A Stress Prediction Method for Machine Tool Beam and Column Assembly Based on Amortization Difference Hint Learning

Abstract

This invention discloses a method for predicting assembly stress of machine tool crossbeams and columns based on amortized difference cue learning. The method includes: constructing a high-fidelity assembly stress field dataset of the crossbeams and columns of a gantry milling machine under different assembly conditions, thereby obtaining high-fidelity stress residual labels and physical information difference cue fields for each grid node of the crossbeam; constructing a 22-dimensional analytical mechanical feature based on the high-fidelity assembly stress field dataset, and then combining the high-fidelity stress residual labels to obtain low-fidelity analytical stress labels; training an assembly stress field prediction model using the high- and low-fidelity analytical stress labels, and then predicting the nodal equivalent stress field of the crossbeam under assembly conditions. This invention can explicitly indicate the location of stress concentration caused by tilt angle differences and improve the utilization efficiency of inexpensive analytical labels under the condition of scarce finite element samples, and can be used for assembly compliance verification, stress concentration location, and reassembly decision-making.

Description

Technical Field

[0001] This invention relates to a machine tool assembly stress prediction method, which relates to the fields of digital assembly of large CNC machine tools, structural state perception and artificial intelligence-assisted engineering analysis, and specifically to a machine tool beam and column assembly stress prediction method based on amortization difference prompt learning. Background Technology

[0002] Large gantry milling machines are used to process workpieces measuring meters or larger. Their crossbeams and left and right columns form the main load-bearing frame. The crossbeams typically require a forced fit assembly between the two columns, and the assembly condition of the crossbeam-column joint directly affects the overall machine's geometric accuracy, rigidity retention, and long-term operational stability. Due to manufacturing errors, foundation adjustment errors, and installation errors, the forward and backward tilt angles of the left and right columns are difficult to be perfectly consistent. This mismatch in tilt angles can lock assembly stress within the crossbeam and columns, creating localized stress concentrations at the crossbeam ends, connection areas, and cavity corners.

[0003] The aforementioned assembly stresses are mainly distributed within the structure and near the contact interfaces. Conventional strain gauges, displacement sensors, or geometric detection equipment cannot directly obtain the complete three-dimensional nodal stress field. In engineering, it is often necessary to determine whether the current assembly state can be accepted, or whether it is necessary to disassemble the crossbeams and readjust the column posture, based on whether the assembly stresses exceed the allowable range. Therefore, rapidly predicting the assembly stress field under given double column inclination angles and crossbeam geometric nodes is an important foundation for achieving assembly compliance verification and proactive reassembly decisions.

[0004] Existing analytical mechanics methods can establish the relationship between tilt angle difference and macroscopic bending moment and stress based on beam bending theory, with relatively low computational cost. However, they typically simplify beams to beams with uniform cross-sections, making it difficult to accurately represent local stress concentrations caused by hollow structures, local connections, contact nonlinearities, and complex boundary conditions. The finite element method can obtain high-fidelity stress fields under detailed geometry and contact conditions, but it requires resolving the problem every time the tilt angle of the left and right columns is changed, resulting in high computational and modeling costs and making it unsuitable for repeated use in a large number of assembly states.

[0005] Neural networks and neural operators can learn the mapping from assembly parameters to the overall response, offering high online prediction speeds. However, existing methods typically append the left and right column inclination angles directly to the network input as global scalars, or discretize the assembly error into several levels. Such inputs only indicate the current assembly condition; they cannot pinpoint at the node level where the bending effect induced by the inclination angle difference should be amplified along the beam span. The model needs to learn the spatial organization of stress concentration using only a small number of high-fidelity samples, which can easily lead to over-smoothing of the stress field and omission of local peaks.

[0006] On the other hand, the number of high-fidelity finite element labels is limited, while analytical models can generate a large number of low-fidelity labels with macroscopic trend information at low cost. If low-fidelity labels are directly mixed with high-fidelity labels for training, the systematic bias of the analytical model in the contact area and near the cavity may be carried into the final prediction model; if low-fidelity labels are completely discarded, it will result in insufficient utilization of cheap physical knowledge. Therefore, a technical solution is needed that can amortize the reliable shared trends in low-fidelity analytical labels into a unified prediction operator and use scarce finite element labels to correct only the high-fidelity residuals. Summary of the Invention

[0007] To address the problems existing in the background technology, this invention provides a method for predicting the assembly stress of machine tool crossbeam columns based on amortized difference cue learning. This invention solves the problems of lacking node-level spatial mechanics cues for global tilt angle parameters, high cost of obtaining high-fidelity finite element labels, and the tendency for low-fidelity analytical labels to easily propagate model biases to the final prediction results. The method converts the tilt angle difference between the two columns into a node-level bending moment gradient cue that continuously varies along the crossbeam span. Furthermore, through a two-stage approach of low-fidelity analytical label pre-training and finite element label fine-tuning, it learns the shared macroscopic stress trend and local high-fidelity corrections separately.

[0008] The technical solution adopted in this invention is:

[0009] The present invention provides a method for predicting the assembly stress of a machine tool crossbeam and column based on amortization difference hint learning, comprising:

[0010] Step S1: Establish finite element simulation models of the crossbeam and column of the gantry milling machine under different assembly conditions, and extract the simulation parameters of the crossbeam and column under each assembly condition to construct a high-fidelity assembly stress field dataset.

[0011] Step S2: Based on the high-fidelity assembly stress field dataset, obtain the high-fidelity stress residual label for each assembly condition and the physical information difference indication field of each mesh node of the beam in the finite element simulation model.

[0012] Step S3: Based on the high-fidelity assembly stress field dataset, construct analytical mechanical features including eight-dimensional linear bending features, nine-dimensional square and absolute value features, and five-dimensional Legendre higher-order modal features. Then, combine the high-fidelity stress residual labels to obtain low-fidelity analytical stress labels for each assembly condition.

[0013] Step S4: Based on the physical information difference prompt field and analytical mechanical characteristics under each assembly condition, construct the node input matrix. Input the node input matrix, high-fidelity stress residual label and low-fidelity analytical stress label into the shared neural operator network for two-stage amortized training to obtain the assembly stress field prediction model. Input the node coordinates of each grid node of the beam and the column inclination angle of the two columns in the three-dimensional mesh model of the beam and column under the assembly condition to be predicted into the assembly stress field prediction model. After processing, output the nodal stress residual prediction field of the beam under the current assembly condition, and then obtain the predicted nodal equivalent stress field of the beam.

[0014] In step S1, the column tilt angles of the two columns are changed within the preset assembly tolerance range of the column of the gantry milling machine, thereby constructing a finite element simulation model of the beam column under different assembly conditions; the simulation parameters of the beam column include the node coordinates and node equivalent stress of each mesh node on the beam in the finite element simulation model, as well as the column tilt angles of the two columns and the tilt angle error between them.

[0015] In step S2, the average value of the nodal equivalent stress of each grid node in the high-fidelity assembly stress field dataset under the current assembly condition is obtained as the spatial average stress, and the nodal equivalent stress of each grid node is subtracted from the spatial average stress to obtain the high-fidelity stress residual label.

[0016] In step S2, the average value of the column inclination angles of the two columns in the high-fidelity assembly stress field dataset under the current assembly condition is taken as the average inclination angle, and the inclination angle error is taken as the signed differential inclination angle. The average inclination angle and the signed differential inclination angle under each assembly condition are standardized to obtain the standardized average inclination angle and the standardized signed differential inclination angle. The node coordinates of each grid node are dimensionlessly normalized in the span direction, height direction and depth direction of the beam to obtain normalized coordinates. The normalized coordinates include span normalized coordinates, height normalized coordinates and depth normalized coordinates. For each grid node, the product of the standardized signed differential inclination angle and the span normalized coordinate is taken as the spatial modulation amount. The standardized average inclination angle, the standardized signed differential inclination angle and the spatial modulation amount are used to construct the physical information difference indication field of the current grid node.

[0017] In step S3, the analytical mechanical characteristics are as follows:

[0018] in, Represents the analytical mechanical characteristics of mesh node j; , and These represent the linear bending characteristics, square and absolute value characteristics, and Legendre higher-order mode characteristics of mesh node j, respectively. Indicates transpose; Indicates the mean dip angle; Indicates the signed difference tilt angle; , and These represent the span-normalized coordinates, height-normalized coordinates, and depth-normalized coordinates of grid node j, respectively. , and These represent linear bending, parabolic bending, and uniform angle bending, respectively. and These represent second-order and third-order Legendre polynomials, respectively.

[0019] In step S3, the analytical mechanical features are standardized column by column to obtain a standardized feature matrix. Then, the analytical coefficients are obtained by combining the high-fidelity stress residual labels and calibrating them with ridge regression with regularization terms. Based on the analytical coefficients, the initial low-fidelity analytical stress labels are obtained. The initial low-fidelity analytical stress labels are standardized to obtain the final low-fidelity analytical stress labels.

[0020] In step S4, the node input matrix is ​​constructed by splicing the normalized coordinates of each grid node of the beam, the physical information difference prompt field, and the analytical mechanical features. During the two-stage amortized training, the first stage of pre-training is performed, using low-fidelity analytical stress labels as the supervision signal for the shared neural operator network, and calculating the verification loss based on the high-fidelity stress residual labels as the selection criterion. When the verification loss for consecutive preset pre-training rounds is not lower than the minimum verification loss among all pre-training rounds, or when the preset maximum training round is reached, the first stage of pre-training is stopped. The network parameters of the shared neural operator network with the minimum verification loss among the executed training rounds are selected to obtain the pre-trained shared neural operator network, and the selected network parameters are used as the initial parameters for the second stage of fine-tuning training. Then, the second stage of fine-tuning training is performed, using the high-fidelity stress residual labels as the supervision signal for the pre-trained shared neural operator network to fine-tune the neural operator parameters of the pre-trained shared neural operator network, obtaining the final trained assembly stress field prediction model.

[0021] In step S4, after processing, the assembly stress field prediction model outputs the standardized stress residual prediction values ​​of each grid node in the beam under the current assembly state. The standardized stress residual prediction values ​​are de-standardized to obtain the nodal stress residual prediction values ​​with actual stress units for each grid node, thereby constructing the nodal stress residual prediction field. When the spatial average stress under the current assembly state is obtained, the spatial average stress is added to the nodal stress residual prediction values ​​of each grid node to obtain the predicted nodal equivalent stress of each grid node, thereby constructing the predicted nodal equivalent stress field of the beam.

[0022] The electronic device of the present invention includes: a memory and a processor coupled to each other, wherein the memory stores program data, and the processor invokes the program data to execute the method described above.

[0023] The present invention provides a computer-readable storage medium having program data stored thereon, which, when executed by a processor, implements the method described above.

[0024] The beneficial effects of this invention are:

[0025] 1) This invention multiplies the differential tilt angle with the beam span coordinates to form a continuous node-level prompt, making the linear bending moment gradient induced by the tilt angle mismatch explicitly visible at the network input, reducing the difficulty for the model to search for stress concentration locations on its own with only a few samples.

[0026] 2) This invention uses analytical mechanical features to generate low-fidelity labels and enhance node inputs simultaneously, achieving dual utilization of the same physical knowledge; the analytical labels are only responsible for warm-up and startup, and are not used as final high-fidelity supervision, which can reduce the transmission of analytical model bias to the final predictor.

[0027] 3) This invention uses the verification loss to select the first-stage weights, so that the pre-training stops in time after absorbing the shared macro trend, and then uses finite element labels to make targeted corrections to local peaks and nonlinear residuals.

[0028] 4) This invention uses neural operators to perform node-level prediction on complete irregular point clouds, which can directly output the stress residuals of the entire beam. The online inference speed is significantly higher than that of resolving the finite element problem for each assembly state.

[0029] 5) The prediction results of this invention can be used for assembly allowable stress verification, stress concentration area location, column posture adjustment and reassembly decision-making, and can serve as a source of stress information for digital twins of large gantry machine tools and assembly quality monitoring. Attached Figure Description

[0030] Figure 1 This is a flowchart illustrating the overall process of the method of the present invention.

[0031] Figure 2 This is a schematic diagram illustrating the application scenario of the present invention in the prediction of stress field during the assembly of the crossbeam and column of a gantry milling machine.

[0032] Figure 3 This is a comparison diagram of the prediction results of the method of the present invention and the baseline neural operator in an embodiment of the present invention, wherein, Figure 3 (a) is a comparison graph of the mean absolute error of the prediction results of the method of the present invention and the baseline neural operator. Figure 3 (b) is a comparison graph of the root mean square error of the prediction results of the method of the present invention and the baseline neural operator. Figure 3(c) is a comparison chart of the maximum error of the prediction results of the method of the present invention and the baseline neural operator;

[0033] Figure 4 This is a comparison chart of the training process and comprehensive indicators of different neural operators in embodiments of the present invention, wherein, Figure 4 (a) is a comparison of the validation loss curves for different neural operators. Figure 4 (b) is a comparison of the final residual determination coefficients for different neural operators. Figure 4 (c) in the figure is a comparison of the root mean square error of the final test for different neural operators;

[0034] Figure 5 This is a comparison diagram of the predicted stress and finite element stress scatter plots of each neural operator on the test grid node in the embodiments of the present invention;

[0035] Figure 6 This is a comparison chart of three-dimensional stress field prediction and error under representative assembly conditions in the embodiments of the present invention;

[0036] Figure 7 This is a comparison diagram of the stress field and signed error of the upper flange section of the crossbeam under representative assembly conditions in an embodiment of the present invention.

[0037] Figure 8 This is a diagram showing the ablation results of key components in an embodiment of the present invention;

[0038] Figure 9 This is a two-dimensional visualization of the potential features of grid nodes before and after training in an embodiment of the present invention. Detailed Implementation

[0039] The present invention will be further described below with reference to the accompanying drawings and embodiments. It should be noted that the following embodiments are used to explain the present invention and not to limit the scope of protection of the present invention. Equivalent substitutions or conventional adjustments made by those skilled in the art without departing from the basic concept of the present invention should all fall within the scope of protection of the present invention.

[0040] like Figure 1 As shown, the machine tool crossbeam and column assembly stress prediction method based on amortization difference hint learning of the present invention is as follows:

[0041] This embodiment takes the crossbeam body of a large gantry milling machine as the prediction object, such as... Figure 2 As shown, the crossbeam is forcibly assembled between the left and right columns, with fixed constraints at the bottom of the columns. Different assembly error states are created by changing the front and rear tilt angles of the left and right columns. The prediction process of this invention can be deployed on an assembly site computer, digital twin platform, or machine tool assembly quality management system. If the predicted stress exceeds a preset threshold, the system can output column posture adjustment suggestions or reassembly instructions; if the predicted stress meets the requirements, an assembly status acceptance result is generated.

[0042] In practice, a 3D mesh model of the crossbeam and columns of the gantry milling machine is first created to obtain the crossbeam and column assembly. Within the preset assembly tolerance range of the gantry milling machine's columns, the column inclination angles of the two columns are changed. The preset assembly tolerance range is the range of variation for the column inclination angles. The column inclination angle is the angle between each column and the vertical y-axis of the 3D mesh model. Then, ANSYS Mechanical is used to construct finite element simulation models of the crossbeam and columns of the gantry milling machine under different assembly conditions. The finite element model retains the crossbeam cavity, connection parts, and the left and right column structures. The von Mises equivalent stress of the crossbeam nodes after assembly is solved for different left and right column inclination angles. Then, simulation parameters of the crossbeam and columns under each assembly condition are extracted to construct a high-fidelity assembly stress field dataset. The simulation parameters of the crossbeam and columns include the node coordinates and node equivalent stress of each mesh node on the crossbeam in the finite element simulation model, specifically the von Mises equivalent stress, as well as the column inclination angles of the two columns and the inclination angle error between them. In practice, this is the left column inclination angle minus the right column inclination angle. Under different assembly conditions, the bottom position of the column remains unchanged, the length of the crossbeam column remains unchanged, and the column inclination angles of the two columns may be different. The inclination direction is along the vertical plane perpendicular to the crossbeam. After the column inclination angle changes, the crossbeam may bend or twist. In order to ensure that the neural operator can establish a one-to-one correspondence of node mapping between assembly conditions, the finite element model under each assembly condition uses the same crossbeam mesh division, node coordinates and node numbers. That is, the number of nodes and node numbers in the high-fidelity assembly stress field dataset constructed under each assembly condition remain unchanged.

[0043] In practice, a total of 100 assembly scenarios were set up. Left column tilt angle. The range is from 0.040° to 0.085°, right column tilt angle The range is from 0.040° to 0.175°, with the left column inclination angle taking values ​​at 0.005° intervals, and the right column inclination angle constrained to be no less than the left column inclination angle, with the absolute value of the difference between the two not exceeding 0.090°. Before constructing the physical information difference indication field and analyzing the mechanical characteristics, the angle is converted from degrees to radians. The equivalent stress of N=45668 nodes of the beam body is output for each working condition.

[0044] Then, based on the high-fidelity assembly stress field dataset, high-fidelity stress residual labels for each assembly condition and physical information difference hint fields for each mesh node of the beam in the finite element simulation model are obtained. When obtaining the high-fidelity stress residual labels, the average value of the nodal equivalent stress of each mesh node in the high-fidelity assembly stress field dataset under the current assembly condition is obtained as the spatial average stress. The nodal equivalent stress of each mesh node is subtracted from the spatial average stress to obtain the high-fidelity stress residual label. The average value centering process can suppress the near-constant component dominated by self-weight and with small variation with tilt angle, so that the neural operator focuses on learning the non-uniform spatial variation induced by tilt angle error. Specifically, the nodal equivalent stress of the i-th assembly condition is represented as the sum of the spatial average stress and the spatially distributed stress residual. The spatial average stress is used to characterize the approximately uniform stress formed by self-weight and common assembly components, and the stress residual is used to characterize the spatial non-uniform stress caused by tilt angle error, i.e., the high-fidelity stress residual label. The decomposition relationship of the nodal equivalent stress is as follows:

[0045]

[0046] in, Assembly parameters indicating the current assembly condition The nodal equivalent stress at spatial location 'a' of the lower grid node. =( , ), and These are the column inclination angles of the two columns; Assembly parameters indicating the current assembly condition The average spatial stress is as follows; This indicates a high-fidelity stress residual label centered on the average value of the operating conditions.

[0047] When acquiring the physical information difference prompt field, the average of the column tilt angles of the two columns in the high-fidelity assembly stress field dataset under the current assembly condition is taken as the average tilt angle, and the tilt angle error is taken as the signed difference tilt angle. Signed difference tilt angle as follows:

[0048]

[0049] in, Indicates the average tilt angle, used to describe the common tilt component of the two columns; This represents the differential tilt angle defined by the left-to-right sign convention, used to describe the tilt angle mismatch component that causes asymmetric bending of the beam.

[0050] The average tilt angle and the signed differential tilt angle under each assembly condition are standardized to obtain the standardized average tilt angle and the standardized signed differential tilt angle. The standardization process is as follows:

[0051]

[0052] Among them, b and Let them represent the value to be standardized and its standardized value, respectively. and These are the mean and standard deviation of each value to be standardized. Specifically, if b is the average tilt angle, then the mean and standard deviation are obtained based on the average tilt angle under each assembly condition.

[0053] The coordinates of each grid node are dimensionlessly normalized in the span, height, and depth directions of the beam to obtain normalized coordinates. These normalized coordinates include span normalized coordinates, height normalized coordinates, and depth normalized coordinates. Specifically, the normalized coordinates of grid node j in the span, height, and depth directions of the beam are as follows:

[0054]

[0055]

[0056]

[0057] in, , and Let x represent the span normalized coordinates, height normalized coordinates, and depth normalized coordinates of grid node j, respectively. All are dimensionless coordinates with values ​​ranging from [-1, 1]; j y j and z j These represent the three-dimensional coordinates of mesh node j; x min and x max Let represent the minimum and maximum coordinates of the grid nodes of the beam in the x-direction, respectively, and y represent the minimum and maximum coordinates of the grid nodes in the y-direction, respectively. min and y max These represent the minimum and maximum coordinates of the grid nodes of the beam in the y-direction, respectively, and the z-direction coordinates are also represented. min and z max These represent the minimum and maximum coordinates of the grid nodes of the beam in the z-direction, respectively. and These represent the midpoints of the y-axis and z-axis ranges of each grid node of the beam, respectively; h y and h z These represent the y-axis radius and z-axis radius of each grid node of the beam, respectively.

[0058] For each grid node, the product of the standardized signed differential dip angle and the span normalized coordinates is used as the spatial modulation quantity. The standardized average dip angle, the standardized signed differential dip angle, and the spatial modulation quantity are used to construct the physical information difference cue field of the current grid node. The three-channel physical information difference cue field of grid node j is shown below. for:

[0059]

[0060] Wherein, the symbol ~ represents standardization. , and These represent the standardized mean tilt angle, the standardized signed differential tilt angle, and the spatial modulation amount, respectively.

[0061] First Channel Second Channel Broadcast to all mesh nodes to characterize the global assembly loading status; the third channel passes through... Spatially modulating the differential tilt angle allows the linear bending moment gradient from the Euler-Bernoulli beam theory to be explicitly input into the neural operator before prediction. In this embodiment, the third cue channel continuously varies along the beam span from one end to the other, and its sign and amplitude synchronously reflect the direction and degree of mismatch in the tilt angles of the left and right columns. This channel is related to the node height. ,depth The combined effect of subsequent analysis of bending characteristics enables the network to distinguish different responses at the ends of the beam, the upper and lower flanges, the web, and the corners of the cavity.

[0062] Then, based on the Euler-Bernoulli beam bending theory and a high-fidelity assembly stress field dataset, the analytical mechanical features, including eight-dimensional linear bending characteristics, nine-dimensional square and absolute value characteristics, and five-dimensional Legendre higher-order modal characteristics, are constructed as follows:

[0063] in, The analytical mechanical characteristics of mesh node j are represented. ; , and These represent the linear bending characteristics, square and absolute value characteristics, and Legendre higher-order mode characteristics of mesh node j, respectively. Indicates transpose; Indicates the mean dip angle; Indicates the signed difference tilt angle; , and These represent the span-normalized coordinates, height-normalized coordinates, and depth-normalized coordinates of grid node j, respectively. This represents the coupling term between the bending moment component induced by the differential tilt angle and the neutral axis distance; and its The product describes the parabolic bending moment response under distributed loads; Used to compensate for non-uniform responses in the depth direction; , and These represent linear bending, parabolic bending, and uniform angle bending, respectively. and These represent second-order and third-order Legendre polynomials, respectively.

[0064] Analytical mechanical features are used to characterize uniform tilt response, linear bending moment distribution induced by differential tilt angle, parabolic bending moment distribution corresponding to distributed load, neutral axis distance of cross section, non-negative equivalent stress characteristics, and higher-order stress gradients near beam ends and cavities. The construction of analytical mechanical features is based on the beam bending normal stress relationship, as follows:

[0065]

[0066] in, Let M(a) represent the normal bending stress of the beam, where a represents the position of a grid node in the beam, c represents the distance from the current grid node to the neutral axis of the cross section, M(a) represents the bending moment at position a of the beam, and I1 represents the second moment of the cross section.

[0067] Linear bending moment distribution corresponding to the differential tilt angle Parabolic bending moment distribution They are represented as follows:

[0068]

[0069] in, Indicates a positive correlation. This represents the span normalized coordinates of the current grid node.

[0070] Based on the above mechanism, this embodiment constructs twenty-two-dimensional analytical mechanical features.

[0071] The first group consists of eight-dimensional linear bending features. The simplified quantities for linear bending, parabolic bending, and uniform angle bending are defined as follows:

[0072]

[0073] The second group consists of nine-dimensional square and absolute value characteristics. Among them, the square and absolute value transformation is used to characterize the nonnegativity of von Mises equivalent stress, the quadratic characteristics of stress tensor combination, and the interaction between different bending moment components.

[0074] The third group consists of five-dimensional Legendre higher-order modal features. The second and third Legendre polynomials are:

[0075]

[0076] in, The input is a polynomial.

[0077] Higher-order modal features are used to supplement the stress gradients that exhibit higher-order variations near the beam ends, cavity edges, and section corners. The analytical mechanical characteristics are obtained by stitching together the three sets of features. .

[0078] Then, the analytical mechanical features are standardized column by column to obtain a standardized feature matrix. Combined with the high-fidelity stress residual label, the analytical coefficients are obtained through ridge regression with regularization terms. Based on the analytical coefficients, the initial low-fidelity analytical stress label is obtained. The initial low-fidelity analytical stress label is standardized to obtain the final low-fidelity analytical stress label.

[0079] In specific implementation, the k-th dimension feature in the analytical mechanical characteristics of the i-th working condition and the j-th grid node is... Standardize column by column as follows:

[0080]

[0081] in, The k-th dimension feature represents the analytical mechanical characteristics of the i-th assembly condition and the j-th mesh node after standardization. and Representing the k-th dimension features respectively The mean and standard deviation across all grid nodes; when When the value is less than a preset threshold, i.e., close to zero, the k-th dimension feature is retained. Instead of implementing standardization.

[0082] The standardized features are stacked into a standardized feature matrix. Then, the analytical coefficients were obtained through ridge regression. as follows:

[0083]

[0084] in, I represents the ridge regularity coefficients; I represents the identity matrix. This indicates a high-fidelity stress residual label.

[0085] Ridge regularization coefficient in this embodiment Take 10 -3 Analytical coefficients Finite element stress residuals are calibrated using only the training set, without using validation and test sets, thus avoiding information leakage. Low-fidelity analytical labels can reproduce the macroscopic bending trend caused by the inclination difference of the two columns, but are not required to accurately recover the local peaks at the cavity edges and connecting regions; these high-fidelity residuals are corrected by second-stage finite element fine-tuning.

[0086] The low-fidelity analytical stress label corresponding to mesh node j of the i-th assembly condition. for:

[0087]

[0088] in, Represents the normalized coordinates of grid node j; This represents the 22-dimensional normalized analytical mechanical eigenvector of grid node j under the i-th assembly condition. The normalized eigenvector of each grid node under each assembly condition is transposed to form a normalized eigenma matrix. The row corresponding to the current working condition and grid node is the standardized feature matrix. This is a column vector formed by transposing the 22-dimensional standardized analytical mechanical eigenvectors of each grid node under each assembly condition.

[0089] To ensure that the losses in the first and second phases of training are on the same scale, the global mean of high-fidelity stress residual labels is used. and standard deviation The low-fidelity analytical stress label is standardized as follows:

[0090]

[0091] in, This represents the final low-fidelity analytical stress label after standardization.

[0092] Then, a node input matrix is ​​constructed based on the physical information difference cue field and analytical mechanical features under each assembly condition. The node input matrix is ​​obtained by concatenating the normalized coordinates of each grid node of the beam, the physical information difference cue field, and the analytical mechanical features. In specific implementation, the number of channels of the complete node input matrix is ​​3+3+22=28. The node input matrix, high-fidelity stress residual labels, and low-fidelity analytical stress labels are input into the shared neural operator network for two-stage amortized training. During training, each assembly condition contains 45668 complete beam grid nodes, without node downsampling, and the training batch is one assembly condition. The input of the shared neural operator network is an N×28 node input matrix, and the output is an N×1 normalized stress residual prediction value. The training uses the Adam optimizer with a weight decay of 1×10. -6The gradient norm is clipped to 1.0, and the learning rate decay coefficient during the plateau period of the validation error is 0.5.

[0093] When conducting two-stage amortized training, the first stage is pre-training, with a maximum of 150 training rounds and an initial learning rate of 1×10⁻⁶. -4 The finite element method (FEM) optimization process stops early after 25 rounds. Low-fidelity analytical stress labels are used as supervision signals for the shared neural operator network. Optimization indices are obtained based on high-fidelity stress residual labels on the validation set. Training stops when the optimization index reaches its minimum value. Specifically, the optimization objective for the first stage is established as follows:

[0094]

[0095]

[0096] in, and These represent the neural operator parameters of the shared neural operator network after the first stage of training and during training, respectively. This represents the operation of averaging the assembly conditions indexed by i. Let represent the set of assembly conditions; l represents the mean squared error loss function; after each round, the mean squared error loss function is used to calculate the validation loss on the validation set. When the validation loss is continuous... The number of training rounds did not fall below the minimum validation loss recorded in previous rounds, or reach the maximum number of training rounds in the first phase. Pre-training is stopped, and the network parameters saved when the validation loss is minimized are restored. This embodiment... =25、 =150. The second stage corresponds to... =45; Represents a shared neural operator network; This represents the node input matrix under the i-th assembly condition; This represents the final low-fidelity analytical stress label for the i-th assembly condition; This represents the normalized coordinates of each grid node of the beam. N represents the number of grid nodes in the beam; This indicates the physical information difference indication field under the i-th assembly condition. ; This represents the standardized feature matrix under the i-th assembly condition. .

[0097] To avoid overfitting the analytical approximation error by the neural operator, the validation loss is continuously calculated during the first stage of training, and the training rounds are selected according to the following selection criteria:

[0098]

[0099] in, This represents the optimal training round in the first stage, i.e., the training round when the finite element verification error is minimized. This indicates the maximum number of training rounds in the first phase; This represents the mean square error obtained based on high-fidelity stress residual labels; and Let t represent the training epoch and the optimal training epoch, respectively. The parameters of the neural operator are as follows.

[0100] At the end of each training epoch, the validation loss is simultaneously calculated on the finite element validation condition, and the network parameters with the minimum validation loss are saved. This mechanism allows the network to absorb shared macroscopic trends in the parsed low-fidelity labels, while terminating pre-training before parsing bias begins to dominate.

[0101] The neural operator parameters of the shared neural operator network after the first stage of training are saved as the initial parameters for the second stage of fine-tuning training, thus obtaining the pre-trained shared neural operator network.

[0102] Then, a second stage of fine-tuning training is performed. Using high-fidelity stress residual labels as supervision signals, the neural operator parameters of the pre-trained shared neural operator network are fine-tuned to obtain the final trained assembly stress field prediction model. Specifically, the second stage starts from... Starting from this point, fine-tuning is performed using high-fidelity stress residual labels as monitoring signals, and the optimization objective for the second stage is established as follows:

[0103]

[0104] in, This represents the neural operator parameters of the pre-trained shared neural operator network after the second stage of training. This represents the high-fidelity stress residual label under the i-th assembly condition.

[0105] The second phase can use a different learning rate, maximum number of training epochs, and preset early stopping epochs than the first phase. Specifically, the total training budget for the second phase is 400 epochs minus the number of epochs selected in the first phase, with an initial learning rate of 5 × 10⁻⁶. -4 The network is stopped early at round 45, allowing it to focus on correcting contact nonlinearity, stress concentration near cavities, and local three-dimensional effects that cannot be described by analytical theory, based on the macroscopic mechanical trends it has already absorbed.

[0106] The second stage uses the neural operator parameters saved in the first stage as initial parameters, employing the same N×28 input matrix and shared neural operator structure, and fine-tuning them using finite element high-fidelity stress residual labels. Both stages use mean squared error as the data loss, but it can also be replaced with mean absolute error, Huber loss, or a composite loss including stress gradient constraints, depending on the actual noise level.

[0107] The shared neural operator network specifically uses the slice attention-based Transformer neural operator from the paper "Transolver: A Fast Transformer Solver for PDEs on General Geometries" as a shared backbone. It includes 2 Transformer layers, 2 attention heads, 32 slice tokens, a hidden dimension of 32, an MLP expansion ratio of 2, GELU activation, and no dropout. The shared neural operator aggregates N irregular point cloud nodes into S learning slice tokens, which is less than the number of nodes. After performing attention and multilayer perceptron operations among the learning slice tokens, the features are mapped back to each node, and the scalar stress residual prediction value of each node is output. This reduces the high computational cost of direct node attention to a computational cost related to the square of the number of slices.

[0108] Finally, the nodal coordinates of each grid node of the beam and the column inclination angles of the two columns in the 3D mesh model of the beam and columns under the current assembly state are input into the assembly stress field prediction model. The assembly stress field prediction model can output the standardized stress residual prediction values ​​of each grid node in the beam under the current assembly state in one forward calculation. The standardized stress residual prediction values ​​are then de-standardized to obtain the nodal stress residual prediction values ​​of each grid node with actual stress units, with physical units of MPa, and thus construct the nodal stress residual prediction field. When the spatial average stress under the current assembly state is obtained, the spatial average stress is added to the nodal stress residual prediction values ​​of each grid node to obtain the predicted nodal equivalent stress of each grid node, and thus construct the predicted nodal equivalent stress field of the beam. The spatial average stress can be obtained from a pre-calibrated average stress model, simplified self-weight analysis, benchmark finite element calculation, or assembly measurement. When the spatial average stress is not obtained, the nodal stress residual prediction field can be directly used to characterize the non-uniform stress distribution caused by the mismatch of column inclination angles and to locate stress concentration areas. The complete node equivalent stress field or the predicted field of node stress residuals can be compared with the corresponding preset thresholds to generate assembly acceptance results or reassembly instructions.

[0109] Predicted nodal equivalent stress as follows:

[0110]

[0111]

[0112] in, Represents the spatial average stress component; This represents the predicted value of the inverse-standardized stress residual; and This represents the standard deviation and mean of the global standard deviation and global mean used when standardizing the high-fidelity stress residual labels during the model training phase. This represents the predicted value of the stress residual.

[0113] The spatial average stress component can be obtained from a pre-calibrated average stress model, simplified self-weight analysis, a small number of reference finite element calculations, or assembly measurements; when this component is not available, the non-uniform stress concentration induced by the tilt angle can still be directly used to locate the stress residual field.

[0114] For assembly compliance verification tasks, this invention uses the stress residual prediction field to locate the stress concentration area caused by the mismatch in the tilt angles of the left and right columns. When the average stress of the working condition is obtained by simplifying the self-weight model, the benchmark finite element working condition or other methods, the complete node equivalent stress field can be further restored and compared with the allowable stress of the material or the assembly preset threshold to make a reassembly decision.

[0115] In practical implementation, this invention employs five-fold cross-validation to evaluate its method against comparative methods. In each fold, the assembly conditions are divided into 60% training set, 20% validation set, and 20% test set, with the same data partitioning used across all methods. The training set is used for ridge regression parameter calibration of the low-fidelity model and two-stage training of the neural operator. The validation set does not participate in network parameter gradient updates; in the first stage, it is used to calculate the validation loss based on high-fidelity finite element labels and selectively save pre-trained weights; in the second stage, it is used for network parameter optimization, learning rate adjustment, and early stopping. The test set is only used for final prediction performance evaluation after model training is complete and does not participate in model training or parameter selection. Comparison methods include DeepONet (Deep Operator Network), ONO (Orthogonal Neural Operator), UPT (Universal Physics Transformer), Transolver (A Fast Transformer Solver for PDEs on General Geometries), GAOT (Geometry-Aware Operator Transformer), and GNOT (General Neural Operator Transformer).

[0116] like Figure 3 of (a) Figure 3 (b) and Figure 3 As shown in (c), the prediction error is calculated in MPa after destandardization. The smaller the root mean square error (RMSE) and mean absolute error (MAE), the better. The present invention outperforms the comparison method of each baseline neural operator in terms of both the mean absolute error (MAE) and root mean square error (RMSE) in the five-fold test, achieving the lowest value, indicating that the present invention has a good advantage in overall prediction accuracy. In terms of the maximum error (MaxErr), the present invention maintains a low level, close to the best-performing comparison method, indicating that the present invention can better control local extreme prediction errors while improving overall prediction accuracy, and has a more stable stress field prediction performance.

[0117] like Figure 4 of (a) Figure 4 (b) and Figure 4 As shown in (c), the MSE verification loss variation curves and stress residual determination coefficients R for different methods are presented respectively. 2 And the comparison results of the root mean square error (RMSE) of the test set. Figure 4 (a) shows that during the second stage of high-fidelity finite element stress residual label fine-tuning, the verification loss of the method of the present invention gradually decreases with the training rounds and eventually converges to a low level, indicating that the method of the present invention can further utilize high-fidelity finite element data to effectively correct the network parameters on the basis of low-fidelity parsing label pre-training. Figure 4 In (b), the stress residual determination coefficient R 2 The stress residual determination coefficient R0 is used to characterize the degree of agreement between the predicted stress residual and the high-fidelity finite element stress residual. 2 The bigger the better, R 2 The closer the value is to 1, the higher the consistency between the predicted result and the true value of the finite element. The stress residual determination coefficient R0 of the proposed method, GNOT method, GAOT method, Transolver method, UPT method, ONO method, and DeepONet method is... 2 The values ​​are 0.8201, 0.7420, 0.139, 0.7103, 0.7366, 0.4232, and 0.5739, respectively, with the method of the present invention achieving the highest stress residual determination coefficient R. 2 This indicates that the present invention has a better fitting ability for the spatial variation law of stress residual. Figure 4(c) shows the root mean square error (RMSE) of each method on the test set. A smaller value indicates a lower prediction error. The RMSEs of the DeepONet, ONO, UPT, Transolver, GAOT, GNOT, and the method of this invention are 2.832 MPa, 3.284 MPa, 2.226 MPa, 2.334 MPa, 4.024 MPa, 2.203 MPa, and 1.834 MPa, respectively. The method of this invention achieves the lowest RMSE. In summary... Figure 4 (b) and Figure 4 As shown in (c), the average root mean square error of the five-fold test using the method of the present invention is 1.834 MPa, and the stress residual determination coefficient R0 is... 2 The root mean square error is 0.820, which is about 16.8% lower than the baseline neural operator GNOT, indicating that the method of the present invention has good advantages in terms of stress residual prediction accuracy and overall fitting consistency.

[0118] like Figure 5 As shown, to facilitate a direct comparison of the recovery effects of each method on the equivalent stress of complete nodes, under each test condition, the predicted nodal stress residual values ​​output by each method were denormalized and added to the spatial average stress components corresponding to the test condition to obtain the predicted von Mises equivalent stress of each node. Simultaneously, the nodal von Mises equivalent stress calculated by the finite element method was used as the high-fidelity finite element true value for comparison. In the figure, the horizontal axis represents the nodal von Mises equivalent stress calculated using the finite element method (FEM), and the vertical axis represents the corresponding nodal von Mises equivalent stress recovered by each method. Each scatter point corresponds to a test mesh node, and the dashed line represents the ideal prediction relationship y=x. The closer the scatter point is to this dashed line, the higher the consistency between the prediction result and the finite element true value. The root mean square error (RMSE) of the ONO method is 2.753 MPa, the mean absolute error (MAE) is 1.380 MPa, and the stress residual determination coefficient R0 is [not specified]. 2 The value was 0.6712; the RMSE of the UPT method was 2.130 MPa, the MAE was 1.042 MPa, and the R... 2 The value was 0.8031; the RMSE of the Transolver method was 2.190 MPa, the MAE was 1.088 MPa, and the R... 2 The value was 0.7918; the RMSE of the GAOT method was 3.923 MPa, the MAE was 1.889 MPa, and the R... 2 The value was 0.3321; the RMSE of the GNOT method was 2.061 MPa, the MAE was 1.007 MPa, and the R...2 The value is 0.8157; the RMSE of the method of the present invention is 1.226 MPa, the MAE is 0.631 MPa, and the R... 2 The value is 0.9138. It can be seen that the scatter points of the method of this invention are more concentrated near the ideal relationship line, indicating that it has better consistency in the response of nodes with different stress levels and higher node-level prediction accuracy. Figure 5 The complete nodal equivalent stress in the data is only used for result comparison and display. The spatial average stress component is recovered using the known spatial average stress of the corresponding finite element working condition, and does not indicate that the neural operator independently predicted the spatial average stress component.

[0119] like Figure 6 As shown, the three-dimensional stress field prediction and error comparison results of the crossbeam under representative assembly conditions are presented. The representative assembly conditions are a left column inclination angle of 0.055° and a right column inclination angle of 0.115°. The root mean square error (RMSE) of the DeepONet method is 3.14 MPa, the mean absolute error (MAE) is 1.86 MPa, and the stress residual determination coefficient R0 is [missing value]. 2 The root mean square error (RMSE) of the ONO method is 2.91 MPa, the mean absolute error (MAE) is 1.77 MPa, and the stress residual determination coefficient R0 is 0.586. 2 The root mean square error (RMSE) of the UPT method is 2.45 MPa, the mean absolute error (MAE) is 1.42 MPa, and the stress residual determination coefficient R0 is 0.646. 2 The root mean square error (RMSE) of the Transolver method is 2.51 MPa, the mean absolute error (MAE) is 1.45 MPa, and the stress residual determination coefficient R0 is 0.749. 2 The root mean square error (RMSE) of the GNOT method is 2.36 MPa, the mean absolute error (MAE) is 1.36 MPa, and the stress residual determination coefficient R0 is 0.737. 2 The root mean square error (RMSE) of the ADL method of this invention is 1.50 MPa, the mean absolute error (MAE) is 1.02 MPa, and the stress residual determination coefficient R0 is 0.766. 2 The value is 0.906, which shows that the present invention can relatively completely maintain the local stress concentration morphology near the beam cavity.

[0120] like Figure 7The figure shows the predicted nodal equivalent stress field of the upper flange section of the crossbeam under a representative assembly condition in this embodiment of the invention, along with a comparison of the signed error. To maintain consistency with the aforementioned complete stress field results, the predicted nodal stress residuals output by each method are denormalized and added to the spatial average stress component corresponding to the test condition to obtain the nodal von Mises equivalent stress field for comparison and demonstration; the finite element true value represents the nodal von Mises equivalent stress obtained by finite element calculation. The prediction result represents the nodal equivalent stress distribution of the upper flange section of the crossbeam recovered by each method, and the error (predicted value - finite element true value) represents the difference between the predicted equivalent stress of the corresponding node and the finite element true value, where a positive value indicates that the predicted value is higher than the finite element true value, and a negative value indicates that the predicted value is lower than the finite element true value. The prediction results show that the finite element true value exhibits significant non-uniform stress concentration in the lightweight hole of the crossbeam and its adjacent area. Methods such as DeepONet, ONO, and UPT exhibit varying degrees of smoothing in regions of high local stress gradients. Transolver and GNOT can recover some local stress variations, while the method of this invention predicts stress high-value regions that are closer to the true values ​​in terms of location and distribution. Quantitative results show that the root mean square error (RMSE) of the method of this invention is 1.50 MPa, the mean absolute error (MAE) is 1.02 MPa, and the stress residual determination coefficient R0 is [missing information]. 2 The error value is 0.906, which is better than other comparative methods shown in the figure. As can be seen from the signed error field below, the positive and negative error distribution range of the method of the present invention is small at the hole edge and in the high stress gradient region, indicating that it has a good ability to preserve the location and spatial variation of local stress concentration.

[0121] like Figure 8 The diagram shows the ablation comparison results of the key components of this invention. Specifically, removing two modules means simultaneously removing the physical information difference prompt field and the first-stage low-fidelity analytical label pre-training, retaining only the shared neural operator backbone for high-fidelity training; removing the difference prompt means canceling the three-channel physical information difference prompt field, while keeping the other inputs and training process unchanged; removing the first-stage pre-training means retaining the physical information difference prompt field and analytical mechanical features, but canceling the low-fidelity analytical stress label pre-training, and directly using high-fidelity finite element stress residual label training; the complete method of this invention represents the complete method that simultaneously uses the physical information difference prompt field and two-stage amortized training. Figure 8 The upper part presents the nodal equivalent stress field prediction results and corresponding error distributions for the finite element true value, the GNOT method, various ablation variants, and the complete method of this invention. The error diagram is used to reflect the magnitude of the nodal error between the prediction results of each method and the finite element true value. It can be seen that after removing the difference indication, a larger range of prediction deviations appear in the beam cavity and local high stress areas, while the error distribution of the complete method of this invention is smaller overall. Figure 8The following section further presents the validation loss variation, root mean square error (RMSE), mean absolute error (MAE), and coefficient of determination (R) of the test stress residual for each method. 2 The RMSE values ​​for the GNOT method, the method with two modules removed, the method with difference hints removed, the method with the first-stage pre-training removed, and the method of the complete invention were 2.34 MPa, 2.86 MPa, 2.86 MPa, 1.88 MPa, and 1.80 MPa, respectively; the corresponding MAE values ​​were 1.24 MPa, 1.73 MPa, 1.71 MPa, 1.05 MPa, and 0.95 MPa, respectively; and the corresponding stress residual determination coefficient R0 was [missing value]. 2 The values ​​were 0.744, 0.620, 0.620, 0.836, and 0.850, respectively. The results show that removing the physical information difference cues significantly reduced the prediction performance, indicating that node-level spatial cues play a major role in characterizing the asymmetric stress response caused by the mismatch in the inclination angles of the left and right columns. Even after removing the low-fidelity analytical labels from the first-stage pre-training while retaining the difference cues, the model still exhibits good predictive ability, but both its RMSE and MAE increase, indicating that the first-stage pre-training can further improve the model initialization and high-fidelity fine-tuning effects. The complete method of this invention achieves the lowest test RMSE and MAE, and the highest R... 2 This indicates that the difference-indicating field and the two-stage amortization training have complementary effects.

[0122] like Figure 9 The figure shows a two-dimensional visualization of the latent features of grid nodes before and after training for the shared neural operator of this invention. The Uniform Manifold Approximation and Projection (UMAP) is used to map the high-dimensional latent features of nodes within the neural operator to a two-dimensional space, allowing observation of the organization of different node features in the latent space. In the figure, the horizontal and vertical axes represent UMAP dimension 1 and UMAP dimension 2, respectively. Each scatter point corresponds to a beam grid node, and the color of the scatter point indicates the stress level corresponding to that node. The stress unit for the nodes in the color bars is MPa. Figure 9 The left side shows the distribution of latent features of nodes under random initialization before model training. At this time, nodes with different stress levels are highly mixed in the latent space, and the stress differences between neighboring nodes are more obvious. The nearest neighbor correlation coefficient r in the latent space is 0.74, and the normalized mean absolute error is 0.35. Figure 9The right side shows the distribution of latent node features after the second stage of high-fidelity fine-tuning. Nodes with different stress levels exhibit a more continuous gradient organization along the latent space, and the local distribution relationship between high-stress and low-stress nodes is clearer. The correlation coefficient between the nearest neighbors in the latent space increases to 0.83, and the normalized mean absolute error decreases to 0.28. The correlation coefficient *r* measures the consistency between the local neighborhood relationship of nodes and their stress levels in the latent feature space; a larger value indicates a more consistent local organization and stress variation. The normalized mean absolute error measures the average difference in stress levels between nearest neighbors in the latent space; a smaller value indicates higher stress consistency within the local neighborhood. Therefore, the increase in *r* and the decrease in the normalized mean absolute error after training indicate that, after two stages of training, the latent node features learned by the neural operator form a clearer local organizational structure for stress levels, thus providing an auxiliary explanation for the ability of this invention to identify and predict local stress concentration areas.

[0123] The above embodiments illustrate that the present invention solves the problem of lack of node-level spatial clues in global assembly parameters by using physical information difference prompting fields, improves the utilization efficiency of inexpensive analytical labels through two-stage amortized training, and can predict the beam assembly stress field that is difficult to measure directly with low online computing costs.

[0124] Finite element contact settings, material parameters, mesh element selection, and basic neural network operations not described in detail in this specification can all be implemented using techniques known in the art.

[0125] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, optical storage, etc.) containing computer-usable program code. The solutions in the embodiments of this application can be implemented using various computer languages. This application is described with flowcharts of methods, systems, and computer program products according to embodiments of this application.

[0126] Although preferred embodiments of this application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, this invention is intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of this application.

[0127] Obviously, those skilled in the art can make various modifications and variations to this application without departing from the spirit and scope of this application. Therefore, if these modifications and variations of this application fall within the scope of the equivalent technology of this invention, this application also intends to include these modifications and variations.

Claims

1. A method for predicting the assembly stress of a machine tool crossbeam and column based on amortization difference hint learning, characterized in that, include: Step S1: Establish finite element simulation models of the crossbeam and column of the gantry milling machine under different assembly conditions, and extract the simulation parameters of the crossbeam and column under each assembly condition to construct a high-fidelity assembly stress field dataset. Step S2: Based on the high-fidelity assembly stress field dataset, obtain the high-fidelity stress residual label for each assembly condition and the physical information difference indication field of each mesh node of the beam in the finite element simulation model; Step S3: Based on the high-fidelity assembly stress field dataset, construct analytical mechanical features including linear bending features, square and absolute value features, and Legendre higher-order modal features, and then combine the high-fidelity stress residual labels to obtain low-fidelity analytical stress labels for each assembly condition. Step S4: Based on the physical information difference prompt field and analytical mechanical characteristics under each assembly condition, construct the node input matrix. Input the node input matrix, high-fidelity stress residual label and low-fidelity analytical stress label into the shared neural operator network for two-stage amortized training to obtain the assembly stress field prediction model. Input the node coordinates of each grid node of the beam and the column inclination angle of the two columns in the three-dimensional mesh model of the beam and column under the assembly condition to be predicted into the assembly stress field prediction model. After processing, output the nodal stress residual prediction field of the beam under the current assembly condition, and then obtain the predicted nodal equivalent stress field of the beam.

2. The method for predicting the assembly stress of machine tool crossbeam and column based on amortization difference prompting learning according to claim 1, characterized in that: In step S1, the column tilt angles of the two columns are changed within the preset assembly tolerance range of the column of the gantry milling machine, thereby constructing a finite element simulation model of the beam column under different assembly conditions; the simulation parameters of the beam column include the node coordinates and node equivalent stress of each mesh node on the beam in the finite element simulation model, as well as the column tilt angles of the two columns and the tilt angle error between them.

3. The method for predicting the assembly stress of machine tool crossbeam and column based on amortization difference prompting learning according to claim 2, characterized in that: In step S2, the average value of the nodal equivalent stress of each grid node in the high-fidelity assembly stress field dataset under the current assembly condition is obtained as the spatial average stress, and the nodal equivalent stress of each grid node is subtracted from the spatial average stress to obtain the high-fidelity stress residual label.

4. The method for predicting the assembly stress of machine tool crossbeam and column based on amortization difference prompting learning according to claim 2, characterized in that: In step S2, the average value of the column tilt angles of the two columns in the high-fidelity assembly stress field dataset under the current assembly condition is taken as the average tilt angle, and the tilt angle error is taken as the signed differential tilt angle. The average tilt angle and the signed differential tilt angle under each assembly condition are standardized to obtain the standardized average tilt angle and the standardized signed differential tilt angle. The coordinates of each grid node are dimensionlessly normalized in the span, height, and depth directions of the beam to obtain normalized coordinates. The normalized coordinates include span normalized coordinates, height normalized coordinates, and depth normalized coordinates. For each grid node, the product of the standardized signed differential tilt angle and the span normalized coordinate is used as the spatial modulation quantity. The standardized average tilt angle, the standardized signed differential tilt angle, and the spatial modulation quantity are used to construct the physical information difference indication field of the current grid node.

5. The method for predicting the assembly stress of machine tool crossbeam and column based on amortization difference prompting learning according to claim 4, characterized in that: In step S3, the analytical mechanical characteristics are as follows: in, Represents the analytical mechanical characteristics of mesh node j; , and These represent the linear bending characteristics, square and absolute value characteristics, and Legendre higher-order mode characteristics of mesh node j, respectively. Indicates transpose; Indicates the mean dip angle; Indicates the signed difference tilt angle; , and These represent the span-normalized coordinates, height-normalized coordinates, and depth-normalized coordinates of grid node j, respectively. , and These represent linear bending, parabolic bending, and uniform angle bending, respectively. and These represent second-order and third-order Legendre polynomials, respectively.

6. The method for predicting the assembly stress of machine tool crossbeam and column based on amortization difference prompting learning according to claim 4, characterized in that: In step S3, the analytical mechanical features are standardized column by column to obtain a standardized feature matrix. Then, the analytical coefficients are obtained by combining the high-fidelity stress residual labels and calibrating them through ridge regression. Based on the analytical coefficients, the initial low-fidelity analytical stress labels are obtained. After standardizing the initial low-fidelity analytical stress labels, the final low-fidelity analytical stress labels are obtained.

7. The method for predicting the assembly stress of machine tool crossbeam and column based on amortization difference prompting learning according to claim 4, characterized in that: In step S4, the node input matrix is ​​constructed by splicing the normalized coordinates of each grid node of the beam, the physical information difference prompt field, and the analytical mechanical features. During the two-stage amortized training, the first stage of pre-training is performed. Low-fidelity analytical stress labels are used as the supervision signal for the shared neural operator network during pre-training, and the verification loss is calculated based on the high-fidelity stress residual labels. When the verification loss for consecutive preset pre-training rounds is not lower than the minimum verification loss among all pre-training rounds, or when the preset maximum training round is reached, the first stage of pre-training is stopped. The network parameters of the shared neural operator network with the minimum verification loss among the executed training rounds are selected to obtain the pre-trained shared neural operator network. Then, the second stage of fine-tuning training is performed, using the high-fidelity stress residual labels as the supervision signal for the pre-trained shared neural operator network to fine-tune the neural operator parameters of the pre-trained shared neural operator network, obtaining the final trained assembly stress field prediction model.

8. The method for predicting the assembly stress of machine tool crossbeam and column based on amortization difference prompting learning according to claim 1, characterized in that: In step S4, the assembly stress field prediction model outputs the standardized stress residual prediction values ​​of each grid node in the beam under the current assembly state. The standardized stress residual prediction values ​​are then de-standardized to obtain the nodal stress residual prediction values ​​of each grid node, thereby constructing the nodal stress residual prediction field. When the spatial average stress under the current assembly state is obtained, the spatial average stress is added to the predicted value of the nodal stress residual of each grid node to obtain the predicted nodal equivalent stress of each grid node, and then the predicted nodal equivalent stress field of the beam is constructed.

9. An electronic device, characterized in that, include: A memory and a processor are coupled to each other, wherein the memory stores program data, and the processor invokes the program data to perform the method as described in any one of claims 1-8.

10. A computer-readable storage medium storing program data thereon, characterized in that, When the program data is executed by the processor, it implements the method as described in any one of claims 1-8.

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