A geometry-guided manifold neural operator-based method for predicting deformation fields and its application.

Abstract

A manifold neural operator deformation field prediction method based on geometric guidance and its application are used for quickly predicting deformation field functions of different parts under different residual stress field functions, characterized by: the part geometry is gridded and a geometric graph is established, the geometric feature information Z is obtained by mapping the neural network to a low-dimensional manifold g , the input function feature information Z is extracted by combining the geometric feature information Z g and the input function σ , and then the learning of the deformation field prediction neural operator under different geometries is guided by fusing the geometric feature information, that is, d(x) = f(x, Z g , Z σ ), and finally the deformation field prediction of different part geometries under different input functions is realized. The present application can quickly give the deformation field according to the part geometry and the input function, and is suitable for the scene of quickly predicting the deformation field for geometry optimization, machining and the like.

Description

Technical Field

[0001] This invention belongs to the fields of computational mechanics and intelligent manufacturing, and in particular, it is a method for rapidly predicting machining deformation fields using geometrically guided neural operators. Specifically, it is a deformation field prediction method based on geometrically guided manifold neural operators and its application. Background Technology

[0002] During machining, structural components are prone to deformation, which severely affects assembly accuracy, fatigue life, and overall performance, especially in large and complex structural components in fields such as aerospace. Machining deformation arises from the release and redistribution of residual stress fields, resulting in both overall and localized deformation. Effective control of machining deformation requires extensive process optimization and iteration for both online and offline control, as well as predicting deformation fields under different residual stress fields. This places higher demands on the accuracy and efficiency of machining deformation prediction. Therefore, accurate and rapid prediction of the machining deformation field of parts is crucial for optimizing machining processes, controlling deformation, and improving machining quality. Currently, machining deformation field prediction has become one of the key technological requirements in the fields of intelligent manufacturing and advanced manufacturing.

[0003] Existing methods for predicting machining deformation mainly include numerical methods based on the finite element method (FEM) and data-driven methods based on deep learning. The finite element method offers high simulation accuracy and is suitable for deformation prediction under fixed geometry and specific physical quantities reflecting the stress field, including residual stress and deformation forces. However, the computational cost of the finite element method increases exponentially with geometric complexity and problem size, resulting in high computation time and memory requirements. Furthermore, when the geometry, stress field, or deformation force changes, the finite element method typically requires remodeling and recalculation, leading to low prediction efficiency and difficulty in meeting the efficiency and real-time requirements for predicting machining deformation fields in actual production.

[0004] Deep learning-based methods for predicting machining deformation fields leverage the powerful nonlinear fitting capabilities of neural networks to learn complex mapping relationships between stress fields, deformation forces, and deformation from large amounts of data, exhibiting a certain level of prediction accuracy and generalization ability. However, traditional neural networks can only establish discrete mapping relationships between stress, deformation forces, and partial deformation quantities, making it difficult to establish a mapping relationship from stress fields and deformation forces to deformation fields. Neural operators, by learning the mapping between parameter functions and solution functions of partial differential equations, offer a new approach to predicting machining deformation fields. However, existing neural operator techniques are mainly applied to fixed geometric domains, and their applicability in terms of geometric representation and computational accuracy remains limited for complex structural components with varying geometries. Furthermore, current research largely focuses on simple geometries or two-dimensional planar domains, while predicting deformation fields in complex three-dimensional geometric domains remains challenging. Summary of the Invention

[0005] The purpose of this invention is to address the problems of high computation time and memory requirements, as well as limited application areas and adaptability of existing machining deformation prediction methods. This invention proposes a geometry-guided manifold neural operator-based deformation field prediction method and its applications. It represents the part geometry as a geometric graph, maps it to a low-dimensional manifold using a graph neural network, extracts global geometric feature information, and combines this with an input function mapping to obtain input feature information Z. σ This allows functions under different geometries to be mapped to the same latent manifold, thereby enabling the learning of the deformation field prediction operator d(x)=f(x,Z) in Banach space via a neural network. g Z σ Ultimately, this enables the prediction of deformation fields for different parts with different geometry under different input functions.

[0006] The technical solution of this invention is:

[0007] A geometry-guided manifold neural operator-based deformation field prediction method and its application are proposed, including: for the problem of predicting the machining deformation field of different structural parts, the part geometry is first expressed as a geometric graph G = (V, E), and the geometric graph is mapped to a low-dimensional manifold through a geometry embedding module, and geometric feature information Z is extracted from it. g Extracted geometric feature information Z g Together with the input function, the input feature information Z is extracted by the encoder module. σ Finally, the input feature information Z is established through the query module. σ Geometric feature information Z g The mapping relationship between the output deformation field d(x) and the geometric information is used to guide the learning of the neural operator for predicting the deformation field under different geometries.

[0008] d(x)=f(x,Z g Z σ ) (Formula 1)

[0009] Where x is the geometric space coordinate position.

[0010] The geometric graph is G = (V, E), where V represents the node features after geometric meshing, and E represents the edge features between nodes. The node feature V represents the coordinates of the geometric points, and the edge feature E represents the connectivity between nodes.

[0011] The geometric embedding module uses a graph neural network (GNN) to extract global geometric feature information Z from the geometric graph. g ,Right now,

[0012] Z g =GNN(G) (Formula 2)

[0013] The encoder module transmits geometric feature information Z... g The input function value σ(x) is combined to generate the input feature information Z. σ The specific mapping relationship is as follows:

[0014] Z σ =Encoder(σ(x), Z) g ), (Formula 3)

[0015] Here, Encoder represents the neural network structure used for feature extraction. The input function value σ(x) is the residual stress field; the residual stress field is obtained through the deformation force method.

[0016] The input to the neural network is the coordinate x of each grid point. i Input value σ i and geometric feature information Z g The output is the local stress characteristic z corresponding to that point. x After obtaining the local input features of all grid points, the global input feature information Z is obtained by summing and averaging. σ ,Right now

[0017] z i =g(x i , σ i Z g ) (Formula 4)

[0018] Z σ =Aggregate(z1, ... z) n ) (Formula 5)

[0019] Here, g is a neural network.

[0020] The query module is based on the input feature information Z σ Geometric feature information Z g and the coordinates of the query point x q Output deformation field prediction value d(x) q The mapping relationship is as follows:

[0021] d(x q ) = Query(Z σ Z g x q ), (Formula 6)

[0022] Where Query represents the query network; by traversing the nodes within the query geometry, the deformation field function d(x) is obtained.

[0023] This invention can be applied to the prediction of deformation fields during the processing of aircraft frame and beam structural components.

[0024] The beneficial effects of this invention are:

[0025] 1. This invention is applicable to the geometric domains of different parts, and has applicability and generalization.

[0026] 2. This method can quickly predict the deformation field of a part;

[0027] 3. This method supports prediction under multi-resolution sampling conditions and has discrete invariance of input and output. Attached Figure Description

[0028] Figure 1 The geometrically guided neural operator framework diagram and overall application concept diagram of the present invention.

[0029] Figure 2 This is a framework diagram of the geometric embedding module of the present invention.

[0030] Figure 3 This is a framework diagram of the encoding-query module of the present invention. Detailed Implementation

[0031] The present invention will be further described below with reference to the accompanying drawings and embodiments, but the present invention is not limited to these embodiments.

[0032] The following example, using the prediction of deformation field during the processing of aircraft frame and beam structural components, further illustrates the prediction method of the present invention.

[0033] like Figure 1 As shown.

[0034] This example illustrates a typical problem in the manufacturing field. Aircraft frame and beam structural components are representative of this issue, and processing deformation is a key quality indicator in the manufacturing process of these components. The specific prediction steps are as follows:

[0035] 1. Taking aircraft frame and beam structural components as examples, these components often have different geometric and stress field functions. By inputting the part geometry and corresponding stress field into a geometry-guided neural operator, the corresponding part machining deformation field can be quickly predicted. The overall idea is as follows: Figure 1 As shown;

[0036] 2. Collect deformation force data during processing to infer the residual stress field σ(x);

[0037] 3. First, the part is geometrically meshed and represented as a geometric graph G = (V, E), where V is the feature of each mesh node, and the feature of each node is v = (x...). v y v , z v );

[0038] 4. The framework of the geometry embedding module is as follows: Figure 2As shown, the geometric graph is input into a graph neural network (GNN) to obtain global geometric feature information, that is,

[0039]

[0040] 5. Among them, This represents the feature of node v in the l-th layer of the graph neural network. This is the information that node v obtains at level l+1.

[0041] φ and ψ are the features of the neighboring nodes s of node v. φ and ψ represent the neural network; MaxPool is the maximum pooling method; L is the total number of layers in the graph neural network; Z... g It is global geometric feature information extracted through a graph neural network;

[0042] 6. The acquired global geometric feature information Z g The coordinates of each node x i =(x i y i , z i and nodal stress value σ i =σ(x i Input the encoding module to obtain the local stress characteristic information of each node. i ,Right now,

[0043] z i =g(x i , σ i Z g ) (Formula 4)

[0044] The global stress field characteristic information Z is obtained by aggregating and averaging the stress characteristic information of all nodes. σ ,Right now

[0045] Z σ =Aggregate(z1, ... z) n ) (Formula 5)

[0046] 7. The stress field characteristic information Z σ Geometric feature information Z g and the coordinates of the query point x q =(x q y q , z q The combined input query module outputs the predicted deformation field value d(x) corresponding to the query point. q The mapping relationship is as follows:

[0047] d(x q ) = Query(Z σ Z g x q), (Formula 6)

[0048] Where Query represents the query network; by traversing the deformation of the nodes within the query geometry, the deformation field function d(x) is obtained, such as... Figure 3 As shown.

[0049] The parts not covered in this invention are the same as or can be implemented using existing technologies.

Claims

1. A geometric guide based manifold neural operator deformation field prediction method, characterized in that: For the machining deformation field prediction problem of different structural parts, firstly, the part geometry is expressed as a geometry graph, and the geometry graph is mapped to a low-dimensional manifold through a geometry embedding module and the geometry feature information Z g is extracted g ; The geometry feature information Z σ is extracted together with the input function through the encoder module, and finally the mapping relationship among the input feature information Z σ , the geometry feature information Z g and the output deformation field d(x) is established through the query module, and the learning of the deformation field prediction neural operator under different geometries is guided by fusing the geometry information, that is, d(x) = f(x, Z g ,Z σ ) (Equation 1) Wherein, x is the geometric spatial coordinate position.

2. The method of claim 1, wherein: The geometry is G=(V, E), wherein V is the node feature after geometric gridding, and E is the edge feature between nodes. Wherein, the node feature V represents the coordinates of the geometric point, and the edge feature E represents the connectivity between nodes.

3. The method of claim 1, wherein: The geometric embedding module is a neural network, and the neural network is a point cloud neural network, a point cloud-Transformer network or a graph neural network; the neural network is a graph neural network (GNN), and global geometric feature information Z of a geometric graph is extracted through the graph neural network g That is, Z g = GNN(G) (Equation 2).

4. The method of claim 1, wherein: The input function is a physical quantity function that causes or has a physical relationship with the deformation of the part; the physical quantity function is a stress field function or a deformation force function.

5. The method of claim 1, wherein: The encoder module generates the input feature information Z g by combining the geometric feature information Z σ and the input function value σ(x). The specific mapping relationship is: Z σ = Encoder(σ(x), Z g ), (Equation 3) Wherein, Encoder represents a neural network structure for feature extraction.

6. The method of claim 1, wherein: The query module is based on the input feature information Z σ Geometric feature information Z g and the coordinates of the query point x q Output deformation field prediction value d(x) q The mapping relationship is as follows: d(x q ) = Query(Z σ , Z g , x q ), (Equation 4) Wherein, Query represents a query network; by traversing the deformation amount of the nodes in the query geometry, the deformation field function d(x) is obtained.

7. The method of claim 1, wherein: The neural operator is constructed through two mapping modules, namely an encoding mapping module and a query mapping module, which are used to approximate the mapping relationship of the input function to the deformation field, that is, f=Query o Encoder (Formula 5).

8. The method of claim 1, wherein: The input function includes residual stress field, deformation force or residual stress field and deformation force; the residual stress field is obtained by measurement or prediction method, preferably deformation force method; the deformation force is obtained by deformation force monitoring device.

9. The method of claim 3, wherein, The input to the neural network is the coordinate x of each grid point. i Input value σ i and geometric feature information Z g The output is the local input feature z corresponding to that point. x After obtaining the local input features of all grid points, the global input feature information Z is obtained by summing and averaging. σ ,Right now, z i = g(x i , σ i , Z g ) (Equation 6) Z σ = Aggregate(z1,…z n ) (Formula 7) Wherein, g is a neural network.

10. The geometry-guided manifold neural operator deformation field prediction method of claim 1, wherein It is applied to the processing deformation field prediction of aircraft frame, beam and other structural parts.

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