Topological optimization method based on physical information neural network (PINN)

Abstract

The invention discloses a topological optimization method based on a physical information neural network (PINN). The topological optimization method comprises the following steps of data preparation, neural network design, loss function definition, dynamic sampling strategy and optimization process implementation. Specifically, the method comprises the following steps: firstly, acquiring the center coordinates of each unit, then inputting the unit coordinates into a sine representation network, outputting a unit density value, calculating displacement through finite element analysis, then calculating a flexibility value according to node displacement so as to obtain loss, and finally, carrying out back propagation on the loss and updating the network weight. The method has the advantages that the deep learning technology is combined with the physical information neural network, so that the structural performance is improved, the dependence on experimental data is reduced, and the optimization efficiency and precision are improved. Particularly, the structure of the neural network is different from that of a conventional neural network, and deep embedding of physical information is considered in the design of the neural network, so that the prediction accuracy and the generalization ability of the network are improved.

Description

Technical Field

[0001] The present invention relates to a mechanical structure design and optimization method, and in particular to a method and system for topological optimization of an engine bracket using physical information neural network (PINN) and deep learning technology. Background Art

[0002] In the fields of mechanical engineering and aerospace, the performance of structures is crucial to the reliability and safety of overall equipment operation. Traditional topology optimization approaches rely heavily on massive amounts of experimental data and a trial-and-error process, resulting in low optimization efficiency and difficulty in improving accuracy. This makes it difficult to meet the stringent demands for rapid and precise structural optimization in today's complex operating conditions.

[0003] Therefore, developing efficient and accurate topology optimization technology has become a top priority and is the core driving force for promoting structural design changes in the industry and improving product quality and competitiveness. Summary of the Invention

[0004] Purpose of the Invention: This invention provides a topology optimization method based on a physical information neural network (PINN). Its core is to integrate PINN with deep learning techniques to achieve superior topology optimization of complex structures. By deeply embedding PINN into a physical knowledge system, it effectively eliminates the rigid dependence on large amounts of data, comprehensively improving optimization efficiency and accuracy. This method will inject strong impetus into the leapfrog development of structural design in mechanical engineering and aerospace, and open up a new path.

[0005] Technical solution: A topology optimization method based on physical information neural network (PINN) includes the following steps:

[0006] S1: Divide the structure into multiple units and obtain the center coordinates of each unit;

[0007] S2: Input the unit coordinates into the sinusoidal representation network SIREN, which consists of a coordinate input layer, a hidden layer, and a density output layer. The coordinate input layer receives the center coordinates of the structural unit as input. These coordinates are the basis of network prediction and are used to process the input coordinates. The density output layer uses the coordinate information processed by the hidden layer to finally output the density value of each unit. This density value is used for subsequent operations such as flexibility calculation. The design of the hidden layer takes into account the deep embedding of physical information to improve the accuracy of the prediction. The output layer outputs the weight value of each unit, which is used to control the distribution of materials in the structure. The design of the SIREN network focuses on predicting the material distribution of each unit in the structure, providing key weight information for topology optimization, thereby achieving effective control of material usage and optimization of structural performance.

[0008] S3: Calculate the displacement by finite element analysis based on the density value of each unit, and solve the displacement field U = F / J based on the stiffness matrix J and the load vector F;

[0009] S4: Calculate the loss, which includes flexibility loss and volume loss;

[0010] S5: Backpropagate the loss, update the network parameters using the Adam optimizer, and update the network weights;

[0011] S6: Determine whether the stopping condition is met. If the total loss change rate is less than the preset threshold 0.0001 or the maximum number of iterations is 100, the optimization is terminated. Otherwise, repeat the above S2-S6.

[0012] Furthermore, neural network partitioning includes partitioning the network. The present invention involves dividing the structure to be optimized into multiple discrete units, each unit representing an independent part of the structure for separate physical information processing and optimization. This partitioning strategy allows the neural network to process the local characteristics of the structure more finely, thereby improving the accuracy and efficiency of the overall optimization. The unit partitioning is based on the geometric characteristics of the structure, load distribution, boundary conditions, and expected stress and strain concentration areas. In this way, it is possible to ensure that the network has a higher resolution in key areas, thereby more accurately simulating and predicting the physical behavior of the structure.

[0013] Furthermore, the cell center coordinates serve as input to the neural network, predicting the density of each cell. Accurately determining the center coordinates is crucial to the network's predictive accuracy. Through this detailed network partitioning, the method of the present invention can more accurately simulate and predict the structure's performance under different operating conditions, achieving more efficient and accurate topology optimization. This network design not only improves optimization efficiency but also enhances the network's generalization and predictive accuracy by deeply embedding physical information.

[0014] Furthermore, the hidden layer includes 3 layers, the activation function is sin(wx+b), and w is initialized to 30.

[0015] Furthermore, the loss function includes volume loss and compliance loss to achieve the goal of structural optimization. The loss function is defined as follows:

[0016] Total loss function Consists of two parts: compliance loss and volume loss And an adaptive loss weight term λ is used to dynamically adjust the influence of the two.

[0017] The specific formula is as follows:

[0018]

[0019] The flexibility loss is defined as:

[0020]

[0021] Here, U is the displacement vector, J is the stiffness matrix, and Co is the flexibility of the initial structure, which is used as a regularization term to avoid excessive flexibility loss.

[0022] Volume loss:

[0023] It is defined as: where ρ is the density distribution, is the volume of the initial structure. The adaptive loss weight term λ is used to dynamically program the impact of flexibility loss and volume loss on the total loss. Its calculation formula is as follows:

[0024] λ=min{λ0+α*maxIter*Δλ, λmax}

[0025] Among them, λo is the initial weight value, α is the number of iterations, Δλ is the weight increment, and λ max is the maximum weight value. By defining this loss function, the method of the present invention can balance the flexibility and volume of the structure during the optimization process, thereby achieving optimal design of structural performance. This loss function design not only improves optimization efficiency but also enhances the network's generalization ability and prediction accuracy by deeply embedding physical information. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 Design schematic diagram for structural loads;

[0027] Figure 2 Schematic diagram of the optimal topology (finite element model);

[0028] Figure 3 This is the SIREN network architecture diagram;

[0029] Figure 4 Flow chart of the method of the present invention. DETAILED DESCRIPTION

[0030] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the present invention will be further described below.

[0031] Example 1:

[0032] Step 1 (corresponding to claim 1-S1): Divide the structure into multiple units and obtain the center coordinates of each unit.

[0033] The initial design area is discretized into a finite element mesh using finite element software (such as ANSYS), and units are divided according to the geometric characteristics, load distribution and boundary conditions of the structure, and the center coordinates of each unit are recorded.

[0034] Step 2. Input the cell coordinates into the sine representation network (SIREN) and output the density value of each cell.

[0035] The SIREN network structure is: input layer (unit center coordinates) → three hidden layers (activation function: sin(wx+b), with w initialized to 30) → output layer (density value p). The hidden layers use the SIREN activation function, whose sinusoidal characteristics simulate the periodic physical behavior of structural vibration and deformation, achieving a deep fusion of physical laws and neural networks. The network captures displacement changes through periodic characteristics.

[0036] The frequency parameter w (initialized to 30) of the sinusoidal activation function is directly related to the structural characteristic dimensions and load frequency. By fitting the periodic modes of structural deformation (such as the spatial distribution period of stress and strain), physical constraints are explicitly embedded in the network architecture, ensuring that the output density distribution conforms to the laws of mechanics. The hidden layer uses the SIREN activation function, whose sinusoidal characteristics simulate the periodic physical behavior of structural vibration and deformation, achieving a deep fusion of physical laws and neural networks. The network captures displacement changes through periodic characteristics.

[0037] Step 3: Perform finite element analysis based on the density value and calculate the displacement vector.

[0038] The density output by SIREN is mapped to the finite element model. According to the stiffness matrix J and the load vector F, the displacement field U = F / J is solved.

[0039] Step 4: Calculate compliance loss and volume loss

[0040] Compliance loss (where C0 is the initial compliance): Volume loss (constrained volume fraction Vf):

[0041]

[0042] Step 5: Backpropagate the total loss:

[0043] Update network weight max

[0044] The adaptive weight λ is dynamically adjusted according to the formula:

[0045] λ=min{λ0+α·max Iter·Δλ, λ max}Where λ0 is the initial weight value, α is the iteration coefficient, Δλ is the weight increment, and λmax is the maximum weight value. The Adam optimizer is used to update the network parameters, and the learning rate is set to 10 -3 .

[0046] Step 6: Determine whether the stop condition is met

[0047] If the total loss change rate is less than 0.0001 or the number of iterations is greater than or equal to 100, the optimization is terminated, otherwise return to steps 2-6.

[0048] The above description is merely a preferred embodiment of the present invention and does not limit the present invention in any way. Any person skilled in the art who, without departing from the scope of the present invention, makes any equivalent substitution, modification, or other changes to the technical solution and technical content disclosed in the present invention shall be deemed to be within the scope of the present invention and still fall within the scope of protection of the present invention.

Claims

1. A topology optimization method based on physical information neural network (PIN), characterized in that: The following steps are involved: S1: Divide the structure into multiple units and obtain the center coordinates of each unit; S2: Input the unit coordinates into a sinusoidal representation network (SIREN), which consists of a coordinate input layer, a hidden layer, and a density output layer. The coordinate input layer receives the center coordinates of the structural units as input, which form the basis of network prediction and are used to process the input coordinates. The density output layer uses the coordinate information processed by the hidden layer to ultimately output the density value of each unit, which is used for subsequent operations such as flexibility calculation. S3: Calculate the displacement by finite element analysis based on the density value of each unit, and solve the displacement field U = F / J based on the stiffness matrix J and the load vector F; S4: Calculate the loss, which includes flexibility loss and volume loss; S5: Backpropagate the loss, update the network parameters using the Adam optimizer, and update the network weights; S6: Determine whether the stopping condition is met. If the total loss change rate is less than the preset threshold 0.0001 or the maximum number of iterations is 100, the optimization is terminated. Otherwise, repeat the above S2-S6.

2. The topology optimization method based on physical information neural network (PINN) according to claim 1 is characterized in that: Neural network partitioning includes the division of the network, dividing the structure to be optimized into multiple discrete units. Each unit represents an independent part of the structure for separate physical information processing and optimization. The basis for unit division is the geometric characteristics of the structure, load distribution, boundary conditions and expected stress and strain concentration areas.

3. The topology optimization method based on physical information neural network (PINN) according to claim 2 is characterized in that: The center coordinates of the cells are used as input to the neural network to predict the density of each cell.

4. The topology optimization method based on physical information neural network (PINN) according to claim 3 is characterized in that: The hidden layer includes 3 layers, the activation function is sin(wx+b), and w is initialized to 30.

5. The topology optimization method based on physical information neural network (PINN) according to claim 4 is characterized in that: The loss function is defined as follows: The total loss function Consists of two parts Component: Flexibility loss and volume loss And an adaptive loss weight term λ is used to dynamically adjust the influence of the two, The specific formula is as follows: The flexibility loss is defined as: Here, U is the displacement vector, J is the stiffness matrix, and Co is the flexibility of the initial structure, which is used as a regularization term to avoid excessive flexibility loss. Volume loss: Where: Here ρ is the density distribution, is the volume of the initial structure. The adaptive loss weight term λ is used to dynamically program the impact of flexibility loss and volume loss on the total loss. The calculation formula is as follows: λ=min{λ0+α*maxIter*Δλ, λmax} Where λo is the initial weight value, α is the number of iterations, Δλ is the weight increment, and λ max is the maximum weight value.

6. The topology optimization method based on physical information neural network (PINN) according to claim 5 is characterized in that: Based on the established finite element model, a mathematical model is constructed to solve the problem of minimizing the structural flexibility under volume constraints. The model defines an optimization problem, where the objective function is the flexibility of the structure. Where F represents the load vector, U represents the displacement vector, and the optimization variable ρ represents the material distribution. Its value range is limited to 0 and 1 to ensure that the volume fraction of the material does not exceed the preset upper limit. During the optimization process, a random initialization method is used to generate the initial population. The position of each individual in the decision space is determined by the formula, where X min and X max They represent the lower and upper bounds of the j-th dimension respectively. This method ensures the diversity of the initial population and provides search space for the subsequent optimization process.

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