Material tension and compression modulus evolution law inversion method based on machine learning

Abstract

The invention discloses a material tension and compression modulus evolution law inversion method based on machine learning. The method comprises the following steps: carrying out a four-point bending experiment on a material sample; displacement data of deformation field data in the surface deformation information form a two-dimensional numerical matrix, and discrete cosine transform is utilized to transform the numerical matrix to obtain a transformed frequency domain data matrix; determining the size of the main characteristic matrix according to an accumulated energy retention rate principle, cutting the transformed frequency domain data matrix to obtain the main characteristic matrix, filling the main characteristic matrix to the original size by using zero, and converting the main characteristic matrix back to a spatial domain through inverse transformation to obtain a noise-reduced displacement matrix; after initial material moduli of the material sample in different stress states are preset, a neural network model is built; constructing a model loss function; and optimizing neural network model parameters. The neural network model is used for replacing the role of a finite element program in a parameter inversion method, the parameter inversion speed is greatly increased, and meanwhile, the material moduli in different stress states are solved through inversion.

Description

Technical Field

[0001] The present invention relates to the technical field of solid mechanics, and more specifically, to an inversion method for the evolution law of the tensile and compressive moduli of materials based on machine learning. Background Art

[0002] During the actual working process of engineering structures, materials are extremely prone to damage due to the action of external loads. The accumulation and evolution of damage will significantly reduce the mechanical properties of materials, and even cause damage to the corresponding components, thereby affecting the safe operation of the overall structure. In solid mechanics, the measurement of Young's modulus is of great significance for characterizing the damage of materials. Therefore, studying the evolution and distribution of the modulus of materials under load has a positive effect on ensuring the safe operation of engineering structures.

[0003] In the current field of solid mechanics, the main methods for determining the unknown modulus of materials under load are experimental testing methods and inversion methods. The experimental testing method is based on traditional mechanical experiments. The material sample is made into a standard part and strain gauges are arranged. A uniaxial tensile or compressive load is applied to the standard part until the material fails. By measuring the stress-strain relationship of the material during the loading process, the modulus of the material is calculated and determined. However, this method can only measure the modulus of the material under a single stress state, and it is not applicable to the determination of the modulus of the material under different stress states of tension and compression at the same time. In uniaxial tensile or compressive tests, the standard part is prone to slipping or breaking due to improper pre-tightening force at the clamping end, or premature failure of the specimen caused by eccentric tension. These problems will affect the accuracy of the experimental results. Moreover, for brittle or quasi-brittle materials, when only minor deformation occurs before failure, the requirements for deformation measurement technology are relatively high. The inversion methods are mainly divided into the virtual field method and the finite element model correction method, and these methods can well overcome or avoid the above disadvantages. The inversion method uses the measured data as a constraint, uses numerical methods for optimization, and finally inversely obtains the required material parameters by continuously adjusting the variables in the model. The virtual field method selects several virtual displacement fields that satisfy the displacement boundary conditions and continuity conditions according to the number of material parameters to be solved, and establishes a relationship between the measured strain, the external load, and the unknown material parameters by the virtual work principle for solution. The virtual field method is a method for inversely identifying the mechanical parameters of materials based on the full-field deformation measurement results, and has a high calculation efficiency. It has relatively strict requirements for the initial assumption conditions, such as the virtual displacement assumption that needs to satisfy the plane stress, plane strain, and mechanical constraint conditions, which are often difficult to meet in experiments simulating real working conditions. Therefore, its universality and practicality are relatively low.

[0004] The finite element model correction method is used to establish a finite element simulation model corresponding to the experiment, apply the same load and displacement boundary conditions, and construct an objective function between the calculated deformation field data and the measured deformation field data. The material parameters to be determined are iteratively optimized through an optimization algorithm to make the finite element calculation results of the model as consistent with the real physical state as possible, so as to inversely obtain the material parameters. However, this method has the following disadvantages: the finite element calculation is prone to non-convergence during the iteration process, resulting in the interruption of the inversion process; the finite element program needs to be repeatedly called during the inversion process, which is very time-consuming; during the experimental loading process, the deformation measurement of the specimen is easily affected by noise, and when the load level is low, the noise effect is obvious, thus significantly affecting the inversion accuracy. Therefore, it is a technical problem that urgently needs to be solved in this field.

[0005] Chinese Patent Document 1 (Application No.: 2024113732590, Application Date: September 29, 2024) discloses a method for detecting the tensile and compressive properties of pipeline cold insulation materials. Figure 1 It is a method flow chart of the method for detecting the tensile and compressive properties of pipeline cold insulation materials provided by Chinese Patent Document 1; referring to Figure 1 As shown, the tensile and compressive property detection method is as follows: detection preparation, sampling from the pipeline cold insulation materials according to the standard method. When sampling for detection, the sampling points should avoid the defect area and be evenly distributed in the cold insulation layer; data test execution, through the test execution module, detect the texture strength on the pipeline surface, as well as the tensile and compressive tests of the structure; data analysis and processing, based on the test execution module, output a detection analysis report on the tensile and compressive properties of the pipeline cold insulation materials through the data analysis and evaluation module. The data analysis and evaluation module includes an image texture strength evaluation unit, a predicted tensile strength unit under cold insulation performance, and a pressure stability evaluation unit; data upload, upload the data collected by the test execution module to the data acquisition terminal. Using the above scheme cannot solve the above technical problems either.

[0006] Chinese Patent Document 2 (Application No.: 2024109618291, Application Date: July 18, 2024) discloses a method for inverse analysis of mechanical parameters of deep rock masses based on multi-source exploration information, including the following steps: S1. Obtain rock mechanical parameters, which include uniaxial compressive strength of rock, cohesion of rock, and internal friction angle of rock; S2. Obtain rock mass structure parameters, which include rock mass integrity coefficient; S3. Obtain rock mass engineering parameters, which include tunnel burial depth, blasting disturbance coefficient, and groundwater influence correction coefficient; S4. Use the calculation model of the Hoek-Brown criterion to calculate the corresponding rock mass mechanical parameters according to the rock mechanical parameters, rock mass structure parameters, and rock mass engineering parameters. The rock mass mechanical parameters include uniaxial compressive strength of rock mass, elastic modulus of rock mass, cohesion of rock mass, and internal friction angle of rock mass; S5. Take the rock mechanical parameters, rock mass structure parameters, and rock mass engineering parameters as input information, and the corresponding rock mass mechanical parameters as output information to construct a sample database, and establish a deep learning neural network model. Use the sample database to train the model to obtain an inverse analysis model of deep rock mass mechanical parameters; S6. Use the inverse analysis model of deep rock mass mechanical parameters to inverse the deep rock mass mechanical parameters. This is essentially a data-driven method that relies on multi-source field data and requires a large amount of data sets for model training, belonging to a data-intensive method; in addition, it is specifically designed for deep rock masses (such as tunnel engineering) and emphasizes the adaptability of the actual construction scenario. Adopting the above technical solution cannot solve the above technical problems. Summary of the Invention

[0007] In view of this, the present invention provides a method for inverse analysis of the evolution law of material tensile and compressive moduli based on machine learning to solve the problems in the prior art that in the finite element calculation during the iteration process, it is easy to diverge, resulting in the interruption of the inverse analysis process; during the inverse analysis process, it is necessary to repeatedly call the finite element program, which is very time-consuming; during the experimental loading process, the deformation measurement of the specimen is easily affected by noise, and when the load level is low, the noise effect is obvious, thus significantly affecting the inverse analysis accuracy.

[0008] The present application provides a method for inverse analysis of the evolution law of material tensile and compressive moduli based on machine learning, which is characterized by including the following steps:

[0009] Conduct a four-point bending experiment on a material specimen, and use the digital image correlation method to obtain the surface deformation information of the material specimen during the loading process. The surface deformation information of the material specimen includes deformation field data, and define the plane coordinates of finite scattered points in the deformation field data and the displacement data corresponding thereto;

[0010] Construct a two-dimensional numerical matrix from the displacement data of the deformation field data in the surface deformation information, and use the discrete cosine transform to transform the numerical matrix to obtain the transformed frequency-domain data matrix; confirm the size of the main feature matrix according to the cumulative energy retention rate principle, and crop the transformed frequency-domain data matrix to obtain the main feature matrix. Fill the main feature matrix with zeros to its original size, and then transform it back to the spatial domain through inverse transformation to obtain the denoised displacement matrix;

[0011] The expression of the cumulative energy retention rate principle is:

[0012]

[0013] In the formula: M and N represent the size of the transformed frequency-domain data matrix, n represents the size of the main feature matrix obtained by cropping, P represents the energy retention rate, which is a decimal between 0 and 1; A ij 2 represents the energy of the elements in the frequency-domain data matrix before cropping, where i and j represent the row number and column number of the elements in the frequency-domain data matrix, represents the energy of the elements in the main feature matrix after cropping, where p and q represent the row number and column number of the elements in the main feature matrix after cropping;

[0014] After presetting the initial material modulus of the material specimen under different stress states, use the plane coordinates of the finite scattered points in the deformation field data as the input of the neural network, and perform non-linear transformation through the neural network model, using the displacement data of the corresponding scattered points as the network output data;

[0015] Construct a model loss function according to the control equation satisfied by the four-point bending problem, the model boundary conditions equivalent to the real experiment, and the error between the measured displacement data and the network output displacement data. Among them, the measured displacement data is the denoised displacement matrix, and the model loss function includes control term loss, boundary term loss and data term loss;

[0016] When using the minimum loss function in the model loss function to train and optimize the initial material modulus, by adjusting the weights of the control term loss, the boundary term loss and the data term loss, and simultaneously optimizing the hyperparameters of the neural network model until the preset convergence condition is met, and finally determine the target material modulus.

[0017] Optionally, the initial material modulus includes tensile modulus and compressive modulus;

[0018] Perform a four-point bending experiment on the material specimen, and use the digital image correlation method to obtain the surface deformation information of the material specimen during the loading process. The surface deformation information of the material specimen includes deformation field data. Define the plane coordinates of the finite scattered points in the deformation field data and the corresponding displacement data as follows:

[0019] A two-dimensional four-point bending model is established using finite element software, and the two-dimensional four-point bending model corresponds to the longitudinal section of the material specimen in the actual experiment;

[0020] Given material properties are assigned to the two-dimensional four-point bending model, including the tensile modulus, the compressive modulus, and the Poisson's ratio;

[0021] Boundary conditions and loads identical to those in the actual experiment are set;

[0022] Finite element mesh division is performed on the two-dimensional four-point bending model to obtain the deformation field data in the horizontal and vertical directions.

[0023] Optionally, the governing equation satisfied by the four-point bending problem is:

[0024]

[0025] In the formula: represents the partial derivative, E represents the material modulus, μ represents the Poisson's ratio, x and y represent coordinates respectively, u and v represent the displacements in the x and y directions respectively, f x and f y represent body forces;

[0026] The model boundary conditions equivalent to those in the actual experiment include displacement boundaries and stress boundaries, and their expressions are:

[0027]

[0028] In the formula, represents the actual displacement at the boundary, l represents the cosine value of the angle between the outer normal direction of the boundary and the x-axis, m represents the cosine value of the angle between the outer normal direction of the boundary and the y-axis, and represent the external forces acting on the boundary;

[0029] The network output data includes network output displacement data.

[0030] Optionally, the expression of the control term loss is:

[0031]

[0032] The expression of the boundary term loss is:

[0033]

[0034] The expression of the data term loss is:

[0035] loss_data = [(u net , v net)-(u true ,v true )] 2 ,

[0036] where loss_r represents the control term loss, loss_bc represents the boundary term loss, loss_data represents the data term loss, and (u net ,v net ) represents the network output displacement data, and (u true ,v true ) represents the measured displacement data.

[0037] Optionally, the expression for adjusting the weights of the control term loss, the boundary term loss, and the data term loss is:

[0038] loss = a × loss_r + b × loss_bc + c × loss_data;

[0039] where loss represents the total loss, and a, b, and c are weight coefficients respectively;

[0040] The hyperparameters of the neural network model include the learning rate.

[0041] Compared with the prior art, the method for inverse analysis of the evolution law of the tensile and compressive moduli of materials provided by the present invention has at least achieved the following beneficial effects:

[0042] First, using a neural network model to replace the role of the finite element program in the parameter inverse analysis method, the parameter inverse analysis speed is greatly improved, and the material moduli under different stress states are inversely solved at the same time;

[0043] Second, by processing the measured deformation field data through a data processing program based on the discrete cosine transform, the problem of noise affecting the inverse analysis accuracy of the material modulus is solved, the inverse analysis of the material modulus at the full stress level is realized, and the computing resources are saved, that is, the measured deformation data containing noise can be effectively processed, the inverse analysis accuracy is guaranteed, the inverse analysis efficiency is greatly improved, the computing resources are saved, and the evolution law of the material modulus under different stress states (such as tensile stress state and compressive stress state) can be efficiently obtained;

[0044] Third, writing the relevant physical information of the problem to be solved into the model loss function can accelerate the training convergence of the neural network model and improve the physical interpretability of the neural network model;

[0045] Fourth, taking the initial material moduli under different stress states (such as tensile stress state and compressive stress state) as independent input features or model parameters to participate in the optimization training of the neural network model can improve the accuracy and efficiency of the neural network model and enhance its robustness;

[0046] Fifth, compared with Chinese Patent Document 2, this embodiment mainly relies on physical information drive, greatly reducing the dependence of parameter inversion on data. It can invert material parameters with high precision and efficiency with a small amount of known experimental observation data, and has stronger versatility, not limited to specific engineering scenarios. It can be understood that with physical information drive as the core, the requirement for parameter inversion that depends on data is significantly reduced. Even when the experimental observation data is limited, it can still invert material parameters efficiently and with high precision. In addition, the inversion method for the evolution law of the tensile and compressive modulus of this material has strong versatility, is applicable to a variety of engineering scenarios, and is not restricted by specific conditions.

[0047] Of course, it is not necessary for any product implementing the present invention to simultaneously achieve all the above-mentioned technical effects.

[0048] Other features and advantages of the present invention will become clear from the following detailed description of the exemplary embodiments of the present invention with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] The drawings incorporated in and constituting a part of this specification illustrate embodiments of the present invention and, together with the description, are used to explain the principles of the present invention.

[0050] Figure 1 It is a flowchart of the method for detecting the tensile and compressive properties of the pipe insulation material provided in Chinese Patent Document 1;

[0051] Figure 2 It is a schematic structural diagram of the inversion method for the evolution law of the tensile and compressive modulus of materials provided by the present invention;

[0052] Figure 3 It is a schematic diagram of the present invention using the discrete cosine transform to transform the numerical matrix to obtain the transformed frequency-domain data matrix;

[0053] Figure 4 It is a schematic diagram of the neural network model provided by the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0054] Now, various exemplary embodiments of the present invention will be described in detail with reference to the accompanying drawings. It should be noted that: unless otherwise specifically stated, the relative arrangements of components and steps, numerical expressions, and numerical values set forth in these embodiments do not limit the scope of the present invention.

[0055] The following description of at least one exemplary embodiment is merely illustrative in nature and in no way serves as a limitation to the present invention or its application or use.

[0056] Technologies, methods, and devices known to those of ordinary skill in the relevant art may not be discussed in detail, but where appropriate, such technologies, methods, and devices should be considered as part of the specification.

[0057] In all examples shown and discussed herein, any specific values should be construed as merely exemplary and not as a limitation. Thus, other examples of the exemplary embodiments may have different values.

[0058] It should be noted that like reference numerals and letters refer to like items in the following figures, and thus, once an item is defined in one figure, further discussion thereof in subsequent figures is not required.

[0059] Referring to Figures 2 - 4 as shown, Figure 2 is a schematic structural diagram of an inversion method for the evolution law of the tensile and compressive modulus of materials based on machine learning provided by the present invention; Figure 3 is a schematic diagram of using the discrete cosine transform to transform a numerical matrix to obtain a transformed frequency-domain data matrix. Among them, the two-dimensional numerical matrix A1 represents the matrix before transformation, and the transformed frequency-domain data matrix A2 represents the matrix after transformation. A1 and A2 have the same size, with the number of rows M and the number of columns N. Inside the dashed box is an n main ×n main square matrix, and n main is the size of the main eigenmatrix. According to the principle of the discrete cosine transform, this square matrix represents the most important signal, that is, the main information of the displacement data; Figure 4 is a schematic diagram of the neural network model provided by the present invention. Among them, u and v are the network output data (such as the network output displacement data), and N d represents the neural network model, x and y are the network input information (such as the plane coordinates of finite scattered points in the deformation field data), and θ d represents the hyperparameter; the present embodiment provides an inversion method for the evolution law of the tensile and compressive modulus of materials based on machine learning, including the following steps:

[0060] Step 100: Perform a four-point bending experiment on the material specimen, and use the digital image correlation method to obtain the surface deformation information of the material specimen during the loading process. The surface deformation information of the material specimen includes deformation field data, and defines the plane coordinates of finite scattered points in the deformation field data and the corresponding displacement data;

[0061] Specifically, continuing to refer to Figure 2 as shown, the inversion method for the evolution law of the tensile and compressive modulus of materials based on machine learning provided by the present embodiment can be an inversion method for the evolution law of the material modulus based on machine learning, or an inversion method for predicting and inverting the material modulus based on machine learning.

[0062] The above-mentioned material specimen includes a standard material specimen, which has unified specifications and performance requirements and is used to meet specific test needs. In practical applications, using standard specimens for testing can greatly improve test efficiency and accuracy.

[0063] In the above four-point bending test, the two ends of the material specimen are fixed by two support points, and forces are applied by two loading points in the middle to form bending. By measuring the deformation, the mechanical properties of the material specimen can be evaluated.

[0064] The above digital image correlation method DIC is a non-contact optical measurement technique. By comparing the images of the surface of the material specimen before and after deformation, the deformation field data is calculated. The surface of the material specimen needs to have a random speckle pattern to track the deformation.

[0065] During the four-point bending experiment, the digital image correlation method DIC provides the surface deformation information of the material specimen. The surface deformation information of the material specimen includes: displacement and strain. Among them, the displacement is calculated by tracking the feature points in the image and finding the corresponding positions of these feature points in the deformed image, so as to calculate the displacement data; based on the image matching algorithm, by comparing the digital images before and after deformation and using image processing software to analyze the pixel changes in the images, the strain distribution on the surface of the object is calculated.

[0066] The above deformation field data describes the distribution and variation laws of physical quantities such as displacement, strain, and stress at each point on the surface or inside of the material specimen when it deforms under the action of force or other external factors. Specifically, defining the plane coordinates of finite scattered points in the deformation field data means selecting a series of representative points on the surface of the material specimen, and the positions of these points can be determined by a plane coordinate system. Then, by measuring or calculating the displacements of these points before and after deformation, the displacement data corresponding to each point is obtained. These displacement data reflect the movement of each point in the material specimen during the deformation process, and thus a distribution map of the deformation field data can be constructed.

[0067] The plane coordinates and displacement data of the above finite scattered points, where the plane coordinates: the points on the surface of the material specimen are represented by two-dimensional coordinates (x, y); the displacement data: the displacement of each point after loading is represented by a vector (u, v), where u is the displacement in the x direction and v is the displacement in the y direction.

[0068] Step 102: Construct a two-dimensional numerical matrix from the displacement data of the deformation field data in the surface deformation information, perform a transformation on the numerical matrix using the discrete cosine transform to obtain a transformed frequency-domain data matrix; confirm the size of the main feature matrix according to the cumulative energy retention rate principle, crop the transformed frequency-domain data matrix to obtain the main feature matrix, fill the main feature matrix with zeros to the original size, and then transform it back to the spatial domain through inverse transformation to obtain a denoised displacement matrix;

[0069] Specifically, when establishing a neural network model, first preprocess the deformation field data in the surface deformation information. Further, preprocess the measured noisy deformation field data, such as implementing it based on the discrete cosine transform.

[0070] Combined with Figure 2 and Figure 3 As shown, first collect the displacement data of the deformation field data in the surface deformation information, and arrange the displacement data of the deformation field data in the collected surface deformation information into a two-dimensional numerical matrix according to the spatial position. Assuming there are M points in the x direction and N points in the y direction, the two-dimensional numerical matrix is M×N, where each element represents the displacement value at the corresponding position.

[0071] Apply the discrete cosine transform (DCT) to each row and each column of the two-dimensional numerical matrix respectively, which is implemented by calling the DCT function in the math library. For example, apply the discrete cosine transform (DCT) to each row of the two-dimensional numerical matrix to obtain an intermediate matrix, and then apply DCT to each column of the intermediate matrix to obtain the transformed frequency domain data matrix (as shown in Figure 3 ). The transformed frequency domain data matrix has a good frequency domain energy concentration. The low-frequency signals are concentrated in the upper left corner of the matrix, and the high-frequency signals are often noise distributed in the lower right corner. Suppress the high-frequency noise information by reasonably selecting the size of the main feature matrix to crop the transformed frequency domain data matrix, so as to achieve data dimensionality reduction and noise reduction. For example, select the appropriate size of the main feature matrix according to the cumulative energy retention rate principle [as shown in the following formula (1)], that is, calculate the size of the main feature matrix using the cumulative energy retention rate principle [as shown in the following formula (1)], that is, determine the number of rows / columns of the main feature matrix size; crop the transformed frequency domain data matrix by selecting the appropriate size of the main feature matrix to obtain the main feature matrix, so as to retain the main low-frequency information. The main feature matrix is then transformed back to the spatial domain through the inverse transform to obtain the denoised displacement matrix.

[0072] The above high-frequency noise information mainly comes from factors such as the noise of the image acquisition device, environmental vibration, uneven speckle patterns, and the sensitivity of the image processing algorithm to noise. By cropping the high-frequency components in the frequency domain data matrix, the impact of these noises on the image quality can be significantly reduced, thereby improving the clarity and signal-to-noise ratio of the image.

[0073] The above discrete cosine transform (DCT) is a mathematical tool that transforms data from the spatial domain to the frequency domain. The main advantage of DCT is its high frequency domain energy concentration, with low-frequency signals concentrated in the upper left corner of the transformed matrix and high-frequency signals distributed in other regions.

[0074] The expression of the above cumulative energy retention rate principle is:

[0075]

[0076] Where: M and N represent the sizes of the transformed frequency-domain data matrix, n represents the size of the main feature matrix obtained by cropping, P represents the energy retention rate, which is a decimal between 0 and 1; A ij 2 represents the energy of the elements in the frequency-domain data matrix before cropping. Among them, i and j represent the row number and column number of the elements in the frequency-domain data matrix, represents the energy of the elements in the main feature matrix after cropping. Among them, p and q represent the row number and column number of the elements in the main feature matrix after cropping.

[0077] It should be noted that: Cropping the size of the main feature matrix can retain the main low-frequency information and remove the secondary high-frequency information. The main feature matrix is transformed back to the spatial domain through an inverse transformation (such as the inverse discrete cosine transform). The data after the inverse transformation (the displacement matrix after noise reduction) is the result after noise reduction. Since the high-frequency noise information is removed, the obtained signal or image should be clearer and have less noise than the original one.

[0078] Taking the simulation experiment as an example, the horizontal displacement data of the scattered points in the local area of the two-dimensional four-point bending model are taken. 50 scattered points can be taken along the x direction and 60 scattered points can be taken along the y direction, that is, M = 50, N = 60, and a displacement matrix with noise of size 50x60 is obtained. The frequency-domain data matrix is obtained through the discrete cosine transform, and the size of the frequency-domain data matrix remains unchanged.

[0079] The sum of the squares of each element in the above frequency-domain data matrix, that is, the denominator part in formula (1), represents the total energy of the frequency-domain data matrix. P represents the energy retention rate, which is a decimal between 0 and 1. The closer it is to 1, the greater the energy accumulation ratio, and at the same time, it will also contain more noise signals.

[0080] The frequency-domain data matrix is cropped, and the area corresponding to 95% of the total energy is selected as the main feature matrix, that is, P = 0.95. The numerator part is calculated through formula (1) to further determine the size of the main feature matrix, that is, the value of n.

[0081] Assume n = 40, then the main feature matrix with a size of 40×40 after cropping can represent 95% of the information of the frequency-domain data matrix. Since the cropped area is located in the lower right corner of the frequency-domain data matrix, which is the aggregation area of secondary high-frequency information, it can be considered that the main feature matrix after cropping can represent most of the information of the frequency-domain data matrix.

[0082] After filling the cropped main feature matrix with 0 elements to the original size, that is, 50x60, it is transformed back to the spatial domain through the inverse discrete cosine transform to obtain the displacement matrix after noise reduction (such as the horizontal displacement matrix after noise reduction). The noise reduction processing of the vertical displacement data after noise reduction is the same. The displacement matrix after noise reduction is used for subsequent related calculations of the neural network.

[0083] Step 104: After obtaining the initial material moduli of the preset material specimen under different stress states, use the planar coordinates of the finite scattered points in the deformation field data as the input of the neural network, and perform non-linear transformation through the neural network model, with the displacement data corresponding to the scattered points as the network output data;

[0084] Specifically, in combination with Figure 2 and Figure 4 as shown, the neural network model adopts the form of a multi-layer perceptron ( Figure 3 ). After obtaining the initial material moduli of the preset material specimen under different stress states, such as the initial material modulus E t0 under the preset tensile stress state and the initial material modulus E c0 under the compressive stress state, the initial material modulus E t0 and the initial material modulus E c0 are used for the fitting calculation of the neural network and the composition of the model loss function.

[0085] Use the planar coordinates of the finite scattered points in the deformation field data in Step 100 as the network input information. Through the fitting calculation of the neural network, use the displacement data corresponding to the finite scattered points in the deformation field data as the network output data (such as the network output displacement).

[0086] Network input information: Planar coordinates (x, y) of finite scattered points;

[0087] Network output data: Displacement data (u, v) corresponding to the finite scattered points in the deformation field data;

[0088] The neural network learns the mapping relationship between the input and output, and fits the displacement distribution in the deformation field data. The specific steps are as follows: Collect the planar coordinates (x, y) of finite scattered points and the displacement data (u, v) corresponding to the finite scattered points in the deformation field data, and divide them into a training set and a test set; Select a suitable neural network model. Optionally, a multi-layer perceptron structure (such as Figure 4 as shown), which is further a fully connected network. The fully connected network consists of 1 input layer, 3 hidden layers, and 1 output layer. Both the input layer and the output layer are dual-channel. The input is the planar coordinates (x, y) of finite scattered points, and the network output data are the displacement components (u, v) in the x and y directions; Each hidden layer has 64 neurons and uses the Tanh activation function.

[0089] The initial material modulus E t0 under the preset tensile stress state and the initial material modulus E c0 under the compressive stress state can be defined as trainable parameters in the neural network model, and the initial material modulus E t0 under the preset tensile stress state and the initial material modulus E c0The training optimization of the hyperparameters of the neural network model (such as the learning rate) is carried out independently, and the initial material modulus E under the preset tensile stress state t0 and the initial material modulus E under the preset compressive stress state c0 are also relatively independent in training optimization, thereby improving the robustness of the network structure.

[0090] The hyperparameters of the above neural network model refer to the network depth (i.e., the number of hidden layers passed in the path from the input layer to the output layer), the network width (i.e., the number of neurons in each layer), the learning rate, etc.

[0091] During the training process of the neural network model, it is necessary to comprehensively adjust and optimize by combining the loss values, loss change curves, and inversion results of various losses (such as control term loss, boundary term loss, and data term loss). If the loss values of various losses are all large, it may indicate insufficient expression ability of the neural network. It is necessary to consider increasing the network depth and network width. At the same time, attention should be paid to avoiding overfitting caused by excessive increase in the scale of the neural network. The loss change curve can be observed. If the loss change curve shows an upward trend, it indicates that overfitting may exist. At this time, it is necessary to appropriately reduce the number of network layers or neurons. The learning rate determines the step size of parameter update of the neural network model. If the loss change curve oscillates or even diverges in a large range, it indicates that the learning rate is too large and needs to be appropriately reduced, or the learning rate is set to decay with the step size; if the loss values of various losses do not decrease significantly and the inversion results do not change significantly for a long time, it indicates that the learning rate is too small and the learning rate can be appropriately increased.

[0092] Step 106: Construct a model loss function according to the control equation satisfied by the four-point bending problem, the model boundary conditions equivalent to the real experiment, and the error between the measured displacement data and the network output displacement data. The measured displacement data is the displacement matrix after noise reduction. The model loss function includes control term loss, boundary term loss, and data term loss;

[0093] The control equation satisfied by the four-point bending problem is:

[0094]

[0095] In the formula: denotes the partial derivative, E denotes the material modulus, μ denotes the Poisson's ratio, x and y denote coordinates respectively, u and v denote displacements in the x and y directions respectively, f x and f y denote body forces.

[0096] The model boundary conditions equivalent to the real experiment include displacement boundaries and stress boundaries, and their expressions are:

[0097]

[0098] In the formula, represents the true displacement at the boundary, l represents the cosine value of the angle between the outer normal direction of the boundary and the x-axis, m represents the cosine value of the angle between the outer normal direction of the boundary and the y-axis, and represent the external forces acting on the boundary.

[0099] The above control term loss represents the control term loss of the control equation, and this control term loss comes from the specific description equation of the problem to be solved. In the four-point bending problem, the control equation is obtained by combining the geometric equation (describing the relationship between strain and displacement), the constitutive equation (describing the relationship between stress and strain), and the equilibrium differential equation (describing the relationship between stress and external force balance); the control term loss is used to measure the deviation between the numerical solution and these control equations to ensure that the solution satisfies the physical laws.

[0100] The expression of the control term loss is:

[0101]

[0102] In the formula: loss_r represents the control term loss, represents the partial derivative, E represents the material modulus, μ represents the Poisson's ratio, x and y respectively represent coordinates, u and v respectively represent the displacements in the x and y directions, f x and f y represent the body forces. In the four-point bending problem, the body forces f x and f y are both 0, the initial material modulus E is set to 9.8 GPa, and the Poisson's ratio μ is set to 0.14. Taking the simulation experiment as an example, taking the coordinates (x, y) of the scattered points in the local area of the two-dimensional four-point bending model as the network input, the corresponding network output (u, v) can be obtained, and substituting it into Equation (4) for the corresponding partial derivative After calculation, the loss value m1 can be obtained. As the model is trained, the value of the material modulus E is continuously updated, and the loss value m1 also changes accordingly.

[0103] The boundary term loss represents the boundary term loss of the displacement and stress boundary conditions, and this boundary term loss comes from the same model boundary conditions as the experiment, including the displacement boundary and the stress boundary. Specifically, that is, this boundary term loss includes the displacement boundary condition (specifying the displacement on the boundary) and the stress boundary condition (specifying the stress on the boundary), that is, the above boundary term loss is usually used in numerical simulation to ensure that the boundary conditions of the model are consistent with the experimental conditions. These boundary conditions can include the displacement boundary condition (specifying the displacement on the boundary) and the stress boundary condition (specifying the stress on the boundary).

[0104] The expression of the boundary term loss is:

[0105]

[0106] In the formula, loss_bc represents the boundary term loss, represents the true displacement at the boundary, represents the partial derivative, E represents the material modulus, μ represents the Poisson's ratio, x and y represent coordinates respectively, and u and v represent displacements in the x and y directions respectively, and represents the external force applied at the boundary, l represents the cosine value of the angle between the external normal direction of the boundary and the x-axis, and m represents the cosine value of the angle between the external normal direction of the boundary and the y-axis.

[0107] In the four-point bending problem, the boundary conditions mainly consider the two indenter positions and the two support points. At the indenter position, it is a stress boundary, and it is subjected to a downward pressure F along the y direction. The cosine value l of the angle between the external normal direction of the boundary and the x-axis is 0, and the cosine value m of the angle between the external normal direction of the boundary and the y-axis is 1. At the support point position, it is a displacement boundary, and the displacements in both the x and y directions are 0 here. The initial material modulus is set to 9.8 GPa, and the Poisson's ratio μ is set to 0.14. Taking the simulation experiment as an example, in the network output data of the two-dimensional four-point bending model, the displacements corresponding to the boundary are taken to participate in the calculation of the boundary term loss. Substituting into Equation (5), the loss value m2 can be obtained. As the model is trained, the value of the material modulus E is continuously updated, and the loss value m2 also changes accordingly.

[0108] The expression of the data term loss is:

[0109] loss_data = [(u net , v net ) - (u true , v true )] 2 Equation (6),

[0110] In the formula, loss_data represents the data term loss, (u net , v net ) represents the network output displacement data, and (u true , v true ) represents the measured displacement data.

[0111] The network output data includes the network output displacement data. That is, the data term loss is the data term loss representing the difference between the network output displacement and the measured displacement. This data term loss directly measures the gap between the neural network output displacement and the measured displacement and is an important item for judging the convergence of the model. The collocation points of the control term loss and the boundary term loss are obtained through the Latin hypercube sampling technique, which ensures the randomness and uniform distribution of the collocation points in the sample space.

[0112] Through Latin hypercube sampling, the collocation points of the control term loss and the boundary term loss can be more evenly distributed in the material specimen space, thereby improving the accuracy and reliability of simulation or calculation. This method not only reduces the deviation caused by sample aggregation but also ensures the comprehensiveness and representativeness of the collocation points.

[0113] The above-mentioned Latin hypercube sampling is a random sampling technique aimed at reducing the correlation between input variables, thereby improving the accuracy of simulation or optimization. It divides the value range of each input variable into the same intervals and randomly selects a value within each interval to ensure the randomness and uniformity of the samples.

[0114] Step 108: When training and optimizing the initial material modulus using the minimized loss function in the model loss function, by adjusting the weights of the control term loss, the boundary term loss, and the data term loss, and simultaneously optimizing the hyperparameters of the neural network model until the preset convergence condition is met, the target material modulus is finally determined.

[0115] Specifically, by adjusting the weights of the above-mentioned control term loss, boundary term loss, and data term loss, the fitting degree of the neural network model among physical laws, boundary conditions, and experimental data can be balanced. For example, if the weight of the data term loss is large, the neural network model is more inclined to fit the experimental data; if the weight of the control term loss is large, the neural network model will pay more attention to conforming to physical laws.

[0116] The above-mentioned hyperparameters include the learning rate, batch size, number of network layers, etc. By optimizing the hyperparameters of the learning rate, batch size, and number of network layers, the training efficiency and accuracy of the neural network model can be improved. Common methods include grid search, random search, or Bayesian optimization.

[0117] During the training process, the neural network model continuously adjusts the parameters through backpropagation and the gradient descent method to minimize the loss function. The training continues until the loss function reaches the preset convergence condition (such as the loss value being lower than the threshold), and then the accurate material modulus, which is the target material modulus, is obtained.

[0118] The process of minimizing the loss function is the process by which the initial material modulus continuously approaches the true value. Briefly, the model loss function is used to measure the gap between the observed displacement and the network output displacement. When the loss value output by the model loss function is less than the threshold, it is approximately considered that the observed displacement and the network output displacement are consistent, and the target material modulus at this time can be considered the true modulus, which is the final result.

[0119] The expression for adjusting the weights of the control term loss, boundary term loss, and data term loss is:

[0120] loss = a×loss_r + b×loss_bc + c×loss_data Equation (7),

[0121] In the formula, a, b, and c are weight coefficients respectively, loss represents the total loss, loss_r represents the control term loss, loss_bc represents the boundary term loss, and loss_data represents the data term loss.

[0122] Each part of the loss measures different aspects of the model performance. To make each part of the loss contribute significantly to the total loss loss and thus improve the overall performance of the model, it is necessary to adjust the weight coefficients so that the values of each part of the loss are in the same order of magnitude. Taking the simulation experiment as an example, the initial weight coefficients are a = b = c = 1. After training for 5000 steps, the total loss loss and each part of the loss show a continuous downward trend. At this time, loss = 7.4682, loss_r = 0.9097, loss_bc = 6.3751, loss_data = 0.1834. The boundary term loss loss_bc makes the main contribution to the total loss loss, that is, it is necessary to adjust the weight coefficient of the data term loss loss_data so that the data term loss loss_data is as close as possible to the other two parts of the loss in the same order of magnitude. After adjustment, the weight coefficients are a = 0.1, b = 0.01, c = 1. After training for 5000 steps, the total loss loss and each part of the loss show a continuous downward trend. At this time, loss = 0.13, loss_r = 0.0515, loss_bc = 0.0359, loss_data = 0.0426. The values of each part of the loss are in the same order of magnitude, and the contribution distribution to the total loss is balanced, and the overall performance of the model reaches the best.

[0123] That is, the method for inverting the evolution law of the tensile and compressive modulus of materials based on machine learning mainly includes three steps: measuring the deformation field of the material specimen in the four-point bending experiment, establishing a neural network model, and optimizing the model parameters. The inversion idea of the initial material modulus is to fit and calculate the deformation field on the surface of the material specimen through the neural network model, add physical information describing the mechanical problem (such as physical equation constraints, initial conditions, boundary conditions, and conservation and balance of physical quantities, etc.) to each loss to construct a complete and reasonable model loss function, and train the neural network model by minimizing the loss function in the model loss function, so as to invert the distribution law of the initial material modulus of the material specimen under different stress states.

[0124] Compared with the prior art, the method for inverting the evolution law of the tensile and compressive modulus of materials based on machine learning provided in this embodiment has at least achieved the following beneficial effects:

[0125] First, use the neural network model to replace the role of the finite element program in the parameter inversion method, greatly improving the parameter inversion speed and simultaneously inverting the material modulus under different stress states;

[0126] Second, process the measured deformation field data through a data processing program based on the discrete cosine transform to solve the problem that noise affects the inversion accuracy of material modulus, realize the inversion of material modulus under the full stress level, save computing resources, that is, be able to effectively process the measured deformation data containing noise, ensure the inversion accuracy, and at the same time greatly improve the inversion efficiency, save computing resources, and efficiently obtain the modulus evolution law of materials under different stress states (such as tensile stress state and compressive stress state);

[0127] Third, write the relevant physical information of the problem to be solved into the model loss function to accelerate the training convergence of the neural network model and improve the physical interpretability of the neural network model;

[0128] Fourth, use the initial material modulus under different stress states (such as tensile stress state and compressive stress state) as independent input features or model parameters to participate in the optimization training of the neural network model, which can improve the accuracy and efficiency of the neural network model and enhance its robustness;

[0129] Fifth, compared with Chinese Patent Document 2, this embodiment is mainly driven by physical information, greatly reducing the dependence of parameter inversion on data. It can invert material parameters with high precision and efficiency with a small amount of known experimental observation data, and has stronger versatility, not limited to specific engineering scenarios. It can be understood that with physical information driving as the core, the parameter inversion demand for data dependence is significantly reduced. Even when the experimental observation data is limited, it can still invert material parameters efficiently and with high precision. In addition, the inversion method of the material tension-compression modulus evolution law has strong versatility and is applicable to a variety of engineering scenarios without being restricted by specific conditions.

[0130] In an optional embodiment, the initial material modulus includes the tensile modulus and the compressive modulus;

[0131] Perform a four-point bending experiment on the material specimen. During the loading process, obtain the surface deformation information of the material specimen by the digital image correlation method. The surface deformation information of the material specimen includes deformation field data. Define the plane coordinates of the finite scattered points in the deformation field data and the corresponding displacement data, including:

[0132] Use finite element software to establish a two-dimensional four-point bending model, and the two-dimensional four-point bending model corresponds to the longitudinal section of the material specimen in the real experiment;

[0133] Assign given material properties to the two-dimensional four-point bending model, including the tensile modulus, the compressive modulus, and the Poisson's ratio;

[0134] Set the same boundary conditions and loads as in the real experiment;

[0135] Perform finite element network division on the two-dimensional four-point bending model to obtain the deformation field data in the horizontal and vertical directions.

[0136] Specifically, the above initial material modulus includes tensile modulus and compressive modulus. Through four-point bending experiments, the plane coordinates of finite scattered points in the deformation field data and the corresponding displacement data (such as scattered point displacement data) are used to analyze and calculate the deformation of the material specimen, thereby providing basic data for the inversion of the tensile modulus and compressive modulus of the material. The specific steps are as follows:

[0137] 1. Establish a geometric model

[0138] Geometric modeling: Create a two-dimensional four-point bending model in finite element software to simulate the longitudinal section of the material specimen in the actual experiment. It is usually rectangular, with the length and thickness being the same as those of the actual specimen.

[0139] Assign material properties

[0140] Material properties: Assign material properties to the two-dimensional four-point bending model, including:

[0141] Tensile modulus (E t ): The stiffness of the material specimen when it is stretched.

[0142] Compressive modulus (E c ): The stiffness of the material specimen when it is compressed.

[0143] Poisson's ratio (μ): The ratio of the transverse strain to the longitudinal strain of the material specimen when it is stressed.

[0144] 3. Set boundary conditions and loads

[0145] Boundary conditions: Simulate the constraint conditions in the actual experiment, such as applying fixed supports or simply supported boundary conditions at both ends of the material specimen;

[0146] Load conditions: Apply the same load as in the experiment to the material specimen. For example, in a four-point bending experiment, apply two symmetric concentrated forces.

[0147] 4. Finite element mesh generation

[0148] Mesh generation: Divide the geometric model into finite element meshes, ensuring that the mesh density is high enough to capture the deformation and stress distribution, especially in the stress concentration areas.

[0149] 5. Solve and analyze the results

[0150] Solve: Run the finite element analysis to calculate the response of the two-dimensional four-point bending model under the given loads and boundary conditions.

[0151] Deformation field data: Obtain the deformation field data in the horizontal direction (x-direction) and vertical direction (y-direction), including displacement and strain distributions. Among them, in the deformation field data:

[0152] Horizontal deformation field (x - direction): It reflects the displacement distribution of the material specimen in the length direction and shows the elongation or shortening of the material specimen during the bending process.

[0153] Vertical deformation field (y - direction): It reflects the displacement distribution of the material specimen in the thickness direction and shows the flexure of the material specimen during the bending process.

[0154] Adopting the above - mentioned scheme, by simulating real experimental conditions, verify the accuracy of material properties (such as tensile modulus, compressive modulus, Poisson's ratio), ensure that the two - dimensional four - point bending model can accurately reflect material behavior; simulate the deformation and stress distribution of the material under four - point bending load, predict its performance in practical applications, and help evaluate the mechanical properties of the material specimen; by simulating different experimental conditions, optimize experimental parameters (such as load magnitude, support position, etc.), reduce the number of experiments, and save costs and time; obtain deformation field data in the horizontal and vertical directions, analyze the stress - strain distribution, identify high - stress areas, and evaluate the material failure risk.

[0155] Application Example

[0156] Taking the inversion of the tensile and compressive moduli of nuclear graphite as an example:

[0157] Step 1: Measure the deformation field of the four - point bending specimen

[0158] Before inverting the initial material moduli (such as tensile modulus E t and compressive modulus E c ), a four - point bending mechanical experiment needs to be carried out on the material specimen to measure and calculate the surface deformation field of the material specimen. In this embodiment, it is represented by the plane coordinates of finite scattered points and the corresponding displacement data. To verify the accuracy of the initial material modulus inversion method proposed in this embodiment, a simulation experiment method is used to generate the four - point bending displacement field of the material specimen. Use finite - element simulation software (such as Abaqus or ANSYS, Abaqus can be used in this embodiment) to establish a two - dimensional four - point bending model corresponding to the longitudinal section of the material specimen in the real experiment; assign given material properties, including tensile modulus E t , compressive modulus E c and Poisson's ratio μ; set the same boundary conditions and loads as in the real experiment; divide the finite - element mesh and calculate the displacement fields in the horizontal and vertical directions. In the above two - dimensional four - point bending model, the network input information (x, y) is used as the input of the subsequent neural network, and the displacement fields in the horizontal and vertical directions (u(x, y), v(x, y)) are processed and participate in the inversion; the given initial material moduli (such as tensile modulus E to and compressive modulus E c0)As the control value of the final inversion result. According to existing research, the influence effect of the noise in the real experimental loading process is close to Gaussian white noise. Therefore, a certain level of Gaussian white noise is added to the deformation field data (such as the displacement field) obtained by simulation calculation to simulate the measured noisy displacement field in the real experiment, and then the displacement data of random scatter points are selected for inverting the initial material modulus.

[0159] Step 2: Establish a neural network model

[0160] (1) Given the preset values of the initial material modulus. The initial material modulus includes the tensile modulus E to and the compressive modulus E c0 . Since it is necessary to invert the initial material modulus under different tensile and compressive stress states, it is necessary to first preset the tensile modulus E t0 of the material under the tensile stress state and the compressive modulus E c0 of the material under the compressive stress state respectively. The preset values of the initial material modulus are used for the fitting calculation of the neural network and the composition of the model loss function. For example, the initial material modulus includes the elastic modulus, and the elastic modulus of nuclear graphite without damage is 9.8 GPa - 10 GPa.

[0161] (2) Preprocessing of the noisy displacement field. If the finally obtained noisy displacement field in Step 1 is directly used for inverting the initial material modulus, it will greatly affect the inversion accuracy and even result in non - convergence. To solve the above problems, it is necessary to process the noisy displacement field. As Figure 3 shown, perform a discrete cosine transform on the numerical matrix composed of the displacement data of the deformation field data in the surface deformation information. First, transform the numerical matrix from the spatial domain to the frequency domain through the forward transform to obtain the frequency - domain coefficient matrix, and then select the appropriate main eigen - matrix size to crop the frequency - domain coefficient matrix according to the cumulative energy retention rate principle [the above formula (1)] to retain the main low - frequency information. The cropped matrix is then transformed back to the spatial domain through the inverse transform to obtain the denoised displacement matrix.

[0162] (3) Build a neural network model. The neural network in this embodiment adopts the Figure 4 shown multi - layer perceptron structure, which includes a total of 1 input layer, 3 hidden layers, and 1 output layer. Both the input layer and the output layer are dual - channel. The network input information is the plane coordinates (x, y) of finite scatter points, and the network output data are the displacement data (u, v) in the x and y directions; each hidden layer has 64 neurons and uses the Tanh activation function. The preset tensile modulus E t0 and the preset compressive modulus E c0 are defined as trainable parameters in the neural network model, and the training and optimization of the tensile modulus E t0 , the compressive modulus E c0 and other hyperparameters of the network (such as the learning rate) are carried out independently. The tensile modulus Et0 and the compressive modulus E c0 The training optimization between them is also relatively independent, thus improving the robustness of the network structure.

[0163] (4) Construct the model loss function. In this embodiment, by writing the description of the relevant physical information of the problem to be solved into the model loss function, the training of the neural network model is constrained, optimizing the dependence of traditional machine learning on a large amount of data sets. While ensuring the inversion accuracy, the inversion efficiency is greatly improved, and at the same time, the physical interpretability of the model is enhanced. The model loss function of this embodiment consists of three parts, including the control term loss (loss_r), the boundary term loss (loss_bc), and the data term loss (loss_data). The control term loss loss_r comes from the specific description equation of the problem to be solved. In the four-point bending problem, the control equation is obtained by combining the geometric equation, the constitutive equation, and the equilibrium differential equation [as shown in the above formula (4)]; the boundary term loss loss_bc comes from the same model boundary conditions as the experiment, including the displacement boundary and the stress boundary [as shown in the above formula (5)]; the data term loss loss_data directly measures the gap between the displacement data output by the neural network and the measured displacement data, and is an important term for judging the convergence of the neural network model. The collocation points of the control term loss and the boundary term loss are obtained by Latin hypercube sampling to ensure the randomness and uniform distribution of the collocation points. (5) Train the neural network. The initial material moduli under different stress states (such as tensile stress state and compressive stress state) are used as independent trainable parameters, and the learning rates are set respectively.

[0164] Define the true modulus E t 、E c and the preset modulus E t0 、E c0 The Euclidean norm of the difference between them is used as the absolute error; the error limit is set to 0.001; when the absolute error of any modulus continuously is less than this limit value, fix this modulus as an invariant parameter and continue to optimize the other modulus until the absolute errors of both are continuously less than the error limit; that is, judge the convergence condition:

[0165] If the error Error t <0.001, fix E t as an invariant parameter and continue to optimize E c ;

[0166] If the error Error c <0.001, fix E c as an invariant parameter and continue to optimize E t ;

[0167] Termination condition: When the error Error t and the error Error cWhen both are continuously less than 0.001, the training ends.

[0168] Adopting the above scheme can accelerate the convergence of neural network training.

[0169] Step 3: Optimize the parameters of the neural network model.

[0170] In the neural network model, E t and E c As trainable parameters, they are automatically trained and optimized by the Adam optimizer during the iteration process. The initial learning rates of E t and E c are both set to 0.01, and the learning rate decay step is set. Every 10,000 training steps, the learning rate decays to 50% of the original. After 3 decays, the learning rate starts to remain unchanged. In addition, since the model loss function consists of three parts [as shown in the above formula (7)], it is necessary to adjust the weight coefficients a, b, and c of each part according to the convergence of the neural network model. The initial weight coefficients a = b = c = 1. The basic idea of adjusting the weight coefficients is to keep the loss values of each part as close as possible in the same order of magnitude. After obtaining the appropriate weight coefficients, use the neural network model to continuously update and optimize the output displacement of the network until the convergence condition is met. At this time, the modulus values E t and E c obtained from the output of the neural network model can be regarded as the true moduli of the material under tensile and compressive stress states.

[0171] The above Adam optimizer (Adaptive Moment Estimation) is an optimization algorithm widely used in deep learning, which is used to update and calculate the parameters in the model to minimize or maximize the loss function.

[0172] Through the above embodiments, it can be seen that the method for inverting the evolution law of the tensile and compressive moduli of materials based on machine learning provided by the present invention at least achieves the following beneficial effects:

[0173] First, use the neural network model to replace the role of the finite element program in the parameter inversion method, greatly improving the parameter inversion speed, and at the same time inverting the material moduli under different stress states;

[0174] Second, process the measured deformation field data through a data processing program based on the discrete cosine transform, solve the problem that noise affects the inversion accuracy of the material modulus, realize the inversion of the material modulus at the full stress level, save computing resources, that is, can effectively process the measured deformation data containing noise, ensure the inversion accuracy, while greatly improving the inversion efficiency, saving computing resources, and efficiently obtaining the modulus of the material under tensile and compressive stress states;

[0175] Third, write the relevant physical information of the problem to be solved into the model loss function to accelerate the training convergence of the neural network model and improve the physical interpretability of the model;

[0176] Fourth, use the initial material moduli under different stress states (such as tension and compression) as independent input features or model parameters to participate in the optimization training of the neural network model, which can improve the accuracy and efficiency of the neural network model and enhance its robustness.

[0177] For the case filed on the same day as this application, the patent title is "Inverse Method for Damage Field of Quasi-Brittle Materials Based on Physics-Informed Neural Networks". The differences between the inverse method for the evolution law of material tensile and compressive moduli based on machine learning in this application and the inverse method for the damage field of quasi-brittle materials based on physics-informed neural networks in the case filed on the same day are at least as follows: 1. This application is for the two-parameter inversion of material tensile and compressive moduli, while the case filed on the same day is for the large-scale parameter inversion of material field variables. The cross-interaction effects between parameters are more complex, and the problem-solving dimensions of the two are completely different; 2. Construct a two-dimensional numerical matrix from the displacement data of the deformation field data in the surface deformation information, and use the discrete cosine transform to transform the numerical matrix to obtain the transformed frequency-domain data matrix; confirm the size of the main feature matrix according to the cumulative energy retention rate principle, crop the transformed frequency-domain data matrix to obtain the main feature matrix, fill the main feature matrix to the original size with zeros, and then transform it back to the spatial domain through inverse transformation to obtain the denoised displacement matrix; 3. The expressions of the control term loss, boundary term loss, and data term loss in this application are not exactly the same as those of the control term loss, boundary term loss, and data term loss in the case filed on the same day. Therefore, the inventive points of the inverse method for the evolution law of material tensile and compressive moduli based on machine learning in this application are different from those of an inverse method for the damage field of quasi-brittle materials based on physics-informed neural networks in the case filed on the same day.

[0178] Although some specific embodiments of the present invention have been described in detail by way of examples, those skilled in the art should understand that the above examples are for illustrative purposes only and not for limiting the scope of the present invention. Those skilled in the art should understand that the above embodiments can be modified without departing from the scope and spirit of the present invention. The scope of the present invention is defined by the appended claims.

Claims

1. A method for inverting the evolution law of material tensile and compressive modulus based on machine learning, characterized in that: The following steps are involved: A four-point bending test is performed on a material sample, and during the loading process, a digital image correlation method is used to obtain surface deformation information of the material sample, wherein the surface deformation information of the material sample includes deformation field data, and plane coordinates of finite scattered points in the deformation field data and displacement data corresponding thereto are defined; The displacement data of the deformation field data in the surface deformation information are used to form a two-dimensional numerical matrix, and the numerical matrix is ​​transformed by discrete cosine transformation to obtain a transformed frequency domain data matrix; The size of the main feature matrix is ​​determined according to the cumulative energy retention rate principle, and the transformed frequency domain data matrix is ​​clipped to obtain the main feature matrix, the main feature matrix is ​​filled with zeros to the original size, and then converted back to the spatial domain through inverse transformation to obtain the displacement matrix after noise reduction; The expression of the cumulative energy retention rate principle is: Where: M and N represent the size of the transformed frequency domain data matrix, n represents the size of the main feature matrix obtained by clipping, and P represents the energy retention rate, which is a decimal between 0 and 1; A ij 2 represents the energy of the elements in the frequency domain data matrix before clipping, where i and j represent the number of rows and columns of the elements in the frequency domain data matrix. represents the energy of the elements in the main feature matrix after clipping, where p and q represent the number of rows and columns of the elements in the main feature matrix after clipping; After the initial material modulus of the material sample under different stress states is preset, the plane coordinates of the finite scattered points in the deformation field data are used as the input of the neural network, and the nonlinear transformation is performed through the neural network model, and the displacement data of the corresponding scattered points are used as the network output data; A model loss function is constructed according to the control equation satisfied by the four-point bending problem, the model boundary conditions equivalent to the real experiment, and the error between the measured displacement data and the network output displacement data, wherein the measured displacement data is the displacement matrix after denoising, and the model loss function includes control term loss, boundary term loss and data term loss; When the initial material modulus is trained and optimized by minimizing the loss function in the model loss function, the weights of the control term loss, the boundary term loss and the data term loss are adjusted, and the hyperparameters of the neural network model are optimized at the same time until the preset convergence conditions are met, and finally the target material modulus is determined.

2. The inversion method for the evolution law of material tensile and compressive modulus based on machine learning according to claim 1 is characterized in that: The initial material modulus includes a tensile modulus and a compression modulus; The four-point bending test is performed on the material sample, and the surface deformation information of the material sample is obtained by using the digital image correlation method during the loading process. The surface deformation information of the material sample includes deformation field data, and the plane coordinates of the finite scattered points in the deformation field data and the corresponding displacement data are defined as follows: A two-dimensional four-point bending model is established by using finite element software, wherein the two-dimensional four-point bending model corresponds to the longitudinal section of the material sample in the actual experiment; Assigning given material properties to the two-dimensional four-point bending model, including the tensile modulus, the compression modulus and Poisson's ratio; Set the same boundary conditions and loads as the actual experiment; Finite element network division is performed on the two-dimensional four-point bending model to obtain the deformation field data along the horizontal direction and the vertical direction.

3. The inversion method for the evolution law of material tensile and compressive modulus based on machine learning according to claim 1 is characterized in that: The governing equations satisfied by the four-point bending problem are: Where: It is expressed as a partial derivative, E represents the material modulus, μ represents the Poisson's ratio, x and y represent the coordinates, u and v represent the displacements in the x and y directions, respectively, and f x and f y It indicates physical strength; The model boundary conditions equivalent to the real experiment include displacement boundary and stress boundary, and their expressions are: In the formula, represents the true displacement at the boundary, l represents the cosine value of the angle between the normal direction outside the boundary and the x-axis, and m represents the cosine value of the angle between the normal direction outside the boundary and the y-axis. and Indicates the external force on the boundary; The network output data includes network output displacement data.

4. The method for inversion of the evolution law of material tensile and compressive modulus based on machine learning according to claim 3 is characterized in that: The expression of the control term loss is: The expression of the boundary term loss is: The expression of the data item loss is: loss_data=[(u net ,v net )-(u true ,v true )] 2 , Where, loss_r represents the control term loss, loss_bc represents the boundary term loss, loss_data represents the data term loss, (u net , v net ) represents the network output displacement data, (u true , v true ) represents the measured displacement data.

5. The inversion method for the evolution law of material tensile and compressive modulus based on machine learning according to claim 1 is characterized in that: The expression for adjusting the weights of the control item loss, the boundary item loss and the data item loss is: loss=a×loss_r+b×loss_bc+c×loss_data; In the formula, loss represents the total loss, a, b and c are weight coefficients respectively; The hyperparameters of the neural network model include a learning rate.

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