| CPC G05B 19/4099 (2013.01) [B23K 31/003 (2013.01); G05B 2219/49007 (2013.01)] | 2 Claims |
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1. A method for constructing a body-in-white (BiW) spot welding deformation prediction model based on a graph convolutional network (GCN), comprising the following steps:
1) acquiring each spot weld and a three-dimensional (3D) coordinate measurement point thereof of a BiW in a production process; extracting a welding feature and 3D coordinates of each spot weld wi to form an eigenvector xi; and extracting designed 3D coordinates at the 3D coordinate measurement point;
wherein wi denotes an i-th spot weld, and xi denotes the eigenvector formed by the welding feature and the 3D coordinates of the spot weld wi;
2) inputting eigenvectors of all spot welds into a deep neural network (DNN) MLP_1, and encoding, by an encoder encoder_1 of the DNN MLP_1, the eigenvectors into hidden space vectors of the spot welds; inputting designed 3D coordinate vectors of all 3D coordinate measurement points into a DNN MLP_2, and encoding, by an encoder encoder_2 of the DNN MLP_2, the designed 3D coordinate vectors into hidden space vectors of the coordinate measurement points; and adding edges to the hidden space vectors of the spot welds and the hidden space vectors of the coordinate measurement points through a k-nearest neighbors (KNN) algorithm to construct a graph topology G;
3) decomposing a Laplacian eigenvector of the constructed graph topology G to acquire frequency domain components, and linearly transforming eigenvalues corresponding to the frequency domain components to construct a multi-layer GCN, wherein each layer of the GCN has a different frequency domain filter to adaptively extract thermodynamic and kinetic information in a neighborhood of each coordinate measurement point of the BiW;
4) inputting the thermodynamic and kinetic information of each coordinate measurement point into a DNN MLP_3; encoding, by an encoder decoder of the DNN MLP_3, the thermodynamic and kinetic information into a 3D coordinate space, and decoding a final deformation at each coordinate measurement point; and outputting a predicted 3D vector of the deformation at each coordinate measurement point; and
5) optimizing the BiW spot welding deformation prediction model;
wherein step 2) specifically comprises: inputting the eigenvectors x1˜xm of all the spot welds into the DNN MLP_1, and encoding, by the encoder encoder_1, the eigenvectors into the hidden space vectors h1˜hm of the spot welds; and inputting the designed 3D coordinate vectors p1˜pn-m of all the coordinate measurement points into the DNN MLP_2, and encoding, by the encoder encoder_2, the designed 3D coordinate vectors into the hidden space vectors hm+1˜hn of the coordinate measurement points, wherein h1˜hm and hm+1˜hn are located in a same vector space to form n discrete vectors h1˜hn; and
adding, based on a metric space of a global coordinate system where h1˜hn are located, edges to the nodes h1˜hn through the KNN algorithm to construct the graph topology G=(H, E), wherein for an arbitrary i-th node, hi∈H, H being a k-dimensional real vector space Rk, that is, H⊆Rk; and
an edge connecting two nodes i and j is eij∈E, wherein E denotes an edge space of the graph topology G, E⊆{(x, y)|(x, y)∈H2}, meaning an arbitrary pair of connected nodes in the graph topology;
hi denotes a discrete vector of an i-th node; i and j denote nodes; m denotes a number of spot welds; n denotes a number of discrete vectors;
wherein in step 3), the decomposing a Laplacian eigenvector of the constructed graph topology G comprises:
31) constructing an adjacency matrix A of the graph topology G, wherein the adjacency matrix A is a 0-1 square matrix of n×n, and an element of the square matrix expresses whether two nodes are adjacent; if the two nodes i, j are adjacent, then aij=1; otherwise, aij=0; and aij is an element of the adjacency matrix, that is, aij∈A;
32) constructing a symmetric normalized Laplacian matrix Lsys of the graph topology G:
Lsys=D−1/2LD−1/2
wherein, D denotes a degree matrix of the graph topology G; and L denotes the Laplace matrix of the graph topology G, which is calculated from the adjacency matrix:
L=D−A
33) subjecting the symmetric normalized Laplacian matrix Lsys of the graph topology G to eigendecomposition (spectral decomposition):
 wherein, U=(u1, u2, ⋅ ⋅ ⋅ , un); ul denotes a column vector, which belongs to the vector space H, that is, ul∈Rk, l=1, 2, ⋅ ⋅ ⋅ , n; and
 denotes an eigenvalue matrix of the symmetric normalized Laplacian matrix Lsys; and λ1˜λn, denote eigenvalues of the symmetric normalized Laplacian matrix Lsys of the graph topology G;
wherein a method for constructing a graph convolutional layer based on the graph topology G comprises: setting an i-th graph convolutional layer with an input feature Xi and an output feature Xi+1, wherein X∈Rn×k; Rn×k denotes a n×k-dimensional real matrix space; n denotes a number of graph nodes; and k denotes a dimension of the hidden space vector;
34) designing a set of filter parameters gθ(Λ) for each channel of the input feature, which is a k-channel graph topology, and convolving each channel of the k-channel graph topology to acquire an eigenmatrix Xi:
 wherein, ĥ(λ1)˜ĥ(λn) denote parameters of a graph filter; and ĥ(λi) denotes a nonlinear function of λi, i={1, 2, . . . , n}; and
35) linearly transforming each channel in the eigenmatrix acquired by convolution to acquire an eigen transformation matrix W∈Rk×k, and acquiring an output data Xi+1 through an element-level nonlinear activation function ReLu:
 wherein, Rk×k denotes a k×k-dimensional real matrix space;
wherein in step 3), the extracting thermodynamic and kinetic information in a neighborhood of each coordinate measurement point of the BiW comprises:
36) connecting the constructed graph convolutional layer by a residual into a deep residual graph convolutional network (DRGCN), wherein the DRGCN comprises L basic residuals, each of which forms the GCN by the graph convolutional layer; and, outputting, by an L-th basic residual of the DRGCN, final thermodynamic and kinetic information on all the spot welds and coordinate measurement points of the BiW;
wherein in step 5), the optimizing the BiW spot welding deformation prediction model comprises: processing, by a L2-norm loss function, actual and predicted 3D vectors of the deformation at each coordinate measurement point; and optimizing, by an adaptive movement estimation algorithm (Adam), L2-norm Loss_Avg of each coordinate measurement point as an optimization target to acquire the BiW spot welding deformation prediction model based on the GCN.
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