A method for predicting post-buckling deflection of cold-rolled strip based on physical information neural network

Abstract

The present invention discloses a method for predicting post-buckling deflection of cold-rolled steel strip based on a physical information neural network, comprising the following steps: Step 1: Collecting geometric parameters of the steel strip, material property parameters of the steel strip, load conditions, and boundary conditions of the steel strip; Step 2: Sampling the steel strip within the solution region, obtaining coordinates of multiple sampling points, and normalizing them to form a training data set; Step 3: Constructing a post-buckling prediction model for cold-rolled steel strip based on a physical information neural network; Step 4: Training the post-buckling prediction model for cold-rolled steel strip based on a physical information neural network using the training data set; Step 5: Collecting coordinates of the points to be predicted in the steel strip, and using the trained post-buckling prediction model for cold-rolled steel strip based on a physical information neural network to predict post-buckling deflection. The present invention combines physical laws with machine learning algorithms to achieve accurate prediction of post-buckling deflection of cold-rolled steel strip.

Description

Technical Field

[0001] The present invention belongs to the technical field of intersection of rolling and artificial intelligence, and in particular relates to a method for predicting post-buckling deflection of cold-rolled strip steel based on a physical information neural network. Background Art

[0002] In engineering practice, many steel strips experience large deflections under load, entering a post-buckling state. Analyzing the large deflections of steel strip structures in this post-buckling state is a key issue in fields such as steel, aerospace, and civil engineering. Accurately predicting structural deformation under this large post-buckling state is crucial for ensuring structural safety and reliability.

[0003] However, traditional methods for predicting post-buckling deformation and plate shape defects of steel strip are mainly based on empirical formulas, analytical methods and finite element simulations. Because the large deflection equilibrium equation of steel strip involves solving high-order nonlinear equations, which are difficult and complex to solve, empirical formulas and analytical methods rely on a large amount of experimental data and simplified assumptions, making it difficult to accurately describe complex nonlinear mechanical behavior. Although finite element simulation can accurately simulate the deformation of steel strip, it has the problems of large amount of calculation and long calculation time, and its ability to handle complex boundary conditions and material properties is limited. As strip production develops towards high precision and high performance, there is an urgent need for an efficient and accurate method to predict the large deflection deformation and plate shape defects of steel strip after buckling. Summary of the Invention

[0004] In order to solve the above technical problems, the purpose of the present invention is to provide a method for predicting the post-buckling deflection of cold-rolled strip based on a physical information neural network to solve high-order nonlinear complex formulas, improve the accuracy and computational efficiency of strip deflection prediction, reduce dependence on computing resources, and better adapt to the complex geometric shape, boundary conditions and nonlinear characteristics of the strip.

[0005] The present invention provides a method for predicting post-buckling deflection of cold-rolled strip steel based on a physical information neural network, comprising:

[0006] Step 1: Collect the geometric parameters of the steel strip, the material property parameters of the steel strip, the load conditions and boundary conditions of the steel strip;

[0007] Step 2: Sample the steel strip within the solution area, obtain the coordinates of multiple sampling points, and perform normalization to form a training data set;

[0008] Step 3: Construct a cold-rolled strip post-buckling prediction model based on physical information neural network;

[0009] Step 4: Use the training data set to train the cold-rolled strip post-buckling prediction model based on the physical information neural network;

[0010] Step 5: Collect the coordinates of the points to be predicted on the strip, and use the trained cold-rolled strip post-buckling prediction model based on physical information neural network to predict the post-buckling deflection.

[0011] The present invention provides a method for predicting the post-buckling deflection of cold-rolled steel strip based on a physical information neural network, which combines physical laws with machine learning algorithms to achieve accurate prediction of the post-buckling deflection of cold-rolled steel strip. The method embeds the strip post-buckling large deflection control equation and the deformation coordination equation as physical constraints into the training process of the neural network, so that the neural network can fully consider the physical properties of the strip during the learning process, thereby improving the accuracy of the strip deflection prediction. Compared with the traditional finite element method, the method of the present invention does not require complex meshing and a large amount of numerical calculations, can significantly improve computational efficiency, and reduce computing time and computing resource consumption. The physical information neural network used in the present invention has a strong nonlinear fitting ability and can automatically learn the complex solutions to the strip post-buckling large deflection problem. Even when the strip has complex geometric shapes, boundary conditions and nonlinear characteristics, it can achieve accurate prediction of deflection. The present invention introduces physical equations as constraints in the training process, reducing the dependence on a large amount of experimental data. Even when the experimental data is limited, relatively accurate prediction results can be obtained. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figure 1 A flowchart of a method for predicting post-buckling deflection of cold-rolled strip based on a physical information neural network provided by the present invention;

[0013] FIG2 is a schematic diagram of the structure of the physical information neural network constructed by the present invention;

[0014] FIG3 is a comparison diagram of the strip deflection predicted by the present invention and that after finite element simulation. DETAILED DESCRIPTION

[0015] The following embodiments of the present invention are described in further detail with reference to the accompanying drawings and examples. The following examples are used to illustrate the present invention but are not intended to limit the scope of the present invention.

[0016] like Figure 1 As shown, the present invention provides a method for predicting post-buckling deflection of cold-rolled strip based on a physical information neural network, comprising:

[0017] Step 1: Collect the geometric parameters of the steel strip, the material properties of the steel strip, the initial load and boundary conditions of the steel strip;

[0018] The geometric parameters of the steel strip include length, width and thickness. In this embodiment, the steel strip has a length L = 500 mm, a width B = 100 mm, and a thickness h = 1.5 mm.

[0019] The material property parameters of the strip steel include: Young's modulus and Poisson's ratio. , Poisson's ratio =0.3.

[0020] Step 2: Sample the steel strip within the solution area, obtain the coordinates of multiple sampling points, and perform normalization to form a training data set.

[0021] In specific implementation, sampling points are generated within the strip's solution domain. Based on the strip's geometry and computational accuracy requirements, a uniform sampling method is used to generate a series of 2,500 sampling points, 50 along its length and 50 along its width. The coordinates (x, y) of these sampling points serve as input data for the neural network, where x represents the strip's length and y represents its width. The coordinates of the sampling points are then normalized to improve the training efficiency and stability of the neural network.

[0022] Step 3: Construct a cold-rolled strip post-buckling prediction model based on a physical information neural network, specifically:

[0023] Step 3.1: Design a multi-layer fully connected neural network, including an input layer, multiple hidden layers, and an output layer. The number of neurons in the input layer is 2, corresponding to the normalized strip length coordinate x and strip width coordinate y respectively. The number of neurons in the output layer is 2, used to output the predicted strip deflection. and stress function F; the number of hidden layers and the number of neurons in each layer are set to 3-5 layers, and the number of neurons in each layer is 28-32, such as Figure 2 As shown in the figure, this architecture can better balance the computational effort and the ability to fit the complex relationship of strip deflection.

[0024] Step 3.2: Select the activation function and choose the hyperbolic tangent function tanh(x) or the rectified linear unit function f(x)=max(0,x) as the activation function in the hidden layer.

[0025] In specific implementation, the hyperbolic tangent function tanh(x) can be used, which can map the neuron output to between −1 and 1 to introduce nonlinear characteristics and enhance the fitting ability of the neural network.

[0026] Step 3.3: Embed the strip post-buckling large deflection control equation, deformation coordination equation, strip geometry equation, physical equation, and the relationship between stress function and stress as physical constraints into the neural network training process.

[0027] The strip post-buckling large deflection control equation is:

[0028]

[0029]

[0030]

[0031] The deformation coordination equation is:

[0032]

[0033]

[0034] The geometric equation of the strip steel is:

[0035]

[0036]

[0037]

[0038] The physical equation is:

[0039]

[0040]

[0041]

[0042] The relationship between the stress function and stress is:

[0043]

[0044]

[0045]

[0046] Wherein, D is the bending stiffness of the cold-rolled strip per unit width; E is the Young's modulus of the cold-rolled strip; h is the thickness of the cold-rolled strip; is Poisson's ratio; is the Laplace operator; F is the internal stress function of the cold-rolled strip; is the deflection of the cold-rolled strip; x is the length coordinate of the cold-rolled strip; y is the width coordinate of the cold-rolled strip; u and v are the displacement components of the strip in the x and y directions; 、 、 is the normal strain of the strip in the x direction, the normal strain of the strip in the y direction and the shear strain of the strip in the xy plane; is the normal stress of the strip in the x direction, the normal stress of the strip in the y direction and the shear stress of the strip in the xy plane.

[0047] Step 3.4: Construct the loss function of the cold-rolled strip post-buckling prediction model based on the equations, boundary conditions, and initial loads:

[0048]

[0049] in, is the loss error of the equation, is the boundary condition loss error, is the initial condition error, determined by the initial load on the strip; They represent the weight coefficients of equation loss error, boundary condition loss error, and initial condition error, respectively, and are used to adjust the relative importance of the loss of each part; n1 is the number of equations, n2 is the number of boundaries, and n3 is the number of initial loads.

[0050]

[0051] in, is the load predicted by the model, is the initial load on the strip.

[0052] Loss error for each boundary condition It is determined based on the boundary conditions of each side of the strip:

[0053] The simply supported boundary satisfies: , ;

[0054] The free boundary satisfies: , ; or satisfy: ;

[0055] The fixed support boundary satisfies: , ; or satisfy: .

[0056] Step 4: Use the training data set to train the cold-rolled strip post-buckling prediction model based on the physical information neural network, specifically:

[0057] Step 4.1: Select the Adam optimization algorithm or the stochastic gradient descent algorithm to optimize the parameters of the neural network; this algorithm can adaptively adjust the learning rate, effectively avoiding falling into local optimal solutions during training and improving training efficiency.

[0058] Step 4.2: During the training process, the normalized coordinates (x, y) of the sampling points are input into the physical information neural network to obtain the predicted deflection. According to the definition of the loss function, the total loss is calculated, and the gradient of the loss function to the neural network parameters is calculated through the back-propagation algorithm.

[0059] Step 4.3: Use the Adam optimization algorithm or the stochastic gradient descent algorithm to update the parameters of the neural network so that the loss function gradually decreases.

[0060] Step 4.4: The training process ends when the maximum number of training iterations is reached or the loss function converges to a value less than a preset threshold.

[0061] In practice, the maximum number of training iterations was set to 30,000. The loss function converged to a preset threshold of 0.01. During actual training, the loss value was recorded every 100 training iterations to observe its convergence.

[0062] Step 5: Collect the coordinates of the points to be predicted on the strip, and use the trained cold-rolled strip post-buckling prediction model based on physical information neural network to predict the post-buckling deflection.

[0063] The coordinates (x, y) of the predicted point are normalized and then input into a trained cold-rolled strip post-buckling prediction model based on a physical information neural network to obtain the predicted normalized deflection. The predicted normalized deflection is then denormalized to obtain the final predicted value of the strip deflection.

[0064] At the same time, this embodiment established a finite element simulation model of a local strip steel with the same parameters and under the same conditions for verification. Figure 3 The comparison between the prediction results and the finite element results of data collection in the local area where the highest point of strip deflection occurs in this embodiment is shown. It can be seen that the prediction results through the physical information neural network and the finite element results are within a certain error range, verifying the effectiveness of the results of this method. At the same time, the time taken for prediction through the physical information neural network is much less than the finite element simulation effect, indicating that this method has improved efficiency and is superior.

[0065] The present invention provides a method for predicting the post-buckling deflection of cold-rolled steel strip based on a physical information neural network. By embedding physical constraints into the training process of the neural network, the neural network can fully consider the physical properties of the steel strip during the learning process, thereby improving the accuracy of the strip deflection prediction, significantly improving the computing efficiency, reducing the computing time and the consumption of computing resources, and achieving accurate prediction of the deflection even when the steel strip has complex geometric shapes, boundary conditions and nonlinear characteristics.

[0066] The above description is only a preferred embodiment of the present invention and is not intended to limit the concept of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for predicting post-buckling deflection of cold-rolled strip based on physical information neural network, characterized in that: include: Step 1: Collect the geometric parameters of the steel strip, the material properties of the steel strip, the initial load and boundary conditions of the steel strip; Step 2: Sample the steel strip within the solution area, obtain the coordinates of multiple sampling points, and perform normalization to form a training data set; Step 3: Construct a cold-rolled strip post-buckling prediction model based on physical information neural network; Step 4: Use the training data set to train the cold-rolled strip post-buckling prediction model based on the physical information neural network; Step 5: Collect the coordinates of the points to be predicted on the strip and use the trained cold-rolled strip post-buckling prediction model based on physical information neural network to predict the post-buckling deflection; The step 3 is specifically as follows: Step 3.1: Design a multi-layer fully connected neural network, including an input layer, multiple hidden layers, and an output layer. The input layer has two neurons, corresponding to the normalized strip length coordinate x and strip width coordinate y, respectively. The output layer has two neurons, used to output the predicted strip deflection and stress functions. The number of hidden layers and the number of neurons in each layer are set to 3-5, with 28-32 neurons per layer. Step 3.2: Select the activation function. In the hidden layer, select the hyperbolic tangent function tanh(x) or the rectified linear unit function f(x) = max(0, x) as the activation function. Step 3.3: Embed the strip post-buckling large deflection control equation, deformation coordination equation, strip geometry equation, physical equation, and the relationship between stress function and stress as physical constraints into the neural network training process; Step 3.4: Construct the loss function of the cold-rolled strip post-buckling prediction model based on the equations, boundary conditions, and initial loads: Among them, L msep is the equation loss error, L mseb is the boundary condition loss error, L msei is the initial condition error, determined by the initial load on the strip; α i , β i 、 They represent the weight coefficients of equation loss error, boundary condition loss error, and initial condition error respectively, n1 is the number of equations, n2 is the number of boundaries, and n3 is the number of initial loads.

2. The method for predicting post-buckling deflection of cold-rolled steel strip based on physical information neural network according to claim 1, characterized in that: The geometric parameters of the strip steel include: length, width and thickness; The material property parameters of the strip steel include: Young's modulus and Poisson's ratio.

3. The method for predicting post-buckling deflection of cold-rolled steel strip based on physical information neural network according to claim 1, characterized in that: The strip post-buckling large deflection control equation is: The deformation coordination equation is: The geometric equation of the strip steel is: The physical equation is: The relationship between the stress function and stress is: Wherein, D is the bending stiffness of the cold-rolled strip per unit width; E is the Young's modulus of the cold-rolled strip; h is the thickness of the cold-rolled strip; μ is the Poisson's ratio; is the Laplace operator; F is the internal stress function of the cold-rolled strip; ω is the deflection of the cold-rolled strip; x is the length coordinate of the cold-rolled strip; y is the width coordinate of the cold-rolled strip; u and v are the displacement components of the strip in the x and y directions; ε x , ε y , γ xy is the normal strain of the strip in the x direction, the normal strain of the strip in the y direction and the shear strain of the strip in the xy plane; σ x , σ y , τ xy is the normal stress of the strip in the x direction, the normal stress of the strip in the y direction and the shear stress of the strip in the xy plane.

4. The method for predicting post-buckling deflection of cold-rolled steel strip based on physical information neural network according to claim 1, characterized in that: L msei =|s 1pred -s 1target | 2 Among them, σ 1pred is the load predicted by the model, σ 1target is the initial load on the strip.

5. The method for predicting post-buckling deflection of cold-rolled steel strip based on physical information neural network according to claim 3, characterized in that: Loss error L for each boundary condition mseb It is determined based on the boundary conditions of each side of the strip: The simply supported boundary satisfies: ω=0, The free boundary satisfies: Or satisfy: The fixed support boundary satisfies: ω=0, Or satisfy:

6. The method for predicting post-buckling deflection of cold-rolled strip based on physical information neural network according to claim 1, characterized in that: The step 4 is specifically as follows: Step 4.1: Select the Adam optimization algorithm or the stochastic gradient descent algorithm to optimize the parameters of the neural network; Step 4.2: During the training process, the normalized coordinates (x, y) of the sampling points are input into the physical information neural network to obtain the predicted deflection. According to the definition of the loss function, the total loss is calculated, and the gradient of the loss function with respect to the neural network parameters is calculated through the back-propagation algorithm. Step 4.3: Use the Adam optimization algorithm or the stochastic gradient descent algorithm to update the parameters of the neural network so that the loss function gradually decreases; Step 4.4: The training process ends when the maximum number of training iterations is reached or the loss function converges to a value less than a preset threshold.

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