Method for predicting displacement of contact surface between crossbeam and column of machine tool based on topographic anchoring average flow

Abstract

The application discloses a machine tool beam-column contact surface displacement prediction method based on topographic anchor average flow. The method comprises the following steps: obtaining the condition data and target normal displacement field of the contact surface to construct a data set; constructing a topographic anchor generation model comprising a variational autoencoder and a latent voxel analysis regressor and training; constructing a latent space average flow generator to construct a condition source distribution with the topographic anchor, sample the source latent variable, and train and learn the residual transport to the target displacement latent variable; during prediction, generating the topographic anchor according to the condition data of the contact surface to be predicted, determining the integral initial value, integrating the few-step ordinary differential equation to obtain the predicted displacement latent variable, and mapping back to the physical space to obtain the normal displacement prediction field. The application replaces the general noise with the topographic anchor, reduces the probability path overlap, maintains the local gradient, and realizes high-precision and rapid prediction.

Description

Technical Field

[0001] This invention belongs to the field of large precision machine tool assembly accuracy prediction, and specifically relates to a method for predicting the displacement of the machine tool beam-column contact surface based on topographic anchored average flow. Background Technology

[0002] Large gantry milling machines are widely used in aerospace, energy, shipbuilding, and large mold manufacturing. The beam-column contact surface bears the weight of the moving beam and the machining load. Local compression, warping, and uneven deformation of the surface are amplified to the tool center point through the long cantilever structure of the beam, resulting in contour deviations and dimensional drift. Therefore, accurately predicting the normal displacement field of the contact surface before actual assembly is a crucial foundation for assembly qualification, pre-assembly performance evaluation, and contact surface scraping. Traditional assembly typically relies on repeated trial assembly, inspection, disassembly, and manual scraping to ensure contact quality. This process is not only time-consuming and costly but also heavily dependent on operator experience, making it difficult to obtain a quantitative displacement distribution of the entire contact surface before formal assembly.

[0003] The beam-column contact surface is typically a complex area with non-convex inner and outer boundaries, multiple bolt holes, and locally hollowed-out structures. Macroscopic flatness, bending and torsion errors of the upper and lower mating surfaces, surface waviness and microscopic roughness, as well as bolt preload distribution, tightening sequence, friction state, and assembly translation and rotation deviations all collectively affect the actual contact state. Large displacement gradients tend to form near bolt hole edges, free boundaries, and locations of abrupt morphological changes, making these areas key areas for assembly quality assessment and scraping. Even with identical nominal geometric dimensions and assembly conditions, the final displacement field may differ due to unmeasured microscopic morphology and variations in the tightening process; therefore, there is a one-to-many conditional distribution relationship between assembly conditions and displacement response.

[0004] High-fidelity finite element contact analysis can describe complex geometric boundaries, bolt preload, and surface morphology, and obtain relatively accurate displacement field results. However, contact problems in large machine tools involve complex meshes and nonlinear contact iterations, and a single solution typically requires a long time. When batch analysis is needed for different surface morphologies, preload, and assembly deviations, the computational cost increases further, making it difficult to meet the needs of rapid evaluation and parameter adjustment in the assembly field. Therefore, the finite element method is more suitable as an offline data generation and mechanism analysis tool, and is not suitable as a direct means of rapid on-site prediction.

[0005] To improve prediction efficiency, existing technologies typically employ deterministic surrogate models such as regression networks and neural operators to learn the mapping relationship between assembly conditions and displacement fields. While these methods offer fast inference speeds, they often compress multiple possible displacement responses under the same conditions into a single conditional mean. This can easily smooth local peaks and steep gradients near bolt holes and free boundaries, allowing the prediction results to reflect the overall deformation trend. However, they struggle to retain local details that are crucial for scraping and identifying abnormal areas, and they also fail to characterize the randomness in the assembly process.

[0006] Generative physics methods such as diffusion models and flow-matching models can learn conditional distributions, but they typically begin iterating from isotropic Gaussian noise independent of the specific contact surface. For contact regions with holes, openwork, and non-convex boundaries, different samples start from similar random states, easily leading to overlapping probabilistic transport paths. The model not only needs to learn the complex residuals caused by local morphology but also needs to regenerate the overall elastic deformation trend determined by structural stiffness and load. When the training samples are limited or the number of inference steps is small, the prediction results are prone to problems such as block artifacts, boundary noise, and convergence instability.

[0007] Using linear analytical estimation as a physical prior can reduce the model's repetitive learning of overall elastic deformation, but directly using simple linear estimation in the original displacement field space still presents adaptation difficulties. The non-convex profile of the contact surface, bolt holes, and multi-scale surface morphology weaken the linear superposition relationship, causing morphology-induced biases in the analytical estimation at different locations, making it difficult to accurately describe the local deformation near the free boundary and bolt holes. Therefore, a displacement prediction method is needed that can generate a dedicated flow starting point based on the morphology of each contact surface, bolt load, and assembly state, and calibrate physical prior biases in a suitable representation space. This method allows the model to primarily learn local residuals that cannot be expressed by analytical estimation, stably preserving local displacement gradients with fewer inference steps, thereby meeting the needs of rapid pre-assembly evaluation, assembly qualification determination, and abnormal contact surface location. Summary of the Invention

[0008] To address the problems existing in the background technology, this invention provides a method for predicting the displacement of the machine tool beam-column contact surface based on topography-anchored average flow. This method solves the technical problems in the prior art where the complex topography features of the interface are difficult to effectively integrate into the generation process, and where traditional generation methods rely on random noise initialization, leading to insufficient accuracy and stability in displacement field prediction. The method of this invention replaces general noise with topography anchors on the contact surface to be predicted, and improves the interpretability of the topography anchors for the latent variables of the target displacement by physically aligning the latent space. This allows the latent space average flow generator to focus on learning the topography-driven residual transport.

[0009] The technical solution adopted by the machine tool beam-column contact surface displacement prediction method of the present invention is as follows:

[0010] S1. Obtain the conditional data of the beam-column contact surface and the corresponding target normal displacement field, and construct the contact surface displacement prediction dataset.

[0011] S2. Construct a topography anchor generation model and train it using a contact surface displacement prediction dataset to obtain a trained topography anchor generation model. The topography anchor generation model includes a variational autoencoder and a latent voxel-by-latest analytical regressor.

[0012] S3. Construct a latent space average flow generator; construct a conditional source distribution based on the trained topography anchor generation model, sample source latent variables from the conditional source distribution, and train the latent space average flow generator to learn the residual transport from source latent variables to target displacement latent variables.

[0013] S4. Obtain the conditional data of the contact surface to be predicted and generate the corresponding topographic anchor. Determine the initial value of the integral based on the topographic anchor. Starting from the initial value of the integral, perform the integration of the ordinary differential equation through the trained latent space average flow generator. Map the latent variable of the predicted displacement obtained by the integral back to the physical space to obtain the predicted normal displacement field of the contact surface to be predicted.

[0014] The conditional data includes spatial conditions and scalar conditions; the spatial conditions include bolt preload distribution, upper contact surface morphology, lower contact surface morphology, bolt distance field, inner boundary distance field, and outer boundary distance field; the scalar conditions include upper contact surface roughness parameters, lower contact surface roughness parameters, upper contact surface waviness parameters, lower contact surface waviness parameters, and assembly offset parameters; the target normal displacement field is the normal displacement field generated after bolt assembly of the beam-column contact surface.

[0015] Step S1 specifically involves:

[0016] S11. Discretize the beam-column contact area into an H×W grid and create a binary frame mask to identify the effective contact area.

[0017] S12. Based on the H×W grid, determine the bolt preload distribution value, upper contact surface morphology value and lower contact surface morphology value at each grid point, and combine the three types of values ​​corresponding to each grid point into the original spatial conditions according to the channels.

[0018] S13. Calculate the normalized Euclidean distance from each grid point to the nearest bolt center, inner free boundary, and outer free boundary to obtain the bolt distance field, inner boundary distance field, and outer boundary distance field, and combine them with the original spatial conditions to form the spatial conditions.

[0019] S14. Obtain the roughness amplitude of the upper contact surface, the roughness amplitude of the lower contact surface, the waviness amplitude of the upper contact surface, the waviness amplitude of the lower contact surface, and the assembly offset parameters of the upper contact surface relative to the lower contact surface, which together constitute the scalar conditions; the spatial conditions and scalar conditions together constitute the condition data of the beam-column contact surface.

[0020] S15. Under the assembly state corresponding to the condition data obtained in step S14, the beam-column contact surface generates a displacement field after bolt assembly; from the displacement field, obtain the normal displacement components at each grid point in the H×W grid; according to the binary frame mask, retain the normal displacement components corresponding to the grid points marked as contact in the binary frame mask as the target normal displacement field.

[0021] S16. Repeat steps S11-S15 several times to collect the target normal displacement field corresponding to different conditions, thereby constructing a contact surface displacement prediction dataset.

[0022] Step S2 specifically involves:

[0023] S21. The target normal displacement field is mapped to the mean and logarithmic variance of the latent variable distribution using the encoder in the variational autoencoder. The latent variable distribution is determined based on the mean and logarithmic variance, and the target displacement latent variable is obtained by reparameter sampling of the latent variable distribution.

[0024] S22. Using a voxel-by-voxel analytical regressor, the original spatial conditions are averaged and then the pooled original spatial conditions and scalar conditions are linearly mapped and fused to obtain the corresponding morphological anchors.

[0025] S23. Utilize the decoder in the variational autoencoder to analyze the latent variable of the target displacement. The reconstructed displacement field is obtained by reconstruction. The effective contact area reconstruction loss is constructed based on the difference between the target normal displacement field and the reconstructed displacement field within the effective contact area. The latent variable distribution regularization loss is constructed based on the difference between the latent variable distribution and the standard normal distribution. The latent variable alignment loss is constructed based on the difference between the mean of the latent variable distribution and the topographic anchor.

[0026] S24. Construct a joint loss consisting of effective contact area reconstruction loss, latent variable distribution regularization loss, and latent variable alignment loss, and train the shape anchor generation model to obtain the trained shape anchor generation model.

[0027] The joint loss is set according to the following formula:

[0028] ;

[0029] ;

[0030] ;

[0031] ;

[0032] in, For joint losses; To effectively address the losses in the contact area; For latent variable distribution regularization loss; For latent variable alignment loss; and All are weighting coefficients; To calculate the expected value of the distribution of latent variables; and These are the mean and variance of the latent variable distribution of the encoder output, respectively; For the decoder in a variational autoencoder; It is a binary box mask; For element-wise product; For the target normal displacement field; For shape anchors.

[0033] Step S3 specifically involves:

[0034] S31. Using the encoder of the trained variational autoencoder and the latent voxel-by-latest analytical regressor, calculate the residual between the mean of the latent variable distribution of each sample in the dataset and the corresponding morphological anchor. Calculate the empirical standard deviation based on the residuals of all samples and construct the conditional source distribution.

[0035] S32. Sample source latent variables from the conditional source distribution, use the source latent variables as the starting point for flow matching of the latent space average flow generator, use the target displacement latent variable as the ending point for flow matching of the latent space average flow generator, use the difference between the two latent variables as the velocity target for flow matching learning, train the latent space average flow generator to learn the residual transport from the source latent variables to the target displacement latent variable, and finally obtain the trained latent space average flow generator.

[0036] Step S32 further includes:

[0037] A linear interpolation path is established between the source latent variable and the target displacement latent variable, with each time step on the linear interpolation path corresponding to a latent variable; the input of the latent space average flow generator includes the latent variables on the linear interpolation path, the time interval, and the conditional data; the latent space average flow generator outputs the average velocity on the given time interval of the linear interpolation path and is trained using flow training loss.

[0038] The flow training loss used during the training of the latent space average flow generator is set according to the following formula:

[0039] ;

[0040] in, For flow training loss; The average velocity predicted by the latent space average flow generator; For speed targets; To stop the gradient; To reconstruct the weights of auxiliary items; and These are the two endpoints of the time interval; For the linear interpolation path at time step Latent variables; The latent variable is the target displacement. These are the source latent variables.

[0041] Step S4 specifically involves:

[0042] S41. Obtain the conditional data of the contact surface to be predicted, and use the latent voxel-by-voxel analytical regressor in the trained morphology anchor generation model to generate the morphology anchor of the contact surface to be predicted based on the original spatial conditions and scalar conditions in the conditional data.

[0043] S42. Determine the initial value of the integral based on the shape anchor of the contact surface to be predicted. Starting from the initial value of the integral, divide the integral interval into K steps. In each step, input the current latent variable, time interval and condition data into the trained latent space average flow generator to obtain the average velocity prediction. Update the latent variable step by step according to the explicit Euler method to obtain the predicted displacement latent variable.

[0044] S43. Input the predicted latent displacement variable into the decoder in the trained topographic anchor generation model, and apply a binary box mask and inverse normalization to the decoding result to obtain the predicted normal displacement field under physical dimensions.

[0045] In step S42: the morphology anchor of the contact surface to be predicted is directly used as the initial value of the integral; or the morphology anchor is used as the mean to construct a conditional source distribution, and the initial value of the integral is independently sampled from the conditional source distribution.

[0046] The beneficial effects of this invention are:

[0047] 1. This invention generates a topographic anchor for each contact surface and uses it as the flow starting point, replacing the initialization noise shared by all instances, reducing the overlap of probabilistic transport paths, and eliminating the need for the latent space average flow generator to repeatedly learn the overall elastic displacement determined by the conditional data.

[0048] 2. This invention utilizes latent variable alignment loss to align the shape anchor with the mean of the latent variable distribution output by the encoder, thereby reducing the shape-induced bias caused by non-convex hollow boundaries and discrete bolt loading, and improving the variance interpretation capability of analytical priors in the latent space.

[0049] 3. This invention employs latent space average flow and few-step ordinary differential equation integration to improve prediction efficiency while suppressing block artifacts caused by general noise initialization, and to maintain high gradient displacement characteristics near bolt holes, inner free boundaries, and outer free boundaries.

[0050] 4. The displacement field and error region output by this invention have clear spatial locations, which can be used for assembly qualification judgment, abnormal contact area location, and scraping or rework guidance before actual fastening; the predicted distribution under the same conditions can be obtained by independently sampling from the condition source distribution. Attached Figure Description

[0051] Figure 1 This is a flowchart of the method of the present invention.

[0052] Figure 2 This is a bar chart comparing the present invention with different baseline methods on various quantitative indicators; wherein, Figure 2 (a) in the figure is a histogram comparison of the average absolute error of pixels; Figure 2 (b) in the figure is a histogram comparing the mean absolute error; Figure 2 (c) in the figure is a histogram comparing relative errors; Figure 2 (d) in the figure is a histogram comparing peak signal-to-noise ratio; Figure 2 (e) in the figure is a histogram comparing structural similarity; Figure 2 (f) in the figure is a histogram comparing the gradient mean square error.

[0053] Figure 3 This is a comparison chart of displacement field prediction results for the sample using different methods; among them, Figure 3 (a) in the figure shows the true displacement field of the sample and the corresponding error plot; Figure 3 (b) in the figure shows the displacement field predicted by the method of the present invention and the corresponding error diagram; Figure 3 (c) in the figure shows the displacement field predicted by the Transolver method and the corresponding error plot; Figure 3 In the diagram, (d) represents the displacement field predicted by the PreDiff method and the corresponding error plot. Figure 3 (e) in the figure represents the displacement field predicted by the FFM method and the corresponding error plot; Figure 3 In the diagram, (f) represents the displacement field predicted by the Diffusion-PDE method and the corresponding error plot.

[0054] Figure 4 The sample is shown as a true displacement field plot with two cut lines.

[0055] Figure 5 These are displacement diagrams of the sample under horizontal and numerical profiles, respectively; where, Figure 5 (a) in the figure is a displacement diagram in the horizontal section; Figure 5(b) in the figure is the displacement diagram in the vertical section.

[0056] Figure 6 This is a comparison chart of ablation results using the method of the present invention; wherein, Figure 6 (a) in the figure shows the true displacement of the sample and the corresponding error plot; Figure 6 (b) in the figure shows the baseline displacement and the corresponding error diagram; Figure 6 (c) in the figure represents the anchor point displacement and the corresponding error diagram; Figure 6 In the diagram, (d) represents the position and corresponding error map obtained by this invention. Detailed Implementation

[0057] The present invention will now be described in more detail with reference to the accompanying drawings and embodiments. However, the present invention is not limited thereto. For those skilled in the art, several improvements and modifications can be made without departing from the principles of the present invention, and these improvements and modifications are also considered to be within the scope of protection of the present invention. Contents not described in detail in this specification are prior art known to those skilled in the art.

[0058] Example 1:

[0059] like Figure 1 As shown, the machine tool beam-column contact surface displacement prediction method of this embodiment includes the following steps:

[0060] S1. Obtain the conditional data of the beam-column contact surface and the corresponding target normal displacement field, and construct the contact surface displacement prediction dataset.

[0061] Conditional data includes spatial conditions. and scalar conditions Spatial conditions This includes bolt preload distribution, macroscopic morphology of the upper contact surface, macroscopic morphology of the lower contact surface, bolt distance field, inner boundary distance field, and outer boundary distance field; scalar conditions. Including the surface roughness parameters of the upper contact surface 1. Lower contact surface roughness parameters upper contact surface waviness parameters Lower contact surface waviness parameters and assembly offset parameters , , The target normal displacement field is the normal displacement field generated at the beam-column contact surface after bolt assembly.

[0062] S11. Discretize the beam-column contact area in the gantry milling machine into an H×W grid and establish a binary bounding mask to identify the effective contact area. Where H and W are the number of rows and columns of the grid, respectively.

[0063] Specifically, binary box mask A binary matrix of the same size as the H×W grid, where elements corresponding to grid points inside the contact area are set to 1, and elements corresponding to grid points outside the contact area are set to 0; a binary frame mask. Used to define the effective area for subsequent loss calculation, distance field calculation, and final prediction results.

[0064] S12. Based on the H×W grid, determine the bolt preload distribution value, upper contact surface macroscopic morphology value, and lower contact surface macroscopic morphology value at each grid point, and combine the three types of values ​​corresponding to each grid point into the original spatial conditions according to the channels. .

[0065] The bolt preload distribution is the local pressure or load distribution under the bolt preload at each grid point; the macroscopic morphology of the upper and lower contact surfaces are the height deviation values ​​of the upper and lower contact surfaces at the corresponding grid points, described by the low-frequency geometric deviation function, respectively. The low-frequency geometric deviation is used to represent the flatness error, bending and twisting of the contact surface.

[0066] S13. Calculate the normalized Euclidean distance from each grid point to the nearest bolt center, inner free boundary, and outer free boundary, respectively, to obtain the bolt distance field, inner boundary distance field, and outer boundary distance field. Compare the bolt distance field, inner boundary distance field, and outer boundary distance field with the original spatial conditions. Together they constitute spatial conditions ;

[0067] Among them, the bolt center is the projection point of the center of each bolt hole on the grid plane of the contact surface; the inner free boundary is the boundary of the holes or hollow structures inside the contact area; and the outer free boundary is the outer contour boundary of the contact area.

[0068] S14. Obtain the roughness amplitude of the upper contact surface, the roughness amplitude of the lower contact surface, the waviness amplitude of the upper contact surface, the waviness amplitude of the lower contact surface, and the assembly offset parameter of the upper contact surface relative to the lower contact surface, which together constitute the scalar condition. Spatial conditions and scalar conditions The conditional data that together constitute the beam-column contact surface.

[0069] The assembly offset parameter is the translational offset of the upper contact surface relative to the lower contact surface along the coordinate directions of the two contact surfaces. , and rotational offset about the normal to the contact surface The assembly offset parameter is the relative position deviation of the upper and lower contact surfaces that is known or can be preset before assembly. Its source is one of the following: measured value, estimated clamping and positioning accuracy value, or working condition value preset according to assembly tolerance.

[0070] S15. Under the assembly state corresponding to the condition data obtained in step S14, the beam-column contact surface generates a displacement field after bolt assembly; from the displacement field, obtain the normal displacement components at each grid point in the H×W grid; based on the binary frame mask... Preserve the binary bounding box mask The normal displacement components corresponding to the grid points marked as contact are used as the target normal displacement field.

[0071] S16. Repeat steps S11-S15 several times to collect the target normal displacement field corresponding to different conditions, thereby constructing a contact surface displacement prediction dataset.

[0072] Specifically, the normal displacement component is the displacement component of the contact surface along the normal direction of the contact surface in the local coordinate system. In this embodiment, the normal displacement field is obtained from the displacement field measured by actual contact surface experiments.

[0073] Furthermore, after obtaining the target normal displacement field corresponding to several different condition data, the condition data and the target normal displacement field are normalized respectively before constructing the contact surface displacement prediction dataset.

[0074] S2. Construct a topography anchor generation model and train it using the contact surface displacement prediction dataset to obtain a trained topography anchor generation model. The topography anchor generation model includes a variational autoencoder and a latent voxel-by-latest analytical regressor.

[0075] S21. Using the encoder in the variational autoencoder, the target normal displacement field is mapped to the mean and logarithmic variance of the latent variable distribution. The latent variable distribution is determined based on the mean and logarithmic variance, and the target displacement latent variable is obtained by reparameter sampling of the latent variable distribution. .

[0076] Specifically, the variational autoencoder includes an encoder and a decoder. The encoder consists of multiple convolutional blocks connected in series, each convolutional block including a convolutional layer, a group normalization layer, and a nonlinear activation layer. The decoder is a mirror image of the encoder, consisting of multiple convolutional blocks connected in series, each convolutional block including a bilinear upsampling layer, a convolutional layer, a group normalization layer, and a nonlinear activation layer. The decoder gradually recovers the spatial dimensions through bilinear upsampling, representing the latent variable of the target displacement. Reconstructed as a displacement field.

[0077] The latent variable distribution parameters output by the encoder are the mean of the latent variable distribution. and logarithmic variance ; by mean and logarithmic variance The latent variable distribution is determined to be a Gaussian distribution N(μ,σ²I); the target displacement latent variable is obtained by reparameter sampling of the latent variable distribution. , ;in, This indicates element-wise multiplication. It is the identity matrix. To obtain from the standard normal distribution The noise vector sampled in the middle; the latent variable of the target displacement. The mean μ of the encoder output is used as the training target for the subsequent latent space average flow generator and is also used as the alignment target for the latent voxel-by-latest analytical regressor.

[0078] S22. Using a potential voxel-by-potential regressor, the original spatial conditions are analyzed. After average pooling, the original spatial conditions after pooling are... and scalar conditions After performing linear mapping separately, the results are fused to obtain the corresponding topographic anchors.

[0079] Specifically, the latent variable of the target displacement output by the variational autoencoder It has a latent space grid size, such as 4×16×24, that is, the latent variables are spatially divided into a latent space grid of 16 rows and 24 columns; each spatial location in the latent space grid is called a latent voxel.

[0080] Voxel-by-voxel regressor receiver spatial conditions The original spatial conditions and scalar conditions ; the original spatial conditions Average pooling to target displacement latent variable The same latent space mesh size is used, and spatial condition weights are set at each latent voxel location. Scalar conditional weights and bias At each latent voxel location, the original spatial conditions after pooling were respectively... and scalar conditions After linear mapping and fusion, the topography anchor is obtained. .

[0081] The morphology anchor is obtained by processing the latent voxel regressor according to the following formula. :

[0082] ;

[0083] in, Indicates average pooling; For bias; the topographic anchor is the latent variable of the target displacement. A latent space tensor of the same size is used as the center of the subsequent conditional source distribution.

[0084] Furthermore, the original spatial conditions Includes bolt preload distribution, macroscopic morphology of the upper contact surface, and macroscopic morphology of the lower contact surface; scalar conditions. It includes the roughness amplitude of the upper contact surface, the roughness amplitude of the lower contact surface, the waviness amplitude of the upper contact surface, the waviness amplitude of the lower contact surface, and the assembly offset parameter of the upper contact surface relative to the lower contact surface; the bolt distance field, the inner boundary distance field, and the outer boundary distance field are geometric indicators, which are not input into the latent voxel analytical regressor, but are directly input into the subsequent latent space average flow generator.

[0085] S23. Utilize the decoder in the variational autoencoder to analyze the latent variable of the target displacement. The reconstructed displacement field is obtained by reconstruction. The effective contact area reconstruction loss is constructed based on the difference between the target normal displacement field and the reconstructed displacement field within the effective contact area. The latent variable distribution regularization loss is constructed based on the difference between the latent variable distribution and the standard normal distribution. The latent variable alignment loss is constructed based on the difference between the mean of the latent variable distribution and the topographic anchor.

[0086] S24. Construct a joint loss consisting of effective contact area reconstruction loss, latent variable distribution regularization loss, and latent variable alignment loss, and train the shape anchor generation model to obtain the trained shape anchor generation model.

[0087] The joint loss is set according to the following formula:

[0088]

[0089]

[0090]

[0091]

[0092] in, For joint losses; To effectively address the losses in the contact area; For the regularized loss of the latent variable distribution, the 1 in the formula represents the standard normal distribution. The variance; For latent variable alignment loss; and All are weighting coefficients; To calculate the expectation of each dimension of the latent variable distribution within the parentheses; and These are the mean and variance of the latent variable distribution of the encoder output, respectively; For the decoder in a variational autoencoder; It is a binary box mask; For element-wise product; For the target normal displacement field; These are the original spatial conditions; Scalar condition; As a topographic anchor; It is an L2 norm.

[0093] Effective contact area reconstruction loss Used to train the decoder, enabling the decoder to learn from the latent variables of the target displacement. The target normal displacement field is reconstructed, and the reconstruction error is only within the binary frame mask. Calculated within the effective contact area of ​​the identifier; latent variable distribution regularized loss. Used to constrain the distribution of latent variables Approximately standard normal distribution Latent variable alignment loss The shape anchor generated by the latent voxel-by-latest regressor is used to align with the mean of the latent variable distribution of the variational autoencoder. Alignment, that is, applying physical alignment constraints to the latent space of the variational autoencoder, so that the topographic anchor directly corresponds to the analytical displacement estimate in the latent space; this alignment process makes the latent space of the variational autoencoder a physically aligned latent space, thereby calibrating the analytical estimation bias and improving the variance interpretation capability of the analytical prior.

[0094] S3. Construct a latent space average flow generator; based on the trained topography anchor generation model, construct a conditional source distribution, sample source latent variables from the conditional source distribution, and train the latent space average flow generator to learn the latent variables from the source latent variables to the target displacement latent variables. Residual transport.

[0095] The latent space average flow generator is a neural network used to predict the latent space average velocity; the latent space average velocity is the average velocity over a given time interval along the linear interpolation path from the source latent variable to the target displacement latent variable.

[0096] S31. Using the encoder of the variational autoencoder and the latent voxel-by-latest analytical regressor in the trained morphology anchor generation model, calculate the residual between the mean of the latent variable distribution of each sample in the contact surface displacement prediction dataset and the corresponding morphology anchor. Calculate the empirical standard deviation based on the residuals of all samples and construct the conditional source distribution.

[0097] Specifically, in the trained shape anchor generation model, the parameters of both the encoder and the latent voxel-by-latest analytical regressor are frozen. For each sample in the dataset, the mean of the latent variable distribution is obtained using the encoder. The morphological anchor was obtained using a voxel-by-voxel regressor. Calculate the residual ; Calculate the residuals of all samples empirical standard deviation .

[0098] Constructing conditional source distribution based on topography anchor As the mean, with A Gaussian distribution with covariance:

[0099]

[0100] in, For joint conditional data; As a topographic anchor; These are the source latent variables obtained by sampling from the conditional source distribution.

[0101] S32. Sample source latent variables from the conditional source distribution, using the source latent variables as the starting point for flow matching in the latent space average flow generator, and using the target displacement latent variables... As the endpoint of flow matching for the latent space average flow generator, the difference between two latent variables (source latent variable and target displacement latent variable) is used. The difference between the source and target displacement latent variables is used as the velocity target for flow matching learning. The latent space average flow generator is trained to learn the flow from the source latent variable to the target displacement latent variable. The residual transport is used to obtain the trained latent space average flow generator.

[0102] In source latent variables and target displacement latent variables A linear interpolation path is established between them, and at each time step on the linear interpolation path... Corresponding to a latent variable The input to the latent space average flow generator includes latent variables on the linear interpolation path. Time interval And conditional data; the latent space average flow generator outputs the average velocity over a given time interval along a linear interpolation path. And it is trained using streaming training loss.

[0103] Specifically, from the conditional source distribution Source latent variables obtained by mid-sampling In the source latent variable and target displacement latent variables Establish a linear interpolation path between them:

[0104]

[0105] in, , Corresponding to the latent variable end of the target displacement, Corresponding to the latent variable end; For time step latent variables The speed target is Time range For any continuous time interval on the linear interpolation path, satisfying .

[0106] The loss function used during the training of the latent space average flow generator includes an average flow consistency term and a state reconstruction auxiliary term; the average flow consistency term is used to constrain the predicted average velocity to be consistent with the velocity target; the state reconstruction auxiliary term is used to constrain the velocity from the target velocity. Starting from the latent variables of the time step, and passing through the average velocity The latent variables obtained after integration and Latent variables of time step Consistent.

[0107] The flow training loss used during latent space average flow generator training is set according to the following formula:

[0108]

[0109] in, For flow training loss; The average velocity predicted by the latent space average flow generator; For speed targets; To stop the gradient; To reconstruct the weights of auxiliary items; and Let the two endpoints of the time interval satisfy the following condition: ; For the linear interpolation path at time step Latent variables; The latent variable is the target displacement. These are the source latent variables.

[0110] Specifically, the latent space average flow generator adopts a diffusion converter structure, which includes a token embedding layer, a position encoding layer, multiple converter blocks, and an output deblocking layer connected in series.

[0111] The token embedding layer will embed latent variables on the linear interpolation path. The tokens are embedded in blocks of 2×2 size; the position coding layer superimposes sinusoidal position codes onto the token sequences; each transformer block includes a multi-head self-attention layer, an adaptive normalized modulation layer, and a feedforward network layer connected in series. The modulation signal of the adaptive normalized modulation layer is encoded by time interval and scalar condition. Encoding and Spatial Conditions The encoding is generated jointly; the output deblocking layer restores the token sequence output by the transform block to... Average velocity prediction for the same size.

[0112] In this embodiment, the latent space average flow generator specifically adopts the following structure: latent variables on the linear interpolation path The dimensions are 4×16×24 (channels×height×width), the patch size is 2×2, the token sequence length is 8×12=96, the transformer depth is 6, the hidden dimension is 256, the number of attention heads is 4, the hidden dimension of the feedforward network is 1024, and the number of parameters is approximately 9.6M.

[0113] Furthermore, during training, scalar conditions are discarded with a preset probability, enabling the latent space average flow generator to learn both conditional and unconditional average velocities simultaneously. During inference, the conditional and unconditional average velocities are weighted and combined to obtain the guiding average velocity used for integral updates.

[0114] S4. Obtain the conditional data of the contact surface to be predicted and generate the corresponding topographic anchor. Determine the initial value of the integral based on the topographic anchor. Starting from the initial value of the integral, perform the integration of the ordinary differential equation through the trained latent space average flow generator. Map the latent variable of the predicted displacement obtained by the integral back to the physical space to obtain the predicted normal displacement field of the contact surface to be predicted.

[0115] S41. Obtain the conditional data of the contact surface to be predicted, and use the latent voxel-by-latest analytical regressor in the trained morphology anchor generation model to determine the original spatial conditions in the conditional data. The scalar conditions are used to generate the topographic anchor of the contact surface to be predicted.

[0116] S42. Determine the initial value of the integral based on the shape anchor of the contact surface to be predicted. Starting from the initial value of the integral, divide the integral interval into K steps. In each step, input the current latent variable, time interval and condition data into the trained latent space average flow generator to obtain the average velocity prediction. Update the latent variable step by step according to the explicit Euler method to obtain the predicted displacement latent variable.

[0117] Specifically, the morphology of the contact surface to be predicted is directly used as the initial value for integration;

[0118] Alternatively, a conditional source distribution can be constructed using the topographic anchor as the mean. One or more initial integral values ​​can be independently sampled from the conditional source distribution. If multiple initial integral values ​​are used, each initial integral value can be integrated separately to obtain multiple independent prediction samples (predicted latent displacement variables) under the same conditions.

[0119] In this embodiment, the topographic anchor of the contact surface to be predicted obtained in S41 is used as the initial value for the integration of the ordinary differential equation. ; Change the integration interval from the source end To the target end Divide the data into K steps, with each step having a length of K. For the k-th step, k=0,1,…,K-1, the current latent variable is... Let be the latent variable during the k-th integration step; where k=0, This is the initial value for the integral; when k > 0, The latent variables are obtained after updating by explicit Euler method in step k-1.

[0120] Current latent variables The endpoint of the time interval corresponding to step k and The latent space average flow generator, trained with complete conditional data input, outputs the average velocity prediction at the k-th step. Update latent variables using explicit Euler method:

[0121]

[0122] in, The guided average velocity is obtained by guiding the combination of the k-th step average velocity output from the latent space average flow generator. The calculation method is as follows:

[0123]

[0124] in, The average velocity output by the latent space average flow generator when complete conditional data is input. The average velocity output by the latent space average flow generator when the scalar condition is discarded; To guide the scale; after K-step integration, the predicted latent displacement variables are obtained. In this embodiment, K is 10.

[0125] S43. Input the predicted latent displacement variable into the decoder in the trained topographic anchor generation model, and apply a binary box mask and inverse normalization to the decoding result to obtain the predicted normal displacement field under physical dimensions.

[0126] Specifically, the predicted displacement latent variables obtained from S42 Input the decoder frozen after training in S2 The decoder outputs a reconstructed displacement field. The displacement field will be reconstructed. With binary box mask Element-wise multiplication is performed to zero out the predicted values ​​outside the contact area, yielding the masked displacement field. :

[0127]

[0128] in, For element-wise product; It is a binary bounding mask that identifies the valid grid points within the contact area.

[0129] Using the mean and standard deviation of the target normal displacement field saved during the training phase, the displacement field after masking is... By performing inverse normalization, the predicted normal displacement field under the physical dimensions is obtained. :

[0130]

[0131] in, The standard deviation of the target normal displacement field during the training phase; The mean of the target normal displacement field during the training phase; the predicted normal displacement field. This is the predicted result of the normal displacement of the beam-column contact surface.

[0132] Furthermore, if step S42 uses a conditional source distribution to sample multiple initial integral values ​​to obtain multiple predicted displacement latent variables, step S43 is executed for each predicted displacement latent variable to obtain multiple normal displacement prediction field samples under the same conditional data; the multiple normal displacement prediction field samples are used to evaluate the prediction uncertainty and the range of contact state fluctuations.

[0133] Furthermore, multiple normal displacement prediction field samples can be used to calculate the prediction mean and prediction standard deviation: the prediction mean is the average value of each normal displacement prediction field sample at the same grid point, and the prediction standard deviation is the standard deviation of each normal displacement prediction field sample at the same grid point; the prediction mean is used to characterize the expected displacement field under the given data conditions, and the prediction standard deviation is used to characterize the displacement fluctuation range under the given data conditions.

[0134] Example 2:

[0135] This embodiment takes the prediction of the normal displacement U3 of the bolted connection between the beam and column of a large gantry milling machine as an example to illustrate the specific construction method of the contact surface displacement prediction dataset, the training configuration of the topography anchor generation model and the latent space average flow generator, and the evaluation method of the prediction results.

[0136] The contact surface has an outer contour, an inner hollow area, and multiple bolt holes. Local displacement propagates through the beam structure and affects the machining accuracy of the tool center point. The contact surface displacement prediction dataset in this embodiment is constructed using finite element simulation; that is, the dataset construction process in steps S11 to S16 of embodiment 1 is specifically implemented using finite element simulation in this embodiment. Static finite element models are established on three contact surface geometric variants with different aspect ratios and bolt numbers, using the same solution settings and material parameters for all three variants. For each sample, upper and lower mating surface morphologies are generated, and bolt preload and assembly offset parameters are randomly set. , , After static finite element analysis, the normal displacement components on the finite element mesh are mapped to the H×W mesh through interpolation.

[0137] Each mating surface morphology consists of three superimposed components: macroscopic morphology, waviness, and microscopic roughness.

[0138]

[0139] in, The coordinates of the grid points on the H×W grid; This is a quadratic low-order morphology with the center of the contact surface as the origin, used to describe bending and twisting, and its expression is:

[0140]

[0141] in, and They are respectively direction and The coefficient of the quadratic term in the direction, The cross term coefficient; This is a band-limited random ripple obtained by spectral synthesis using sinusoidal components of random direction, wavelength, and phase. For spatially independent Gaussian micro-roughness, satisfying:

[0142]

[0143] in, This represents the roughness amplitude.

[0144] After stacking, zero-mean correction is performed to eliminate unwanted rigid body offsets. The upper and lower contact surfaces are sampled independently to form a multi-scale, non-Gaussian gap morphology.

[0145] In this embodiment, the macroscopic quadratic form parameters A and B are in the range [-2.5, 2.5] × 10⁻⁶. -7 Range sampling, parameter C is in [-1.5, 1.5] × 10 -7 Range sampling; ripple wavelength is 30–180 mm, ripple amplitude is 0.005–0.015, ripple component number is 8; roughness amplitude is 0.005–0.010.

[0146] The finite element mesh output is mapped to a uniform H×W mesh using a binary box mask. The effective frame-shaped contact area is identified, and the target normal displacement field is denoted as... In this embodiment, the size of the target normal displacement field is 1×64×96.

[0147] The spatial condition S consists of six channels: bolt preload distribution, macroscopic morphology of the upper contact surface, macroscopic morphology of the lower contact surface, bolt distance field, inner boundary distance field, and outer boundary distance field. The three distance fields are the normalized Euclidean distances from the grid point to the nearest bolt center, the inner free boundary, and the outer free boundary, respectively, used to explicitly provide bolt hole location and non-convex boundary information to the latent space average flow generator.

[0148] Scalar conditions This includes the roughness amplitude and waviness amplitude of the upper and lower contact surfaces, as well as assembly offset parameters. , , Original spatial conditions and scalar conditions Combination as joint conditions .

[0149] In this embodiment, the contact surface displacement prediction dataset contains 3000 finite element samples, 1000 for each geometric variant, of which 2700 are used for training and 300 for validation; all variants appear in both the training and validation sets. The target normal displacement field and conditional data are normalized based on the training set statistics, and the loss and evaluation metrics are only used in binary bounding box masks. Calculated within the effective contact area of ​​the sign.

[0150] In this embodiment, the encoder consists of multiple concatenated convolutional blocks, each including a concatenated convolutional layer, a group normalization layer, and a nonlinear activation layer. The latent variable distribution parameters output by the encoder are the mean of the latent variable distribution. and logarithmic variance ; by mean and logarithmic variance The latent variable distribution is determined; the latent variable distribution is a Gaussian distribution. The latent variables of the target displacement are obtained by reparameter sampling of the latent variable distribution. , The dimensions are 4×16×24.

[0151] The decoder is mirrored in the encoder setup and consists of multiple concatenated convolutional blocks. Each concatenated convolutional block includes a cascaded bilinear upsampling layer, a convolutional layer, a group normalization layer, and a nonlinear activation layer. The decoder gradually recovers the spatial dimensions through bilinear upsampling, representing the latent variable of the target displacement. Reconstructed as a displacement field.

[0152] The voxel-by-voxel regressor uses the original space conditions. and scalar conditions Original spatial conditions After average pooling to the latent space grid, a linear mapping is performed at each latent voxel location using independent weights. Shape anchors are generated according to:

[0153]

[0154] in, , and It allows for variation with latent voxel position to describe the spatial non-uniform effect of conditions on displacement.

[0155] The distance field is input to the latent space average flow generator to provide geometric boundary information, but not to the latent voxel-by-latest analytical regressor, because the distance field is a geometric indicator rather than a nonlinear elastic predictor.

[0156] The topography anchor generation model is trained on the training set using the joint loss from Example 1.

[0157] After training convergence, calculate the training set residuals. empirical standard deviation , which serves as the standard deviation of the conditional source distribution.

[0158] Coefficient of determination This represents the proportion of latent space variance explained by the latent voxel-by-latest analytical regressor; for the deterministic residual components anchored to the regression objective, we have ,in The residuals of all samples in the training set variance The mean of the latent variable distribution of the target displacement for all samples in the training set. The variance.

[0159] From a Bayesian perspective, conditional Gaussian priors The KL divergence between the encoded posterior and the mean difference term includes the mean difference term. This term is proportional to the latent variable alignment loss, and and Proportional. Among them, For joint conditional data; As a topographic anchor; The variance parameter of the conditional Gaussian prior measures the degree of dispersion of the prior distribution around the topographic anchor. It is an identity matrix.

[0160] The variational autoencoder target retains the pointing The latent variable distribution regularization loss, combined with the latent variable alignment loss, constitutes a mixed objective, rather than a strict lower bound of evidence for any single conditional prior model.

[0161] Freeze the completed variational autoencoder training. For each joint conditional data... From the conditional source distribution latent variables of sampling source .

[0162] make This represents the latent target displacement obtained by freezing the encoder, using a linear interpolation path. The speed target is Therefore, the morphological anchor source end is located at The latent variable end of the target displacement is located at .

[0163] The latent space average flow generator employs a diffusion transformer structure. Latent variables on the linear interpolation path... It is segmented and embedded as a token sequence and superimposed with a sinusoidal positional code. This is determined by the time interval and scalar condition. and spatial conditions The encoding generates an adaptive layer normalized zero-initialized modulation signal, and conditional information is injected into each converter block. The output token is then de-blocked to recover the signal. Average velocity prediction for the same size.

[0164] In this embodiment, the latent space average flow generator has a patch size of 2, a transformer depth of 6, a hidden dimension of 256, and an attention head of 4; the variational autoencoder has approximately 0.57M parameters, and the latent space average flow generator has approximately 9.6M parameters.

[0165] Latent space average flow generator output time interval average speed During training, samples are taken from the logit-normal distribution. , and And set with a preset flow ratio of 0.5. This causes the corresponding samples to degenerate into standard flow matching. Here, the logit-normal distribution is a probability distribution defined on the interval [0,1], and the flow ratio is the proportion of samples with the time interval set to zero length during training.

[0166] along The training loss for directional Jacobian vector product flow is:

[0167]

[0168] The variational autoencoder and the latent space average flow generator are trained sequentially using the AdamW optimizer. The variational autoencoder is trained and frozen first, followed by the training of the latent space average flow generator. The average flow generator is trained using learning rate warm-up, cosine scheduling, and parameter exponential moving average.

[0169] The specific configuration is as follows: the topography anchor generation model and the latent space average flow generator are trained for 500 and 700 epochs respectively, with a batch size of 16 and a learning rate of 2×10⁻⁶ for both. -4The EMA decay of the latent space average flow generator is 0.9999. , , measured The probability of discarding scalar conditions during training is 0.10. , =0.5.

[0170] Obtain the bolt preload distribution, macroscopic morphology of the upper and lower contact surfaces, distance field, roughness parameters, waviness parameters, and assembly offset parameters of the contact surface to be predicted, and normalize them in the same way as in the training phase.

[0171] The topography anchor of the contact surface to be predicted is generated by the voxel-by-voxel regressor. The topographic anchor is used as the initial value for the integral of the ordinary differential equation, that is, in Direct settings on the terminal .

[0172] In this embodiment, K is set to 10. After integration, the latent displacement variable will be predicted. The input is a frozen decoder, and the result is multiplied by a binary box mask. Then, by inverse normalization, the predicted normal displacement field in millimeters is obtained.

[0173] To further demonstrate the beneficial effects of the present invention:

[0174] Under the same data partitioning, conditional input, and training budget, the method of this embodiment is compared with deterministic neural operators and generative solvers starting from general noise. Evaluation metrics include normalized pixel mean absolute error, dimensional mean absolute error, relative L2 error, peak signal-to-noise ratio, structural similarity, and gradient mean square error.

[0175] Experimental results show that the normalized pixel mean absolute error of this invention is 2.70 × 10⁻⁶. -3 The physical mean absolute error is 1.10 × 10⁻⁶. -3 The relative L2 error was 17.70%, the peak signal-to-noise ratio was 31.22 dB, the structural similarity was 0.8733, and the mean square error of the gradient was 1.79 × 10⁻⁶ mm. -6 mm².

[0176] Figure 2 , Figure 3 and Figure 4 A comparison of the method of this invention (MoMF) with other existing methods shows that deterministic neural operators can recover the overall displacement shape but are prone to smoothing boundary gradients, while generative models based on general noise are prone to leaving block artifacts; the present invention has a lower and more uniform error compared to existing technologies.

[0177] in, Figure 2This is a bar chart comparing the present invention (MoMF) with different baseline methods (Universal Physical Neural Operator UPT, Physical Attention Neural Operator Transolver, Predictive Diffusion Model PreDiff, Flow Matching Model FFM, Scoring Inference Model SI, and Partial Differential Diffusion Model Diffusion-PDE) on various quantitative indicators. Figure 2 (a) in the figure is a histogram comparison of the average absolute error of pixels; Figure 2 (b) in the figure is a histogram comparing the mean absolute error; Figure 2 (c) in the figure is a histogram comparing relative errors; Figure 2 (d) in the figure is a histogram comparing peak signal-to-noise ratio; Figure 2 (e) in the figure is a histogram comparing structural similarity; Figure 2 (f) in the figure is a histogram comparing the gradient mean square error. Figure 3 A comparison chart of displacement field prediction results for the sample using different methods; Figure 3 In the diagram (a), the actual displacement field of the sample and the corresponding error plot are shown. The left side is the actual displacement plot, and since the actual displacement plot has no error, the right side of the error plot is empty. Figure 3 (b) in the figure shows the displacement field predicted by the method of the present invention and the corresponding error diagram; Figure 3 (c) in the figure shows the displacement field predicted by the Transolver method and the corresponding error plot; Figure 3 In the diagram, (d) represents the displacement field predicted by the PreDiff method and the corresponding error plot. Figure 3 (e) in the figure represents the displacement field predicted by the FFM method and the corresponding error plot; Figure 3 In the diagram, (f) represents the displacement field predicted by the Diffusion-PDE method and the corresponding error plot.

[0178] Figure 4 and Figure 5 This indicates that, when comparing horizontal and vertical slices along the bolt location, the prediction curve of this invention can follow the local peaks and valleys near the free boundary caused by the bolt. Specifically, Figure 4 The true displacement field diagrams are shown below two sections: section A at the horizontal position (y=35.0mm) and section B at the vertical position (x=40.0mm). Figure 5 (a) is the displacement diagram at the horizontal profile y=35.0mm; Figure 5 (b) is the displacement diagram in the vertical section x=40.0mm; where FNO is the Fourier neural operator, which is compared with existing deterministic physical field prediction methods in this application.

[0179] Figure 6The ablation results show that, starting with the general noise average flow, and then sequentially adding the morphological anchor flow initiation point and the physical alignment latent space, the error gradually shrinks from dispersed blocky noise to a lower error with no obvious spatial structure. Among these, Figure 6 In the diagram (a), the true displacement of the sample and the corresponding error plot are shown. The left side is the true displacement plot, and since the true displacement plot has no error, the right side of the error plot is empty. Figure 6 (b) in the figure shows the displacement and corresponding error plot obtained by the FFM method; Figure 6 (c) in the figure represents the displacement and corresponding error map predicted by the anchor point (FFM method + topography anchor generation model of this invention); Figure 6 In the diagram, (d) represents the predicted location and corresponding error map obtained by this invention.

[0180] In assembly applications, the predicted displacement field can locate the high deviation area driven by the shape in the contact surface, providing a quantitative reference for judging whether the assembly is qualified and for scraping or rework of the contact surface before actual assembly.

[0181] The above embodiments are merely preferred embodiments provided to fully illustrate the present invention, and the scope of protection of the present invention is not limited thereto. Equivalent substitutions or modifications made by those skilled in the art based on the present invention are all within the scope of protection of the present invention. The scope of protection of the present invention is defined by the claims.

Claims

1. A method for predicting the displacement of the machine tool beam-column contact surface based on topographically anchored average flow, characterized in that, Includes the following steps: S1. Obtain the conditional data of the beam-column contact surface and the corresponding target normal displacement field, and construct the contact surface displacement prediction dataset; S2. Construct a topography anchor generation model, and train the topography anchor generation model using the contact surface displacement prediction dataset to obtain the trained topography anchor generation model; the topography anchor generation model includes a variational autoencoder and a latent voxel-by-latest analytical regressor. S3. Construct a latent space average flow generator; construct a conditional source distribution based on the trained topography anchor generation model, sample source latent variables from the conditional source distribution, and train the latent space average flow generator to learn the residual transport from source latent variables to target displacement latent variables; S4. Obtain the conditional data of the contact surface to be predicted and generate the corresponding topographic anchor. Determine the initial value of the integral based on the topographic anchor. Starting from the initial value of the integral, perform the integration of the ordinary differential equation through the trained latent space average flow generator. Map the latent variable of the predicted displacement obtained by the integral back to the physical space to obtain the predicted normal displacement field of the contact surface to be predicted.

2. The method for predicting the displacement of the machine tool beam-column contact surface according to claim 1, characterized in that: The conditional data includes spatial conditions and scalar conditions; the spatial conditions include bolt preload distribution, upper contact surface morphology, lower contact surface morphology, bolt distance field, inner boundary distance field, and outer boundary distance field; the scalar conditions include upper contact surface roughness parameters, lower contact surface roughness parameters, upper contact surface waviness parameters, lower contact surface waviness parameters, and assembly offset parameters; the target normal displacement field is the normal displacement field generated after bolt assembly of the beam-column contact surface.

3. The method for predicting the displacement of the machine tool beam-column contact surface according to claim 1, characterized in that, Step S1 specifically involves: S11. Discretize the beam-column contact area into an H×W grid and establish a binary frame mask to identify the effective contact area; S12. Based on the H×W grid, determine the bolt preload distribution value, upper contact surface morphology value and lower contact surface morphology value at each grid point, and combine the three types of values ​​corresponding to each grid point into the original spatial conditions according to the channels. S13. Calculate the normalized Euclidean distance from each grid point to the nearest bolt center, inner free boundary, and outer free boundary to obtain the bolt distance field, inner boundary distance field, and outer boundary distance field, and combine them with the original spatial conditions to form the spatial conditions. S14. Obtain the roughness amplitude of the upper contact surface, the roughness amplitude of the lower contact surface, the waviness amplitude of the upper contact surface, the waviness amplitude of the lower contact surface, and the assembly offset parameters of the upper contact surface relative to the lower contact surface, which together constitute the scalar conditions; the spatial conditions and scalar conditions together constitute the condition data of the beam-column contact surface. S15. Under the assembly state corresponding to the condition data obtained in step S14, the beam-column contact surface generates a displacement field after bolt assembly; from the displacement field, obtain the normal displacement components at each grid point in the H×W grid; according to the binary frame mask, retain the normal displacement components corresponding to the grid points marked as contact in the binary frame mask as the target normal displacement field; S16. Repeat steps S11-S15 several times to collect the target normal displacement field corresponding to different conditions, thereby constructing a contact surface displacement prediction dataset.

4. The method for predicting the displacement of the machine tool beam-column contact surface according to claim 3, characterized in that, Step S2 specifically involves: S21. The target normal displacement field is mapped to the mean and logarithmic variance of the latent variable distribution using the encoder in the variational autoencoder. The latent variable distribution is determined based on the mean and logarithmic variance, and the target displacement latent variable is obtained by reparameter sampling of the latent variable distribution. S22. Using a voxel-by-voxel analytical regressor, the original spatial conditions are averaged and then the pooled original spatial conditions and scalar conditions are linearly mapped and fused to obtain the corresponding morphological anchors. S23. The target displacement latent variable is reconstructed using the decoder in the variational autoencoder to obtain the reconstructed displacement field. The effective contact area reconstruction loss is constructed based on the difference between the target normal displacement field and the reconstructed displacement field within the effective contact area. The latent variable distribution regularization loss is constructed based on the difference between the latent variable distribution and the standard normal distribution. The latent variable alignment loss is constructed based on the difference between the mean of the latent variable distribution and the topographic anchor. S24. Construct a joint loss consisting of effective contact area reconstruction loss, latent variable distribution regularization loss, and latent variable alignment loss, and train the shape anchor generation model to obtain the trained shape anchor generation model.

5. The method for predicting the displacement of the machine tool beam-column contact surface according to claim 4, characterized in that: The joint loss is set according to the following formula: ； ； ； ； in, For joint losses; To effectively address the losses in the contact area; For latent variable distribution regularization loss; For latent variable alignment loss; and All are weighting coefficients; In order to achieve expectations; and These are the mean and variance of the latent variable distribution of the encoder output, respectively; For the decoder in a variational autoencoder; It is a binary box mask; For element-wise product; For the target normal displacement field; For shape anchors.

6. The method for predicting the displacement of the machine tool beam-column contact surface according to claim 1, characterized in that, Step S3 specifically involves: S31. Using the encoder and latent voxel-by-latest analytical regressor of the trained variational autoencoder, calculate the residual between the mean of the latent variable distribution of each sample in the dataset and the corresponding morphological anchor. Calculate the empirical standard deviation based on the residuals of all samples and construct the conditional source distribution. S32. Sample source latent variables from the conditional source distribution, use the source latent variables as the starting point for flow matching of the latent space average flow generator, use the target displacement latent variable as the ending point for flow matching of the latent space average flow generator, use the difference between the two latent variables as the velocity target for flow matching learning, train the latent space average flow generator to learn the residual transport from the source latent variables to the target displacement latent variable, and finally obtain the trained latent space average flow generator.

7. The method for predicting the displacement of the machine tool beam-column contact surface according to claim 6, characterized in that, Step S32 further includes: A linear interpolation path is established between the source latent variable and the target displacement latent variable, with each time step on the linear interpolation path corresponding to a latent variable; the input of the latent space average flow generator includes the latent variables on the linear interpolation path, the time interval, and the conditional data; the latent space average flow generator outputs the average velocity on the given time interval of the linear interpolation path and is trained using flow training loss.

8. The method for predicting the displacement of the machine tool beam-column contact surface according to claim 6, characterized in that: The flow training loss used during the training of the latent space average flow generator is set according to the following formula: ； in, For flow training loss; The average velocity predicted by the latent space average flow generator; For speed targets; To stop the gradient; To reconstruct the weights of auxiliary items; and These are the two endpoints of the time interval; For the linear interpolation path at time step Latent variables; The latent variable is the target displacement. These are the source latent variables.

9. The method for predicting the displacement of the machine tool beam-column contact surface according to claim 1, characterized in that, Step S4 specifically involves: S41. Obtain the conditional data of the contact surface to be predicted, and use the latent voxel-by-voxel analytical regressor in the trained morphology anchor generation model to generate the morphology anchor of the contact surface to be predicted based on the original spatial conditions and scalar conditions in the conditional data. S42. Determine the initial value of the integral based on the shape anchor of the contact surface to be predicted. Starting from the initial value of the integral, divide the integral interval into K steps. In each step, input the current latent variable, time interval and condition data into the trained latent space average flow generator to obtain the average velocity prediction. Update the latent variable step by step according to the explicit Euler method to obtain the predicted displacement latent variable. S43. Input the predicted latent displacement variable into the decoder in the trained topographic anchor generation model, and apply a binary box mask and inverse normalization to the decoding result to obtain the predicted normal displacement field under physical dimensions.

10. The method for predicting the displacement of the machine tool beam-column contact surface according to claim 9, characterized in that, In step S42: The morphology of the contact surface to be predicted is directly used as the initial value for integration; Alternatively, a conditional source distribution can be constructed using the shape anchor as the mean, and the initial integral value can be independently sampled from the conditional source distribution.

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