pair is less than a set threshold.

[0072] The third category can indicate that both the first and second values ​​exist in the corresponding initial state pair, and the noise level of the first and / or second values ​​in the corresponding initial state pair is not less than a set threshold.

[0073] The fourth category can indicate that the first or second value is missing in the corresponding initial state pair, and the noise level of the first or second value present in the corresponding initial state pair is not less than a set threshold.

[0074] In the embodiments of this disclosure, the threshold can be preset, such as 5%, 10%, etc., and this disclosure does not limit it.

[0075] As an example, suppose the initial state pair corresponding to monitoring point 1 includes (a, b), and the threshold is set to 10%, where:

[0076] When both the first value a and the second value b exist in the initial state pair (a, b), and the noise levels of both the first value a and the second value b are less than 10%, the data category of the initial state pair (a, b) is determined to be the first category.

[0077] When the first value 'a' is missing in the initial state pair (a,b) and the noise level of the existing second value 'b' is less than 10%, the data category of the initial state pair (a,b) is determined to be the second category; when the second value 'b' is missing in the initial state pair (a,b) and the noise level of the existing first value 'a' is less than 10%, the data category of the initial state pair (a,b) is determined to be the second category.

[0078] When both the first value a and the second value b exist in the initial state pair (a,b), and the noise level of the first value a and / or the second value b is not less than 10%, the data category of the initial state pair (a,b) is determined to be the third category.

[0079] When the first value 'a' in the initial state pair (a,b) is missing, and the noise level of the existing second value 'b' is not less than 10%, the data category of the initial state pair (a,b) is determined to be the fourth category; when the second value 'b' in the initial state pair (a,b) is missing, and the noise level of the existing first value 'a' is less than 10%, the data category of the initial state pair (a,b) is determined to be the fourth category.

[0080] In another possible implementation of this disclosure, when neither the first value of the stress state nor the second value of the strain state exists in the initial state pair corresponding to the monitoring point, the initial state pair corresponding to the monitoring point can be deleted.

[0081] In this embodiment of the disclosure, for any monitoring point, the initial state pairs corresponding to the monitoring point can be divided according to the data category to which each initial state pair belongs, thereby obtaining at least one subset corresponding to the monitoring point.

[0082] It should be noted that the number of subsets corresponding to monitoring points can be, but is not limited to, one, and this disclosure does not impose any restrictions on this.

[0083] It should also be noted that each subset can have a corresponding data category.

[0084] Using the example above, for monitoring point 1, after dividing the multiple initial state pairs corresponding to monitoring point 1 according to the data category to which each initial state pair belongs, the resulting subsets corresponding to monitoring point 1 include subset A and subset B. In subset A, the data category to which each initial state pair belongs is the first category, that is, the data category corresponding to subset A is the first category. In subset B, the data category to which each initial state pair belongs is the third category, that is, the data category corresponding to subset B is the third category.

[0085] Step 204: For any subset corresponding to the monitoring point, based on the data category corresponding to the subset, use the corresponding data preprocessing method to preprocess the initial state pair values ​​in the subset to obtain the first state pair values ​​corresponding to the monitoring point.

[0086] In this embodiment of the disclosure, for any subset corresponding to a monitoring point, the initial state pair values ​​in the subset can be preprocessed using the corresponding data preprocessing method based on the data category corresponding to the subset, thereby obtaining the first state pair value corresponding to the monitoring point.

[0087] As an example, suppose the subset corresponding to monitoring point 2 includes subset A, subset B, and subset C. The data preprocessing methods include method 1, method 2, method 3, and method 4. Based on the data category corresponding to subset A, method 1 is used to preprocess the initial state pairs in subset A to obtain the first state pairs corresponding to the monitoring point. Based on the data category corresponding to subset B, method 3 is used to preprocess the initial state pairs in subset B to obtain the first state pairs corresponding to the monitoring point. Based on the data category corresponding to subset C, method 4 is used to preprocess the initial state pairs in subset C to obtain the first state pairs corresponding to the monitoring point.

[0088] Step 205: Based on the finite element geometric model and multiple first state pairs corresponding to each monitoring point, a data-driven algorithm is used to determine the optimal state pair corresponding to each monitoring point.

[0089] The execution process of step 205 can be found in any embodiment of this disclosure, and will not be described in detail here.

[0090] In this embodiment, for any monitoring point, the initial state pairs corresponding to the monitoring point are divided according to the data category to which they belong, to obtain at least one subset corresponding to the monitoring point. For any subset corresponding to the monitoring point, based on the data category of the subset, the initial state pairs in the subset are preprocessed using the corresponding data preprocessing method to obtain the first state pair corresponding to the monitoring point. Therefore, by using the corresponding data preprocessing method based on the data category of each subset, the data accuracy of each subset can be effectively improved.

[0091] In this disclosure, when the data category includes at least one of the first category, second category, third category and fourth category shown in step 203, for any subset corresponding to the monitoring point, in order to clearly illustrate how the initial state pair values ​​in the subset are preprocessed based on the data category corresponding to the subset to obtain the first state pair value corresponding to the monitoring point, another embodiment of this disclosure provides a possible implementation of the mechanical characterization method. Figure 3 is a flowchart of a mechanical characterization method provided by another embodiment of this disclosure.

[0092] As shown in Figure 3, the mechanical characterization method includes steps 301-304.

[0093] Step 301: For any subset corresponding to a monitoring point, in response to the data category corresponding to the subset being the first category, the initial state pair value in the subset is determined as the first state pair value corresponding to the monitoring point.

[0094] In the embodiments of this disclosure, the number of initial state pairs in each subset may be, but is not limited to, one, and this disclosure does not impose any restrictions on this.

[0095] In this embodiment of the disclosure, for any subset corresponding to a monitoring point, when the data category corresponding to the subset is the first category, the initial state pair value in the subset can be determined as the first state pair value corresponding to the monitoring point.

[0096] In other words, when the data category corresponding to the subset is the first category, the initial state pair value in the subset can be directly determined as the first state pair value corresponding to the monitoring point.

[0097] Step 302: In response to the data category corresponding to the subset being the second category, the initial state pair values ​​in the subset are filled with missing values ​​using the method of filling missing values ​​to obtain the first state pair values ​​corresponding to the monitoring point.

[0098] In this embodiment of the disclosure, when the data category corresponding to the subset is the second category, the method of filling missing values ​​can be used to fill the first data of the initial state pair values ​​in the subset to obtain the first state pair values ​​corresponding to the monitoring point.

[0099] Optionally, when the data category corresponding to the subset is the second category, the following steps can be used to perform first data imputation on the initial state pairs in the subset using a method for imputing missing values, so as to obtain the first state pairs corresponding to the monitoring points:

[0100] Step 3021: In response to the data category corresponding to the subset being the second category, obtain the first constitutive model and the first material parameters corresponding to the monitoring point in the target mining area.

[0101] Among them, the first material parameter matches the first constitutive model.

[0102] In this embodiment of the disclosure, after obtaining the first constitutive model corresponding to the monitoring point in the target mining area, the first material parameters matching the first constitutive model can be obtained.

[0103] In other words, the first material parameter depends on the first constitutive model obtained. For example, when the first constitutive model is a linear elastic constitutive model, the first material parameter may include the elastic modulus (e.g., Young's modulus) and Poisson's ratio, or the first material parameter may include Lamé constant and shear modulus; when the first constitutive model is an elastoplastic model, the first material parameter may include density, elastic modulus, and Poisson's ratio.

[0104] In this embodiment of the disclosure, when the data category corresponding to the subset is the second category, the first constitutive model and the first material parameters corresponding to the monitoring point in the target mining area can be obtained.

[0105] Step 3022: Construct the material stiffness matrix corresponding to the monitoring point based on the first constitutive model and the first material parameters corresponding to the monitoring point.

[0106] In this embodiment of the disclosure, a material stiffness matrix corresponding to the monitoring point can be constructed based on the first constitutive model and the first material parameters corresponding to the monitoring point.

[0107] As an example, assuming the first constitutive model corresponding to the monitoring point is a linear elastic constitutive model, and the first material parameters include the elastic modulus and Poisson's ratio, with the elastic modulus being Young's modulus E and the Poisson's ratio being ν, then the Lamé constant λ and shear modulus μ of the material at the monitoring point are respectively:

[0108] The material stiffness matrix C corresponding to the monitoring point is:

[0109] Step 3023: For any initial state pair in the subset, determine the target value in the initial state pair based on the material stiffness matrix corresponding to the monitoring point.

[0110] The target value can be either the first missing value or the second missing value.

[0111] For example, assuming a subset has an initial state pair (a, b), and the material stiffness matrix corresponding to the monitoring point is C, when the first value 'a' in the initial state pair (a, b) is missing, the first value 'a' is the target value that needs to be determined. The target value 'a' can be determined using the following formula: a = C -1 ×b; (4)

[0112] When the second value b is missing from the initial state pair (a, b), the second value b is the target value that needs to be determined. The target value b can be determined using the following formula: b = C -1 ×a; (5)

[0113] Step 3024: Based on the target value, fill in the initial state pair value and determine the filled initial state pair value as the first state pair value corresponding to the monitoring point.

[0114] In this embodiment of the disclosure, the initial state pair can be filled based on the target value, and the initial state pair after filling can be determined as the first state pair corresponding to the monitoring point.

[0115] Using the example above, when the first value 'a' in the initial state pair (a, b) is missing, the initial state pair (a, b) is filled in based on the target value 'a' determined by formula (4). The filled initial state pair is then (C...). -1 ×b,b), can make (C) -1 ×b, b) is determined as the first state pair value corresponding to the monitoring point; when the second value b is missing in the initial state pair value (a, b), the initial state pair value (a, b) is filled based on the target value b determined by formula (5), and the initial state pair value after filling is (a, C -1 ×a), which can be used to represent (a, C) -1 ×a) is determined as the first state pair value corresponding to the monitoring point.

[0116] Therefore, when the data category corresponding to the subset is the second category, the initial state pair values ​​in the subset can be filled with the first data, thereby effectively obtaining the first state pair values ​​corresponding to the monitoring point.

[0117] Step 303: In response to the data category corresponding to the subset being the third category, the initial state pair values ​​in the subset are supplemented with the first data using a data construction method to obtain the first state pair values ​​corresponding to the monitoring point.

[0118] In this embodiment of the disclosure, when the data category corresponding to the subset is the third category, a data construction method can be used to supplement the initial state pair values ​​in the subset with the first data to obtain the first state pair values ​​corresponding to the monitoring point.

[0119] Optionally, when the data category corresponding to the subset is the third category, the following steps can be used to supplement the initial state pair values ​​in the subset with data construction methods to obtain the first state pair values ​​corresponding to the monitoring points:

[0120] Step 3031: In response to the data category corresponding to the subset being the third category, obtain the second constitutive model and second material parameters corresponding to the monitoring point in the target mining area, and obtain the first boundary conditions corresponding to the monitoring point.

[0121] The second material parameter matches the second constitutive model.

[0122] It should be noted that the second constitutive model may be the same as or different from the first constitutive model in step 3021, and this disclosure does not impose any restrictions on this.

[0123] It should also be noted that the second material parameter may be the same as or different from the first material parameter in step 3021, and this disclosure does not impose any restrictions on this.

[0124] The first boundary condition can be, for example, the magnitude of the applied force, the location information of the applied force, etc., and this disclosure does not limit it.

[0125] In this embodiment of the disclosure, when the data category corresponding to the subset is the third category, the second constitutive model and the second material parameters corresponding to the monitoring point in the target mining area can be obtained, and the first boundary condition corresponding to the monitoring point can be obtained. For example, in response to the user's selection operation, the second constitutive model can be obtained from a plurality of pre-configured constitutive models, and in response to the user's input operation, the second material parameters matching the second constitutive model and the first boundary condition corresponding to the monitoring point can be obtained.

[0126] Step 3032: Based on the second constitutive model, second material parameters, and first boundary conditions corresponding to the monitoring point, as well as the finite element geometric model, the second state pair value belonging to the subset is constructed using the finite element method.

[0127] In this embodiment of the disclosure, based on the second constitutive model, second material parameters, and first boundary conditions corresponding to the monitoring point, as well as the finite element geometric model, the finite element method can be used to construct a second state pair value belonging to a subset. For example, based on the second constitutive model, second material parameters, and first boundary conditions corresponding to the monitoring point, as well as the finite element geometric model, the finite element method can be implemented using ANSYS computer-aided engineering software, ABAQUS engineering simulation finite element software, etc., to construct the second state pair value belonging to the subset.

[0128] Optionally, the number of second state values ​​corresponding to the constructed monitoring points can be a first set multiple of the number of initial state pairs in the corresponding subset.

[0129] The first set multiple can be preset, such as any real number from 1 to 2, etc.

[0130] As an example, suppose the data category corresponding to subset B of monitoring point 2 is the third category, the number of initial state pairs in subset B is n, and the first set multiple is 1.2, then the number of second state values ​​corresponding to the constructed monitoring point is 1.2n.

[0131] Step 3033: The constructed second state pair value and the initial state pair value in the subset are both determined as the first state pair value corresponding to the monitoring point.

[0132] In this embodiment of the disclosure, the constructed second state pair value and the initial state pair value in the corresponding subset can both be determined as the first state pair value corresponding to the monitoring point.

[0133] Using the example above, the constructed second state pair values ​​of quantity 1.2n and the initial state pair values ​​of quantity n in subset B can both be determined as the first state pair values ​​corresponding to the monitoring points.

[0134] Therefore, when the data category corresponding to the subset is the third category, the initial state pair values ​​in the subset can be supplemented with the first data, thereby effectively obtaining the first state pair values ​​corresponding to the monitoring point.

[0135] Step 304: In response to the data category corresponding to the subset being the fourth category, the initial state pair values ​​in the subset are processed using methods for filling missing values ​​and data construction to obtain the first state pair values ​​corresponding to the monitoring points.

[0136] In this embodiment of the disclosure, when the data category corresponding to the subset is the fourth category, the method of filling missing values ​​and the data construction method can be used to process the initial state pair values ​​in the subset to obtain the first state pair values ​​corresponding to the monitoring point.

[0137] Optionally, when the data category corresponding to the subset is the fourth category, the following steps can be taken to process the initial state pairs in the subset using methods for filling missing values ​​and data construction to obtain the first state pairs corresponding to the monitoring points:

[0138] Step 3041: In response to the data category corresponding to the subset being the fourth category, the initial state pair values ​​in the subset are imputed with a second data imputation method to obtain the third state pair values.

[0139] It should be noted that the method for performing the second data filling on the initial state values ​​in the subset is similar to the method for performing the first data filling in step 302, and will not be described in detail here.

[0140] Step 3042: Using a data construction method, construct the fourth state pair values ​​belonging to the subset.

[0141] Optionally, the third constitutive model and third material parameters corresponding to the monitoring point in the target mining area are obtained, and the second boundary conditions corresponding to the monitoring point are constructed, wherein the third material parameters are matched with the third constitutive model; based on the third constitutive model, third material parameters and second boundary conditions corresponding to the monitoring point, as well as the finite element geometric model, the fourth state pair value belonging to the subset is constructed using the finite element method.

[0142] It should be noted that the third constitutive model may be the same as or different from the first constitutive model in step 3021, and this disclosure does not impose any restrictions on this.

[0143] It should also be noted that the third material parameter may be the same as or different from the first material parameter in step 3021, and this disclosure does not impose any restrictions on this.

[0144] The second boundary condition can be, for example, the magnitude of the applied force, the location information of the applied force, etc., and this disclosure does not limit it.

[0145] In one possible implementation of this disclosure, when a first subset and a second subset exist simultaneously in the subset corresponding to the monitoring point, wherein the data category corresponding to the first subset is the third category and the data category corresponding to the second subset is the fourth category, when the data construction method is used to construct the second state pair value belonging to the first subset and the fourth state pair value belonging to the second subset respectively, the number of constructed fourth state pair values ​​is a second predetermined multiple of the number of constructed second state pair values.

[0146] The second set multiple can be preset, such as 0.8, 0.9, etc., and this disclosure does not limit it.

[0147] As an example, suppose that the subset corresponding to monitoring point 1 contains both a first subset and a second subset, and the second set multiple is 0.9. Using the data construction method, the number of second state pair values ​​constructed is m. Then, using the data construction method, the number of fourth state pair values ​​constructed is 0.9m.

[0148] Step 3043: Determine both the third state pair value and the fourth state pair value as the first state pair value corresponding to the monitoring point.

[0149] In this embodiment of the disclosure, both the third state pair and the fourth state pair are determined as the first state pair corresponding to the monitoring point, that is, both the third state pair obtained by data filling and the fourth state pair obtained by data construction are determined as the first state pair corresponding to the monitoring point.

[0150] As an example, suppose the subset corresponding to monitoring point 3 includes subsets A, B, C, and D, where:

[0151] When the data category corresponding to subset A is the first category, the initial state pair value in subset A is determined as the first state pair value corresponding to the monitoring point;

[0152] When the data category corresponding to subset B is the second category, the method of filling missing values ​​is used to fill the first data in the initial state pair values ​​in subset B to obtain the first state pair values ​​corresponding to the monitoring point.

[0153] When the data category corresponding to subset C is the third category, the method of filling missing values ​​is used to fill the first data in the initial state pair values ​​in the subset to obtain the first state pair values ​​corresponding to the monitoring point.

[0154] When the data category corresponding to subset D is the fourth category, the initial state pairs in the subset are processed using methods for filling missing values ​​and data construction to obtain the first state pairs corresponding to the monitoring points.

[0155] Therefore, by using different data processing methods to preprocess the initial state pairs in each subset corresponding to the monitoring points, the first state pairs corresponding to the monitoring points can be effectively obtained.

[0156] It should be noted that at least one of steps 301, 302, 303 and 304 can be executed, and when multiple steps are executed, they can be executed in parallel or sequentially, and this disclosure does not impose any restrictions on this.

[0157] In this embodiment, for any subset corresponding to a monitoring point, in response to the data category corresponding to the subset being a first category, the initial state pairs in the subset are determined as the first state pairs corresponding to the monitoring point; in response to the data category corresponding to the subset being a second category, the initial state pairs in the subset are filled with missing values ​​using a first data filling method to obtain the first state pairs corresponding to the monitoring point; in response to the data category corresponding to the subset being a third category, the initial state pairs in the subset are supplemented with data using a data construction method to obtain the first state pairs corresponding to the monitoring point; in response to the data category corresponding to the subset being a fourth category, the initial state pairs in the subset are processed using both the missing value filling method and the data construction method to obtain the first state pairs corresponding to the monitoring point. Thus, on the one hand, data loss is effectively reduced; on the other hand, noise can be smoothed through finite element data construction, effectively reducing the data noise level.

[0158] It is understood that the first state pair value corresponding to the monitoring point can have a corresponding physical state, such as a coal mine mining state, an external force disturbance state, an earthquake disturbance state, etc. In other words, the first state pair value corresponding to the monitoring point is obtained when the monitoring point is in the corresponding physical state. Based on this, in order to clearly illustrate how the optimal state pair value corresponding to each monitoring point is determined by a data-driven algorithm based on the finite element geometric model and multiple first state pairs value corresponding to each monitoring point in any of the above embodiments of this disclosure, another embodiment of this disclosure provides a possible implementation of the mechanical characterization method. Figure 4 is a flowchart of a mechanical characterization method provided in another embodiment of this disclosure.

[0159] As shown in Figure 4, based on any of the above embodiments of this disclosure, the mechanical characterization method includes steps 401-406.

[0160] Step 401: For any physical state, based on the finite element geometric model and multiple first state pairs of each monitoring point in the physical state, perform multiple rounds of iterative process to obtain the optimal state pair of each monitoring point in the physical state.

[0161] The physical state can be, but is not limited to, coal mining state, external force disturbance state, earthquake disturbance state, etc.

[0162] As an example, assuming the physical state is a coal mine mining state, for the coal mine mining state, multiple iterations can be performed based on the finite element geometric model and multiple first state pairs of each monitoring point in the coal mine mining state to obtain the optimal state pair of each monitoring point in the coal mine mining state.

[0163] Step 402: For any round of iteration, obtain the candidate state pair values ​​of each monitoring point in the current round from multiple first state pair values ​​of each monitoring point in the physical state.

[0164] Among them, the candidate state pair values ​​include the third value of the stress state and the fourth value of the strain state.

[0165] As an example, assume the monitoring points include monitoring point 1, monitoring point 2, and monitoring point 3, and the physical state is coal mining. The first state pair value of monitoring point 1 under the coal mining state includes (a 11 ,b 11 ), (a 12 ,b 12 ) and (a 13 ,b 13 The first state pair values ​​of monitoring point 2 under coal mining conditions include (a) 21 ,b 21 ) and (a22 ,b 22 The first state pair values ​​of monitoring point 3 under coal mining conditions include (a) 31 ,b 31 ), (a 32 ,b 32 ), (a 33 ,b 33 ) and (a 34 ,b 34 Then, candidate state pairs for each monitoring point in the current round under the coal mining state can be randomly obtained from multiple first state pairs for each monitoring point under the physical state. For example, the candidate state pairs for each monitoring point in the current round under the coal mining state are (a 11 ,b 11 ), (a 22 ,b 22 ), (a 34 ,b 34 ).

[0166] Step 403: Based on the candidate state pairs and finite element geometric models of each monitoring point in the current round under the physical state, a data-driven algorithm is used to determine the target state pairs of each monitoring point in the current round under the physical state.

[0167] The target state values ​​include the fifth value of the stress state and the sixth value of the strain state.

[0168] In this embodiment of the disclosure, the target state pair value of each monitoring point in the current round under the physical state can be determined by using a data-driven algorithm based on the candidate state pair values ​​and finite element geometric model of each monitoring point in the current round under the physical state.

[0169] As an example, based on the candidate state-to-state pairs and the finite element geometric model of each monitoring point in this round under the physical state, the target state-to-state pairs of each monitoring point in this round under the physical state can be determined according to the following formula:

[0170] In this model, the number of nodes in the finite element geometric model is n, the number of monitoring points is m, σ represents the vector composed of the third value of the stress state in the candidate state pair values ​​of each monitoring point in this round, and ε represents the vector composed of the fourth value of the strain state in the candidate state pair values ​​of each monitoring point in this round. e ε represents the third value of the stress state in the candidate state pair for the e-th monitoring point. e w represents the fourth value of the strain state in the candidate state pair values ​​for the e-th monitoring point. e B represents the weight of the node corresponding to the e-th monitoring point in the finite element geometric model. ej B represents the reciprocal matrix of the shape function between the e-th monitoring point and the j-th node.ei C represents the reciprocal matrix of the shape function between the e-th monitoring point and the i-th node. e For the pre-set intermediate matrix, u i Let η be the displacement driven by the i-th node in the candidate state pair value pair of each monitoring point under the physical state in this round. i f is the Lagrange multiplier corresponding to the i-th node. i σ′ represents the magnitude of the external force on the i-th node, σ′ represents the vector composed of the fifth value of the stress state in the target state pair values ​​of each monitoring point, and ε′ represents the vector composed of the sixth value of the strain state in the target state pair values ​​of each monitoring point.

[0171] Step 404: Based on the distance between the candidate state pair values ​​and the corresponding target state pair values ​​of each monitoring point in the current round under the physical state, determine whether the target state pair value of each monitoring point in the current round under the physical state is the optimal state pair value of the corresponding monitoring point under the physical state.

[0172] Optionally, a first coefficient is determined based on the distance between the third value of the candidate state pair values ​​of each monitoring point in the current round under physical conditions and the fifth value of the corresponding target state pair values; a second coefficient is determined based on the distance between the fourth value of the candidate state pair values ​​of each monitoring point in the current round under physical conditions and the sixth value of the corresponding target state pair values; in response to the first coefficient being less than a first set threshold and the second coefficient being less than a second set threshold, the target state pair value of each monitoring point in the current round under physical conditions is determined to be the optimal state pair value of the corresponding monitoring point under physical conditions.

[0173] Using the example above, σ represents the vector composed of the third value of the stress state in the candidate state pair values ​​of each monitoring point in this round, ε represents the vector composed of the fourth value of the strain state in the candidate state pair values ​​of each monitoring point in this round, σ′ represents the vector composed of the fifth value of the stress state in the target state pair values ​​of each monitoring point, and ε′ represents the vector composed of the sixth value of the strain state in the target state pair values ​​of each monitoring point. The first threshold is set as l1, and the second threshold is set as l2. The first coefficient k1 can be determined according to the following formula: k1=||σ-σ′||; (7)

[0174] The second coefficient k2 is determined according to the following formula: k2=||ε-ε′||; (8)

[0175] When the first coefficient k1 is less than the first set threshold l1 and the second coefficient k2 is less than the second set threshold l2, the target state pair value of each monitoring point in this round under the physical state can be determined as the optimal state pair value of the corresponding monitoring point under the physical state, that is, (σ′, ε′) is the optimal state pair value of each monitoring point under the corresponding physical state.

[0176] Optionally, when the first coefficient is not less than the first set threshold and / or the second coefficient is not less than the second set threshold, it can be determined that the target state pair value of each monitoring point in the current round under the physical state is not the optimal state pair value of the corresponding monitoring point under the physical state.

[0177] Step 405: In response to the target state pair value of each monitoring point in the physical state in this round being the optimal state pair value of the corresponding monitoring point in the physical state, the iteration process is stopped.

[0178] Step 406: In response to the fact that the target state pair value of each monitoring point in the current round is not the optimal state pair value of the corresponding monitoring point in the physical state, execute the next round of iteration.

[0179] It should be noted that in practical applications, steps 405 and 406 are performed selectively.

[0180] In this embodiment, for any physical state, based on the finite element geometric model and multiple first state pairs of each monitoring point in the physical state, multiple iterations are performed to obtain the optimal state pair of each monitoring point in the physical state. For any iteration, candidate state pairs of each monitoring point in the current iteration are obtained from the multiple first state pairs of each monitoring point in the physical state. Based on the candidate state pairs of each monitoring point in the current iteration, a data-driven algorithm is used to determine the target state pairs of each monitoring point in the current iteration. Based on the distance between the candidate state pairs of each monitoring point in the current iteration and the corresponding target state pairs, it is determined whether the target state pairs of each monitoring point in the current iteration are the optimal state pairs of the corresponding monitoring point in the physical state. In response to the target state pairs of each monitoring point in the current iteration being the optimal state pairs of the corresponding monitoring point in the physical state, the iteration process stops. In response to the target state pairs of each monitoring point in the current iteration not being the optimal state pairs of the corresponding monitoring point in the physical state, the next iteration is performed. Therefore, based on the theory of data-driven mechanics, the global optimal state pair values, namely the global optimal stress state and the optimal strain state, can be effectively determined.

[0181] To clearly illustrate the mechanical characterization method of this disclosure, the above process will be explained in detail below with reference to examples.

[0182] Figure 5 is a flowchart illustrating a mechanical characterization method provided in an embodiment of this disclosure.

[0183] As shown in Figure 5, this mechanical characterization method includes steps 510-560.

[0184] Step 510, Data Collection and Data Classification

[0185] Specifically, it may include the following steps 511 to 512:

[0186] Step 511: For any one of the multiple monitoring points in the target mining area, collect the monitoring data corresponding to that monitoring point. The monitoring data includes the location of the monitoring point, the measured stress (referred to as the first value in this disclosure), and the measured strain (referred to as the second value in this disclosure).

[0187] Step 512: Data Classification. Based on the actual situation of the data, it is divided into four categories, labeled A, B, C, and D. Category A data includes data where both measured stress and strain are present, and the noise levels for both are below 10%. Category B data includes data where either measured stress or strain is missing, and the noise levels for both are below 10%. Data with missing measured stress is labeled B-1, and data with missing measured strain is labeled B-2. Category C data includes data where both measured stress and strain are present, and the noise levels for both measured stress and / or measured strain are above 10%. Category D data includes data where either measured stress or measured strain is missing, and the noise levels for the present measured stress or measured strain are above 10%. Data with missing measured stress is labeled D-1, and data with missing measured strain is labeled D-2.

[0188] Step 520: Establish the finite element geometric model

[0189] A finite element geometric model of the actual project (i.e., the target mining area) is established. This model defines nodes, the topological relationships between nodes, the shape functions between nodes, the derivative matrices of the shape functions, and the weights of each node. During the model creation, each monitoring point has a corresponding node within the finite element geometric model.

[0190] Step 530, Data Processing for Category B

[0191] Specifically, it may include the following steps 531 to 534:

[0192] Step 531: For any monitoring data in Category B data, obtain the constitutive model (referred to as the first constitutive model in this disclosure) and material parameters (referred to as the first material parameters in this disclosure) corresponding to the monitoring point in the target mining area. Relevant personnel can estimate the possible constitutive model and material parameters of the monitoring point based on engineering experience. The constitutive model can be, for example, a linear elastic constitutive model, and the material parameters can include, for example, Young's modulus and Poisson's ratio.

[0193] Step 532: Construct the material stiffness matrix based on the constitutive model and material parameters.

[0194] For example, assuming the constitutive model is a linear elastic constitutive model, the Young's modulus of the material is E, and the Poisson's ratio is ν, then the Lamé constant λ of the material at the monitoring point is as shown in formula (1), the shear modulus μ is as shown in formula (2), and the material stiffness matrix C is as shown in formula (3).

[0195] Step 533: Process missing strain measurement data. Traverse the B-1 class of data, assuming the measured stress is a, determine and fill in the corresponding measured strain b as: b = C -1 ×a; (9)

[0196] Step 534: Process missing measured stress data. Traverse the B-2 type data, assuming the measured strain is b, determine and fill in the corresponding measured stress a as: a = C -1 ×b; (10)

[0197] Step 540, C-type data processing

[0198] Specifically, it may include the following steps 541 to 543:

[0199] Step 541, Construction: Using the material stiffness matrix established in Step 530, finite element calculations are performed based on the finite element geometric model established in Step 520. Random boundary conditions can be constructed within a reasonable range. Thus, based on the material stiffness matrix, the finite element geometric model, and the boundary conditions, stress-strain pairs for the corresponding monitoring points in Class C data can be constructed. It should be noted that the number of stress-strain pairs constructed for any given monitoring point can be determined by the number of Class C data points for that monitoring point. For example, the number of stress-strain pairs constructed for a monitoring point can be 1 to 2 times the number of Class C data points for that monitoring point. Furthermore, the specific value of this multiple depends on the noise level of the data; the greater the data noise, the higher the value of this multiple.

[0200] Step 542, Data Appendage (also known as Data Supplementation): For any monitoring point, the constructed stress-strain pair of the monitoring point is appended to the corresponding Class C data of the monitoring point.

[0201] Step 543, Random Arrangement: Randomly arrange the C-class data after the addition of the constructed data, so that the data is evenly mixed and distributed in the storage space of the C-class data.

[0202] Step 550, D-type data processing

[0203] First, process the D-1 and D-2 data according to the processing methods for B-1 and B-2 data in step 530, respectively. Then, add constructed data according to the processing method for C-1 data in step 540. For any monitoring point, the amount of constructed data for the D-1 data at that monitoring point is generally 0.8 to 0.9 times that of the constructed data for the C-1 data at that monitoring point.

[0204] Step 560, Data-Driven Computation

[0205] Specifically, it may include the following steps 561 to 564:

[0206] Step 561: Rearrange the data: For any monitoring point, establish a corresponding dataset. Specifically, merge and store the four types of data (A, B, C, and D) corresponding to the monitoring point after data processing in the corresponding dataset, and randomly rearrange them so that the four types of data are randomly and evenly distributed in the corresponding dataset.

[0207] It should be noted that in this disclosure, each stress-strain pair in the dataset is denoted as the first state pair value.

[0208] Step 562: For a certain physical state, randomly select the "stress-strain" pair of the corresponding monitoring point in the physical state from the dataset corresponding to any monitoring point, and use the selected "stress-strain" pair of the corresponding monitoring point in the physical state as the candidate state pair value of the monitoring point in the physical state.

[0209] Among them, the candidate state pair values ​​include the third value of the stress state and the fourth value of the strain state.

[0210] Step 563: Based on the finite element geometric model and the candidate state pair values ​​of each monitoring point in the physical state, determine the target state pair value of each monitoring point in the physical state according to formula (6).

[0211] The target state values ​​include the third value of the stress state and the fourth value of the strain state.

[0212] Step 564, Error Check:

[0213] A first coefficient is determined based on the distance between the third value of the candidate state pair and the fifth value of the corresponding target state pair at each monitoring point under the physical state. A second coefficient is determined based on the distance between the fourth value of the candidate state pair and the sixth value of the corresponding target state pair at each monitoring point under the physical state. If the first coefficient is less than a first set threshold and the second coefficient is less than a second set threshold, then the target state pair at each monitoring point under the physical state can be determined as the optimal state pair at the corresponding monitoring point under the physical state (also known as the global state pair). At this point, the process of determining the optimal state pair under this physical state can be exited, and the process of determining the optimal state pair under the next physical state can be executed until the process of determining the optimal state pair under all physical states is completed.

[0214] Optionally, if the first coefficient is not less than the first set threshold and / or the second coefficient is not less than the second set threshold, it can be determined that the target state pair value of each monitoring point under the physical state is not the optimal state pair value of the corresponding monitoring point under the physical state; at this time, steps 562-564 can be executed repeatedly until the optimal state pair value under the physical state is determined.

[0215] In the field of coal mine stress monitoring, methods such as fuzzy mathematics, artificial neural networks, big data analysis, and multi-source data fusion are currently used to reduce monitoring data noise and data loss. However, these methods lack the support of mechanical principles and cannot fully solve practical engineering problems.

[0216] In summary, the mechanical characterization method disclosed herein can effectively reduce the noise level of monitoring data and reduce the occurrence of missing data. It adopts the basic theory of data-driven mechanics as support, so that the calculated global stress state conforms to the basic principles of computational mechanics, which can effectively support the prevention and control of coal mine rockburst disasters and the development of deep mining.

[0217] The mechanical characterization method disclosed herein is applicable to scenarios where data is missing, thus having strong applicability. Furthermore, by constructing data using the finite element method, it reduces errors caused by data noise, thereby enhancing the performance of digitally driven mechanical characterization in practical engineering.

[0218] Corresponding to the mechanical characterization method provided in the embodiments of Figures 1 to 4 above, this disclosure also provides a mechanical characterization device. Since the mechanical characterization device provided in the embodiments of this disclosure corresponds to the mechanical characterization method provided in the embodiments of Figures 1 to 4 above, the implementation of the mechanical characterization method is also applicable to the mechanical characterization device provided in the embodiments of this disclosure, and will not be described in detail in the embodiments of this disclosure.

[0219] Figure 6 is a schematic diagram of the structure of a mechanical characterization device provided in an embodiment of this disclosure.

[0220] As shown in Figure 6, the mechanical characterization device 600 may include: an acquisition module 601, a construction module 602, a processing module 603, and a determination module 604.

[0221] The acquisition module 601 is used to acquire multiple initial state pairs corresponding to any one of the multiple monitoring points in the target mining area; wherein the initial state pairs include a first value of stress state and a second value of strain state.

[0222] Module 602 is used to construct the finite element geometric model corresponding to the target mining area; wherein, the finite element geometric model includes multiple nodes, and each monitoring point has a corresponding node in the finite element geometric model.

[0223] The processing module 603 is used to perform data preprocessing on multiple initial state pairs corresponding to any monitoring point to obtain multiple first state pairs corresponding to the monitoring point.

[0224] The determination module 604 is used to determine the optimal state pair value corresponding to each monitoring point based on the finite element geometric model and multiple first state pair values ​​corresponding to each monitoring point, using a data-driven algorithm.

[0225] In one possible implementation of this disclosure, the processing module 603 is configured to: for any monitoring point, divide multiple initial state pairs corresponding to the monitoring point according to the data category to which each initial state pair belongs, so as to obtain at least one subset corresponding to the monitoring point; for any subset corresponding to the monitoring point, perform data preprocessing on the initial state pairs in the subset based on the data category corresponding to the subset, using a corresponding data preprocessing method, so as to obtain a first state pair corresponding to the monitoring point.

[0226] In one possible implementation of this disclosure, the data category includes at least one of a first category, a second category, a third category, and a fourth category, wherein:

[0227] The first category indicates that both the first and second values ​​exist in the initial state pair corresponding to the first category, and the noise levels of both the first and second values ​​in the corresponding initial state pair are less than the set threshold.

[0228] The second category indicates that the first or second value is missing in the corresponding initial state pair, and the noise level of the first or second value present in the corresponding initial state pair is less than a set threshold.

[0229] The third category indicates that both the first and second values ​​exist in the initial state pair corresponding to the third category, and the noise level of the first and / or second values ​​in the corresponding initial state pair is not less than the set threshold.

[0230] The fourth category indicates that the first or second value is missing in the corresponding initial state pair, and the noise level of the first or second value present in the corresponding initial state pair is not less than a set threshold.

[0231] In one possible implementation of this disclosure, the processing module 603 is configured to: for any subset corresponding to a monitoring point, in response to the data category corresponding to the subset being a first category, determine the initial state pair values ​​in the subset as the first state pair values ​​corresponding to the monitoring point; in response to the data category corresponding to the subset being a second category, perform first data filling on the initial state pair values ​​in the subset using a missing value filling method to obtain the first state pair values ​​corresponding to the monitoring point; in response to the data category corresponding to the subset being a third category, perform first data supplementation on the initial state pair values ​​in the subset using a data construction method to obtain the first state pair values ​​corresponding to the monitoring point; and in response to the data category corresponding to the subset being a fourth category, process the initial state pair values ​​in the subset using both the missing value filling method and the data construction method to obtain the first state pair values ​​corresponding to the monitoring point.

[0232] In one possible implementation of this disclosure, the processing module 603 is configured to: in response to the data category corresponding to the subset being a second category, obtain a first constitutive model and a first material parameter corresponding to the monitoring point in the target mining area; wherein the first material parameter matches the first constitutive model; construct a material stiffness matrix corresponding to the monitoring point based on the first constitutive model and the first material parameter corresponding to the monitoring point; for any initial state pair value in the subset, determine a target value in the initial state pair value based on the material stiffness matrix corresponding to the monitoring point; wherein the target value is a missing first value or a missing second value; perform a fill-in process on the initial state pair value based on the target value, and determine the filled initial state pair value as the first state pair value corresponding to the monitoring point.

[0233] In one possible implementation of this disclosure, the processing module 603 is configured to: in response to the data category corresponding to the subset being the third category, obtain the second constitutive model and the second material parameters corresponding to the monitoring point in the target mining area, and construct the first boundary condition corresponding to the monitoring point; wherein the second material parameters match the second constitutive model; based on the second constitutive model, the second material parameters, and the first boundary condition corresponding to the monitoring point, and the finite element geometric model, construct the second state pair value belonging to the subset using the finite element method; and determine the constructed second state pair value and the initial state pair value in the subset as the first state pair value corresponding to the monitoring point.

[0234] In one possible implementation of this disclosure, the processing module 603 is configured to: in response to the data category corresponding to the subset being the fourth category, perform second data filling on the initial state pair values ​​in the subset using a method for filling missing values ​​to obtain a third state pair value; construct a fourth state pair value belonging to the subset using a data construction method; and determine both the third state pair value and the fourth state pair value as the first state pair value corresponding to the monitoring point.

[0235] In one possible implementation of this disclosure, each first state pair value has a corresponding physical state, and there is at least one physical state; the determining module 604 is configured to: for any physical state, based on the finite element geometric model and multiple first state pairs values ​​of each monitoring point in the physical state, perform a multi-round iterative process to obtain the optimal state pair value of each monitoring point in the physical state; for any round of iterative process, obtain candidate state pairs values ​​of each monitoring point in the physical state from the multiple first state pairs values ​​of each monitoring point in the physical state; wherein, the candidate state pairs values ​​include a third value of the stress state and a fourth value of the strain state; based on the candidate state pairs values ​​of each monitoring point in the physical state and the finite element geometric model, adopt... Using a data-driven algorithm, the target state pair values ​​for each monitoring point under the current physical state are determined. These target state pair values ​​include the fifth value of the stress state and the sixth value of the strain state. Based on the distance between the candidate state pair values ​​and the corresponding target state pair values ​​for each monitoring point under the current physical state, it is determined whether the target state pair value for each monitoring point under the current physical state is the optimal state pair value for that monitoring point. If the target state pair value for each monitoring point under the current physical state is the optimal state pair value for that monitoring point, the iteration process stops. If the target state pair value for each monitoring point under the current physical state is not the optimal state pair value for that monitoring point, the next iteration process is executed.

[0236] In one possible implementation of this disclosure, the determining module 604 is configured to: determine a first coefficient based on the distance between the third value of the candidate state pair values ​​of each monitoring point in the current round under physical conditions and the fifth value of the corresponding target state pair values; determine a second coefficient based on the distance between the fourth value of the candidate state pair values ​​of each monitoring point in the current round under physical conditions and the sixth value of the corresponding target state pair values; and determine the target state pair value of each monitoring point in the current round under physical conditions as the optimal state pair value of the corresponding monitoring point under physical conditions in response to the first coefficient being less than a first preset threshold and the second coefficient being less than a second preset threshold.

[0237] To implement the above embodiments, this disclosure also proposes an electronic device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the mechanical characterization method proposed in one aspect of the present disclosure.

[0238] To implement the above embodiments, this disclosure also proposes a non-transitory computer-readable storage medium storing a computer program that, when executed by a processor, implements the mechanical characterization method proposed in one aspect of the present disclosure.

[0239] To implement the above embodiments, this disclosure also proposes a computer program product that, when the instructions in the computer program product are executed by a processor, performs the mechanical characterization method as proposed in one aspect of the embodiments of this disclosure.

[0240] The collection, storage, use, processing, transmission, provision, and disclosure of user personal information involved in this disclosure all comply with the provisions of relevant laws and regulations and do not violate public order and good morals.

[0241] It should be noted that personal information collected from users should be used for legitimate and reasonable purposes and should not be shared or sold outside of these legitimate uses. Furthermore, such collection / sharing should only be conducted after receiving the user's informed consent, including but not limited to notifying the user to read the user agreement / user notice and sign an agreement / authorization that includes authorization of relevant user information before the user uses the function. In addition, any necessary steps must be taken to protect and safeguard access to such personal information data and ensure that others with access to personal information data comply with their privacy policies and procedures.

[0242] This disclosure is intended to provide implementation schemes for users to selectively prevent the use or access to their personal information data. Specifically, this disclosure is intended to provide hardware and / or software to prevent or block access to such personal information data. Once personal information data is no longer needed, risks can be minimized by restricting data collection and deleting data. Furthermore, where applicable, such personal information is de-identified to protect user privacy.

[0243] In the foregoing descriptions of the embodiments, the terms "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., refer to specific features, structures, materials, or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of this disclosure. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0244] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this disclosure, "a plurality of" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0245] Any process or method description in the flowchart or otherwise herein can be understood as representing a module, segment, or portion of code comprising one or more executable instructions for implementing custom logic functions or processes, and the scope of preferred embodiments of this disclosure includes additional implementations in which functions may be performed not in the order shown or discussed, including substantially simultaneously or in reverse order depending on the functions involved, as will be understood by those skilled in the art to which embodiments of this disclosure pertain.

[0246] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-included system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device. More specific examples (a non-exhaustive list) of computer-readable media include: an electrical connection having one or more wires (electronic device), a portable computer disk drive (magnetic device), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Alternatively, the computer-readable medium may be paper or other suitable media on which the program can be printed, since the program can be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in a computer memory.

[0247] It should be understood that various parts of this disclosure can be implemented using hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented using software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0248] Those skilled in the art will understand that all or part of the steps of the methods in the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, the program includes one or a combination of the steps of the method embodiments.

[0249] Furthermore, the functional units in the various embodiments of this disclosure can be integrated into a processing module, or each unit can exist physically separately, or two or more units can be integrated into a module. The integrated module can be implemented in hardware or as a software functional module. If the integrated module is implemented as a software functional module and sold or used as an independent product, it can also be stored in a computer-readable storage medium.

[0250] The storage medium mentioned above can be a read-only memory, a disk, or an optical disk, etc. Although embodiments of the present disclosure have been shown and described above, it is to be understood that the above embodiments are exemplary and should not be construed as limiting the present disclosure. Those skilled in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of the present disclosure.

Claims

1. A method of mechanical characterisation, wherein, The method comprises: For any of the monitoring points in the target mining area, obtaining a plurality of initial state pair values corresponding to the monitoring point; wherein the initial state pair value comprises a first value of a stress state and a second value of a strain state; and Constructing a finite element geometric model corresponding to the target mining area; wherein the finite element geometric model comprises a plurality of nodes, and each monitoring point has a corresponding node in the finite element geometric model; and For any of the monitoring points, data preprocessing is performed on the plurality of initial state pair values corresponding to the monitoring point to obtain a plurality of first state pair values corresponding to the monitoring point; and Based on the finite element geometric model and the plurality of first state pair values corresponding to each monitoring point, a data-driven algorithm is used to determine the optimal state pair value corresponding to each monitoring point.

2. The method of claim 1, wherein, The data preprocessing performed on the plurality of initial state pair values corresponding to any of the monitoring points to obtain a plurality of first state pair values corresponding to the monitoring point comprises: For any of the monitoring points, according to the data category to which each initial state pair value corresponding to the monitoring point belongs, the plurality of initial state pair values corresponding to the monitoring point are divided to obtain at least one subset corresponding to the monitoring point; and For any of the subsets corresponding to the monitoring point, based on the data category corresponding to the subset, the initial state pair values in the subset are data preprocessed using the corresponding data preprocessing method to obtain the first state pair value corresponding to the monitoring point.

3. The method of claim 2, wherein, The data category comprises at least one of a first category, a second category, a third category and a fourth category, wherein: The first category indicates that both the first value and the second value exist in the corresponding initial state pair value, and the noise levels of the first value and the second value in the corresponding initial state pair value are less than a set threshold; The second category indicates that the first value or the second value is missing in the corresponding initial state pair value, and the noise level of the existing first value or existing second value in the corresponding initial state pair value is less than the set threshold; The third category indicates that both the first value and the second value exist in the corresponding initial state pair value, and the noise level of the first value and / or the second value in the corresponding initial state pair value is not less than the set threshold; The fourth category indicates that the first value or the second value is missing in the corresponding initial state pair value, and the noise level of the existing first value or existing second value in the corresponding initial state pair value is not less than the set threshold.

4. The method of claim 3, wherein, The data preprocessing performed on the initial state pair values in any of the subsets corresponding to the monitoring point based on the data category corresponding to the subset to obtain the first state pair value corresponding to the monitoring point comprises: For any of the subsets corresponding to the monitoring point, in response to the data category corresponding to the subset being the first category, the initial state pair values in the subset are determined as the first state pair values corresponding to the monitoring point; and In response to the data category corresponding to the subset being the second category, initial state pair values in the subset are first data filled by using a missing value filling method to obtain first state pair values corresponding to the monitoring point; and In response to the data category corresponding to the subset being the third category, initial state pair values in the subset are first data supplemented by using a data construction method to obtain first state pair values corresponding to the monitoring point; and In response to the data category corresponding to the subset being the fourth category, initial state pair values in the subset are processed by using the missing value filling method and the data construction method to obtain first state pair values corresponding to the monitoring point.

5. The method of claim 4, wherein, The response to the data category corresponding to the subset being the second category, the initial state pair value in the subset is first data filled by using a missing value filling method to obtain the first state pair value corresponding to the monitoring point, comprising: In response to the data category corresponding to the subset being the second category, the first constitutive model and the first material parameter corresponding to the monitoring point in the target mining area are obtained; wherein the first material parameter matches the first constitutive model; and According to the first constitutive model and the first material parameter corresponding to the monitoring point, the material stiffness matrix corresponding to the monitoring point is constructed; For any initial state pair value in the subset, based on the material stiffness matrix corresponding to the monitoring point, a target value in the initial state pair value is determined; wherein the target value is the missing first value or the missing second value; and Based on the target value, the initial state pair value is filled and processed, and the initial state pair value after filling and processing is determined as the first state pair value corresponding to the monitoring point.

6. The method of any one of claims 4-5, wherein, The response to the data category corresponding to the subset being the third category, the initial state pair value in the subset is first data supplemented by using a data construction method to obtain the first state pair value corresponding to the monitoring point, comprising: In response to the data category corresponding to the subset being the third category, the second constitutive model and the second material parameter corresponding to the monitoring point in the target mining area are obtained, and the first boundary condition corresponding to the monitoring point is constructed; wherein the second material parameter matches the second constitutive model; and Based on the second constitutive model, the second material parameter and the first boundary condition corresponding to the monitoring point, and the finite element geometric model, a second state pair value belonging to the subset is constructed by using a finite element method; and The constructed second state pair value and the initial state pair value in the subset are both determined as the first state pair value corresponding to the monitoring point.

7. The method of any one of claims 4-6, wherein, The response to the data category corresponding to the subset being the fourth category, the initial state pair value in the subset is processed by using the missing value filling method and the data construction method to obtain the first state pair value corresponding to the monitoring point, comprising: In response to the data category corresponding to the subset being the fourth category, performing second data filling on the initial state pair values in the subset by using the method for filling missing values to obtain third state pair values; and constructing fourth state pair values belonging to the subset by using a data construction method; and determining the third state pair values and the fourth state pair values as the first state pair values corresponding to the monitoring points.

8. The method of any one of claims 1-7, wherein, Each of the first state pair values has a corresponding physical state, and the physical state is at least one; The data-driven algorithm is used to determine the optimal state pair values corresponding to each of the monitoring points based on the finite element geometric model and the plurality of first state pair values corresponding to each of the monitoring points, including: For any physical state, a plurality of rounds of iteration processes are performed based on the finite element geometric model and the plurality of first state pair values of each of the monitoring points in the physical state to obtain the optimal state pair values of each of the monitoring points in the physical state; and For any round of the iteration process, candidate state pair values of each of the monitoring points in the physical state in the round are obtained from the plurality of first state pair values of each of the monitoring points in the physical state; wherein the candidate state pair values include a third value of the stress state and a fourth value of the strain state; and The data-driven algorithm is used to determine target state pair values of each of the monitoring points in the physical state in the round based on the candidate state pair values of each of the monitoring points in the physical state in the round and the finite element geometric model; wherein the target state pair values include a fifth value of the stress state and a sixth value of the strain state; and Based on the distance between the candidate state pair values of each of the monitoring points in the physical state in the round and the corresponding target state pair values, it is determined whether the target state pair values of each of the monitoring points in the physical state in the round are the optimal state pair values of the corresponding monitoring points in the physical state; and In response to the target state pair values of each of the monitoring points in the physical state in the round being the optimal state pair values of the corresponding monitoring points in the physical state, the iteration process is stopped; and In response to the target state pair values of each of the monitoring points in the physical state in the round not being the optimal state pair values of the corresponding monitoring points in the physical state, the next round of iteration process is performed.

9. The method of any one of claims 1-8, wherein, The distance between the candidate state pair values of each of the monitoring points in the physical state in the round and the corresponding target state pair values, including: a first coefficient is determined based on the distance between the third value in the candidate state pair values of each of the monitoring points in the physical state in the round and the fifth value in the corresponding target state pair values; and a second coefficient is determined based on the distance between the fourth value in the candidate state pair values of each of the monitoring points in the physical state in the round and the sixth value in the corresponding target state pair values; and In response to the first coefficient being less than a first set threshold and the second coefficient being less than a second set threshold, determining a target state pair value of each of the monitoring points in the physical state as an optimal state pair value of the corresponding monitoring point in the physical state.

10. A mechanical characterisation apparatus, wherein, The apparatus comprises: an acquisition module configured to acquire, for any one of a plurality of monitoring points in a target mining area, a plurality of initial state pair values corresponding to the monitoring point; wherein the initial state pair values comprise a first value of a stress state and a second value of a strain state; and a construction module configured to construct a finite element geometric model corresponding to the target mining area; wherein the finite element geometric model comprises a plurality of nodes, and each of the monitoring points has a corresponding node in the finite element geometric model; and a processing module configured to, for any one of the monitoring points, perform data preprocessing on the plurality of initial state pair values corresponding to the monitoring point to obtain a plurality of first state pair values corresponding to the monitoring point; and a determination module configured to determine, based on the finite element geometric model and the plurality of first state pair values corresponding to each of the monitoring points, an optimal state pair value corresponding to each of the monitoring points by using a data-driven algorithm.

11. The apparatus of claim 10, wherein, The processing module is further configured to: for any one of the monitoring points, divide the plurality of initial state pair values corresponding to the monitoring point according to a data category to which each of the initial state pair values corresponding to the monitoring point belongs, to obtain at least one subset corresponding to the monitoring point; and for any one of the subsets corresponding to the monitoring point, perform data preprocessing on the initial state pair values in the subset by using a corresponding data preprocessing method based on the data category corresponding to the subset, to obtain the first state pair values corresponding to the monitoring point. The data category comprises at least one of a first category, a second category, a third category, and a fourth category, wherein:

12. The apparatus of claim 11, wherein, the first category indicates that both the first value and the second value exist in the corresponding initial state pair value, and the noise levels of the first value and the second value in the corresponding initial state pair value are less than a set threshold; the second category indicates that either the first value or the second value is missing in the corresponding initial state pair value, and the noise level of the existing first value or existing second value in the corresponding initial state pair value is less than the set threshold; the third category indicates that both the first value and the second value exist in the corresponding initial state pair value, and the noise level of the first value and / or the second value in the corresponding initial state pair value is not less than the set threshold; and the fourth category indicates that either the first value or the second value is missing in the corresponding initial state pair value, and the noise level of the existing first value or existing second value in the corresponding initial state pair value is not less than the set threshold. The processing module is further configured to:

13. The apparatus of claim 12, wherein, for any one of the subsets corresponding to the monitoring point, in response to the data category corresponding to the subset being the first category, determining the initial state pair values in the subset as the first state pair values corresponding to the monitoring point; and for any one of the subsets corresponding to the monitoring point, in response to the data category corresponding to the subset being the second category, determining the initial state pair values in the subset as the first state pair values corresponding to the monitoring point. ​ In response to the data category corresponding to the subset being the second category, performing first data filling on the initial state pair value in the subset by using a missing value filling method to obtain a first state pair value corresponding to the monitoring point; and In response to the data category corresponding to the subset being the third category, performing first data filling on the initial state pair value in the subset by using a data construction method to obtain a first state pair value corresponding to the monitoring point; and In response to the data category corresponding to the subset being the fourth category, performing processing on the initial state pair value in the subset by using the missing value filling method and the data construction method to obtain a first state pair value corresponding to the monitoring point.

14. The apparatus of claim 13, wherein, The processing module is further configured to: In response to the data category corresponding to the subset being the second category, obtaining a first constitutive model and a first material parameter corresponding to the monitoring point in the target mining area; wherein the first material parameter matches the first constitutive model; and constructing a material stiffness matrix corresponding to the monitoring point according to the first constitutive model and the first material parameter corresponding to the monitoring point; for any initial state pair value in the subset, determining a target value in the initial state pair value based on the material stiffness matrix corresponding to the monitoring point; wherein the target value is the missing first value or the missing second value; and based on the target value, performing filling processing on the initial state pair value, and determining the initial state pair value after the filling processing as the first state pair value corresponding to the monitoring point.

15. The apparatus of any of claims 13-14, wherein, The processing module is further configured to: In response to the data category corresponding to the subset being the third category, obtaining a second constitutive model and a second material parameter corresponding to the monitoring point in the target mining area, and constructing a first boundary condition corresponding to the monitoring point; wherein the second material parameter matches the second constitutive model; and based on the second constitutive model, the second material parameter, and the first boundary condition corresponding to the monitoring point, and the finite element geometric model, constructing a second state pair value belonging to the subset by using a finite element method; and determining the constructed second state pair value and the initial state pair value in the subset as the first state pair value corresponding to the monitoring point.

16. The apparatus of any one of claims 13-15, wherein, The processing module is further configured to: In response to the data category corresponding to the subset being the fourth category, performing second data filling on the initial state pair value in the subset by using the missing value filling method to obtain a third state pair value; and constructing a fourth state pair value belonging to the subset by using a data construction method; and determining the third state pair value and the fourth state pair value as the first state pair value corresponding to the monitoring point.

17. The apparatus of any one of claims 10-16, wherein, Each first state pair value has a corresponding physical state, and the physical state is at least one; the determining module is further configured to: for any physical state, performing a plurality of rounds of iteration processes based on the finite element geometric model and a plurality of first state pair values of each monitoring point in the physical state to obtain an optimal state pair value of each monitoring point in the physical state; and For any round of the iterative process, obtain a candidate state pair value of each of the monitoring points in the physical state from a plurality of the first state pair values of each of the monitoring points in the physical state; wherein the candidate state pair value comprises a third value of the stress state and a fourth value of the strain state; and Based on the candidate state pair value of each of the monitoring points in the physical state and the finite element geometric model, determine a target state pair value of each of the monitoring points in the physical state by using a data-driven algorithm; wherein the target state pair value comprises a fifth value of the stress state and a sixth value of the strain state; and Based on the distance between the candidate state pair value of each of the monitoring points in the physical state and the corresponding target state pair value, determine whether the target state pair value of each of the monitoring points in the physical state is the optimal state pair value of the corresponding monitoring point in the physical state; and In response to the target state pair value of each of the monitoring points in the physical state being the optimal state pair value of the corresponding monitoring point in the physical state, stop the iterative process; and In response to the target state pair value of each of the monitoring points in the physical state not being the optimal state pair value of the corresponding monitoring point in the physical state, perform the next round of the iterative process.

18. The apparatus of any one of claims 10-17, wherein, The determination module is further configured to: determine a first coefficient based on the distance between the third value in the candidate state pair value of each of the monitoring points in the physical state and the fifth value in the corresponding target state pair value; and determine a second coefficient based on the distance between the fourth value in the candidate state pair value of each of the monitoring points in the physical state and the sixth value in the corresponding target state pair value; and In response to the first coefficient being less than a first set threshold value and the second coefficient being less than a second set threshold value, determine that the target state pair value of each of the monitoring points in the physical state is the optimal state pair value of the corresponding monitoring point in the physical state. The computer program product comprises a computer readable storage medium having stored thereon instructions that, when executed by a processor, cause the processor to perform the mechanical characterization method according to any one of claims 1-9. The computer program product comprises a computer readable storage medium having stored thereon instructions that, when executed by a processor, cause the processor to perform the mechanical characterization method according to any one of claims 1-9.

19. An electronic device, comprising: The computer program product comprises a computer readable storage medium having stored thereon instructions that, when executed by a processor, cause the processor to perform the mechanical characterization method according to any one of claims 1-9. The computer program product comprises a computer readable storage medium having stored thereon instructions that, when executed by a processor, cause the processor to perform the mechanical characterization method according to any one of claims 1-9. ​ 20. A non-transitory computer readable storage medium storing a computer program, wherein, ​ 21. A computer program product, wherein, ​

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