Anti-deformation structure lightweight optimization method based on active sampling and physical information neural network

Abstract

The invention discloses an anti-deformation structure lightweight optimization method based on active sampling and a physical information neural network. The invention relates to the technical field of structure optimization, and solves the problem that optimization precision and calculation efficiency cannot be balanced in the prior art. The method is oriented to an anti-deformation structure, the flexibility is used as a minimization target, the usage amount of structural materials is used as a constraint, and a neural network is used as optimization acceleration; the method aims at achieving integration of a deep neural network and structure optimization, achieving an efficient anti-deformation structure optimization design process and proposing an active sampling strategy to reduce the cost of model training. The physical information neural network of the coding bottom layer physical law shows the superiority, and a forward problem can be directly solved in a scene without a training sample; and an active sampling strategy is adopted to reduce the input data volume, so that the training difficulty is reduced, and the training cost is saved. Furthermore, potential energy based on a variational form is calculated for decoupling material properties and displacements of the training collocation and used for the construction of a loss function.

Description

Technical Field

[0001] The present invention relates to the technical field of structural optimization, and in particular to a lightweight optimization method for anti-deformation structures based on active sampling and physical information neural networks. Background Art

[0002] With the development of technology, the optimization design of anti-deformation structures has gradually become an important research direction in the engineering field. This design method is widely used in fields such as parameter identification and structural optimization, aiming to improve the stability and adaptability of structures under complex load conditions. For the optimization of anti-deformation structures, its core goal is to reduce material consumption and manufacturing costs while meeting functional requirements through reasonable design strategies, while improving the diversity and high-performance characteristics of the structure. Although traditional methods such as finite element analysis and variable optimization have solved some problems to a certain extent, their computational efficiency is low and it is difficult to cope with complex nonlinear material distributions. In contrast, although data-driven methods can significantly improve the optimization efficiency, the high sample generation cost and the model's reliance on extrapolation capabilities limit their practical application. Although these methods provide an exploration direction for new structural optimization paradigms, they still face challenges in the trade-off between sample generation costs and extrapolation capabilities.

[0003] In recent years, physical information-driven optimization methods have brought new ideas to the optimization design of anti-deformation structures. This method avoids dependence on large-scale samples by directly embedding the underlying physical laws into the optimization process, thereby achieving zero-sample training and maintaining high prediction accuracy. In particular, under the framework of the energy method, the energy calculation strategy based on variational form can more efficiently describe the mechanical behavior in structural optimization and significantly improve the reliability of the optimization results. Since there is no need to rely on training data, this method can theoretically be applied to any structural optimization problem and shows broad application prospects. However, in practical applications, the complexity of the geometric design domain and its boundary conditions places higher requirements on the accuracy of the optimization results. In addition, the complex nonlinear distribution of materials also increases the difficulty of optimization, resulting in training cost becoming one of the limiting factors. Therefore, how to balance optimization accuracy and computational efficiency is still a key issue that needs to be solved in the field of anti-deformation structural optimization design. Summary of the invention

[0004] The purpose of the present invention is to provide a lightweight optimization method for anti-deformation structures based on active sampling and physical information neural network to solve the problem that the prior art cannot balance the optimization accuracy and computational efficiency.

[0005] The present invention provides a lightweight optimization method for anti-deformation structure based on active sampling and physical information neural network, comprising:

[0006] Step 1: Select the anti-deformation structural part to be optimized and discretize it to obtain the corresponding mesh model. Based on the mesh model of the anti-deformation structural part, establish mesh data including node connection relationship and node coordinates, establish boundary conditions for displacement and load, and set the active sampling threshold ε. s , setting parameters of neural network models involving structural optimization and physical information;

[0007] Step 2: Preprocess the data, including constructing a density filter matrix, calculating the partial derivative matrix of the shape function at each unit integration point, and initializing the density field;

[0008] Step 3: Active sampling threshold ε set in step 1 s Sampling the units actually required, and screening all nodes associated with these units as inputs to the physical information neural network model;

[0009] Step 4: Calculate the grayscale index based on the density field to dynamically configure the trainable parameters of the physical information neural network model;

[0010] Step 5: Train the configured physical information neural network model to the maximum number of iterations, and perform the following in sequence during the iteration process: predict displacement, calculate internal potential energy and external potential energy, construct loss function, and update network trainable parameters; after the training is completed, separate the required node displacement and strain energy density field from the calculation graph;

[0011] Step 6: Convert the strain energy density into the sensitivity vector of the optimization target, calculate the sensitivity vector of the volume constraint, and use the combined density field vector as the optimizer input to obtain the optimized density field vector;

[0012] Step 7: Determine whether the optimization meets the convergence condition. If not, return to step 3 based on the optimized density field vector; if satisfied, output the optimized density field vector.

[0013] Furthermore, the boundary conditions of the load in step 1 are encoded as hard constraints into the training of the physical information neural network model, and its general expression is:

[0014]

[0015] Where g(x) represents the Dirichlet boundary function, l(x) is an auxiliary function to ensure that g(x) only works on the Dirichlet boundary; x represents any node in the geometric domain; represents the displacement amplitude preset by the Dirichlet boundary; Γ D represents the Dirichlet frontier.

[0016] Further, in step one, the load boundary conditions are encoded in vector form and used to calculate the external work in the training of the physics-informed neural network model:

[0017] E ext =f T u.

[0018] Where E ext represents the external work, f represents the load vector; u represents the predicted displacement vector; T represents the transpose.

[0019] Further, in step three, it is necessary to sample the set of elements with a unit density greater than the preset sampling threshold and obtain the set of non-repeating nodes associated with all elements. The sampled set of elements is expressed as:

[0020]

[0021] Where represents the sampled element; Ω represents the entire geometric design domain; ρ represents the element density; τ represents the sampling threshold.

[0022] Further, in step four, it is necessary to calculate the gray-scale index according to the density field. This index is used to indirectly describe the convergence of the density field to reflect the change state of the design variables. This index is calculated by the following formula:

[0023]

[0024] Where M represents the gray-scale index; ρ k represents the density of the k-th element; Ne represents the total number of discrete elements; when the gray-scale index is greater than the preset gray-scale threshold only the network parameters of the backbone neural network are considered as trainable parameters; when the gray-scale index is less than the preset gray-scale threshold the network parameters of the backbone neural network and the coefficient neural network are periodically used as trainable parameters respectively. In the first structural optimization cycle of each period, only the backbone neural network is trained, and in the remaining periods, only the coefficient neural network is trained.

[0025] Further, in step five, the loss function uses the total potential energy function Π(u), which is the difference between the internal potential energy and the external potential energy of the system, and is expressed as:

[0026]

[0027] Where the first term on the right side is the internal potential energy of the system, and the second term is the external potential energy of the system; σ represents the Cauchy stress; ε represents the Cauchy strain; Γ NIndicates the Neumann boundary; u represents the predicted displacement vector; T represents the transpose; Ω represents the entire geometric design domain; f represents the load vector; dv represents the volume element, which is integrated over the entire volume domain; ds represents the line segment element, which is integrated over the load boundary.

[0028] Furthermore, in step five, the internal potential energy of the system is calculated based on the discrete form, the internal potential energy of the element is calculated based on two-point Gaussian integration, and the sum is obtained as the total internal potential energy of the system, expressed as:

[0029]

[0030] where Ω represents the entire geometric design domain; σ represents the Cauchy stress; ε represents the Cauchy strain; dv represents the volume element; Ne and Ng respectively represent the total number of discrete elements and the number of element integration points; σ ij and ε ij respectively represent the Cauchy stress and strain at the j-th integration point of the i-th element; κ j represents the weight at the j-th integration point; T represents the transpose.

[0031] Furthermore, in step six, the sensitivity of the optimization objective is obtained from the strain energy density field output by the physics-informed neural network. When the element strain field is converted into a sensitivity vector, the element strain energy and the elements of the sensitivity vector are required to satisfy a bijective relationship; the sensitivity of the volume constraint is expressed as the actual volume or area vector of the element.

[0032] Furthermore, the convergence criterion in step six is set as:

[0033]

[0034] where f c represents the optimization objective; Ns is a constant integer value; τ stop represents the convergence threshold; f c represents the optimization objective; k represents the index of the corresponding iteration.

[0035] The present invention also provides a computer device, including a processor and a memory. The memory is used to store a computer program, and the processor is used to execute the computer program to perform the above method.

[0036] The present invention has the following beneficial effects:

[0037] The present invention proposes a dynamic configuration neural network composed of a backbone neural network and a coefficient neural network. This network model can dynamically configure the backbone neural network with high training cost or the coefficient neural network with low training cost as the training network according to the gray scale index, so as to reduce the training cost of the physics-informed neural network. The essence of this strategy lies in using the similarity of the pseudo-density field in the continuous optimization cycle to periodically replace the high-cost neural network model.

[0038] The present invention proposes an active sampling strategy, which selectively samples elements according to density and obtains training collocation points, thereby removing collocation points with low contribution to the loss function, and saving computational cost by reducing the amount of input data without sacrificing the accuracy of the physics-informed neural network.

[0039] The present invention uses Gaussian quadrature to calculate the strain energy of elements instead of the strain energy at collocation points, thereby decoupling the displacement prediction from the material at collocation points, and thus enabling accurate assignment of material properties. Description of the Drawings

[0040] In order to more clearly illustrate the technical solutions of the present invention, the drawings required for use in the embodiments will be briefly introduced below. Obviously, for those of ordinary skill in the art, other drawings can also be obtained based on these drawings without creative efforts.

[0041] Figure 1 is a schematic flow chart of the anti-deformation structure lightweight optimization method based on active sampling and physics-informed neural network for this embodiment;

[0042] Figure 2 is the geometric model to be optimized in the specific application embodiment of the present invention;

[0043] Figure 3 is the comparative analysis of the cost of training the physics-informed neural network in the specific application embodiment of the present invention and the structural analysis cost of structural optimization based on finite element analysis. Detailed Embodiments

[0044] To make the objectives, technical solutions, and advantages of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below in conjunction with the specific embodiments and corresponding drawings of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention. The technical solutions provided by each embodiment of the present invention are described in detail below with reference to the drawings.

[0045] Please refer to Figure 1 , a lightweight optimization method for anti-deformation structures based on active sampling and physics-informed neural network provided by the present invention, includes:

[0046] Step 1: Select the anti-deformation structural member to be optimized, discretize it to obtain the corresponding mesh model, establish mesh data including node connection relationships and node coordinates based on the mesh model of the anti-deformation structural member, establish boundary conditions regarding displacement and load, and set the active sampling threshold ε s, set the parameters related to structural optimization and the physical information neural network model.

[0047] Specifically, the boundary conditions of the load in step one are encoded as hard constraints into the training of the physical information neural network model, and its general expression form is:

[0048]

[0049] where g(x) represents the Dirichlet boundary function, and l(x) is an auxiliary function to ensure that g(x) only acts on the Dirichlet boundary; x represents any node within the geometric domain; represents the preset displacement amplitude of the Dirichlet boundary; Γ D represents the Dirichlet boundary.

[0050] Step two: Preprocess the data, including constructing a density filtering matrix, calculating the partial derivative matrix of the shape function at each integration point of the element, and initializing the density field.

[0051] Step three: Based on the active sampling threshold ε set in step one s sample the elements actually required, and screen all the nodes associated with this part of the elements as the input of the physical information neural network model.

[0052] Specifically, in step three, it is necessary to sample the set of elements whose element density is greater than the preset sampling threshold, and obtain the set of non-repeated nodes associated with all elements. The set of sampled elements is expressed as:

[0053]

[0054] where represents the sampled element; Ω represents the entire geometric design domain; ρ represents the element density; τ represents the sampling threshold.

[0055] Step four: Calculate the gray-scale index based on the density field to dynamically configure the trainable parameters of the physical information neural network model.

[0056] Specifically, in step four, it is necessary to calculate the gray-scale index according to the density field. This index is used to indirectly describe the convergence of the density field to reflect the change state of the design variables. This index is calculated by the following formula:

[0057]

[0058] where M represents the gray-scale index; ρ k represents the density of the kth element; Ne represents the total number of discretized elements; when the gray-scale index is greater than the preset gray-scale threshold only consider the network parameters of the backbone neural network as the trainable parameters; when the gray-scale index is less than the preset gray-scale threshold When it is, the network parameters of the backbone neural network and the coefficient neural network are respectively used as trainable parameters periodically, where in the first structural optimization cycle of each period, only the backbone neural network is trained, and in the remaining periods, only the coefficient neural network is trained.

[0059] Step Five: When the configured physical information neural network model is trained to the maximum number of iterations, the following operations are sequentially performed during the iteration process: predicting displacements, calculating internal potential energy and external potential energy, constructing a loss function, and updating the network trainable parameters; after the training is completed, the required nodal displacements and strain energy density fields are separated from the computational graph.

[0060] Specifically, the external potential energy is the work done by external forces. In Step Five, the loss function uses the total potential energy function Π(u), which is the difference between the internal potential energy and the external potential energy of the system, and is expressed as:

[0061]

[0062] where the first term on the right side is the internal potential energy of the system, and the second term is the external potential energy of the system; σ represents the Cauchy stress; ε represents the Cauchy strain; Γ N represents the Neumann boundary; u represents the predicted displacement vector; T represents the transpose; Ω represents the entire geometric design domain; f represents the load vector; dv represents the volume element, which is integrated over the entire volume domain; ds represents the line element, which is integrated over the load boundary.

[0063] Specifically, in Step Five, the internal potential energy of the system is calculated based on the discrete form, the internal potential energy of the element is calculated based on two-point Gaussian quadrature, and the sum is obtained as the total internal potential energy of the system, which is expressed as:

[0064]

[0065] where Ω represents the entire geometric design domain; σ represents the Cauchy stress; ε represents the Cauchy strain; dv represents the volume element; Ne and Ng respectively represent the total number of discrete elements and the number of element integration points; σ ij and ε ij respectively represent the Cauchy stress and strain at the j-th integration point of the i-th element; κ j represents the weight at the j-th integration point; T represents the transpose.

[0066] Step Six: Convert the strain energy density into the sensitivity vector of the optimization objective, calculate the sensitivity vector of the volume constraint, and jointly use the density field vector as the input of the optimizer to obtain the optimized density field vector.

[0067] Specifically, the sensitivity of the optimization objective in Step Six is obtained from the strain energy density field output by the physical information neural network. When the element strain field is converted into the sensitivity vector, the element strain energy and the elements of the sensitivity vector satisfy a bijective relationship; the sensitivity of the volume constraint is expressed as the actual volume and area vector of the element.

[0068] Specifically, the sensitivity of the volume constraint is expressed as the actual volume, i.e., for three-dimensional problems, and as the area vector, i.e., for two-dimensional problems. The convergence criterion in step six is set as follows:

[0069]

[0070] where f c represents the optimization objective; Ns is a constant integer value; τ stop represents the convergence threshold; f c represents; k represents the index of the corresponding iteration.

[0071] Step seven: Determine whether the optimization meets the convergence condition. If not, return to step three based on the optimized density field vector; if it meets, output the optimized density field vector.

[0072] Without loss of generality, this embodiment selects the classical minimum compliance structural optimization problem for analysis. As Figure 2 shown, a cube with a hole is considered as the initial geometric design domain to increase the prediction complexity of the physics-informed neural network. The length, width, and height of the cube are 12 m, 1 m, and 5 m respectively, and the hole diameter is 2.5 m. The left Dirichlet boundary is fully constrained, and the right Neuman boundary condition is a static distributed load applied on the edge. f represents the load vector. The structural compliance is used as the optimization objective, and the ratio of the volume of the optimized structure to the original geometric domain is used as the constraint. The lightweight optimization of the anti-deformation structure based on active sampling and physics-informed neural network is performed.

[0073] This embodiment is implemented through the following scheme: A lightweight optimization method for anti-deformation structures based on active sampling and physics-informed neural networks, specifically including:

[0074] S1: Discretization Figure 2 Discretize the CAD model shown and establish grid data, and extract the node coordinates and the node connection relationships of each element. The displacement constraints used for training the physics-informed neural network are:

[0075]

[0076] where d x represents the abscissa of the node, l x represents the characteristic length of the geometric model in the X-axis direction; u x and u y respectively represent the displacement of the X degree of freedom and the displacement of the Y degree of freedom output by the network. and respectively represent the actual predicted displacement of the X degree of freedom and the actual predicted displacement of the Y degree of freedom after applying the constraints.

[0077] S2: Set the structure optimization parameters and the hyperparameters of the physics-informed neural network. Among them, the structure optimization parameters include the density penalty exponent, which is taken as 3 in this embodiment; the volume fraction, which is taken as 30% in this embodiment; the active sampling threshold, which is taken as 0.1% in this embodiment; the gray scale index threshold, which is taken as 5% in this embodiment; the number of network layers, which is taken as 5 in this embodiment; the number of neurons in each layer of the network, which is taken as 360 and 48 for the backbone neural network and the coefficient neural network respectively in this embodiment; and the learning rate for model training, which is taken as 0.001 in this embodiment.

[0078] S3: Select, as the analysis object, the discrete model composed of the unit set with unit density greater than the sampling threshold set in S2, and supply the nodes included in the analysis object as input data for the training of the physics-informed neural network.

[0079] S4: Calculate the gray scale index of the density field and compare it with the gray scale index threshold set in S2. When the gray scale index is less than the gray scale index threshold, the dynamic configuration strategy is activated. Select a fixed structure optimization iteration as a cycle. In the first iteration of each cycle, only the backbone neural network is trained, and in the remaining iterations of the current cycle, only the coefficient neural network is trained.

[0080] S5: Enter the physics-informed neural training stage. After training is completed, the predicted displacement field and strain energy density field will be output.

[0081] S6: Convert the strain energy density into the sensitivity vector of the optimization target, calculate the sensitivity vector of the volume constraint, and jointly use the density field vector, etc. as the input of the optimizer to obtain the optimized density field vector;

[0082] S7: Determine whether the optimization meets the convergence condition. If not, return to S3 based on the optimized density field vector; if it meets, output the optimized density field vector.

[0083] The optimization result of this example is as Figure 3 shown, Figure 3 indicating that the method proposed by the present invention is comparable to the traditional finite element-based structure optimization method in terms of computational cost. The method proposed by the present invention is almost the same as the traditional finite element-based structure optimization method in the density distribution of the final optimization result, with differences only at the structural boundaries, and the difference in the structural performance between the two is only 0.46%.

[0084] The present invention also provides a computer device, including a processor and a memory. The memory is used to store a computer program, and the processor is used to execute the computer program to perform the above-mentioned method.

[0085] The above are only the preferred embodiments of the present invention and do not impose any formal restrictions on the present invention. Although the present invention has been disclosed above with the preferred embodiments, it is not intended to limit the present invention. Therefore, any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the technical solution of the present invention shall fall within the scope of protection of the technical solution of the present invention.

Claims

1. A lightweight optimization method for anti-deformation structures based on active sampling and physical information neural network, characterized in that: include: Step 1: Select the anti-deformation structural part to be optimized and discretize it to obtain the corresponding mesh model. Based on the mesh model of the anti-deformation structural part, establish mesh data including node connection relationship and node coordinates, establish boundary conditions for displacement and load, and set the active sampling threshold ε. s , setting parameters of neural network models involving structural optimization and physical information; Step 2: Preprocess the data, including constructing a density filter matrix, calculating the partial derivative matrix of the shape function at each unit integration point, and initializing the density field; Step 3: Active sampling threshold ε set in step 1 s Sampling the units actually required, and screening all nodes associated with these units as inputs to the physical information neural network model; Step 4: Calculate the grayscale index based on the density field to dynamically configure the trainable parameters of the physical information neural network model; Step 5: Train the configured physical information neural network model to the maximum number of iterations, and perform the following in sequence during the iteration process: predict displacement, calculate internal potential energy and external potential energy, construct loss function, and update network trainable parameters; after the training is completed, separate the required node displacement and strain energy density field from the calculation graph; Step 6: Convert the strain energy density into the sensitivity vector of the optimization target, calculate the sensitivity vector of the volume constraint, and use the combined density field vector as the optimizer input to obtain the optimized density field vector; Step 7: Determine whether the optimization meets the convergence condition. If not, return to step 3 based on the optimized density field vector; if satisfied, output the optimized density field vector.

2. The method for lightweight optimization of anti-deformation structure based on active sampling and physical information neural network according to claim 1 is characterized in that: In step 1, the boundary conditions of the load are encoded as hard constraints into the training of the physical information neural network model. The general expression is: Where g(x) represents the Dirichlet boundary function, l(x) is an auxiliary function to ensure that g(x) only works on the Dirichlet boundary; x represents any node in the geometric domain; represents the displacement amplitude preset by the Dirichlet boundary; Γ D represents the Dirichlet frontier.

3. The method for lightweight optimization of anti-deformation structure based on active sampling and physical information neural network according to claim 1 is characterized in that: In step 1, the load boundary conditions are encoded in vector form and used to calculate the external force work in the physical information neural network model training: HAVE BEEN ext =f T u. Where E ext represents external work, f represents the load vector, u represents the predicted displacement vector, and T represents transpose.

4. The method for lightweight optimization of anti-deformation structure based on active sampling and physical information neural network according to claim 1 is characterized in that: In step 3, the unit set whose unit density is greater than the preset sampling threshold needs to be sampled, and the non-repeated node set associated with all units is obtained. The sampling unit set is expressed as: in represents the sampling unit; Ω represents the entire geometric design domain; ρ represents the unit density; τ represents the sampling threshold.

5. The method for lightweight optimization of anti-deformation structure based on active sampling and physical information neural network according to claim 1 is characterized in that: In step 4, the gray index needs to be calculated based on the density field. This index is used to indirectly describe the convergence of the density field to reflect the change state of the design variable. The index is calculated by the following formula: Where M represents the grayscale index; ρ k Represents the kth unit density; Ne represents the total number of discrete units; when the grayscale index is greater than the preset grayscale threshold M, only the network parameters of the backbone neural network are considered as trainable parameters; when the grayscale index is less than the preset grayscale threshold M, the network parameters of the backbone neural network and the coefficient neural network are periodically used as trainable parameters respectively, where the first structural optimization cycle of each cycle only trains the backbone neural network, and the remaining cycles only train the coefficient neural network.

6. The method for lightweight optimization of anti-deformation structure based on active sampling and physical information neural network according to claim 1 is characterized in that: The loss function in step 5 uses the total potential energy function Π(u), which is the difference between the internal potential energy and the external potential energy of the system, expressed as: The first term on the right side is the internal potential energy of the system, and the second term is the external potential energy of the system; σ represents the Cauchy stress; ε represents the Cauchy strain; Γ N represents the Neumann boundary; u represents the predicted displacement vector; T represents the transpose; Ω represents the entire geometric design domain; f represents the load vector; dv represents the volume element, which is integrated over the entire volume domain; ds represents the line segment element, which is integrated over the load boundary.

7. The method for lightweight optimization of anti-deformation structure based on active sampling and physical information neural network according to claim 1 is characterized in that: In step 5, the internal potential energy of the system is calculated based on the discrete form, the internal potential energy of the unit is calculated based on the two-point Gaussian integral, and the total internal potential energy of the system is obtained by summing up, which is expressed as: Where Ω represents the entire geometric design domain; σ represents the Cauchy stress; ε represents the Cauchy strain; dv represents the volume element; Ne and Ng represent the total number of discrete elements and the number of element integration points, respectively; σ ij and ε ij denote the Cauchy stress and strain at the jth integration point of the ith element, respectively; κ j represents the weight of the jth integration point; T represents the transpose.

8. The method for lightweight optimization of anti-deformation structure based on active sampling and physical information neural network according to claim 1 is characterized in that: The sensitivity of the optimization target in step six is ​​obtained from the strain energy density field output by the physical information neural network. It is required that when the unit strain field is converted into a sensitivity vector, the unit strain energy and the sensitivity vector elements satisfy a bijective relationship; the sensitivity of the volume constraint is expressed as the unit actual volume or area vector.

9. The method for lightweight optimization of anti-deformation structure based on active sampling and physical information neural network according to claim 1, characterized in that: The convergence criteria in step 6 are set as: where f c represents the optimization objective; Ns is a constant integer value; τ stop represents the convergence threshold; f c represents the optimization target; k represents the index of the corresponding iteration.

10. A computer device comprising a processor and a memory, wherein the memory is used to store a computer program, wherein: The processor is configured to execute the computer program to perform the method according to any one of claims 1 to 9.

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