Stress intensity prediction method and device based on CGPINNs

Abstract

The invention discloses a stress intensity prediction method and device based on CGPINNs, and the method comprises the steps: building an input layer, a hidden layer and an output layer based on a central difference enhanced physical information neural network, and constructing a physical information neural network model; performing performance evaluation on the physical information neural network model; s2, through construction of a loss function, calculating a point residual error in a PDE domain, weighting the point residual error and incorporating the point residual error into the loss function, and determining an optimal weight combination through experiments and analysis of influences of different weights on a model prediction result; s3, optimizing the first-order moment estimation and the second-order moment estimation of the calculation gradient of the isotropic material through an Adam algorithm, adjusting the learning rate of each parameter according to the first-order moment estimation and the second-order moment estimation, and determining the optimal combination of the optimal learning rate and the central difference step length; s4, predicting the maximum stress intensity value of the composite material according to the stress distribution; the method has the advantages of high prediction accuracy, high stability, strong generalization ability and the like.

Description

Technical Field

[0001] The present invention relates to the field of computational mechanics and artificial intelligence technology, and in particular to a stress intensity prediction method and device based on CGPINNs. Background Art

[0002] In the field of engineering, accurately predicting the maximum stress intensity of a structure is crucial to ensuring the safety and reliability of the structure. Traditional stress intensity calculation methods, such as analytical methods and finite element methods, have many limitations when facing complex structures and multi-scale problems. The analytical method is only applicable to structures with simple geometric shapes and boundary conditions, and it is difficult to solve complex structures; although the finite element method is widely used, it is computationally expensive and inefficient when dealing with multi-scale problems.

[0003] With the development of artificial intelligence technology, physical information neural networks (PINNs) provide a new way to solve such problems. PINNs integrate physical laws into neural networks, reduce the dependence on large amounts of data, and improve the generalization ability of the model. However, the accuracy of traditional PINNs still needs to be improved when dealing with high-precision and multi-scale maximum stress intensity predictions. Although gradient-enhanced physical information neural networks (GPINNs) attempt to improve, they face problems of numerical instability and error accumulation when calculating first-order derivatives, which affects the accuracy of predictions.

[0004] Therefore, the present application provides a stress intensity prediction method and device based on CGPINNs. Summary of the invention

[0005] The technical problem to be solved by the present invention is that the accuracy of traditional PINNs in processing high-precision and multi-scale maximum stress intensity prediction still needs to be improved. Although gradient enhanced physical information neural networks (GPINNs) attempt to improve, they face the problems of numerical instability and error accumulation when calculating the first-order derivative, which affects the accuracy of the prediction. Therefore, a stress intensity prediction method and device based on CGPINNs are provided, and the stress intensity prediction method based on CGPINNs includes:

[0006] S1. Based on the central difference enhanced physical information neural network, the input layer, hidden layer and output layer are established to construct a physical information neural network model; obtain data, import the data into the physical information neural network model, obtain the calculated data, divide the calculated data into a test set, a validation set and a training set, and evaluate the performance of the physical information neural network model through the training set and the validation set;

[0007] S2. Construct the loss function, calculate the residual of the point in the PDE domain and incorporate it into the loss function with weights, assign values ​​to the weights, judge the impact of the weights on the model prediction results, and determine the optimal weight combination;

[0008] S3. Optimize the first-order moment estimation and second-order moment estimation of the gradient calculated for isotropic materials through the Adam algorithm, adjust the learning rate of each parameter according to the first-order moment estimation and the second-order moment estimation, and determine the best combination of the optimal learning rate and the central difference step size;

[0009] S4. Based on the stress distribution, the Euler-Bernoulli beam theory is used to consider the influence of boundary conditions and predict the maximum stress intensity value of the composite material.

[0010] Optionally, the central difference enhanced physical information neural network is used to establish an input layer, a hidden layer and an output layer, and construct a physical information neural network model, including:

[0011] S1.1. Based on the central difference enhanced physical information neural network, the input layer, hidden layer and output layer are established to construct the physical information neural network model;

[0012] S1.2. Obtain some data and pre-process the data.

[0013] Lu: = f (-Δu = f);

[0014] S1.3. Using partial differential equations to process neurons within the boundary:

[0015]

[0016] S1.4. After introducing time, perform partial differentiation on the neuron:

[0017]

[0018] S1.5. Normalize the data so that data of different magnitudes and properties are in the same order of magnitude, perform weighted summation on the input data and perform nonlinear transformation through activation functions;

[0019] S1.6. The data processed by steps S1.2-S1.5 enters the input layer of the physical information neural network model, passes through the input layer, hidden layer and output layer in sequence, and is output from the output layer to obtain the prediction result of stress intensity.

[0020] Optionally, the specific performance evaluation formula in the performance evaluation of the physical information neural network model through the training set and the validation set includes:

[0021]

[0022] Among them, α * It represents the optimal architecture that the neural network architecture of the physical information neural network model is searching for, ω *It represents the parameters of the optimal architecture that the neural network architecture of the physical information neural network model is searching for.

[0023] Optionally, the specific calculation process of the Adam algorithm includes:

[0024] Calculate the gradient g corresponding to the number of iterations t t , the specific calculation formula is:

[0025]

[0026] Update the first moment estimate:

[0027] m t =β1m t-1 +(1-β1)g t ;

[0028] Update the second moment estimate:

[0029]

[0030] Perform bias correction on the first-order moment estimate and the second-order moment estimate:

[0031]

[0032] Update the parameters θ:

[0033]

[0034] Among them, θ is the optimized parameter, t is the current iteration number, α is the learning rate, β1 and β2 are exponential decay rates, and ε is a number used to prevent division by zero.

[0035] Alternatively, the forward problem of the Euler-Bernoulli beam theory can be described as:

[0036]

[0037] where x∈[0,π], t∈[0,1], w i (i=1,2) is the lateral displacement of the first point and the acceleration of the second beam, is the acceleration of the corresponding beam, is the curvature of the corresponding beam, E i is the moment of inertia of the beam, I i is the density of the beam, ρ i is the cross-sectional area of ​​the beam, A i is the stiffness of the Winkler foundation connecting the two beams, and k is the lateral force acting on the two beams.

[0038] Optionally, the total loss function is expressed as:

[0039]

[0040] MSE PDE =MSE P +MSE G +MSE C ;

[0041] Among them, MSE PDE is the partial differential equation error, MSE BC is the boundary condition error, MSE P , MSE G and MSE C are the errors of the equilibrium equation, geometric equation and constitutive equation, respectively. and are the weights of the loss function respectively;

[0042] Weight The specific expression of the error equation is:

[0043]

[0044] The specific expression of boundary error is:

[0045]

[0046] Among them, N P is the data of randomly generated internal particles, N b The number of points to randomly generate boundary points.

[0047] The second aspect of the present invention further provides a stress intensity prediction device based on CGPINNs, the stress intensity prediction device based on CGPINNs comprising:

[0048] A neural network building module is used to build an input layer, a hidden layer and an output layer based on a central difference enhanced physical information neural network, and construct a physical information neural network model; obtain data, import the data into the physical information neural network model, obtain the calculated data, divide the calculated data into a test set, a validation set and a training set, and evaluate the performance of the physical information neural network model through the training set and the validation set;

[0049] The loss function weight determination module is used to calculate the residual of the points in the PDE domain and incorporate them into the loss function through the construction of the loss function. The optimal weight combination is determined through experiments and analysis of the impact of different weights on the model prediction results.

[0050] Algorithm optimization module, used to optimize the first-order moment estimation and second-order moment estimation of the gradient calculated for isotropic materials through the Adam algorithm, adjust the learning rate of each parameter according to the first-order moment estimation and the second-order moment estimation, and determine the best combination of the optimal learning rate and the central difference step size;

[0051] The stress intensity prediction module is used to predict the maximum stress intensity value of the composite material based on the stress distribution and the influence of boundary conditions using the Euler-Bernoulli beam theory.

[0052] The third aspect of the present invention further provides an electronic device, the electronic device comprising a memory and at least one processor, the memory storing instructions and data;

[0053] The at least one processor calls the instructions and data in the memory so that the electronic device executes each step of the stress intensity prediction method based on CGPINNs as described in any one of the above items.

[0054] A fourth aspect of the present invention further provides a readable storage medium having instructions and data stored thereon, wherein the instructions, when executed by a processor, implement the various steps of any of the above-mentioned methods for stress intensity prediction based on CGPINNs.

[0055] The implementation of the present invention has the following beneficial effects:

[0056] 1. Based on the stress distribution obtained by CGPINNs, the present invention effectively learns the parameters required for stress intensity prediction with the help of optimized loss functions and training algorithms, thereby predicting the maximum stress intensity. Taking into account the uncertainty of factors such as new structural designs or different load conditions, CGPINNs can reduce numerical instability in the process of solving PDE with the help of the symmetry of central differences. This enables the model to reliably provide stress intensity predictions when facing various complex working conditions and structural characteristics, providing stable support for the safety assessment and design of engineering structures.

[0057] 2. The present invention adopts the CGPINNs method, which can converge to an accurate solution more quickly by using the loss function solution process and the advantages of the Adam optimizer, further improving the computational efficiency. This improvement enables us to more accurately predict the stress distribution and dynamic changes of materials under stress, providing solid scientific support for the design of composite material structures in aerospace, automobile manufacturing, construction engineering and other fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 is a flow chart of a stress intensity prediction method based on CGPINNs provided by the present invention;

[0059] Figure 2 It is a schematic diagram of the physical information neural network model provided by the present invention;

[0060] Figure 3 are the displacements of ω1(x, t) (left) and ω2(x, t) (right) under the Euler-Bernoulli beam theory provided by the present invention;

[0061] Figure 4 The MSE provided by the present invention BC In ω c =0.1,ω c = Error curve at 0.01;

[0062] Figure 5 The MSE provided by the present invention PDE In ω c =0.1,ω c = Error curve at 0.01;

[0063] Figure 6 A schematic diagram of the structure of a stress intensity prediction device based on CGPINNs provided by the present invention;

[0064] Figure 7 It is a schematic diagram of the structure of an electronic device provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0065] The embodiment of the present invention provides a stress strength prediction method based on CGPINNs, including S1. establishing an input layer, a hidden layer and an output layer based on a central difference enhanced physical information neural network to construct a physical information neural network model; acquiring data, importing the data into the physical information neural network model, obtaining calculated data, dividing the calculated data into a test set, a validation set and a training set, and evaluating the performance of the physical information neural network model through the training set and the validation set; S2. constructing a loss function, calculating the point residual in the PDE domain and weighting it into the loss function, assigning weights by assignment, judging the influence of the weights on the model prediction results, and determining the optimal weight combination; S3. optimizing the first-order moment estimation and the second-order moment estimation of the gradient calculated for isotropic materials through the Adam algorithm, adjusting the learning rate of each parameter according to the first-order moment estimation and the second-order moment estimation, and determining the optimal combination of the optimal learning rate and the central difference step size; S4. predicting the maximum stress strength value of the composite material according to the stress distribution and the influence of the boundary conditions by using the Euler-Bernoulli beam theory; the present invention solves the problem that the accuracy of traditional PINNs in processing high-precision and multi-scale maximum stress strength prediction still needs to be improved. Although gradient-enhanced physically-informed neural networks (GPINNs) attempt to improve on this, they face problems of numerical instability and error accumulation when calculating first-order derivatives, which affects the accuracy of predictions.

[0066] The terms "first", "second", "third", "fourth", etc. (if any) in the specification and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that the data used in this way can be interchanged where appropriate, so that the embodiments described herein can be implemented in an order other than that illustrated or described herein. In addition, the terms "including" or "having" and any variations thereof are intended to cover non-exclusive inclusions, for example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units that are clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0067] For ease of understanding, the specific process of the embodiment of the present invention is described below. Figure 1 and Figure 6-7 In the embodiment of the present invention, the first embodiment of the stress intensity prediction method based on CGPINNs includes:

[0068] S1. Based on the central difference enhanced physical information neural network, the input layer, hidden layer and output layer are established to construct a physical information neural network model; obtain data, import the data into the physical information neural network model, obtain the calculated data, divide the calculated data into a test set, a validation set and a training set, and evaluate the performance of the physical information neural network model through the training set and the validation set;

[0069] Among them, the input layer, hidden layer and output layer are established based on the central difference enhanced physical information neural network, and the construction of the physical information neural network model specifically includes:

[0070] S1.1. Based on the central difference enhanced physical information neural network, the input layer, hidden layer and output layer are established to construct a physical information neural network model; the number of hidden layers can be flexibly adjusted to adapt to different structural complexities, and the activation functions of the hidden layer nodes are diverse. As the number of hidden layers increases, the learning ability of the network is enhanced, and it can capture more complex potential relationships between stress intensity and input parameters;

[0071] S1.2. Obtain some data and pre-process the data.

[0072] Lu: = f (-Δu = f);

[0073] In this formula, u is an unknown function, f is a known function, and Δ is the Laplace operator.

[0074] S1.3. Using partial differential equations to process neurons within the boundary:

[0075]

[0076] S1.4. After introducing time, perform partial differentiation on the neuron:

[0077]

[0078] S1.5. Normalize the data so that data of different magnitudes and properties are in the same order of magnitude, perform weighted summation on the input data and perform nonlinear transformation through activation functions;

[0079] In this embodiment, relevant parameters are reasonably preprocessed so that parameters of different magnitudes and properties are within the same magnitude range, which is convenient for network learning.

[0080] S1.6. The data processed by steps S1.2-S1.5 enters the input layer of the physical information neural network model, passes through the input layer, hidden layer and output layer in turn, and is output from the output layer to obtain the predicted result of stress intensity. The predicted value is presented in scalar form, intuitively giving the key stress intensity index of the structure under given conditions, which is convenient for direct comparison with the allowable stress of the material, so as to quickly evaluate the safety and reliability of the structure. The output layer has a certain degree of scalability, which can provide more information for further analysis of the local stress state and force direction characteristics of the structure, and maintain the simplicity and computational efficiency of the model.

[0081] In addition, the specific performance evaluation formulas for evaluating the performance of the physical information neural network model through the training set and the validation set include:

[0082]

[0083] Among them, α * It represents the optimal architecture that the neural network architecture of the physical information neural network model is searching for, ω * It represents the parameters of the optimal architecture that the neural network architecture of the physical information neural network model is searching for.

[0084] S2. Construct the loss function, calculate the residual of the point in the PDE domain and incorporate it into the loss function with weights, assign values ​​to the weights, judge the impact of the weights on the model prediction results, and determine the optimal weight combination;

[0085] Among them, the total loss function is expressed as:

[0086]

[0087] MSE PDE =MSE P +MSE G +MSE C ;

[0088] Among them, MSEPDE is the partial differential equation error, MSE BC is the boundary condition error, MSE P , MSE G and MSE C are the errors of the equilibrium equation, geometric equation and constitutive equation, respectively. and are the weights of the loss function respectively;

[0089] Weight The specific expression of the error equation is:

[0090]

[0091] The specific expression of boundary error is:

[0092]

[0093] Among them, N P is the data of randomly generated internal particles, N b The number of points to randomly generate boundary points.

[0094] S3. Optimize the first-order moment estimation and second-order moment estimation of the gradient calculated for isotropic materials through the Adam algorithm, adjust the learning rate of each parameter according to the first-order moment estimation and the second-order moment estimation, and determine the best combination of the optimal learning rate and the central difference step size;

[0095] The specific calculation process of the Adam algorithm includes:

[0096] Calculate the gradient g corresponding to the number of iterations t t , the specific calculation formula is:

[0097]

[0098] Update the first moment estimate:

[0099] m t =β1m t-1 +(1-β1)g t ;

[0100] Update the second moment estimate:

[0101]

[0102] Perform bias correction on the first-order moment estimate and the second-order moment estimate:

[0103]

[0104] Update the parameters θ:

[0105]

[0106] Among them, θ is the optimized parameter, t is the current number of iterations, α is the learning rate, β1 and β2 are exponential decay rates, and ε is a number used to prevent division by zero, and the specific value of this number is very small.

[0107] S4. Based on the stress distribution, the Euler-Bernoulli beam theory is used to consider the influence of boundary conditions and predict the maximum stress intensity value of the composite material.

[0108] See also Figure 1-7 The second embodiment of the stress intensity prediction method based on CGPINNs in the embodiment of the present invention includes:

[0109] Step S1. Establish an input layer, a hidden layer and an output layer based on a central difference enhanced physical information neural network to construct a physical information neural network model; obtain data, import the data into the physical information neural network model, obtain the calculated data, divide the calculated data into a test set, a validation set and a training set, and evaluate the performance of the physical information neural network model through the training set and the validation set;

[0110] Among them, the input layer, hidden layer and output layer are established based on the central difference enhanced physical information neural network, and the construction of the physical information neural network model specifically includes:

[0111] S1.1. Based on the central difference enhanced physical information neural network, the input layer, hidden layer and output layer are established to construct a physical information neural network model; the number of hidden layers can be flexibly adjusted to adapt to different structural complexities, and the activation functions of the hidden layer nodes are diverse. As the number of hidden layers increases, the learning ability of the network is enhanced, and it can capture more complex potential relationships between stress intensity and input parameters;

[0112] S1.2. Obtain some data and pre-process the data.

[0113] Lu: = f (-Δu = f);

[0114] In this formula, u is an unknown function, f is a known function, and Δ is the Laplace operator.

[0115] S1.3. Using partial differential equations to process neurons within the boundary:

[0116]

[0117] S1.4. After introducing time, perform partial differentiation on the neuron:

[0118]

[0119] S1.5. Normalize the data so that data of different magnitudes and properties are in the same order of magnitude, perform weighted summation on the input data and perform nonlinear transformation through activation functions;

[0120] In this embodiment, relevant parameters are reasonably preprocessed so that parameters of different magnitudes and properties are within the same magnitude range, which is convenient for network learning.

[0121] S1.6. The data processed by steps S1.2-S1.5 enters the input layer of the physical information neural network model, passes through the input layer, hidden layer and output layer in turn, and is output from the output layer to obtain the predicted result of stress intensity. The predicted value is presented in scalar form, intuitively giving the key stress intensity index of the structure under given conditions, which is convenient for direct comparison with the allowable stress of the material, so as to quickly evaluate the safety and reliability of the structure. The output layer has a certain degree of scalability, which can provide more information for further analysis of the local stress state and force direction characteristics of the structure, and maintain the simplicity and computational efficiency of the model.

[0122] In addition, the specific performance evaluation formulas for evaluating the performance of the physical information neural network model through the training set and the validation set include:

[0123]

[0124] Among them, α * It represents the optimal architecture that the neural network architecture of the physical information neural network model is searching for, ω * It represents the parameters of the optimal architecture that the neural network architecture of the physical information neural network model is searching for.

[0125] Step S2. Calculate the residual of the point in the PDE domain by constructing the loss function and incorporate it into the loss function with weights. The selection of weights is crucial to the model performance. Determine the optimal weight combination by experiments and analyzing the impact of different weights on the model prediction results. For example, when dealing with different types of PDE problems, such as the Poisson equation, the diffusion-reaction equation, etc., we can calculate the weights of ω respectively. f ,ω b ,ω c (central difference correlation weight) and other weights are adjusted, the model performance is evaluated on the validation set, and the weight combination that minimizes the prediction error is selected;

[0126] The loss function is as follows:

[0127] Next, the process of processing the boundary condition residuals and weighting them is:

[0128] For example, for the Dirichlet boundary condition:

[0129]

[0130] So, the process of dealing with the additional loss term is:

[0131] The additional loss term is calculated according to the central difference formula, such as adding the corresponding central difference loss term to the Poisson equation:

[0132] One-dimensional Poisson equation:

[0133]

[0134] The central difference loss term is:

[0135] L=ω f L f +ω i L i +ω c L c ;

[0136] Two-dimensional Poisson equation:

[0137]

[0138] The central difference loss term is:

[0139] L=ω f L f +ω b L b +ω i L i +ω c1 L c1 (T c1 )+ω c2 L c2 (T c2 );

[0140] S3. The Adam algorithm is used to optimize the first-order moment estimate (mean) and second-order moment estimate (variance) of the gradient of isotropic materials, and the learning rate of each parameter is adjusted according to these two estimated values. This can effectively handle complex nonlinear relationships and quickly optimize model parameters to improve the accuracy of stress intensity prediction. During model training:

[0141] At each iteration t, the gradient g is calculated t :

[0142]

[0143] Update the first moment estimate:

[0144] m t =β1m t-1 +(1-β1)g t ;

[0145] Update the second moment estimate:

[0146]

[0147] Perform bias correction on the first-order moment estimate and the second-order moment estimate:

[0148]

[0149] Update the parameters θ:

[0150]

[0151] Among them, θ is the optimized parameter, t is the current iteration number, α is the learning rate, β1 and β2 are exponential decay rates, and ε is a very small number used to prevent division by zero.

[0152] The Adam algorithm dynamically adjusts the learning rate according to the gradient information of different parameters, so that the model can effectively learn on data with different structures and working conditions.

[0153] S4. Based on the stress distribution, the peak stress area is searched with the help of Euler-Bernoulli beam theory to predict the maximum stress intensity value of the composite material.

[0154] The Euler-Bernoulli beam theory is based on the following assumption: the cross section of the beam perpendicular to the beam axis before deformation remains flat and perpendicular to the beam axis after deformation. This assumption is called the plane section assumption. This means that during the bending process of the beam, the points on the cross section only undergo displacement perpendicular to the cross section, without lateral shear deformation. The specific steps are as follows:

[0155] The forward problem of Euler-Bernoulli beam theory can be described as:

[0156]

[0157] where x∈[0,π], t∈[0,1], w i (i=1,2) is the lateral displacement of the first point and the acceleration of the second beam, is the acceleration of the corresponding beam, is the curvature of the corresponding beam, E i is the moment of inertia of the beam, I i is the density of the beam, ρ i is the cross-sectional area of ​​the beam, A i is the stiffness of the Winkler foundation connecting the two beams, and k is the lateral force acting on the two beams.

[0158] The present invention is further described in detail below with reference to the prediction process of the maximum stress in the embodiments.

[0159] by Figure 3 This shows the limiting initial and boundary conditions:

[0160]

[0161] And external forces:

[0162]

[0163] The Euler-Bernoulli beam theory calculates the lateral displacements of the two beams ω1(x, t) (left) and ω2(x, t) (right) based on the above constraints:

[0164] ω1(x,t)=sin(x)cos(t);

[0165]

[0166] By solving the bending equation and combining the boundary conditions, the maximum stress intensity is calculated.

[0167] Figure 4 and Figure 5 The MSE is shown respectively BC In ω c =0.1,ω c = 0.01 error curve and MSE PDE In ω c =0.1,ω c = 0.01 error curve. MSE PDE Not only the residual information is utilized, but also the central difference is adopted instead of the derivative calculation to alleviate the impact of error superposition.

[0168] Based on the optimization solution process of the loss function and the advantages of Euler-Bernoulli beam theory in describing the bending behavior of beams, we can significantly improve the convergence speed of the calculation process and reach an accurate solution more quickly, thereby further improving the overall calculation efficiency. This important improvement enables us to more accurately and efficiently predict the stress distribution and dynamic changes of materials under complex stress states, providing more solid scientific support for the design of composite materials in key fields such as aerospace, automobile manufacturing, and construction engineering.

[0169] The above describes the stress intensity prediction method based on CGPINNs in the embodiment of the present invention. The following describes the stress intensity prediction device based on CGPINNs in the embodiment of the present invention. Figure 6In the embodiment of the present invention, the stress intensity prediction device based on CGPINNs includes the following for the above embodiment:

[0170] The neural network establishment module 601 is used to establish an input layer, a hidden layer and an output layer based on the central difference enhanced physical information neural network, and construct a physical information neural network model; obtain data, import the data into the physical information neural network model, obtain the calculated data, divide the calculated data into a test set, a validation set and a training set, and evaluate the performance of the physical information neural network model through the training set and the validation set;

[0171] The loss function weight determination module 602 is used to calculate the residual of the point in the PDE domain and incorporate it into the loss function by weight through the construction of the loss function, and determine the optimal weight combination through experiments and analysis of the impact of different weights on the model prediction results;

[0172] Algorithm optimization module 603, used for optimizing the first-order moment estimation and the second-order moment estimation of the gradient calculated for the isotropic material by using the Adam algorithm, adjusting the learning rate of each parameter according to the first-order moment estimation and the second-order moment estimation, and determining the best combination of the optimal learning rate and the central difference step size;

[0173] The stress intensity prediction module 604 is used to predict the maximum stress intensity value of the composite material based on the stress distribution and taking into account the influence factors of the boundary conditions using the Euler-Bernoulli beam theory.

[0174] above Figure 6 The stress intensity prediction device based on CGPINNs in the embodiment of the present invention is described in detail from the perspective of modular functional entities, and the electronic device in the embodiment of the present invention is described in detail from the perspective of hardware processing.

[0175] Figure 7 7 is a schematic diagram of the structure of an electronic device provided by an embodiment of the present invention. The electronic device 700 may have relatively large differences due to different configurations or performances, and may include one or more processors 710 (for example, one or more processors) and a memory 720, and one or more storage media 730 (for example, one or more storage devices, including RAM\FLASH, etc.) storing application programs 733 or data 732. Among them, the memory 720 and the storage medium 730 may be temporary storage or permanent storage. The program stored in the storage medium 730 may include one or more modules (not shown in the figure), and each module may include a series of instruction operations in the electronic device 700. Furthermore, the processor 710 may be configured to communicate with the storage medium 730 to execute a series of instruction operations in the storage medium 730 on the electronic device 700.

[0176] The electronic device 700 may also include one or more power supplies 740, one or more input / output interfaces 750, and / or one or more operating systems 731, such as FreeRTOS, Android, etc. It will be appreciated by those skilled in the art that Figure 7 The structure of the electronic device shown does not constitute a limitation on the electronic device, and may include more or less components than shown in the figure, or combine some components, or arrange the components differently.

[0177] The present invention also provides a computer-readable storage medium, which may be a non-volatile computer-readable storage medium or a volatile computer-readable storage medium. Instructions are stored in the computer-readable storage medium. When the instructions are executed on a computer, the computer executes the steps of a stress intensity prediction method based on CGPINNs.

[0178] Those skilled in the art can clearly understand that, for the convenience and brevity of description, the specific working process of the above-described system, device, or unit can refer to the corresponding process in the aforementioned method embodiment and will not be repeated here.

[0179] If the integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention is essentially or the part that contributes to the prior art or all or part of the technical solution can be embodied in the form of a software product. The computer software product is stored in a storage medium, including several instructions for a computer device (which can be a personal computer, mobile device, server, or network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM), random access memory (RAM), disk or optical disk and other media that can store program codes.

[0180] As described above, the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features thereof may be replaced by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A stress intensity prediction method based on CGPINNs, characterized in that: include: S1. Based on the central difference enhanced physical information neural network, the input layer, hidden layer and output layer are established to construct a physical information neural network model; obtain data, import the data into the physical information neural network model, obtain the calculated data, divide the calculated data into a test set, a validation set and a training set, and evaluate the performance of the physical information neural network model through the training set and the validation set; S2. Construct the loss function, calculate the residual of the point in the PDE domain and incorporate it into the loss function with weights, assign values ​​to the weights, judge the impact of the weights on the model prediction results, and determine the optimal weight combination; S3. Optimize the first-order moment estimation and second-order moment estimation of the gradient calculated for isotropic materials through the Adam algorithm, adjust the learning rate of each parameter according to the first-order moment estimation and the second-order moment estimation, and determine the best combination of the optimal learning rate and the central difference step size; S4. Based on the stress distribution, the Euler-Bernoulli beam theory is used to consider the influence of boundary conditions and predict the maximum stress intensity value of the composite material.

2. The stress intensity prediction method based on CGPINNs according to claim 1, characterized in that: The central difference enhanced physical information neural network is used to establish an input layer, a hidden layer and an output layer, and construct a physical information neural network model, including: S1.

1. Based on the central difference enhanced physical information neural network, the input layer, hidden layer and output layer are established to construct the physical information neural network model; S1.

2. Obtain some data and pre-process the data. Lu: = f (-Δu = f); S1.

3. Using partial differential equations to process neurons within the boundary: S1.

4. After introducing time, perform partial differentiation on the neuron: S1.

5. Normalize the data so that data of different magnitudes and properties are in the same order of magnitude, perform weighted summation on the input data and perform nonlinear transformation through activation functions; S1.

6. The data processed by steps S1.2-S1.5 enters the input layer of the physical information neural network model, passes through the input layer, hidden layer and output layer in sequence, and is output from the output layer to obtain the prediction result of stress intensity.

3. The stress intensity prediction method based on CGPINNs according to claim 1, characterized in that: The specific performance evaluation formula for the performance evaluation of the physical information neural network model through the training set and the validation set includes: Among them, α * It represents the optimal architecture that the neural network architecture of the physical information neural network model is searching for, ω * It represents the parameters of the optimal architecture that the neural network architecture of the physical information neural network model is searching for.

4. The stress intensity prediction method based on CGPINNs according to claim 1, characterized in that: The specific calculation process of the Adam algorithm includes: Calculate the gradient g corresponding to the number of iterations t t , the specific calculation formula is: Update the first moment estimate: m t =β1m t-1 +(1-β1)g t ; Update the second moment estimate: v t =β2v t-1 +(1-β2)g 2 t ; Perform bias correction on the first-order moment estimate and the second-order moment estimate: Update the parameters θ: Among them, θ is the optimized parameter, t is the current iteration number, α is the learning rate, β1 and β2 are exponential decay rates, and ε is a number used to prevent division by zero.

5. The stress intensity prediction method based on CGPINNs according to claim 1, characterized in that: The forward problem of the Euler-Bernoulli beam theory can be described as: where x∈[0,π], t∈[0,1], w i (i=1,2) is the lateral displacement of the first point and the acceleration of the second beam, is the acceleration of the corresponding beam, is the curvature of the corresponding beam, E i is the moment of inertia of the beam, I i is the density of the beam, ρ i is the cross-sectional area of ​​the beam, A i is the stiffness of the Winkler foundation connecting the two beams, and k is the lateral force acting on the two beams.

6. The stress intensity prediction method based on CGPINNs according to claim 1, characterized in that: The total loss function is expressed as: MSE PDE =MSE P +MSE G +MSE C ; Among them, MSE PDE is the partial differential equation error, MSE BC is the boundary condition error, MSE P , MSE G and MSE C are the errors of the equilibrium equation, geometric equation and constitutive equation, respectively. and are the weights of the loss function respectively; Weight The specific expression of the error equation is: The specific expression of boundary error is: Among them, N P is the data of randomly generated internal particles, N b The number of points to randomly generate boundary points.

7. A stress intensity prediction device based on CGPINNs, characterized in that: include: A neural network building module is used to build an input layer, a hidden layer and an output layer based on a central difference enhanced physical information neural network, and construct a physical information neural network model; obtain data, import the data into the physical information neural network model, obtain the calculated data, divide the calculated data into a test set, a validation set and a training set, and evaluate the performance of the physical information neural network model through the training set and the validation set; The loss function weight determination module is used to calculate the residual of the points in the PDE domain and incorporate them into the loss function through the construction of the loss function. The optimal weight combination is determined through experiments and analysis of the impact of different weights on the model prediction results. Algorithm optimization module, used to optimize the first-order moment estimation and second-order moment estimation of the gradient calculated for isotropic materials through the Adam algorithm, adjust the learning rate of each parameter according to the first-order moment estimation and the second-order moment estimation, and determine the best combination of the optimal learning rate and the central difference step size; The stress intensity prediction module is used to predict the maximum stress intensity value of the composite material based on the stress distribution and the influence of boundary conditions using the Euler-Bernoulli beam theory.

8. An electronic device, comprising a memory and at least one processor, characterized in that: Instructions and data are stored in the memory; The at least one processor calls the instructions and data in the memory so that the electronic device executes the various steps of the stress intensity prediction method based on CGPINNs as described in any one of claims 1-6.

9. A readable storage medium having instructions and data stored thereon, characterized in that: When the instructions are executed by the processor, the various steps of the stress intensity prediction method based on CGPINNs as claimed in any one of claims 1 to 6 are implemented.

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