Geometric guidance-based manifold neural operator deformation field prediction method and application thereof

Abstract

A manifold neural operator deformation field prediction method based on geometric guidance and an application thereof are used for rapidly predicting deformation field functions of different parts under different residual stress field functions, and are characterized in that the parts are geometrically gridded, a geometric graph is established, the geometric graph is mapped to a low-dimensional manifold through a neural network, geometric feature information Zg is obtained, and the geometric feature information Zg is calculated. And combining the geometric feature information Zg and the input function to extract the feature information Zsigma of the input function, further guiding the learning of a deformation field prediction neural operator under different geometries by fusing the geometric feature information, namely, d (x) = f (x, Zg, Zsigma), and finally realizing the deformation field prediction of different part geometries under different input functions. The deformation field can be rapidly given according to part geometry and input functions, and the method is suitable for geometric optimization, machining and other scenes requiring rapid prediction of the deformation field.

Description

Technical Field

[0001] The present invention belongs to the fields of computational mechanics and intelligent manufacturing, and in particular, is a method for rapidly predicting machining deformation fields through geometrically guided neural operators, and is specifically a method for predicting deformation fields of manifold neural operators based on geometric guidance and its application. Background Art

[0002] During the machining process, structural parts are prone to machining deformation, which seriously affects the assembly accuracy, fatigue life and overall performance of the product. Especially in large and complex structural parts in the fields of aerospace, the problem of machining deformation is particularly prominent. The machining deformation of structural parts is due to the release and redistribution of the residual stress field, which not only produces overall deformation but also local deformation. In order to effectively control machining deformation, both online and offline machining deformation control require a large number of machining process optimization iterations to predict the deformation field under different residual stress fields, which puts higher requirements on the accuracy and efficiency of machining deformation. Therefore, accurate and rapid prediction of the machining deformation field of parts is of great significance for optimizing the machining process, controlling deformation and improving machining quality. At this stage, machining deformation field prediction has become one of the key technical requirements in the field of intelligent manufacturing and advanced manufacturing.

[0003] Existing machining deformation prediction methods mainly include numerical calculation methods based on the finite element method (FEM) and data-driven methods based on deep learning. The finite element method has high simulation accuracy and is suitable for deformation prediction under conditions of fixed geometry and specific physical quantities reflecting stress fields, including residual stress fields and deformation forces. However, the amount of calculation of the finite element method increases exponentially with the increase of geometric complexity and problem size, and the calculation time and memory requirements are high. In addition, when the geometric shape or stress field or deformation force changes, the finite element method usually needs to be re-modeled and re-calculated, and the prediction efficiency is low, which makes it difficult to meet the requirements of efficiency and real-time performance of machining deformation field prediction in actual production.

[0004] The deep learning-based deformation field prediction method relies on the powerful nonlinear fitting ability of neural networks, and can learn the complex mapping relationship between stress field, deformation force and deformation from a large amount of data, with certain prediction accuracy and generalization ability. However, traditional neural networks can only establish the mapping relationship between discrete stress, deformation force and partial deformation, and it is difficult to establish the mapping relationship between stress field, deformation force and deformation field. Neural operators provide new ideas for the prediction of machining deformation field by learning the mapping between parameter functions and solution functions of partial differential equations. However, the existing neural operator technology is mainly applied to fixed geometric domains, and its applicability in geometric representation and calculation accuracy is still limited for complex structural parts with variable geometric shapes. At the same time, current research is mostly focused on simple geometry or two-dimensional plane domains, and deformation field prediction in complex three-dimensional geometric domains is still challenging. Summary of the invention

[0005] The purpose of this invention is to solve the problems of high computing time and memory requirements and limited application fields and adaptability of existing machining deformation prediction methods, and to invent a deformation field prediction method based on geometry-guided manifold neural operator and its application. 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 the input function mapping to obtain the input feature information Z σ , and then map the functions under different geometries to the same underlying manifold, so as to learn the deformation field prediction operator d(x)=f(x,Z g , Z σ ), and finally realize the deformation field prediction of different part geometries under different input functions.

[0006] The technical solution of the present invention is:

[0007] A geometry-guided manifold neural operator deformation field prediction method and its application include: for the machining deformation field prediction problem of different structural parts, the part geometry is first expressed as a geometric graph G = (V, E), the geometric graph is mapped to a low-dimensional manifold through a geometric embedding module, and geometric feature information Z is extracted from it. g ; Extracted geometric feature information Z g Together with the input function, it passes through the encoder module to extract the input feature information Z 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 output deformation field d(x) guides the learning of the deformation field prediction neural operator under different geometries by fusing geometric information, that is.

[0008] d(x)=f(x,Z g , Z σ ) (Formula 1)

[0009] Among them, x is the geometric space coordinate position.

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

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

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

[0013] The encoder module converts the 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:

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

[0015] Where 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 by the deformation force method;

[0016] The input to the neural network is the coordinates 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 the 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 query point coordinates x q Output deformation field prediction value d(x q ), the mapping relationship is:

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

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

[0023] The present invention can be applied to the prediction of deformation field during machining of aircraft frame and beam structural parts.

[0024] The beneficial effects of the present invention are:

[0025] 1. The present 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 parts;

[0027] 3. This method supports prediction under multi-resolution sampling conditions and has discrete invariance of input and output. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 The geometry-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 DESCRIPTION

[0031] The present invention is further described below in conjunction with the accompanying drawings and embodiments, but the present invention is not limited to the embodiments.

[0032] The prediction method of the present invention is further described below by taking the prediction of deformation field in the processing of aircraft frame and beam structural parts as an example.

[0033] like Figure 1 shown.

[0034] This example is a typical problem in the manufacturing field. Aircraft frame and beam structural parts are representative in the manufacturing field. Processing deformation is a key quality indicator in the manufacturing process of frame and beam structural parts. The specific prediction steps are:

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

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

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

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

[0039]

[0040] 5. Among them, represents the features of node v in the l-th layer of the graph neural network, is the information obtained by node v at layer l+1,

[0041] is the feature of node v’s neighbor node s. φ and ψ are neural networks; MaxPool is the maximum pooling; L is the total number of layers of the graph neural network; Z g It is the global geometric feature information extracted by the graph neural network;

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

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

[0044] The stress characteristic information of all nodes is aggregated and averaged to obtain the global characteristic information Z of the stress field 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 query point coordinates x q =(x q ,y q , z q ) combined with the input query module, and outputs the deformation field prediction value d(x) corresponding to the query point q ), the mapping relationship is:

[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 in the query geometry, the deformation field function d(x) is obtained, such as Figure 3 shown.

[0049] The present invention does not involve parts that are the same as the prior art or can be implemented by using the prior art.

Claims

1. A geometry-guided manifold neural operator deformation field prediction method, characterized by: In order to predict the machining deformation field of different structural parts, the part geometry is first expressed as a geometric graph, and the geometric graph is mapped to a low-dimensional manifold through a geometric embedding module to extract the geometric feature information Z g ; Geometric feature information Z g Together with the input function, it passes through the encoder module to extract the input feature information Z 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 output deformation field d(x) guides the learning of the deformation field prediction neural operator under different geometries by fusing geometric information, that is. d(x)=f(x,Z g , Z σ ) (Formula 1) Among them, x is the geometric space coordinate position.

2. The method according to claim 1, characterized in that: The geometric graph is G=(V, E), where V is the node feature after geometric meshing, and E is the edge feature between nodes; The node feature V represents the coordinates of the geometric point, and the edge feature E represents the connectivity between nodes.

3. The method according to claim 1, characterized in that: 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 preferably a graph neural network (GNN), and the global geometric feature information Z of the geometric graph is extracted through the graph neural network. g ,Right now, Z g =GNN(G) (Formula 2).

4. The method according to claim 1, characterized in that: 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 preferably a stress field function or a deformation force function.

5. The method according to claim 1, characterized in that: The encoder module converts the geometric feature information Z g , and the input function value σ(x) are combined to generate the input feature information Zσ. The specific mapping relationship is: Z σ = Encoder(σ(x), Z g ), (Equation 3) Encoder represents the neural network structure used for feature extraction.

6. The method according to claim 1, characterized in that: The query module is based on the input feature information Zσ, geometric feature information Z g and the query point coordinates x q Output deformation field prediction value d(x q ), the mapping relationship is: d(x q ) = Query(Z σ , Z g , x q ), (Equation 4) Where Query represents the query network; by traversing the deformation of the nodes in the query geometry, the deformation field function d(x) is obtained.

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

8. The method according to claim 1, characterized in that: 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 neural network structure according to claim 3, characterized in that: The input of 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 the 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 ) (Formula 6) FROM σ =Aggregate(z1,…z n )( equation7) Here, g is a neural network.

10. A method for predicting deformation field based on geometrically guided manifold neural operators according to claim 1, characterized in that It is used in the prediction of deformation field during machining of aircraft frame and beam structural parts.

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