A structure collision analysis method and system based on domain decomposition PINN

Abstract

The application relates to the technical field of ship structure collision response analysis, in particular to a structure collision analysis method and system based on domain decomposition PINN, the method comprises the following steps: carrying out calculation domain division based on the contact relationship between an impact object and a structure, generating training point coordinates of each subdomain and corresponding boundaries, uniformly scaling the training point coordinates and multidimensional parameters, taking the training point coordinates after scaling as input to construct a collision analysis model, constructing a loss function to calculate the total loss of a submodel, configuring an independent optimizer for each allocated neural network, and outputting complete structure collision displacement field and stress field prediction results, the application can accurately capture stress concentration phenomena in the structure collision process, avoids the stress concentration capture failure problem caused by the discontinuous boundary conditions of the traditional PINN and the oscillation problem of the finite element method in the high gradient area, and improves the prediction accuracy and stability of the structure collision displacement field and the stress field.

Description

Technical Field

[0001] This invention relates to the field of ship structural collision response analysis technology, and in particular to a structural collision analysis method and system based on domain decomposition PINN. Background Technology

[0002] In the field of collision response analysis and strength assessment of ship structures, solid mechanics problems are usually described by partial differential equations. However, most of these equations are difficult to obtain analytical solutions. Therefore, numerical discretization methods have become the core means of obtaining approximate solutions in engineering. The finite element method is currently the most widely used computational framework, but it still has inherent defects that are difficult to overcome: On the one hand, the accuracy of its solution is highly dependent on the mesh quality. Generating high-quality meshes in complex three-dimensional ship structures is not only time-consuming and laborious, but may also lead to mesh distortion due to geometric complexity. On the other hand, the robustness of the finite element method is extremely sensitive to the discretization scheme and the order of the approximate polynomial. Numerical oscillations are prone to occur in the high gradient stress region caused by ship collisions, which seriously affects the accuracy of collision strength assessment.

[0003] Physical Information Neural Networks (PINNs), as an emerging numerical method, have seen rapid development in solving forward and inverse problems in solid mechanics due to their advantages of not relying on grids and being able to directly incorporate physical constraints. However, existing structural response prediction methods based on PINNs are mostly applicable to homogeneous materials or continuous boundary conditions. When faced with problems involving discontinuous loads, such as ship collisions, the limitations of the traditional single-domain, single-network PINN architecture become apparent. During a ship collision, the contact between the impactor and the hull leads to abrupt changes in boundary conditions. This discontinuity is not only reflected at the boundary but also extends into the interior of the hull material, causing a significant decrease in the prediction accuracy of traditional PINNs in local high-gradient regions. Although the domain decomposition PINN method has been proven to effectively handle problems such as discontinuous multi-material properties and improves the solution accuracy by assigning independent neural networks to different regions, its application to structural impact problems with complex discontinuous boundary conditions, such as ship collisions and groundings, remains relatively scarce. At present, there is a need for a structural collision analysis method and system based on domain decomposition PINNs. Summary of the Invention

[0004] To address the issues of traditional PINN (Physical PINN) failing to capture structural collision stress concentration and having low accuracy in assessing collision intensity due to discontinuous boundary conditions, this invention provides a structural collision analysis method and system based on domain decomposition PINN.

[0005] Firstly, the present invention provides a structural collision analysis method based on domain decomposition PINN, which adopts the following technical solution: A structural collision analysis method based on domain decomposition PINN includes: The multi-dimensional parameters of the structure to be analyzed are obtained, and the computational domain is divided based on the contact relationship between the impactor and the structure, generating the coordinates of training points for each subdomain and its corresponding boundary. Feature length, feature displacement, and elastic modulus are selected as feature quantities, and the coordinates of training points and multi-dimensional parameters are scaled to a uniform order of magnitude. A collision analysis model is constructed using the scaled training point coordinates as input, including the basic architecture of the model based on a fully connected neural network, and a hyperbolic tangent activation function is embedded within the basic architecture; Assign corresponding neural networks to each subdomain and its corresponding boundary based on the subdomain type, and construct a loss function to calculate the total loss of the sub-model; An independent optimizer is configured for each assigned neural network, and the network is trained until the total loss function converges through an iterative process of gradient clearing, backpropagation, and parameter updates. The predicted point coordinates of each subdomain are generated, scaled, and then input into the corresponding trained neural network. The prediction results of each subdomain are merged, and the complete prediction results of the structural collision displacement field and stress field are output.

[0006] Furthermore, the generation of training point coordinates for each subdomain and its corresponding boundary includes identifying the contact area through the contact parameters between the impactor and the structure to be analyzed, determining the intersection point of the free boundary and the contact boundary, dividing the computational domain according to the intersection point and the impact direction to obtain several independent subdomains and dividing them into corresponding subdomain boundaries, and forming an interface between adjacent subdomains to constrain the continuity of physical quantities. According to a preset density rule, training points are uniformly generated along the coordinate axes of the structural geometric coordinate system within each subdomain, at the subdomain boundary, and at the interface between adjacent subdomains.

[0007] Furthermore, the uniform scaling of training point coordinates and multi-dimensional parameters includes using selected feature quantities as a uniform scaling reference, and scaling the training point coordinates, displacement boundary conditions, elastic matrix, traction force boundary conditions, and volume force according to the uniform scaling reference. The feature length is determined by selecting the feature dimension of the structure to be analyzed in the impact direction. The feature dimension is calculated based on the maximum geometric span and the feature width of the key stress area in the impact direction of the structure. The uniform scaling expression is: , in, , , , and These correspond to the scaled training point coordinates, displacement boundary conditions, elasticity matrix, traction force boundary conditions, and volume force, respectively. , E and E represent the characteristic length, characteristic displacement, and elastic modulus, respectively. , , , and These are the coordinates of the training points before scaling, the displacement boundary conditions, the elastic matrix, the traction boundary conditions, and the volume force.

[0008] Furthermore, the collision analysis model constructed using scaled training point coordinates as input includes a basic architecture consisting of an input layer, a hidden layer, and an output layer. The input layer receives the scaled training point coordinates, which are then processed layer by layer by the hidden layer. Finally, the output layer outputs the scaled displacement and scaled stress corresponding to the training points. The hidden layer adopts a hierarchical progressive connection structure, with adjacent layer neurons transmitting data through a fully connected manner. For two-dimensional structural collision problems, the hidden layer is configured according to the serial logic of the input layer, hidden layer group, and output layer. For three-dimensional structural collision problems, the number of layers is increased based on the two-dimensional configuration, and the number of neurons in each hidden layer remains consistent. The number of neurons in the input layer matches the dimension of the training point coordinates, and the number of neurons in the output layer matches the sum of the dimensions of the displacement vector and the stress tensor.

[0009] Furthermore, the embedding of hyperbolic tangent activation functions within the infrastructure includes embedding hyperbolic tangent activation functions between adjacent hidden layers of the fully connected neural network and between the last hidden layer and the output layer. The output of the previous layer of neurons in the infrastructure is weighted, summed, and biased before being input to the hyperbolic tangent activation function for nonlinear transformation. The transformed result is used as the input of the next layer of neurons.

[0010] Furthermore, the step of assigning corresponding neural networks to each subdomain and its corresponding boundary according to the subdomain type includes defining subdomains containing contact boundaries as first-class subdomains and subdomains not containing contact boundaries as second-class subdomains. Based on the subdomain classification results, the collision analysis model is instantiated into two independent networks with the same structure. The weight coefficient of the traction boundary in the first-class neural network is higher than that in the second-class neural network. Subdomains of type I and their corresponding boundaries are uniformly assigned to the first-class neural network, and subdomains of type II and their corresponding boundaries are uniformly assigned to the second-class neural network. Subdomains of the same type share the same neural network to achieve optimized allocation of computing resources.

[0011] Further, the construction of the loss function to calculate the total loss of the sub-model includes constructing the control equation loss, boundary condition loss, and interface continuity loss, and performing a weighted sum to obtain the total loss function. The control equation loss is calculated based on the mean square error of the residual between the momentum conservation equation and the constitutive equation. The boundary condition loss is calculated based on the mean square error of the difference between the neural network prediction value and the given boundary condition. The interface continuity loss is calculated based on the mean square error of the difference in physical quantities at the same interface of adjacent subdomains. The control equation loss is expressed as follows: , in, The loss of the control equation for the i-th neural network is... This represents the i-th neural network. The stress in tensor form represents the output of the neural network. The stress, represented by the Voigt notation, is the output of the neural network. The strain, represented by the Voigt notation, is calculated from the displacement output by the neural network.

[0012] Furthermore, the training until the total loss function converges includes configuring an independent optimizer for each neural network corresponding to each subdomain. The training process is executed iteratively. At the beginning of each iteration, the gradient data generated in the previous training round is cleared. Then, backpropagation calculation is performed based on the total loss function through an automatic differentiation mechanism to obtain the gradient information of each neural network parameter. Finally, the parameters of the neural network are iteratively updated based on the gradient information. The iterative update expression is: , in, For the updated neural network parameters, For learning rate, This is an estimate of the first-order momentum. This is an estimate of the second-order momentum. It is a very small constant.

[0013] Furthermore, the output of complete structural collision displacement and stress field prediction results includes inputting the scaled prediction point coordinates into the neural network trained on the corresponding subdomains to obtain the scaled displacement and scaled stress of each subdomain prediction point, restoring the actual displacement and actual stress of each subdomain prediction point through inverse scaling operation, and merging the prediction results of each subdomain according to the spatial positional relationship of the subdomains to output complete structural collision displacement and stress field prediction results. The expression for the inverse scaling operation is: , in, This is the actual displacement. This represents the scaled displacement of the neural network output. For actual stress, The scaled stress is the output of the neural network.

[0014] Secondly, a structural collision analysis system based on domain decomposition PINN includes: The data acquisition module is configured to: acquire multi-dimensional parameters of the structure to be analyzed, divide the computational domain based on the contact relationship between the impactor and the structure, and generate the coordinates of training points for each subdomain and its corresponding boundary. The preprocessing module is configured to: select feature length, feature displacement and elastic modulus as feature quantities, and perform uniform scaling on the training point coordinates and multi-dimensional parameters; The model module is configured to: construct a collision analysis model with scaled training point coordinates as input, including a fully connected neural network as the basic architecture of the model, and embed a hyperbolic tangent activation function within the basic architecture; The transformation module is configured to: assign corresponding neural networks to each subdomain and its corresponding boundary according to the subdomain type, and construct a loss function to calculate the total loss of the sub-model; The training module is configured to: configure an independent optimizer for each assigned neural network, and train until the total loss function converges through an iterative process of gradient clearing, backpropagation, and parameter updates; The output module is configured to: generate the predicted point coordinates of each subdomain, scale them, input them into the corresponding trained neural network, merge the prediction results of each subdomain, and output the complete prediction results of the structural collision displacement field and stress field.

[0015] In summary, the present invention has the following beneficial technical effects: 1. This invention divides the computational domain based on the contact relationship between the impactor and the structure, generates subdomains containing interfaces and training points, and constructs a collision analysis model using uniform scaling combined with a fully connected neural network and a hyperbolic tangent activation function. Through iterative training with an independent optimizer and inverse scaling and merging of prediction results, it achieves accurate capture of stress concentration phenomena during structural collision without relying on external training data. This effectively avoids the stress concentration capture failure problem caused by discontinuous boundary conditions in traditional PINN and the oscillation problem of the finite element method in high gradient regions, significantly improving the prediction accuracy and stability of structural collision displacement and stress fields.

[0016] 2. This invention decomposes the computational domain into independent subdomains based on contact relationships and sets interface constraints, enabling each subdomain's neural network to learn local mechanical responses in a targeted manner. The hyperbolic tangent activation function ensures the accuracy of residual calculations for higher-order partial differential equations. A weighted fusion total loss function with multiple loss terms strengthens physical constraints and interface continuity. Independent optimizers achieve precise convergence of each neural network, resulting in efficient fitting of the nonlinear response to structural collisions. This simplifies the process of collision analysis for complex structures, reduces reliance on computational resources, and eliminates the need for large amounts of labeled training data. It also expands the engineering application scenarios of the PINN method in ship structural collision analysis and strength assessment.

[0017] 3. This invention eliminates the impact of differences in parameter magnitudes on training results through a unified scaling mechanism. It adopts a hierarchical, progressive, fully connected neural network architecture to adapt to two-dimensional and three-dimensional structural collision problems. Based on the subdomain type, it configures the neural network weight ratio differently. Combined with the iterative training process of gradient clearing, backpropagation, and adaptive parameter updates, it achieves a balance between model training efficiency and prediction accuracy. It ensures the continuity of physical quantities at the interface in the prediction results, provides a reliable technical means for rapid and accurate evaluation of structural collision response, and helps to shorten the structural design cycle and optimize the structural collision resistance performance. Attached Figure Description

[0018] Figure 1 This is a flowchart of the structural collision analysis method based on domain decomposition PINN proposed in this invention; Figure 2 This is a schematic diagram of the impact process of the two-dimensional structure in an embodiment of the present invention; Figure 3 This is a schematic diagram of the domain decomposition scheme of the method of the present invention for two-dimensional structures subjected to multi-directional impacts. Figure 4 This is a schematic diagram of the neural network and loss function in an embodiment of the present invention; Figure 5 This is a graph showing the prediction results of the domain decomposition PINN method in an embodiment of the present invention, wherein... Figure 5 (a) shows the predicted displacement components in the X direction. Figure 5 (b) shows the predicted displacement components in the Y direction. Figure 5 (c) shows the predicted results of the normal stress components in the X direction. Figure 5 (d) shows the predicted results of the normal stress components in the Y direction. Figure 5 (e) shows the predicted results of the shear stress components. Figure 5 (f) shows the predicted equivalent stress; Figure 6 This is a diagram showing the calculation results of the finite element method in an embodiment of the present invention, wherein, Figure 6 (a) shows the calculation results of the displacement components in the X direction. Figure 6 (b) shows the calculation results of the displacement components in the Y direction. Figure 6 (c) shows the calculation results of the normal stress components in the X direction. Figure 6 (d) shows the calculated results of the normal stress components in the Y direction. Figure 6 (e) shows the calculation results of the shear stress components. Figure 6 (f) shows the equivalent stress calculation results; Figure 7 This is a comparison of local details of the prediction results from the domain decomposition PINN method and the finite element method in an embodiment of the present invention. Figure 7 (a) shows the comparison results of the displacement components in the X direction. Figure 7 (b) shows the comparison results of the displacement components in the Y direction. Figure 7 (c) shows the comparison results of the normal stress components in the X direction. Figure 7 (d) shows the comparison results of the normal stress components in the Y direction. Figure 7 (e) shows the comparison results of shear stress components. Figure 7 (f) shows the results of the equivalent stress comparison. Detailed Implementation

[0019] The present invention will be further described in detail below with reference to the accompanying drawings.

[0020] Example 1: Refer to Figure 1 This embodiment of a structural collision analysis method based on domain decomposition PINN includes: The multi-dimensional parameters of the structure to be analyzed are obtained, and the computational domain is divided based on the contact relationship between the impactor and the structure, generating the coordinates of training points for each subdomain and its corresponding boundary. Feature length, feature displacement, and elastic modulus are selected as feature quantities, and the coordinates of training points and multi-dimensional parameters are scaled to a uniform order of magnitude. A collision analysis model is constructed using the scaled training point coordinates as input, including the basic architecture of the model based on a fully connected neural network, and a hyperbolic tangent activation function is embedded within the basic architecture; Assign corresponding neural networks to each subdomain and its corresponding boundary based on the subdomain type, and construct a loss function to calculate the total loss of the sub-model; An independent optimizer is configured for each assigned neural network, and the network is trained until the total loss function converges through an iterative process of gradient clearing, backpropagation, and parameter updates. The predicted point coordinates of each subdomain are generated, scaled, and then input into the corresponding trained neural network. The prediction results of each subdomain are merged, and the complete prediction results of the structural collision displacement field and stress field are output.

[0021] Specifically, a structural collision analysis method based on domain decomposition PINN includes the following steps: like Figure 1 As shown, S1, obtain the multi-dimensional parameters of the structure to be analyzed, and divide the computational domain based on the contact relationship between the impactor and the structure, generating the training point coordinates of each subdomain and its corresponding boundary. First, multi-dimensional parameters of the structure to be analyzed are obtained. These parameters include the structure's geometric dimensions, material properties, impactor-related parameters, and boundary constraint parameters, such as solid-wall constraints, free boundaries, and symmetrical boundaries, along with their corresponding constraint conditions. Material properties include the elastic modulus E and Poisson's ratio. Impactor-related parameters include the impactor's geometry, impact velocity, and impact direction. Then, a contact determination model is established using the contact parameters between the impactor and the structure. These parameters include the impact direction vector of the impactor, the initial contact position coordinates between the impactor and the structure, and the geometric topological information of the structural surface. A geometric intersection detection algorithm is used to identify the contact area: for two-dimensional structural impact... In collision problems, the impacting object is simplified into line segments or polygons, and the structure to be analyzed is simplified into a polygonal outline. The contact area is determined by judging the intersection relationships between line segments and polygon edges, and the overlapping areas between polygons. For 3D structural collision problems, the impacting object is simplified into a curved surface or polyhedron, and the structure to be analyzed is simplified into a polyhedron model. The contact area is accurately located through spatial curved surface intersection detection and polyhedron volume overlap calculation. At the edge of the identified contact area, a distinction is made between free boundaries and contact boundaries. Free boundaries are unconstrained boundaries or boundaries only subject to environmental loads, while contact boundaries represent boundaries in direct contact with the impacting object. A boundary tracing algorithm is used to traverse the structural outline to obtain the coordinate set of the intersection points of the free and contact boundaries. Where n is the number of boundary points, Let i be the i-th boundary point. In a two-dimensional problem, the z-coordinate is 0.

[0022] Then, using the coordinate set P of the boundary point and the impact direction vector The computational domain is divided for the core parameters, where, The direction of impact of the impactor on the structure. Let v be the components of the impact direction vector along the x, y, and z axes of the structural geometric coordinate system, taking values ​​in the interval [-1, 1]. For a two-dimensional structural collision problem, construct a straight line L passing through each intersection point and parallel to the impact direction vector v. i The equation of the line is ,and ≠0 and ≠0, if If = 0, then the equation of the line is: ,like If = 0, then the equation of the line is: Where x, y, and z are the coordinate variables of any point on the dividing plane. , Let x and y be the x and y coordinates of the i-th intersection point, which is a necessary point for the line to pass through, ensuring that the dividing line passes through the intersection of the free boundary and the contact boundary. and The slope of the line is determined by the components of the impact direction vector on the x and y axes, so that the dividing line is consistent with the impact direction. This ensures that the subdomain can specifically capture the local mechanical response caused by the impact. The original computational domain is divided into several independent two-dimensional subdomains by this set of lines, and the original structural boundary through which the dividing line passes is synchronously divided into the boundary of the corresponding subdomain. Two-dimensional interfaces are formed between adjacent subdomains.

[0023] For the three-dimensional structure collision problem, construct a surface S passing through each intersection point and tangent to the impact direction vector v. i The surface equation is determined based on the structural geometry and impact direction. If the structure is a regular geometric shape (such as a cuboid or cylinder), the surface can be a plane or a quadratic surface. The plane equation is... ,in, Let z be the z-coordinate of the i-th boundary point. The original computational domain is divided into several independent three-dimensional subdomains by this set of surfaces. The original structural boundary passed through by the dividing surface is synchronously divided into the boundary of the corresponding subdomain, and a three-dimensional interface is formed between adjacent subdomains.

[0024] like Figure 2 , Figure 3 As shown, the following rules must be followed during the computational domain segmentation process: the volume or area difference between the segmented subdomains should not exceed 30%. If the difference exceeds this, the position of the segmenting line or surface should be adjusted to ensure that the scale of each subdomain is balanced. For multi-directional impact scenarios, there are multiple impact vectors v1, v2, ..., v in different directions. k To avoid intersections or overlapping subdomains between segmented straight lines / surfaces, adjacent and non-contact subdomains are merged to reduce computational complexity. Finally, training points are generated according to a preset density rule, determined based on the accuracy requirements of the structural collision problem. The training point spacing d ranges from 0.001m to 0.01m; in this embodiment, d=0.005m is selected. For each subdomain, points are evenly distributed along each coordinate axis direction within the subdomain at a spacing d, using the structural geometric coordinate system (x-axis, y-axis, z-axis) as a reference. The coordinates of the training points within the two-dimensional subdomain are obtained using the formula (…). ) generated, where, , These represent the minimum and maximum values ​​of the subdomain along the x-axis, respectively. , , respectively, represent the minimum and maximum values ​​of the subdomain along the y-axis, and i is the index of the point along the x-axis. j is the index of the point along the y-axis. The coordinates of training points within the three-dimensional subdomain are obtained through the formula. Generate, where , These are the minimum and maximum values ​​of the subdomain along the z-axis, respectively, where k is the index of the points along the z-axis. At the boundaries of each subdomain and the interfaces between adjacent subdomains, points are uniformly distributed along the geometric contours of the boundaries or interfaces at the same interval d. For straight or planar boundaries, points are directly generated according to the uniform distribution formula mentioned above. For curved or surface boundaries, the curve or surface is first discretized into several segments of broken lines or surfaces, with the length of each segment not exceeding d. Then, points are uniformly distributed at interval d on each segment of broken line or surface to ensure that the density of training points on the boundaries and interfaces is consistent with that inside the subdomain. Finally, a complete set of training point coordinates containing the interior of the subdomain, the boundaries of the subdomain, and the interfaces is formed, providing a data foundation for subsequent parameter scaling and model training.

[0025] S2. Select feature length, feature displacement and elastic modulus as feature quantities, and perform uniform scaling on the training point coordinates and multi-dimensional parameters. After completing the computational domain partitioning and training point coordinate generation in step S1, the next step is to unify the parameter scaling. By selecting feature length, feature displacement, and elastic modulus as core feature quantities, a unified scaling benchmark is established. First, the feature quantities are determined and selected, including the feature length. The characteristic dimensions are calculated using the characteristic dimensions of the structure under analysis in the impact direction, which are derived from the maximum geometric span of the structure in the impact direction. and the characteristic width of the key stress area It is determined according to the weighted average formula, which is as follows: ,in, This is a weighting coefficient, ranging from 0.6 to 0.8, which can be adjusted based on the structural stress characteristics. If the width of critical stress areas, such as near the contact boundary or the expected stress concentration area, significantly affects the collision response, it can be reduced. Values, in this embodiment Maximum geometric span The structure's vector in the impact direction The projection onto the surface is obtained by calculating the difference between the maximum and minimum projected coordinates of all points on the structural boundary in the impact direction, which represents the characteristic width of the key stress area. The maximum width of the contact area along the vertical direction of the impact is determined by identifying the contour of the contact area and calculating its size range perpendicular to the impact direction.

[0026] Characteristic displacement The displacement magnitude or engineering experience value is selected based on the preset displacement magnitude for structural collision problems, for common scenarios such as ship structural collisions. The range of values ​​is In this embodiment, the following is selected If known boundary displacement conditions exist, the absolute value of the displacement can be used as... To ensure that the displacement parameters are within a reasonable range after scaling, the elastic modulus E is an inherent property parameter of the structural material to be analyzed, which is directly extracted from the multi-dimensional parameters obtained in step S1. In this embodiment, the structural material is steel, and the elastic modulus E is... .

[0027] Once the feature quantities are determined, they are used as a unified scaling benchmark to scale the training point coordinates, displacement boundary conditions, elasticity matrix, traction force boundary conditions, and volume force respectively. The unified scaling expression is as follows: , in, , , , and These correspond to the scaled training point coordinates, displacement boundary conditions, elasticity matrix, traction force boundary conditions, and volume force, respectively. , E and E represent the characteristic length, characteristic displacement, and elastic modulus, respectively. , , , and These are the coordinates of the training points before scaling, the displacement boundary conditions, the elastic matrix, the traction boundary conditions, and the volume force.

[0028] For the training point coordinate x, it is the three-dimensional coordinate value generated in step S1 (the third dimension is 0 in a two-dimensional problem), which is obtained by dividing the coordinate components of each training point by the feature length. To achieve uniformity in the magnitude of coordinate parameters and ensure that the scaled coordinates are consistent. Within the range [0,10], to avoid difficulties in initializing the weights of the neural network input layer due to excessively large or small coordinate values; for the displacement boundary condition u, including the preset displacement constraint values ​​of each boundary of the structure, such as the displacement of the solid wall boundary being 0, the given displacement of the impact boundary, etc., each displacement component is divided by the characteristic displacement. , to scale the displacement Concentrated in the [-10, 10] interval, it fits the input range of neural network activation functions; for the elasticity matrix C, which is a matrix describing the elastic properties of the material, the expression for the elasticity matrix corresponding to the two-dimensional structure is: , in, It is Poisson's ratio, and in this embodiment, it is the elastic modulus. for Poisson's ratio The elasticity is 0.3. The elastic matrix corresponding to the three-dimensional structure is determined according to the theory of mechanics of materials. Each element in the elastic matrix is ​​divided by the elastic modulus E to achieve dimensionless processing of the elastic matrix and eliminate the fluctuation of the matrix element magnitude caused by the difference in material stiffness. For the traction force boundary condition t, which is the distributed force on the structural boundary, it is obtained by multiplying each component of the traction force vector by the characteristic length. Then divide by the elastic modulus E and the characteristic displacement The product of the ... The magnitudes are consistent to ensure that the values ​​match the scaled values ​​of other parameters; for the volume force f, each component of the volume force vector is multiplied by the feature length. The square of the value, divided by the elastic modulus E and the characteristic displacement The product of the volume force and the load parameters is used to normalize the magnitude of the volume force, thus avoiding the loss of calculation accuracy in the governing equations due to the large difference between the volume force value and other load parameters.

[0029] The following constraints must be followed during scaling: scaling of all parameters must be based on the same set of features. , And E, ensure that the scaling reference is consistent; for two-dimensional structural collision problems, only the coordinates, displacements, traction forces, and volume force components in the x and y directions are scaled, while the relevant parameters in the z direction remain unchanged; after scaling, the scaling results of each parameter need to be verified to ensure that the scaled parameters are consistent. , , , and All values ​​are within the range [-100, 100]. If a value exceeds this range, the feature value is adjusted. or The values ​​are then rescaled until all parameters meet the required scale, laying the data foundation for the subsequent construction and training of the neural network.

[0030] S3. Construct a collision analysis model using the scaled training point coordinates as input, including the basic architecture of the model based on a fully connected neural network, and embed the hyperbolic tangent activation function inside the basic architecture; The hierarchical structure of the model's basic architecture is determined. This architecture consists of an input layer, hidden layers, and an output layer connected in series. Neurons at each layer use a fully connected approach for data transmission, ensuring that the output of neurons in the previous layer is completely transmitted to all neurons in the next layer, achieving full feature fusion and mapping. The number of neurons in the input layer is strictly matched to the dimension of the training point coordinates: for two-dimensional collision problems, the training point coordinates are... For two-dimensional vectors, the number of neurons in the input layer is set to 2; for three-dimensional collision problems, the coordinates of the training points are... A three-dimensional vector, with the number of neurons in the input layer set to 3. The input layer receives the scaled coordinates of the training points from step S2. This is then converted into a vector form that can be processed by the neural network, serving as the initial input features for the model.

[0031] The hidden layers employ a hierarchical, progressive connection structure. The number of layers and neurons is adapted to the dimension of the structural collision problem: For two-dimensional structural collision problems, 5 hidden layers are set, with each layer uniformly configured with 64 neurons. This configuration ensures both model fitting ability and training efficiency, avoiding slow convergence or gradient explosion caused by overly deep or wide network structures. For three-dimensional structural collision problems, due to the need to handle higher-dimensional feature mappings and more complex mechanical response relationships, the number of hidden layers increases to 6-8, while the number of neurons per layer remains at 64. This ensures balanced feature processing capabilities across hidden layers and avoids a sharp increase in computational complexity due to the increased number of layers. The hidden layers are interconnected through a fully connected weight matrix. Let the first layer be... The number of neurons in the hidden layer is , No. The number of neurons in the hidden layer is Then the fully connected weight matrix between the two layers The dimension is Bias vector The dimension is The initial values ​​of the weight matrix and bias vector are determined using the Xavier initialization method, meaning the elements of the weight matrix follow a range... The neurons are uniformly distributed within the layer, and the initial value of the bias vector is set to 0 to ensure that the output of each neuron is within a reasonable range in the initial stage. The number of neurons in the output layer matches the sum of the displacement vector dimension and the stress tensor dimension: for a two-dimensional structural collision problem, the displacement vector is... A two-dimensional vector, the stress tensor is represented using the Voigt notation as follows: The vector is three-dimensional, therefore the number of neurons in the output layer is set to 2+3=5, corresponding to the two components of two-dimensional displacement and the three components of two-dimensional stress, respectively; for the three-dimensional structural collision problem, the displacement vector is... A three-dimensional vector, the stress tensor, is represented using the Voigt notation as follows: Since it is a six-dimensional vector, the number of neurons in the output layer is set to 3+6=9, corresponding to the three components of three-dimensional displacement and the six components of three-dimensional stress, respectively. The output layer receives the output features of the last hidden layer, and after linear transformation, outputs the scaled displacement and scaled stress corresponding to the training points, thus completing the mapping from coordinate features to mechanical response.

[0032] The hyperbolic tangent (Tanh) activation function is embedded within the infrastructure. The applicability of various common activation functions in this method is shown in Table 1. Table 1 shows the applicability of common activation functions in this method;

[0033] Embedding locations include between adjacent hidden layers and between the last hidden layer and the output layer, ensuring that the input of each layer undergoes a nonlinear transformation, thus improving the model's ability to fit the nonlinear mechanical response to structural collisions. The activation function works by: the output vector of the previous layer's neurons... With the corresponding weight matrix Perform matrix multiplication and then superimpose the bias vectors. The linear transformation result is obtained. Its mathematical expression is ,in This is the output vector of the l-th layer neuron. For the first layer to the first The weight matrix of the layer, For the first Layer bias vector, For the first The linear input of the layer neurons will be linear input The input is subjected to a nonlinear transformation by the hyperbolic tangent activation function, the mathematical expression of which is: This function has continuous derivatives of any order in the real number range, and its output value ranges from [-1, 1]. It effectively prevents gradient explosion while simultaneously capturing both global trend fitting and local nonlinear details. Furthermore, as an odd function, it possesses good symmetry, which helps in gradient balancing and accelerates training convergence. The result after activation function transformation... As the first The output of each layer of neurons is passed to the next layer for feature mapping, until the output of the last hidden layer is transformed by the activation function and then input to the output layer to complete the linear transformation and output the final result.

[0034] The following constraints must be followed during model construction: the number of neurons in the input, hidden, and output layers must be strictly matched according to the dimension of the structural collision problem to ensure data dimension consistency; the initialization method for the weight matrix and bias vector should uniformly adopt Xavier initialization to avoid training difficulties caused by improper initial parameters; the embedding position of the hyperbolic tangent activation function must cover all adjacent layers, and no nonlinear transformation of any layer should be omitted; for two-dimensional and three-dimensional structural collision problems, the number of layers and neurons in the hidden layers must be executed according to the preset configuration. If adjustments are required, it must be ensured that the number of neurons in each hidden layer is consistent after adjustment, and the number of layers matches the problem complexity, ensuring that the model can fully fit the mechanical response without wasting computational resources or causing training non-convergence due to excessive structural complexity. Ultimately, a collision analysis model with a regular structure and strong mapping ability is constructed, laying the foundation for subsequent subdomain neural network allocation and model training.

[0035] S4. Assign corresponding neural networks to each subdomain and its corresponding boundary according to the subdomain type, and construct a loss function to calculate the total loss of the sub-model; like Figure 4As shown, all subdomains divided in step S1 are traversed, and the subdomains are defined according to whether they contain contact boundaries. Subdomains containing the contact boundary between the impactor and the structure are defined as Class I subdomains. These subdomains directly bear impact loads, and the boundary conditions are discontinuous, requiring higher accuracy in capturing the mechanical response. Subdomains that do not contain contact boundaries but only contain free boundaries, solid wall constraint boundaries, or symmetrical boundaries are defined as Class II subdomains. The mechanical response of these subdomains is relatively smooth, and the boundary conditions are continuous. Based on the subdomain classification results, the collision analysis model constructed in step S3 is instantiated into two independent neural networks with the same structure, denoted as the first type of neural network and the second type of neural network, respectively. The basic architecture of the two types of networks (number of layers of input layer, hidden layer, output layer, number of neurons, and activation function type) is completely identical, with the only difference being the traction boundary weight coefficient in the boundary condition loss calculation. The traction boundary weight coefficient of the first type of neural network ranges from 0.6 to 0.8, while that of the second type of neural network ranges from 0.2 to 0.4. Through differentiated weight configuration, the first type of neural network focuses more on fitting the load transfer characteristics of the contact boundary, thereby improving the prediction accuracy of the stress concentration area. The allocation rule is as follows: all Class I subdomains and their corresponding boundaries are uniformly allocated to the first type of neural network, and all Class II subdomains and their corresponding boundaries are uniformly allocated to the second type of neural network. Subdomains of the same type share the same neural network, eliminating the need to instantiate a network separately for each subdomain, thereby optimizing the allocation of computing resources and reducing the computational complexity in multi-subdomain scenarios. For multi-subdomain partitioning scenarios caused by multi-directional impacts, if there are multiple adjacent Class II subdomains, they can be further merged into a single logical subdomain and share the same second type of neural network, ensuring computational efficiency without affecting prediction accuracy.

[0036] After the neural network assignment is completed, a loss function is constructed to quantify the deviation between the model's predicted values ​​and the actual mechanical response. The loss function consists of three parts: governing equation loss, boundary condition loss, and interface continuity loss, all calculated based on mean squared error (MSE). The core formula is as follows: ,in, This is the error matrix; if it is a vector, it degenerates into vector form. Let F0 be the square of the Frobenius norm of the error matrix, and for vectors it be the square of the 2-norm. The formula calculates the number of training points involved in the error and accurately measures the overall level of prediction bias by averaging the squared errors.

[0037] The first part involves constructing the governing equation loss, which is based on the residual calculation of the momentum conservation equation and the constitutive equation. This ensures that the model prediction results satisfy the fundamental physical laws of solid mechanics. For the i-th neural network... The expression for the loss in its governing equation is: , in, The loss of the control equation for the i-th neural network is... This represents the i-th neural network. The stress in tensor form represents the output of the neural network. The stress output of the neural network is represented by Voigt notation. In a two-dimensional problem, the stress tensor is converted into a three-dimensional vector using Voigt notation. In a three-dimensional problem, it is converted into a 6-dimensional vector. , The strain, expressed in Voigt notation, is calculated from the displacement output by the neural network. The strain calculation follows geometric equations in a two-dimensional problem. In three-dimensional problems, calculations are performed using expanded calculations based on the geometric equations of solid mechanics. The divergence of the stress tensor reflects the conservation of momentum. In this expression, the first term... Calculate the residual mean square error of the momentum conservation equation to ensure that the prediction results satisfy the force equilibrium condition; the second term Calculate the residual mean square error of the constitutive equations to ensure that stress and strain satisfy the elastic constitutive relation of the material. Average the losses of the governing equations of all neural networks to obtain the total governing equation loss. ,in, This represents the total number of neural networks.

[0038] The second part involves constructing the boundary condition loss, which is calculated based on the difference between the boundary displacements and traction forces predicted by the neural network and the given boundary conditions, ensuring that the model meets the boundary constraints of the structure. For the i-th neural network, the expression for its boundary condition loss is: , in, Let be the boundary condition loss of the i-th neural network. This represents the number of boundaries of the i-th neural network (the boundaries do not include the interfaces between adjacent regions). Indicates the dimension of the problem being analyzed; This represents the displacement component in the k-th dimension on the j-th boundary of the corresponding region output by the i-th neural network. This represents the component of the j-th displacement boundary condition in the k-th dimension of the region corresponding to the i-th neural network. This represents the stress in tensor form on the j-th boundary of the corresponding region of the i-th neural network output. Let represent the normal vector of the j-th boundary of the region corresponding to the i-th neural network. This represents the k-th component of the dot product of the stress tensor and the boundary normal vector output by the neural network. This represents the component of the j-th traction boundary condition in the k-th dimension of the region corresponding to the i-th neural network. This represents the weight of the k-th component of the j-th displacement boundary condition corresponding to the i-th neural network region. This represents the weight of the k-th component of the j-th traction boundary condition corresponding to the i-th neural network region. The total boundary condition loss is obtained by summing the boundary condition losses of all neural networks. .

[0039] The third part is the construction of the interface continuity loss. This loss is calculated based on the displacement and stress differences at the same interface between adjacent subdomains, ensuring the continuity of physical quantities at the interface and avoiding breaks or abrupt changes in the prediction results of the subdomains. For neural networks corresponding to adjacent subdomains with interfaces, the expression for the interface continuity loss is: , in, This represents the number of neighboring regions corresponding to the i-th neural network, which is also the number of interfaces corresponding to the current neural network. and Let represent the stresses, denoted by Voigt, on the current interface at the outputs of the i-th and j-th neural networks, respectively. and These represent the displacements on the current interface output by the i-th and j-th neural networks, respectively. For the case where the two neural networks correspond to two different regions, this expression simplifies to... After calculating the governing equation loss, boundary condition loss, and interface loss separately, the total loss is obtained by weighted summation of each loss: , in, , , These are the corresponding weights, in this embodiment This weight configuration ensures that the model follows basic physical laws while also taking into account boundary constraints and interface continuity requirements, providing a precise loss metric for subsequent model training.

[0040] The following constraints must be followed during the implementation of this step: the subdomain type division must be strictly based on whether it includes contact boundaries to ensure unambiguous classification; the basic architecture of the two types of neural networks must be completely consistent, with only the traction boundary weight coefficients being configured differently; all calculations of the loss function are based on the parameters scaled up in step S2 to ensure uniformity of magnitude; the weight values ​​of the total loss function need to be adjusted according to the problem dimension and the number of subdomains, with the core principle being that the control equation loss weight is not less than 0.4 and the interface continuity loss weight is not less than 0.1 to ensure the dominant role of physical constraints.

[0041] S5. Configure an independent optimizer for each assigned neural network and train it until the total loss function converges through an iterative process of gradient clearing, backpropagation, and parameter updates. For each type of neural network assigned to the steps, a separate Adam optimizer is configured. The core parameters of the two optimizers can be set differently according to the subdomain type to ensure adaptation to the mechanical response characteristics of different subdomains. The core parameters of the optimizers include the learning rate. First-order momentum decay coefficient Second-order momentum decay coefficient and a very small constant, learning rate The step size for controlling parameter updates is used. The first type of neural network corresponds to the I-class subdomain (including the contact boundary), where the mechanical response is complex and stress concentration exists. The learning rate is set to a value of [value missing]. In this embodiment, The second type of neural network corresponds to the Class II subdomain (no contact boundary), exhibiting a smooth mechanical response, and the learning rate is set to [value missing]. In this embodiment, the value is taken as... First-order momentum decay coefficient The default value is 0.9, used for estimating first-order momentum using exponential moving averages, reflecting the recent trend of the parameter update gradient; the second-order momentum decay coefficient... The default value is 0.999, used for estimating second-order momentum using exponential moving averages, reflecting the recent squared trend of the parameter update gradient; a minimal constant. Values This is used to avoid the case where the denominator in the iterative update expression is zero, while ensuring the stability of numerical calculations.

[0042] After the optimizer is configured, start the iterative training process of the neural network. The specific steps are as follows: Gradient clearing: At the beginning of each iteration, the optimizer's gradient clearing interface is called to reset all gradient data of the neural network parameters, including the weight matrix W and bias vector b, from the previous training round to 0. ,in This represents all trainable parameters of the neural network. This operation avoids the interference of residual gradient data from the previous round on the parameter update of the current round, ensuring that the gradient calculation of each iteration is based only on the loss value of the current round, thus guaranteeing the stability and convergence efficiency of the training process.

[0043] Backpropagation and gradient calculation: Based on the total loss function constructed in step S4, the total loss function is calculated with respect to each neural network parameter through an automatic differentiation mechanism, such as the torch.autograd module in the PyTorch framework or the tf.GradientTape in the TensorFlow framework. gradient information The automatic differentiation mechanism traces backward along the forward propagation path of the neural network, sequentially calculating the partial derivatives of the total loss function with respect to the parameters of the output layer, hidden layer, and input layer, ultimately obtaining a complete gradient vector. This gradient vector reflects the degree and direction of each parameter's influence on the total loss, providing a basis for parameter updates. During gradient calculation, the gradients of the two types of neural networks are calculated independently without interference, ensuring that each network's parameter updates only adapt to the loss changes in its corresponding subdomain.

[0044] Parameter Iterative Update: Based on the gradient calculation results, the parameters of each neural network are updated using a pre-defined iterative update expression. The update expression is: , in, For the updated neural network parameters, For learning rate, This is an estimate of the first-order momentum. This is an estimate of the second-order momentum. For a minimal constant, the first-order momentum estimate is... and second-order momentum estimates It is calculated using the exponential moving average, and the specific formula is as follows: , , in, and The bias correction term is used to compensate for the problem of the initial momentum estimate being too small. During the parameter update process, the parameters of the two types of neural networks are updated independently. That is, the first type of neural network updates its own parameters only based on the loss gradient of its corresponding subdomain, and the second type of neural network does the same, so as to achieve accurate fitting of the mechanical response of each neural network to the corresponding subdomain.

[0045] During iterative training, the trend of the total loss function needs to be monitored in real time to determine whether the training has converged. The convergence criteria include the following two categories, and training can be stopped if either category is met: The first category is that within a preset number of consecutive rounds (set to 100 rounds in this example), the absolute value of the change in the total loss function is less than the convergence threshold. The first type indicates that the loss function has stabilized and further training cannot significantly improve the model accuracy. The second type is when the training rounds reach the preset maximum number of rounds (set to 5000 rounds in this embodiment). At this point, regardless of whether the loss function still has room for decrease, training is stopped. The convergence threshold and the maximum number of training rounds need to be adjusted according to the complexity of the structural collision problem. The maximum number of rounds can be appropriately reduced for two-dimensional problems and increased accordingly for three-dimensional problems. The core principle is to balance training efficiency while ensuring model accuracy.

[0046] S6. Generate the predicted point coordinates of each subdomain, scale them, input them into the corresponding trained neural network, merge the prediction results of each subdomain, and output the complete prediction results of the structural collision displacement field and stress field.

[0047] The coordinates of predicted points in each subdomain are generated. The generation range of the predicted points corresponds to the spatial range of each subdomain divided in step S1. The generation rule is consistent with the logic of generating training point coordinates, but the density can be adjusted according to the accuracy requirements. After generating the coordinates of predicted points in each subdomain, the coordinates of the predicted points are scaled according to the uniform scaling rule in step S2. The scaled coordinates of each subdomain are then input into the corresponding trained neural network. Through the forward propagation calculation of the neural network, the scaled displacement corresponding to each predicted point is output. and scaled stress Then, the scaled displacement and stress are restored to their actual physical quantities through inverse scaling. The inverse scaling expression is as follows: , in, This is the actual displacement. This represents the scaled displacement of the neural network output. For actual stress, The scaled stress output by the neural network can be converted into displacement and stress data with actual physical meaning by inverse scaling.

[0048] After inverse scaling, the actual displacement of each subdomain is determined according to its spatial relationship. and actual stress The prediction results are then stitched together: First, a global coordinate system is established, and the coordinates of the prediction points in each subdomain are mapped to the global coordinate system to ensure that the coordinates of the prediction points at the subdomain boundaries and interfaces correspond one-to-one in the global coordinate system. For overlapping prediction points at the interfaces, the average value of the output results of the two types of neural networks is taken as the final value to avoid abrupt changes in physical quantities at the interfaces and to ensure the continuity of the merged results. For prediction points in non-interface regions, the inverse scaling results of the corresponding neural networks are directly retained. During the merging process, the positional correlation of the prediction results of each subdomain needs to be verified through a spatial coordinate matching algorithm to ensure that there are no conflicting results in overlapping areas or missing results in blank areas. Finally, a complete prediction point cloud data covering the entire original computational domain is formed, and each prediction point contains global coordinates, actual displacement vectors, and actual stress tensor information.

[0049] Finally, based on the complete predicted point cloud data, the predicted displacement and stress fields of the structure are output: the displacement field results are presented in the form of displacement component cloud maps and displacement vector maps, clearly showing the magnitude and direction of displacement at each location of the structure; the stress field results are presented in the form of stress component cloud maps and equivalent stress cloud maps. The equivalent stress is calculated according to the fourth strength theory, specifically divided into equivalent stress for three-dimensional problems and equivalent stress for two-dimensional problems, with the following formula: , , in, For the equivalent stress of a three-dimensional problem, For the equivalent stress of a two-dimensional problem, Let these be the normal stress components at the predicted point in the global coordinate system of the structure, corresponding to tensile or compressive stresses along the x-axis, y-axis, and z-axis, respectively. The shear stress components of the predicted point in the global coordinate system of the structure are respectively the shear stress in the xy plane, xz plane, and yz plane. They are also predicted and output by the neural network and obtained by inverse scaling. The sign of the shear stress is determined by whether the shear direction is consistent with the coordinate system. At the same time, the statistical results of key parameters are output, including the maximum displacement value and location, the maximum stress value and location, the maximum equivalent stress value and location, etc., to provide a quantitative basis for the assessment of structural collision strength and realize high-precision prediction of structural collision displacement field and stress field.

[0050] Example 2: The difference between this example and Example 1 is that this example provides a specific experiment for a structural collision analysis method based on domain decomposition PINN: like Figure 5 , Figure 6 As shown, Figure 5 (a) shows the predicted displacement components in the X direction. Figure 5 (b) shows the predicted displacement components in the Y direction. Figure 5 (c) shows the predicted results of the normal stress components in the X direction. Figure 5 (d) shows the predicted results of the normal stress components in the Y direction. Figure 5 (e) shows the predicted results of the shear stress components. Figure 5 (f) shows the predicted equivalent stress. Figure 6 (a) shows the calculation results of the displacement components in the X direction. Figure 6 (b) shows the calculation results of the displacement components in the Y direction. Figure 6 (c) shows the calculation results of the normal stress components in the X direction. Figure 6 (d) shows the calculated results of the normal stress components in the Y direction. Figure 6 (e) shows the calculation results of the shear stress components. Figure 6(f) shows the equivalent stress calculation results. This embodiment takes the response problem of the longitudinal girder structure of a large ship under the condition of running aground as the research object to verify the effectiveness of the method of the present invention in the collision analysis of complex structures. The longitudinal girder height is 1000mm and the rib spacing is 2000mm. Considering the structural symmetry, only one side of the current longitudinal girder segment is analyzed, that is, the calculation domain is a square area of ​​1000mm×1000mm. The material is high-strength steel with an elastic modulus of [missing value]. Poisson's ratio To facilitate a more intuitive presentation of the results, the model was inverted. In the collision scenario, the reef was simplified to a cylinder with a radius of 0.5m, which contacts the bottom of the ship along the inner normal direction of the outer plate and acts on the middle region of the current longitudinal girder segment, thereby causing a significant local response in the longitudinal girder structure of that region.

[0051] Based on the contact relationship between the cylindrical reef and the longitudinal girder, a two-dimensional linear segmentation algorithm is used to divide the 1000mm×1000mm computational domain into two subdomains along the impact direction (the direction of the inner normal of the outer plate). The subdomain containing the contact boundary is the Class I subdomain, and the other side is the Class II subdomain. Adjacent subdomains form an interface. Training points are generated at intervals of 0.004m inside each subdomain, at the boundary, and at the interface, for a total of 62,500 training points. Then, parameter scaling is performed sequentially, and the scaled data is input into a fully connected neural network. Prediction points are generated at intervals of 0.002m, scaled, and input into the trained neural network. After inverse scaling, the prediction results of each subdomain are merged to obtain the displacement field and stress field of the ship's bottom longitudinal girder structure.

[0052] In this embodiment, the prediction results of the method of the present invention are compared with those of the traditional finite element method (FEM). The comparison data of key displacement and stress parameters are shown in Table 2 below: Table 2 is a comparison table of the results of the method of the present invention and the finite element method in the embodiments;

[0053] The comparison results show that the displacement and stress distributions in the proposed method are basically consistent with those in the finite element method. In detail, the proposed method effectively captures stress concentrations caused by discontinuous boundary conditions. Table 2 compares the maximum displacement and stress values ​​(absolute values) of the proposed method and the finite element method, and calculates the relative errors. The relative error of the maximum displacement value is smaller than the relative error of the maximum stress value. The X-direction component of the displacement... The relative error of the absolute maximum value is approximately 2%, while the Y-direction component... The relative error of the absolute maximum value does not exceed 1%. Stress components and The relative error of the absolute maximum value does not exceed 3%, stress components The absolute maximum value and equivalent stress The relative error does not exceed 6%. For example, the detailed comparison between this embodiment and the finite element method at the discontinuities in the upper boundary conditions... Figure 7 As shown, Figure 7 (a) to Figure 7 In (f), the left figure of each subplot represents the result of this method, and the right figure represents the finite element result. Figure 7 (a) shows the comparison results of the displacement components in the X direction. Figure 7 (b) shows the comparison results of the displacement components in the Y direction. Figure 7 (c) shows the comparison results of the normal stress components in the X direction. Figure 7 (d) shows the comparison results of the normal stress components in the Y direction. Figure 7 (e) shows the comparison results of shear stress components. Figure 7 (f) shows the equivalent stress comparison results, with displacement in mm and stress in MPa. The contour lines of this method are smoother near this location, while the contour lines of the finite element results have obvious jagged edges.

[0054] Example 3: This example provides a structural collision analysis system based on domain decomposition PINN, including: The data acquisition module is configured to: acquire multi-dimensional parameters of the structure to be analyzed, divide the computational domain based on the contact relationship between the impactor and the structure, and generate the coordinates of training points for each subdomain and its corresponding boundary. The preprocessing module is configured to: select feature length, feature displacement and elastic modulus as feature quantities, and perform uniform scaling on the training point coordinates and multi-dimensional parameters; The model module is configured to: construct a collision analysis model with scaled training point coordinates as input, including a fully connected neural network as the basic architecture of the model, and embed a hyperbolic tangent activation function within the basic architecture; The transformation module is configured to: assign corresponding neural networks to each subdomain and its corresponding boundary according to the subdomain type, and construct a loss function to calculate the total loss of the sub-model; The training module is configured to: configure an independent optimizer for each assigned neural network, and train until the total loss function converges through an iterative process of gradient clearing, backpropagation, and parameter updates; The output module is configured to: generate the predicted point coordinates of each subdomain, scale them, input them into the corresponding trained neural network, merge the prediction results of each subdomain, and output the complete prediction results of the structural collision displacement field and stress field.

[0055] The above are all preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Therefore, all equivalent changes made in accordance with the structure, shape and principle of the present invention should be covered within the scope of protection of the present invention.

Claims

1. A structural collision analysis method based on domain decomposition PINN, characterized in that, include: The multi-dimensional parameters of the structure to be analyzed are obtained, and the computational domain is divided based on the contact relationship between the impactor and the structure, generating the coordinates of training points for each subdomain and its corresponding boundary. Feature length, feature displacement, and elastic modulus are selected as feature quantities, and the coordinates of training points and multi-dimensional parameters are scaled to a uniform order of magnitude. A collision analysis model is constructed using the scaled training point coordinates as input, including the basic architecture of the model based on a fully connected neural network, and a hyperbolic tangent activation function is embedded within the basic architecture; Assign corresponding neural networks to each subdomain and its corresponding boundary based on the subdomain type, and construct a loss function to calculate the total loss of the sub-model; An independent optimizer is configured for each assigned neural network, and the network is trained until the total loss function converges through an iterative process of gradient clearing, backpropagation, and parameter updates. The predicted point coordinates of each subdomain are generated, scaled, and then input into the corresponding trained neural network. The prediction results of each subdomain are merged, and the complete prediction results of the structural collision displacement field and stress field are output.

2. The structural collision analysis method based on domain decomposition PINN according to claim 1, characterized in that, The process of generating training point coordinates for each subdomain and its corresponding boundary includes identifying the contact area through the contact parameters between the impactor and the structure to be analyzed, determining the intersection point of the free boundary and the contact boundary, dividing the computational domain according to the intersection point and the impact direction to obtain several independent subdomains and dividing them into corresponding subdomain boundaries, and forming an interface between adjacent subdomains to constrain the continuity of physical quantities. According to a preset density rule, training points are uniformly generated along the coordinate axes of the structural geometric coordinate system within each subdomain, at the subdomain boundary, and at the interface between adjacent subdomains.

3. The structural collision analysis method based on domain decomposition PINN according to claim 1, characterized in that, The unified scaling of training point coordinates and multi-dimensional parameters includes using selected feature quantities as a unified scaling benchmark, and scaling the training point coordinates, displacement boundary conditions, elastic matrix, traction force boundary conditions, and volume force according to the unified scaling benchmark. The feature length is determined by selecting the feature dimension of the structure to be analyzed in the impact direction. The feature dimension is calculated based on the maximum geometric span and the feature width of the key stress area in the impact direction of the structure. The unified scaling expression is: ， in, , , , and These correspond to the scaled training point coordinates, displacement boundary conditions, elasticity matrix, traction force boundary conditions, and volume force, respectively. , E and E represent the characteristic length, characteristic displacement, and elastic modulus, respectively. , , , and These are the coordinates of the training points before scaling, the displacement boundary conditions, the elastic matrix, the traction boundary conditions, and the volume force.

4. The structural collision analysis method based on domain decomposition PINN according to claim 1, characterized in that, The collision analysis model, constructed using scaled training point coordinates as input, comprises a basic architecture consisting of an input layer, a hidden layer, and an output layer. The input layer receives the scaled training point coordinates, which are then processed layer by layer by the hidden layer. Finally, the output layer outputs the scaled displacement and stress corresponding to the training points. The hidden layer adopts a hierarchical progressive connection structure, with adjacent layer neurons transmitting data through a fully connected manner. For two-dimensional structural collision problems, the hidden layer is configured in a series logic of input layer, hidden layer group, and output layer. For three-dimensional structural collision problems, the number of layers is increased based on the two-dimensional configuration, and the number of neurons in each hidden layer remains consistent. The number of neurons in the input layer matches the dimension of the training point coordinates, and the number of neurons in the output layer matches the sum of the dimensions of the displacement vector and the stress tensor.

5. The structural collision analysis method based on domain decomposition PINN according to claim 1, characterized in that, The method of embedding hyperbolic tangent activation functions within the infrastructure includes embedding hyperbolic tangent activation functions between adjacent hidden layers of the fully connected neural network and between the last hidden layer and the output layer. In the infrastructure, the output of the previous layer of neurons is weighted, summed, and biased before being input to the hyperbolic tangent activation function for nonlinear transformation. The transformed result is used as the input of the next layer of neurons.

6. The structural collision analysis method based on domain decomposition PINN according to claim 1, characterized in that, The process of assigning corresponding neural networks to each subdomain and its corresponding boundary based on the subdomain type includes defining subdomains containing contact boundaries as first-class subdomains and subdomains not containing contact boundaries as second-class subdomains. Based on the subdomain classification results, the collision analysis model is instantiated into two independent networks with the same structure. The weight coefficient of the traction boundary in the first-class neural network is higher than that in the second-class neural network. Subdomains of type I and their corresponding boundaries are uniformly assigned to the first-class neural network, and subdomains of type II and their corresponding boundaries are uniformly assigned to the second-class neural network. Subdomains of the same type share the same neural network to achieve optimized allocation of computing resources.

7. The structural collision analysis method based on domain decomposition PINN according to claim 1, characterized in that, The construction of the loss function calculates the total loss of the sub-model, including the construction of the control equation loss, boundary condition loss, and interface continuity loss, and performs a weighted sum to obtain the total loss function. The control equation loss is calculated based on the mean square error of the residual between the momentum conservation equation and the constitutive equation. The boundary condition loss is calculated based on the mean square error of the difference between the neural network prediction value and the given boundary condition. The interface continuity loss is calculated based on the mean square error of the difference in physical quantities at the same interface of adjacent subdomains. The control equation loss is expressed as follows: ， in, The loss of the control equation for the i-th neural network is... This represents the i-th neural network. The stress in tensor form represents the output of the neural network. The stress, represented by the Voigt notation, is the output of the neural network. The strain, represented by the Voigt notation, is calculated from the displacement output by the neural network.

8. The structural collision analysis method based on domain decomposition PINN according to claim 1, characterized in that, The training until the total loss function converges includes configuring an independent optimizer for each neural network corresponding to each subdomain. The training process is executed iteratively. At the beginning of each iteration, the gradient data generated in the previous training round is cleared. Then, backpropagation calculation is performed based on the total loss function through an automatic differentiation mechanism to obtain the gradient information of each neural network parameter. Finally, the parameters of the neural network are iteratively updated based on the gradient information. The iterative update expression is: ， in, For the updated neural network parameters, For learning rate, This is an estimate of the first-order momentum. This is an estimate of the second-order momentum. It is a very small constant.

9. The structural collision analysis method based on domain decomposition PINN according to claim 1, characterized in that, The complete structural collision displacement and stress field prediction results are output by inputting the scaled prediction point coordinates into the neural network trained on the corresponding subdomains, obtaining the scaled displacement and stress of each subdomain prediction point, restoring the actual displacement and stress of each subdomain prediction point through inverse scaling, and merging the prediction results of each subdomain according to the spatial position relationship of the subdomains to output the complete structural collision displacement and stress field prediction results. The expression for the inverse scaling operation is as follows: ， in, This is the actual displacement. This represents the scaled displacement of the neural network output. For actual stress, The scaled stress is the output of the neural network.

10. A structural collision analysis system based on domain decomposition PINN, executing the method of claim 1, characterized in that, include: The data acquisition module is configured to: acquire multi-dimensional parameters of the structure to be analyzed, divide the computational domain based on the contact relationship between the impactor and the structure, and generate the coordinates of training points for each subdomain and its corresponding boundary. The preprocessing module is configured to: select feature length, feature displacement and elastic modulus as feature quantities, and perform uniform scaling on the training point coordinates and multi-dimensional parameters; The model module is configured to: construct a collision analysis model with scaled training point coordinates as input, including a fully connected neural network as the basic architecture of the model, and embed a hyperbolic tangent activation function within the basic architecture; The transformation module is configured to: assign corresponding neural networks to each subdomain and its corresponding boundary according to the subdomain type, and construct a loss function to calculate the total loss of the sub-model; The training module is configured to: configure an independent optimizer for each assigned neural network, and train until the total loss function converges through an iterative process of gradient clearing, backpropagation, and parameter updates; The output module is configured to: generate the predicted point coordinates of each subdomain, scale them, input them into the corresponding trained neural network, merge the prediction results of each subdomain, and output the complete prediction results of the structural collision displacement field and stress field.

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