Cold-rolled strip steel post-buckling deflection prediction method based on physical information neural network

Abstract

The invention discloses a cold-rolled strip steel post-buckling deflection prediction method based on a physical information neural network. The cold-rolled strip steel post-buckling deflection prediction method comprises the steps that 1, geometric parameters of strip steel, material attribute parameters of the strip steel, load conditions borne by the strip steel and boundary conditions are collected; 2, sampling the strip steel in the solving area of the strip steel to obtain coordinates of a plurality of sampling points, and normalizing the coordinates to form a training data set; 3, constructing a cold-rolled strip steel post-buckling prediction model based on the physical information neural network; 4, training the cold-rolled strip steel post-buckling prediction model based on the physical information neural network by adopting the training data set; and 5, collecting coordinates of a to-be-predicted point of the strip steel, and performing post-buckling deflection prediction by adopting the trained cold-rolled strip steel post-buckling prediction model based on the physical information neural network. According to the method, the physical law and the machine learning algorithm are combined, and accurate prediction of the post-bending deflection of the cold-rolled strip steel is achieved.

Description

Technical Field

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

[0002] In engineering practice, many strip steels will undergo large - deflection deformation and enter the post - buckling state when subjected to loads. The analysis of the large - deflection deformation of strip steel structures in the post - buckling state is a key issue in fields such as iron and steel, aerospace, and civil engineering. Accurately predicting the deformation of the structure under large post - buckling deflections is crucial for ensuring the safety and reliability of the structure.

[0003] However, traditional methods for predicting the post - buckling deformation and shape defects of strip steel mainly rely on empirical formulas, analytical methods, and finite - element simulations, etc. Since the large - deflection equilibrium equation of strip steel involves the solution of high - order nonlinear equations, which is difficult and complex to solve, empirical formulas and analytical methods rely on a large amount of experimental data and simplified assumptions, and it is difficult to accurately describe complex nonlinear mechanical behaviors. Although finite - element simulations can more accurately simulate the deformation of strip steel, they have problems such as large computational volume, long calculation time, and limited ability to handle complex boundary conditions and material properties. With the development of strip - steel production towards high precision and high performance, there is an urgent need for an efficient and accurate method to predict the large post - buckling deflections and shape defects of strip steel. Summary of the Invention

[0004] To solve the above - mentioned technical problems, the purpose of the present invention is to provide a method for predicting the post - buckling deflection of cold - rolled strip steel based on a physics - informed neural network, so as to solve high - order nonlinear complex formulas, improve the accuracy and calculation efficiency of strip - steel deflection prediction, reduce the dependence on computing resources, and at the same time be able to better adapt to the complex geometric shapes, boundary conditions, and nonlinear characteristics of strip steel.

[0005] The present invention provides a method for predicting the post - buckling deflection of cold - rolled strip steel based on a physics - informed neural network, including:

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

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

[0008] Step 3: Construct a post - buckling prediction model for cold - rolled strip steel based on a physics - informed neural network;

[0009] Step 4: Use the training data set to train the post - buckling prediction model for cold - rolled strip steel based on a physics - informed neural network;

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

[0011] A method for predicting the post-buckling deflection of cold-rolled strip based on the physics-informed neural network of the present invention combines physical laws with machine learning algorithms to achieve accurate prediction of the post-buckling deflection of cold-rolled strip. This method embeds the large deflection control equation and deformation coordination equation of strip post-buckling as physical constraints into the training process of the neural network, enabling the neural network to fully consider the physical properties of the strip during the learning process, thereby improving the accuracy of strip deflection prediction. Compared with the traditional finite element method, the method of the present invention does not require complex mesh generation and a large amount of numerical calculations, can significantly improve the calculation efficiency, and reduce the consumption of calculation time and calculation resources. The physics-informed neural network adopted by the present invention has a strong non-linear fitting ability and can automatically learn the complex solutions of the strip post-buckling large deflection problem. Even in the case of complex strip geometries, boundary conditions and non-linear characteristics, it can also achieve accurate prediction of the deflection. In the training process of the present invention, physical equations are introduced as constraints, reducing the dependence on a large amount of experimental data. Even when the experimental data is limited, relatively accurate prediction results can be obtained. Description of the Drawings

[0012] Figure 1 is a flow chart of a method for predicting the post-buckling deflection of cold-rolled strip based on the physics-informed neural network provided by the present invention;

[0013] Figure 2 is a schematic structural diagram of the physics-informed neural network constructed by the present invention;

[0014] Figure 3 is a comparison diagram of the strip deflection predicted by the present invention and the finite element simulation. Detailed Embodiments

[0015] The following will further describe in detail the specific embodiments of the present invention in conjunction with the drawings and embodiments. The following embodiments are used to illustrate the present invention, but are not used to limit the scope of the present invention.

[0016] As Figure 1 shown, a method for predicting the post-buckling deflection of cold-rolled strip based on the physics-informed neural network of the present invention includes:

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

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

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

[0020] Step 2: Sample the strip steel within the solution region to obtain the coordinates of multiple sampling points, and after normalizing them, form a training dataset.

[0021] Specifically, when implementing, sampling points are generated. Within the solution domain of the strip steel, according to the geometric shape of the strip steel and the calculation accuracy requirements, a uniform sampling method is used to generate a series of sampling points. 50 sampling points are taken in the length direction, and 50 sampling points are taken in the width direction, a total of 2,500 sampling points are generated. The coordinates (x, y) of these sampling points will be used as the input data of the neural network, where x is the coordinate in the length direction of the strip steel, and y is the coordinate in the width direction of the strip steel. Then, the coordinates of the sampling points are normalized to improve the training efficiency and stability of the neural network.

[0022] Step 3: Construct a post-buckling prediction model for cold-rolled strip steel based on a physics-informed neural network, specifically:

[0023] Step 3.1: Design a multi-layer fully connected layer 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 coordinate x in the length direction of the strip steel and the coordinate y in the width direction of the strip steel respectively; the number of neurons in the output layer is 2, used to output the predicted deflection of the strip steel and the stress function F; the number of layers of the hidden layer 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, as Figure 2 shown. This architecture can better balance the computational amount and the fitting ability for the complex relationship of the strip steel deflection.

[0024] Step 3.2: Select an 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.

[0025] Specifically, when implementing, the hyperbolic tangent function tanh(x) can be used. This function can map the neuron output to between -1 and 1 to introduce non-linear characteristics and enhance the fitting ability of the neural network.

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

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

[0028]

[0029]

[0030]

[0031] The deformation compatibility equation is as follows:

[0032]

[0033]

[0034] The strip geometry equation is as follows:

[0035]

[0036]

[0037]

[0038] The physical equation is as follows:

[0039]

[0040]

[0041]

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

[0043]

[0044]

[0045]

[0046] where D is the flexural rigidity 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 the 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 coordinate in the length direction of the cold-rolled strip; y is the coordinate in the width direction of the cold-rolled strip; u and v are the displacement components of the strip in the x and y directions; and and are 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; are 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 post-buckling prediction model for cold-rolled strip steel according to the equations, boundary conditions, and initial loads:

[0048]

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

[0050]

[0051] where, is the load predicted by the model, is the initial load applied to the strip steel.

[0052] Each boundary condition loss error is determined according to the boundary conditions of each side of the strip steel:

[0053] The simply supported boundary satisfies: , ;

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

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

[0056] Step 4: Train the post-buckling prediction model for cold-rolled strip steel based on the physics-informed neural network using the training dataset, 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 avoid getting stuck in local optimal solutions during training, and improve the training efficiency.

[0058] Step 4.2: During the training process, input the normalized coordinates (x,y) of the sampling points into the physics-informed neural network to obtain the predicted deflection, calculate the total loss according to the definition of the loss function, and calculate the gradient of the loss function with respect to the parameters of the neural network through the backpropagation algorithm.

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

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

[0061] Specifically, the maximum number of training iterations is set to 30,000 times. The loss function converges to a preset threshold of 0.01. During actual training, the loss value is recorded every 100 training times to observe its convergence.

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

[0063] Normalize the coordinates (x, y) of the points to be predicted, and then input the normalized coordinates into the trained post-buckling deflection prediction model of cold-rolled strip steel based on the physics-informed neural network to obtain the predicted normalized deflection. At the same time, perform denormalization on the predicted normalized deflection to obtain the final strip steel deflection prediction value.

[0064] At the same time, in this embodiment, a finite element simulation model of the local strip steel with the same parameters and in the same situation is established for verification. Figure 3 It shows the comparison between the prediction results and the finite element results of the data collected in the local area where the strip steel deflection reaches the highest point in this embodiment. It can be seen that the prediction results by the physics-informed neural network are within a certain error range compared with the finite element results, verifying the effectiveness of the results of this method. At the same time, the time required for prediction by the physics-informed neural network is much less than the finite element simulation effect, indicating that this method improves the efficiency and has superiority.

[0065] A method for predicting the post-buckling deflection of cold-rolled strip steel based on the physics-informed neural network of the present invention embeds physical constraints into the training process of the neural network, enabling the neural network to fully consider the physical characteristics of the strip steel during the learning process, thereby improving the accuracy of strip steel deflection prediction, significantly improving the calculation efficiency, reducing the consumption of calculation time and calculation resources, and being able to accurately predict the deflection even in the case of strip steel with complex geometric shapes, boundary conditions, and non-linear characteristics.

[0066] The above are only the preferred embodiments of the present invention and are not intended to limit the idea of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A method for predicting the post - buckling deflection of cold - rolled strip steel based on a physics - informed neural network, characterized in that, Including: Step 1: Collect the geometric parameters of the strip steel, the material property parameters of the strip steel, the initial load and boundary conditions applied to the strip steel; Step 2: Sample the strip steel within the solution region of the strip steel, obtain the coordinates of multiple sampling points and perform normalization processing to form a training data set; Step 3: Construct a post-buckling prediction model for cold-rolled strip steel based on a physics-informed neural network; Step 4: Use the training data set to train the post-buckling prediction model for cold-rolled strip steel based on a physics-informed neural network; Step 5: Collect the coordinates of the points to be predicted of the strip steel, and use the trained post-buckling prediction model for cold-rolled strip steel based on a physics-informed neural network to predict the post-buckling deflection.

2. The method for predicting the post-buckling deflection of cold-rolled strip steel based on a physics-informed neural network according to claim 1, wherein: 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 post-buckling deflection prediction method of cold-rolled strip steel based on the physics-informed neural network according to claim 1, characterized in that The specific content of step 3 is as follows: Step 3.1: Design a multi-layer fully connected layer 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 coordinate x in the length direction of the strip steel and the coordinate y in the width direction of the strip steel respectively; the number of neurons in the output layer is 2, which is used to output the predicted deflection and stress function of the strip steel; 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; Step 3.2: Select an 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 post-buckling large deflection control equation of the strip steel, the deformation compatibility equation, the geometric equation of the strip steel, the physical equation and the relationship between the stress function and the stress as physical constraints into the training process of the neural network; Step 3.4: Construct the loss function of the post-buckling prediction model for cold-rolled strip steel according to the equation, boundary conditions and initial load: wherein, is the equation loss error, is the boundary condition loss error, is the initial condition error, which is determined by the initial load on the strip steel; respectively represent the weight coefficients of the equation loss error, the boundary condition loss error, and the initial condition error. n1 is the number of equations, n2 is the number of boundaries, and n3 is the number of initial loads.

4. The method for predicting the post-buckling deflection of cold-rolled strip steel based on a physics-informed neural network according to claim 3, wherein: The post-buckling large deflection control equation of the strip steel is: The deformation compatibility equation is: The geometric equation of the strip steel is: The physical equation is: The relationship between the stress function and the stress is: Among them, D is the flexural rigidity 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 the 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 coordinate in the length direction of the cold-rolled strip; y is the coordinate in the width direction of the cold-rolled strip; u, v are the displacement components of the strip in the x and y directions; 、 、 are 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; are 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.

5. The method for predicting the post-buckling deflection of cold-rolled strip steel based on a physics-informed neural network according to claim 3, wherein: Among them, is the load predicted by the model, is the initial load on the strip steel.

6. The post-buckling deflection prediction method of cold-rolled strip steel based on the physics-informed neural network according to claim 4, characterized in that, Each boundary condition loss error is determined based on the boundary conditions for each edge of the strip: The simply supported boundary satisfies: , ; The free boundary satisfies: , ; or satisfies: ; The clamped boundary satisfies: , ; or satisfies: .

7. The post-buckling deflection prediction method of cold-rolled strip steel based on the physics-informed neural network according to claim 1, characterized in that The specific content of step 4 is 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, input the normalized coordinates (x,y) of the sampling points into the physics-informed neural network to obtain the predicted deflection. According to the definition of the loss function, calculate the total loss, and calculate the gradient of the loss function with respect to the parameters of the neural network through the backpropagation algorithm; Step 4.3: Use the Adam optimization algorithm or the stochastic gradient descent algorithm to update the parameters of the neural network to gradually reduce the loss function. Step 4.4: When the maximum number of training iterations is reached or the loss function converges to less than a preset threshold, the training process ends.

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