A deep learning-based sparse reconstruction method for the inner raceway profile of a ball screw nut

Abstract

The application discloses a kind of based on deep learning's screw nut inner raceway profile sparse reconstruction method, belong to the technical field of precision geometric quantity measurement, it includes constructing sparse sample set, input model output prediction point cloud;Difference is calculated with full amount point cloud and parameter is updated, and output dense reconstruction model;Scanning to be measured screw nut constructs sparse cross section point cloud set;Decoupling matrix is generated according to lead parameter and plane sparse array is mapped out;Plane sparse array is input into reconstruction model to obtain plane dense prediction array;Multiply inverse matrix inverse solution output three-dimensional dense point cloud set;Three-dimensional dense point cloud and nut distance output deviation data set are calculated.The present application adopts helical space decoupling transformation and deep learning model to carry out intelligent interpolation and upsampling to sparse measurement point cloud, can quickly reconstruct complete inner raceway three-dimensional dense point cloud from small amount of input data, improves the measurement efficiency and precision of complex inner cavity surface.

Description

Technical Field

[0001] This application relates to the field of precision geometric measurement technology, and in particular to a sparse reconstruction method for the inner raceway profile of a lead screw nut based on deep learning. Background Technology

[0002] Ball screw assemblies are widely used components and fundamental parts in the machinery industry, used to convert the rotary motion of a motor into linear motion. The surface accuracy of the raceways inside the ball nut directly affects transmission accuracy and efficiency; therefore, it must be inspected during the production process.

[0003] In related technologies, Chinese invention patent application CN102162717A discloses an automatic detection device and method for the comprehensive error of the inner raceway of a ball nut helix. This method uses a grating ruler and a spectral confocal precision displacement sensor to sample the axial and radial positions of points on the normal cross-sectional curve of the inner raceway of the ball nut under test. By rotating the ball nut under test by a certain angle and repeating the above sampling process multiple times, a series of point data at specific angular positions on the inner raceway surface is obtained.

[0004] Regarding the aforementioned technologies, using sensors to perform multiple indexing scans at different corner positions can only acquire discrete cross-sectional point data, failing to quickly obtain the complete, dense, continuous three-dimensional surface morphology of the inner raceway. The overall detection efficiency is low, making it difficult to achieve a comprehensive and efficient evaluation of the entire deep-hole spiral inner surface morphology. Summary of the Invention

[0005] To address the aforementioned issues, this application provides a sparse reconstruction method for the inner raceway surface of a lead screw nut based on deep learning. It employs a helical space decoupling transformation and a deep learning model to intelligently interpolate and upsample the sparse measurement point cloud, enabling rapid reconstruction of a complete three-dimensional dense point cloud of the inner raceway from a small amount of input data, thereby improving the measurement efficiency and accuracy of complex inner cavity surfaces.

[0006] The above objectives can be achieved through the following approach: A deep learning-based sparse reconstruction method for the inner raceway profile of a lead screw nut includes: acquiring a full set of point cloud samples; extracting the spatial coordinates of the cross-sectional contour along the helical axis of the inner raceway of the lead screw nut at fixed phase angle intervals to construct a sparse sample set; inputting the sparse sample set into a preset sparse point cloud reconstruction model to output a predicted point cloud; calculating the Euclidean distance, cross-sectional radius difference, axial mapping difference, and normal gradient difference between the predicted point cloud and the full set of point cloud samples, and generating a loss function by weighted summation, performing parameter updates, and outputting a dense point cloud reconstruction model; locating the lead screw nut to be tested, and using the lead screw nut to drive an endoscopic rotating laser sensor to perform scanning, extracting and aggregating the spatial coordinate points of the inner surface reflection to construct a point cloud set of the sparse cross-section to be tested; obtaining the nominal lead parameters using the lead screw nut to be tested, and establishing a phase angle based on the nominal lead parameters. A linear mapping relationship with axial displacement is used to generate a helical spatial decoupling transformation matrix. The sparse cross-section point cloud to be measured is input into the helical spatial decoupling transformation matrix to perform a mapping calculation from the three-dimensional cylindrical coordinate system to the two-dimensional plane, outputting a planar sparse coordinate array. The planar sparse coordinate array is input into the dense point cloud reconstruction model. A topological node relationship graph is constructed using the planar sparse coordinate array. Information aggregation operations of neighboring nodes are performed to extract spatial correlation features, and coordinate interpolation mapping is performed to output a planar dense prediction coordinate array. The inverse matrix is ​​obtained using the helical spatial decoupling transformation matrix. The planar dense prediction coordinate array is multiplied by the inverse matrix to perform a three-dimensional spatial inverse calculation, outputting a three-dimensional dense point cloud. The three-dimensional Euclidean distance between the three-dimensional dense point cloud and the lead screw nut to be measured is calculated, outputting a surface deviation dataset.

[0007] Optionally, the step of inputting the sparse sample set into a preset sparse point cloud reconstruction model to output a predicted point cloud includes: extracting full scan data of lead screw nuts from historical processing batches, constructing full point cloud samples, extracting cross-sectional contour spatial coordinates at fixed phase angle intervals along the helical axis, and constructing a sparse sample set; inputting the sparse sample set into the sparse point cloud reconstruction model, performing correlation feature extraction and interpolation operations on the sparse sample set, and outputting a predicted point cloud.

[0008] Optionally, the preset sparse point cloud reconstruction model includes: extracting the spatial coordinate node dimension using the sparse sample set, and extracting the dense coordinate tensor dimension using the full point cloud sample set; constructing an input network layer, a graph neural network layer, and an output network layer based on the spatial coordinate node dimension and the dense coordinate tensor dimension to generate an initial generator network topology; and performing numerical initialization assignment on the neuron connection matrix and bias parameters of the initial generator network topology to generate the sparse point cloud reconstruction model.

[0009] Optionally, the output dense point cloud reconstruction model includes: calculating the coordinate vector norm based on the predicted point cloud and the full point cloud samples to generate the coordinate Euclidean distance; calculating the radial deviation distance based on the predicted point cloud in the local normal section coordinate system to generate the section radius difference; calculating the linear mapping deviation of the axial displacement and phase of the predicted point cloud in the cylindrical coordinate system to generate the axial mapping difference; calculating the direction difference between the predicted point cloud and the surface normal vector and the theoretical contact angle vector to generate the normal gradient difference; weighted summation to generate a loss function; performing backpropagation operation; and outputting the dense point cloud reconstruction model.

[0010] Optionally, the construction of the sparse cross-sectional point set to be tested includes: controlling the endoscopic rotating laser sensor to perform axial feed along the inner raceway helix of the lead screw nut to be tested, and triggering cross-sectional profile sampling at the helix phase angle interval to extract the spatial coordinate points of the inner surface reflection; and performing a three-dimensional spatial coordinate system splicing operation on the spatial coordinate points of the inner surface reflection based on the helix phase angle interval and the axial feed to construct the sparse cross-sectional point set to be tested.

[0011] Optionally, the output planar sparse coordinate array includes: extracting nominal lead parameters using the lead screw nut to be tested, and converting the three-dimensional rectangular coordinates of the sparse cross-section point cloud to be tested into radial distance, phase angle, and axial displacement in a three-dimensional cylindrical coordinate system; constructing a linear mapping operator between the phase angle and the axial displacement based on the nominal lead parameters, and using the linear mapping operator to generate a spiral spatial decoupling transformation matrix; substituting the radial distance, the phase angle, and the axial displacement into the spiral spatial decoupling transformation matrix to perform spatial dimensionality reduction calculation, calculating the two-dimensional planar unfolded coordinates, and outputting a planar sparse coordinate array.

[0012] Optionally, the output planar dense prediction coordinate array includes: calling the dense point cloud reconstruction model to receive the planar sparse coordinate array, using the planar sparse coordinate array to construct a topological node relationship graph, performing information aggregation operations on neighboring nodes to generate spatial correlation features; substituting the spatial correlation features into the dense point cloud reconstruction model, performing nonlinear matrix mapping and dense coordinate interpolation calculations on the feature dimensions, and outputting the planar dense prediction coordinate array.

[0013] Optionally, the output three-dimensional dense point cloud includes: performing an algebraic inversion operation on the spiral space decoupling transformation matrix to generate an inverse matrix; multiplying the planar dense prediction coordinate array by the inverse matrix to perform dimension restoration calculation, and solving for the dense radial distance, dense phase angle, and dense axial displacement in the three-dimensional cylindrical coordinate system; based on the transformation relationship between the three-dimensional cylindrical coordinate system and the three-dimensional rectangular coordinate system, mapping the dense radial distance, the dense phase angle, and the dense axial displacement to the three-dimensional rectangular coordinate system to perform spatial inverse calculation, and splicing to generate a three-dimensional dense point cloud.

[0014] Optionally, the output surface deviation dataset includes: extracting nominal geometric parameters using the lead screw nut to be tested, constructing a theoretical surface point cloud array in a three-dimensional coordinate system based on the nominal geometric parameters; performing spatial node registration between the three-dimensional dense point cloud array and the theoretical surface point cloud array, calculating the three-dimensional spatial Euclidean distance between the registered nodes, and aggregating the results to output the surface deviation dataset.

[0015] Based on the same inventive concept, this application also provides a deep learning-based sparse reconstruction system for the inner raceway profile of a lead screw nut. The system includes: a sparse sample construction module, used to acquire a full set of point cloud samples, extract cross-sectional contour spatial coordinates along the helical axis of the inner raceway of the lead screw nut at fixed phase angle intervals, construct a sparse sample set, and input the sparse sample set into a preset sparse point cloud reconstruction model to output a predicted point cloud; a reconstruction model training module, used to calculate the Euclidean distance, cross-sectional radius difference, axial mapping difference, and normal gradient difference between the predicted point cloud and the full set of point cloud samples, and generate a loss function through weighted summation, perform parameter updates, and output a dense point cloud reconstruction model; an inner surface point cloud acquisition module, used to locate the lead screw nut to be tested, drive an endoscopic rotating laser sensor to perform scanning through the lead screw nut to be tested, extract and aggregate the spatial coordinate points of the inner surface reflection, and construct a point cloud set of the sparse cross-section to be tested; and a helical space decoupling mapping module, used to obtain the nominal lead parameters using the lead screw nut to be tested. The system employs several methods: a linear mapping relationship between phase angle and axial displacement is established based on the nominal lead parameters to generate a helical space decoupling transformation matrix. The sparse cross-section point cloud to be measured is input into the helical space decoupling transformation matrix, and a mapping solution from a three-dimensional cylindrical coordinate system to a two-dimensional plane is performed, outputting a planar sparse coordinate array. A dense point cloud prediction module is used to input the planar sparse coordinate array into the dense point cloud reconstruction model, construct a topological node relationship graph using the planar sparse coordinate array, perform information aggregation operations on neighboring nodes to extract spatial correlation features, and perform coordinate interpolation mapping to output a planar dense prediction coordinate array. A three-dimensional space inverse reconstruction module is used to obtain the inverse matrix using the helical space decoupling transformation matrix, multiply the planar dense prediction coordinate array by the inverse matrix to perform a three-dimensional space inverse solution, and output a three-dimensional dense point cloud. A surface deviation calculation module is used to calculate the three-dimensional Euclidean distance between the three-dimensional dense point cloud and the lead screw nut to be measured, and output a surface deviation dataset.

[0016] Compared with the prior art, this application has the following advantages: 1. By reconstructing sparse sampled point clouds using deep learning, the measurement time for the entire inner raceway of the lead screw nut is shortened, improving detection efficiency. Compared to traditional high-density scanning methods, this method avoids the time-consuming process of point-by-point dense acquisition, enabling rapid online or near-line quality assessment of workpieces while ensuring data integrity. 2. The composite loss function integrates composite losses such as coordinate Euclidean distance, cross-sectional radius difference, axial mapping difference, and normal gradient difference, and weights each error to align the network training objective with actual processing requirements, embedding the process evaluation standards of the inspection field into the deep learning training mechanism. This allows the reconstruction model to not only focus on the positional accuracy of the point cloud but also learn the inherent geometric features of the inner raceway. Therefore, the reconstructed dense point cloud has higher physical realism and geometric accuracy on key functional surfaces, superior to surfaces generated by traditional interpolation algorithms, and can more accurately reflect the true processing quality. 3. An innovative closed-loop processing flow of "sparse scanning—spiral 2D unfolding—planar reconstruction—3D inverse recovery—error evaluation" is constructed. Unlike traditional methods that directly perform interpolation fitting in 3D space, this application reduces the processing difficulty of deep learning models by mapping the complex 3D spiral point cloud to a 2D planar array. This dimensionality reduction allows the model to focus more on learning the microscopic features of the raceway cross-section profile, thereby improving the model's training efficiency and reconstruction accuracy. Ultimately, this method not only achieves topographic reconstruction but also directly outputs surface deviation data, significantly enhancing the method's engineering applicability and robustness in practical detection scenarios.

[0017] Other features and advantages of this application will be set forth in the description which follows, and will be apparent in part from the description, or may be learned by practicing the application. The objectives and other advantages of this application may be realized and obtained by means of the structures pointed out in the description, claims and drawings. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 This is a flowchart illustrating a deep learning-based method for sparse reconstruction of the inner raceway profile of a lead screw nut, according to an embodiment of this application.

[0020] Figure 2 This is a dumbbell diagram comparing various geometric deviations of the surface before and after the introduction of multidimensional physical constraints, according to an embodiment of this application.

[0021] Figure 3 This is a box plot comparing the surface reconstruction deviation distribution of different reconstruction methods according to an embodiment of this application.

[0022] Figure 4 This is a schematic diagram of a sparse reconstruction system for the inner raceway profile of a lead screw nut based on deep learning, according to an embodiment of this application. Detailed Implementation

[0023] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0024] Reference Figure 1 One embodiment of this application proposes a sparse reconstruction method for the inner raceway surface of a lead screw nut based on deep learning. It uses a spiral space decoupling transformation and a deep learning model to intelligently interpolate and upsample the sparse measurement point cloud, which can quickly reconstruct the complete three-dimensional dense point cloud of the inner raceway from a small amount of input data, thereby improving the measurement efficiency and accuracy of complex inner cavity surfaces.

[0025] The method described in this embodiment specifically includes: Obtain full point cloud samples, extract cross-sectional contour spatial coordinates along the helical axis of the inner raceway of the lead screw nut at fixed phase angle intervals, construct a sparse sample set, and input the sparse sample set into a preset sparse point cloud reconstruction model to output the predicted point cloud. The Euclidean distance, cross-sectional radius difference, axial mapping difference, and normal gradient difference are calculated between the predicted point cloud and the full point cloud sample, and a loss function is generated by weighted summation. Parameter updates are performed, and a dense point cloud reconstruction model is output. Position the lead screw nut to be tested, and drive the endoscopic rotary laser sensor to perform scanning through the lead screw nut to extract and aggregate the spatial coordinate points of the inner surface reflection to construct a cloud of points of the sparse cross section to be tested. The nominal lead parameter is obtained using the lead screw nut to be tested. A linear mapping relationship between the phase angle and the axial displacement is established based on the nominal lead parameter to generate a helical space decoupling transformation matrix. The cloud of sparse cross-section points to be tested is input into the helical space decoupling transformation matrix to perform a mapping calculation from a three-dimensional cylindrical coordinate system to a two-dimensional plane and output a planar sparse coordinate array. The planar sparse coordinate array is input into the dense point cloud reconstruction model. A topological node relationship graph is constructed using the planar sparse coordinate array. Information aggregation operation of neighboring nodes is performed to extract spatial correlation features. Coordinate interpolation mapping is performed to output a planar dense prediction coordinate array. The inverse matrix is ​​obtained by using the spiral space decoupling transformation matrix. The planar dense prediction coordinate array is multiplied by the inverse matrix to perform three-dimensional space inverse calculation and output a three-dimensional dense point cloud. The three-dimensional Euclidean distance is calculated using the three-dimensional dense point cloud and the lead screw nut to be tested, and the surface deviation dataset is output.

[0026] Optionally, inputting the sparse sample set into a preset sparse point cloud reconstruction model to output a predicted point cloud includes: Extract full scan data of lead screws and nuts from historical processing batches, construct full point cloud samples, extract cross-sectional profile spatial coordinates at fixed phase angle intervals along the helix axis, and construct a sparse sample set; First, the measurement files of qualified products from historical processing batches are read to extract the full-scale scan data of the lead screw and nut. This data originates from an extremely high-density set of surface coordinates acquired by a high-precision coordinate measuring machine. After cleaning and denoising these surface coordinate sets, a full-scale point cloud sample is constructed. Subsequently, a downsampling scan is simulated under a real-world environment, and discretized data is extracted along the three-dimensional spiral trajectory of the full-scale point cloud sample. Based on a set fixed phase angle interval, the target phase angle of each sampling section is calculated, and the spatial coordinates of the section contour at the target phase angle position are extracted. The extraction logic of this target phase angle follows an equidistant step formula: , in, Representing the The target phase angle of each sampling section; The cross-section index number represents a non-negative integer type, and its maximum value range is determined by the total effective thread stroke length and physical lead of the screw nut to be measured. This represents a fixed phase angle interval. The value of this fixed phase angle interval is not arbitrarily set, but strictly configured according to the mechanical resolution of a single rotation of the stepper motor of the endoscopic rotating laser sensor. All cross-sectional points located at the target phase angle position are combined to construct a sparse sample set for feature input.

[0027] For example, a full point cloud sample containing millions of spatial coordinate points was acquired for a specific type of lead screw nut with an effective working length of 200 mm. Considering the sensor's rotational step accuracy of the actual hardware measurement equipment, the fixed phase angle interval was strictly configured to 90 degrees. Subsequently, along the helical axis, discrete complete cross-sectional profile coordinates were extracted successively at specific phase angle positions such as 0 degrees, 90 degrees, and 180 degrees. These extracted cross-sectional data collectively constitute a sparse sample set, which significantly compresses the amount of underlying stored data while accurately preserving the helical topological geometry of the inner raceway core.

[0028] The sparse sample set is input into the sparse point cloud reconstruction model, and correlation feature extraction and interpolation operations are performed on the sparse sample set to output the predicted point cloud.

[0029] The sparse point cloud reconstruction model is a graph neural network built on an open-source deep learning framework, with neuron parameters initialized. The feature extraction layer receives the established sparse sample set, treating each spatial coordinate point as a discrete node in a high-dimensional graph data structure. It constructs a local adjacency matrix between nodes based on the Euclidean distance of the 3D coordinates, thereby performing relevance feature extraction operations. Through a graph convolution information aggregation mechanism, it learns the spatial geometric correspondence between each coordinate node and its neighboring nodes, thus capturing the consistency of the spiral angle motion of the inner rolling channel. When updating node features through node aggregation, the core network forward computation formula of this feature extraction layer is: , in, Representing the network to complete the first The deep node feature matrix output after layer aggregation operation; This represents a non-linear activation function, used to introduce non-linear feature representation and mapping capabilities to graph neural networks; This represents the local adjacency matrix, which reflects the spatial connection topology of discrete coordinate nodes. Representing the The input node feature matrix of the layer; Representing the The learnable weight matrix within the layer network. The local adjacency matrix is ​​directly calculated from the spatial coordinate distance threshold of each node; the values ​​of the learnable weight matrix are randomly initialized by a normal distribution function in the early stages of model construction, and iteratively updated in subsequent model training stages using backpropagation algorithm combined with a loss function. After completing the relevant feature extraction, the deep node feature matrix output is received and interpolated. The deep node feature matrix is ​​remapped back to three-dimensional physical space using a multilayer perceptron network layer, predicting and generating densely arranged unknown spatial coordinate points between discrete sparse cross-sectional data, ultimately completing the nonlinear generation from sparse input to a high-resolution surface, and outputting a predicted point cloud that matches the point cloud density of the full point cloud sample.

[0030] For example, the feature extraction layer of the sparse point cloud reconstruction model receives a sparse sample set containing only forty discrete cross-sectional slices. The feature extraction layer establishes a local adjacency matrix, connecting the coordinate nodes on a specific cross-section to the physical nodes on its adjacent cross-sections at 90 degrees to the left and right. After multiple matrix multiplications and feature aggregation operations within the network layer, the network layer successfully extracts and understands the curvature evolution characteristics of the inner rolling track Gothic arc. Subsequently, based on the acquired curvature evolution characteristics, interpolation operations are performed to automatically extrapolate and interpolate the missing continuous surface coordinate points within the 89-degree spatial range between two sparse cross-sections differing by 90 degrees. Finally, the model smoothly outputs a set of extremely dense predicted point clouds, presenting a seamless and continuous three-dimensional geometry of the inner rolling track both visually and numerically.

[0031] Optionally, the preset sparse point cloud reconstruction model includes: The spatial coordinate node dimension is extracted using the sparse sample set, and the dense coordinate tensor dimension is extracted using the full point cloud sample set. Establishing the network input and output boundaries of a deep learning model is the first step in constructing the algorithm architecture. Tensor shape reading is performed on the training data, scanning the sparse sample set and counting the total number of discrete spatial coordinate points contained therein, thereby extracting the spatial coordinate node dimension. This spatial coordinate node dimension is strictly defined in the underlying data structure as a dimension of size... The two-dimensional feature matrix. Represents the number of three-dimensional coordinate nodes contained in the sparse sample set, a constant. This represents the coordinates of three orthogonal spatial axes in a three-dimensional Cartesian coordinate system. Similarly, by reading the corresponding full point cloud sample, the dimension of the dense coordinate tensor is extracted. This dimension of the dense coordinate tensor is defined as a dimension of... The two-dimensional feature matrix. This represents the number of dense coordinate nodes that the reconstructed point cloud should contain. This is to meet the engineering requirements for high-precision 3D topography reconstruction. and The relationship between them follows a strict algebraic amplification formula: , in, The point cloud amplification factor parameter represents the number of high-density nodes derived from a single sparse node after the model performs upsampling mapping. The positive integer value of this point cloud amplification factor parameter is uniquely determined by calculating the quotient of the number of nodes in the full point cloud sample set and the number of nodes in the sparse sample set.

[0032] For example, when reading a sparse sample set containing 2048 discrete coordinate points, an input tensor with a spatial coordinate node dimension of 2048 x 3 is established. Subsequently, the corresponding full point cloud sample is read, and it is found to contain 16384 extremely dense surface coordinate points, thus establishing an output tensor with a dense coordinate tensor dimension of 16384 x 3. According to the algebraic amplification formula, 16384 divided by 2048 equals 8, thus clarifying that the point cloud amplification ratio parameter required for subsequent network construction is 8.

[0033] Based on the spatial coordinate node dimension and the dense coordinate tensor dimension, an input network layer, a graph neural network layer, and an output network layer are constructed to generate an initial generator network topology. After establishing accurate input and output tensor boundaries, the cascaded computational layers of the deep learning model are assembled in computer memory. First, a receiver is instantiated based on the spatial coordinate node dimensions. The input network layer for tensor data uses a multilayer perceptron to map low-dimensional physical space coordinates to a higher-dimensional abstract feature space. Subsequently, a network topology construction module is connected to the graph neural network layer to aggregate local geometric topological features within the feature space based on the adjacency matrix. Finally, an output network layer is concatenated at the end of the graph neural network layer according to the dimension of the dense coordinate tensor. This output network layer contains a tensor reshaping operator for dimensionality augmentation, responsible for restoring the aggregated features to a mapping that conforms to the dimension requirements of the dense coordinate tensor. Coordinate matrix. Through this series of concatenation operations, an initial generator network topology with a complete forward data flow path is generated. The initial generator network topology generated at this stage only has a static computational framework and does not yet have substantial feature extraction capabilities.

[0034] Numerical initialization is performed on the neuron connection matrix and bias parameters of the initial generator network topology to generate a sparse point cloud reconstruction model.

[0035] To break the symmetry of the network topology in spatial mapping and prevent fatal obstacles such as vanishing or exploding gradients in the early stages of model training, a numerical injection operation is performed on the initial generator network topology. All convolutional kernels and fully connected layers in the initial generator network topology are traversed, and numerical initialization is performed on the neuron connection matrix and bias parameters. For the assignment of the neuron connection matrix, the parameter initialization module rejects the use of fixed constants without physical basis, and instead adopts a normal distribution variance scaling algorithm. The specific variance calculation formula is as follows: , in, The variance of the probability distribution representing the random initial weights in the neuron connection matrix; This represents the dimension of the input channel in the current network layer, which is objectively determined by the number of node features; a constant. A compensation coefficient set to offset the data variance decay caused by the nonlinear activation function. Based on the calculated distribution variance. The generated values ​​have a mean of zero and a variance of . A Gaussian random number matrix is ​​generated and injected into the neuron connection matrix of each layer. Simultaneously, all bias parameters in the network are initialized to scalar zero. After parameter injection, the previously empty network framework is transformed into a sparse point cloud reconstruction model that can be immediately used for training and inference.

[0036] For example, when processing a hidden layer in the initial generator network topology, it is detected that this layer receives 256 channel features passed from the previous layer. Using a normal distribution variance scaling algorithm, 256 is substituted into the input channel dimension variable to calculate the required weight variance for this layer, which is 2 divided by 256, or 1 / 128. Subsequently, a random number generation function is called to generate a normally distributed random number matrix with a mean of 0 and a variance of 1 / 128, and this matrix is ​​completely assigned to the neuron connection matrix of this hidden layer. Simultaneously, all bias parameters attached to this hidden layer are precisely set to 0. Through this rigorous data-driven assignment, a sparse point cloud reconstruction model with a robust initial state is finally generated.

[0037] Optionally, the output dense point cloud reconstruction model includes: The coordinate vector norm is calculated based on the predicted point cloud and the full point cloud sample to generate the Euclidean distance. The radial deviation distance is calculated based on the predicted point cloud in the local normal section coordinate system to generate the section radius difference. First, the predicted point cloud and the full point cloud samples are extracted, and the nearest neighbor matching pairs are searched node by node in 3D space. For each matching node pair, the coordinate vector norm between them is calculated, thereby generating the Euclidean distance. This Euclidean distance constrains the overall spatial accuracy of the generated point cloud at a macroscopic level. To accurately constrain the microscopic geometry inside the inner raceway, a local normal section coordinate system is established for each coordinate node in the predicted point cloud. This local normal section coordinate system is constructed using the theoretical helical tangent vector of the corresponding node as the normal reference. After establishing this coordinate system, the coordinates of the predicted point cloud are projected into this local normal section coordinate system, and the radial deviation distance from the projection point to the center of the theoretical raceway section is calculated, thereby generating the section radius difference. The core mathematical calculation logic of this section radius difference follows the geometric projection formula: , in, Represents the difference in cross-sectional radii; and These represent the two orthogonal plane coordinate components of a single point in the predicted point cloud under the local normal section coordinate system; The theoretical Gothic radius representing the inner raceway design is directly extracted from the original design drawing database of the lead screw nut. Through this rigorous projection and distance calculation, the complex three-dimensional surface error is reduced to an intuitive two-dimensional cross-sectional dimension deviation.

[0038] For example, when processing a predicted point cloud containing tens of thousands of spatial nodes, one spatial node is selected. This spatial node is projected onto a locally established local normal section coordinate system, yielding a horizontal coordinate of 3 mm and a vertical coordinate of 4 mm. According to the Pythagorean theorem, the actual deviation of this projected point from the theoretical center of the section is 5 mm. Simultaneously, the theoretical Gothic radius of this type of lead screw nut is retrieved from the design drawing database as 5.02 mm. Substituting these values ​​into the geometric projection formula, the absolute difference between 5 mm and 5.02 mm is calculated to be 0.02 mm. This 0.02 mm value is established as the difference in section radius for this spatial node and used for penalty term calculation.

[0039] The linear mapping deviation of the axial displacement and phase of the predicted point cloud in cylindrical coordinates is calculated to generate the axial mapping difference. The directional difference between the predicted point cloud and the surface normal vector and the theoretical contact angle vector is calculated to generate the normal gradient difference. The weighted sum is used to generate the loss function and backpropagation is performed to output the dense point cloud reconstruction model.

[0040] After obtaining the spatial position and cross-sectional geometric errors, error calculation is performed based on the helical kinematic characteristics. The three-dimensional rectangular coordinates of the predicted point cloud are converted to cylindrical coordinates, and the nominal lead parameters are read. Based on the helical equation, the linear mapping deviation between axial displacement and phase angle is calculated to generate the axial mapping difference. Simultaneously, to ensure the accuracy of the ball bearing force direction, a calculus surface fitting algorithm is used to calculate the surface normal vector of each node in the predicted point cloud, and the theoretical contact angle vector generated based on design parameters is read. The difference between these two directions is calculated to generate the normal gradient difference. After collecting these four physical deviation metrics, a weighted summation is performed to generate the loss function. The aggregation formula of this loss function is defined as: , in, The output scalar represents the total loss function. Represents the calculated Euclidean distance between the coordinates; This represents the difference in cross-sectional radii. Represents the difference in axial mapping; Represents the difference in normal gradients. Weight coefficients. , , and The values ​​are not randomly assigned, but dynamically assigned strictly according to the reciprocals of the manufacturing tolerances corresponding to various physical errors. For example, the manufacturing tolerance of the cross-sectional radius is usually at the extremely small micrometer level, while the tolerance of the overall coordinate position is at the larger level of tens of micrometers. By calculating the reciprocal of the tolerances, a larger weight coefficient is given to the terms corresponding to the micrometer-level tolerances, forcing the neural network to prioritize learning high-precision microscopic geometry. After constructing the loss function, backpropagation is performed, and the gradient of the loss function with respect to the neuron connection matrix and bias parameters inside the network is calculated using the chain rule, driving the optimization algorithm to update all parameters along the gradient descent direction. With each training iteration, when the loss function decreases and stabilizes within the convergence threshold range, parameter updates are stopped, and the finally trained dense point cloud reconstruction model is output.

[0041] For example, in a training iteration of a deep learning network, the average Euclidean distance of a batch of predicted point cloud data is calculated to be 0.5 mm, the difference in cross-sectional radius is 0.1 mm, the difference in axial mapping is 0.2 mm, and the difference in normal gradient is 0.05 radians. Manufacturing tolerances for each item are extracted based on the design drawings. Using a tolerance reciprocal mapping algorithm, the weight coefficients for the Euclidean distance are set to 2, the weight coefficients for the difference in cross-sectional radius are 10, the weight coefficients for the difference in axial mapping are 5, and the weight coefficients for the difference in normal gradient are 20. Substituting the values ​​and corresponding weight coefficients into the aggregation formula, multiplication and addition operations are performed to calculate the total loss function scalar value of 4 for the current iteration. Subsequently, backpropagation is activated, using the value 4 as the source of error, calculating the gradient layer by layer and fine-tuning the network weights. After tens of thousands of iterations, the total loss function scalar value gradually approaches 0.01, indicating that the network has extremely accurately grasped the geometric law of the inner raceway of the lead screw nut. At this point, the training process terminates, and the set of network weights permanently stored in the computer's memory constitutes the final output dense point cloud reconstruction model. For example... Figure 2 As shown, by deeply integrating physical laws such as cross-sectional radius, axial mapping, and normal gradient into the loss function, a significant reduction in deviations across various microscopic and macroscopic geometric indices is achieved. This remarkable "dumbbell-shaped" convergence demonstrates that the composite loss function successfully overcomes the blindness of conventional deep learning in generating complex 3D topologies, effectively ensuring the kinematic fidelity of the final reconstructed surface.

[0042] Optionally, constructing the sparse cross-sectional point cloud to be tested includes: The endoscopic rotary laser sensor is controlled to perform axial feed along the inner raceway helix of the lead screw nut to be tested, and cross-sectional profile sampling is triggered at the helix phase angle interval to extract the spatial coordinate points of the inner surface reflection. The probe of the endoscopic rotary laser sensor is inserted deep into the internal cavity of the lead screw nut under test. Based on the pre-read nominal lead of the lead screw nut, the rotational angular velocity and linear feed rate of the endoscopic rotary laser sensor are adjusted to ensure its physical trajectory strictly conforms to the actual helix of the inner raceway. During uniform motion, data is not continuously recorded at high frequency; instead, a high-precision pulse triggering mechanism is used to trigger cross-sectional profile sampling precisely at the helical phase angle interval. The value of the helical phase angle interval is determined jointly by the feature extraction density requirements and the hardware sampling frequency. Each time sampling is triggered, the endoscopic rotary laser sensor emits a linear laser beam and receives the high-frequency reflected signal, resolving it to the spatial coordinates of the inner surface reflection point in a local polar coordinate system. For this discrete triggering mechanism, the step control calculation formula is as follows: , in, This represents the physical axial feed step size of the sensor between single triggered cross-sectional profile sampling actions; The nominal lead of the lead screw nut under test is the absolute straight-line distance traveled along the axis when the helix rotates once. This value is directly derived from the factory specification data of the lead screw nut under test. This represents the set spiral phase angle interval; This represents the constant pi. Through kinematic formulas, the discrete triggering of the angular dimension is precisely transformed into physical positioning in the axial dimension of three-dimensional space.

[0043] For example, for a lead screw nut with a nominal lead of 10 mm, in order to balance computational efficiency and model reconstruction accuracy, the helical phase angle interval is set to half a π radian, i.e., 90 degrees. Substituting 10 mm and half a π radian into the stepping control calculation formula, we calculate 10 mm multiplied by half a π radian and then divided by twice the π constant, finally obtaining a physical axial feed step size of 2.5 mm between single trigger cross-sectional profile sampling actions. Based on this, a high-frequency pulse command is issued, so that the endoscopic rotating laser sensor instantly records a complete two-dimensional cross-sectional profile data every time it rotates 90 degrees and penetrates axially by 2.5 mm, thereby extracting a batch of inner surface reflection spatial coordinate points with clear phase labels.

[0044] Based on the spiral phase angle interval and the axial feed, a three-dimensional spatial coordinate system splicing operation is performed on the reflection spatial coordinate points of the inner surface to construct a cloud of sparse cross-section points to be measured.

[0045] After acquiring a series of discrete two-dimensional planar cross-sections, they need to be unified into the same global coordinate space. The cumulative value of the helical phase angle interval and the corresponding cumulative axial feed position for each cross-section are extracted. For the reflection space coordinate points on the inner surface of each two-dimensional slice, a three-dimensional coordinate system stitching operation is performed using a rotation and translation matrix. The essence of this three-dimensional coordinate system stitching operation is to map the local two-dimensional polar coordinates of the endoscopic rotating laser sensor to the global three-dimensional Cartesian coordinate system of the lead screw nut under test. The core algebraic formula for performing the stitching includes projections in both the horizontal and vertical directions: , , in, and These represent the horizontal and vertical physical coordinate components in the global three-dimensional coordinate system after splicing and transformation; and These represent the transverse and longitudinal measurement values ​​of the spatial coordinate points of the inner surface reflection in the local coordinate system of the acquisition sensor, respectively. This represents the cumulative spiral phase angle corresponding to the current cross section. This value is obtained by accumulating the spiral phase angle intervals experienced from the origin. and These represent the cosine and sine trigonometric functions, respectively. Simultaneously, the depth coordinate components in the global 3D coordinate system are directly assigned the cumulative axial feed value recorded at the current cross-section. By traversing all discrete slices and performing trigonometric projection and coordinate translation operations, the discrete 2D slices are combined according to their actual spatial positions, ultimately constructing a set of sparse cross-section points with strict spatial relative topological relationships.

[0046] For example, we are processing cross-sectional data located at a point with a cumulative helical phase angle of 180 degrees (π radians) and a cumulative axial feed of 5 millimeters. We extract the reflection coordinates of a point on the inner surface of this cross-section, reading its lateral measurement value as 4 millimeters and its longitudinal measurement value as 0 millimeters in the local coordinate system. Substituting the lateral measurement value of 4 millimeters and the cumulative helical phase angle of π radians into the core algebraic formula for splicing, we calculate the cosine of 4 millimeters multiplied by π radians as -1. Subtracting the sine of 0 millimeters multiplied by π radians as 0, we obtain the lateral physical coordinate component in the global 3D coordinate system as -4 millimeters; similarly, we calculate the longitudinal physical coordinate component in the global 3D coordinate system as 0 millimeters. Then, we directly and precisely assign the depth coordinate component of this point a value of 5 millimeters. By performing this type of rotation and translation matrix operation node by node, the original two-dimensional planar contour is perfectly restored to its precise physical position in a three-dimensional cylindrical space, synthesizing a sparse cross-sectional point set to be measured, providing an absolutely realistic physical observation input boundary for the deep learning network.

[0047] Optionally, the output planar sparse coordinate array includes: The nominal lead parameters are extracted using the lead screw nut to be tested, and the three-dimensional rectangular coordinates of the sparse cross-section point set to be tested are transformed into radial distance, phase angle and axial displacement in a three-dimensional cylindrical coordinate system. The three-dimensional spiral structure exhibits high nonlinearity in Cartesian coordinates, and direct processing can lead to difficulties in convergence of deep learning models. Therefore, a coordinate transformation is performed. First, the nominal lead parameters of the lead screw nut to be tested are read. Then, all three-dimensional Cartesian coordinates in the sparse cross-section point cloud set are traversed, and trigonometric functions are used to transform them one by one into spatial features in three-dimensional cylindrical coordinates. The perpendicular distance from the coordinate point to the spiral central axis is calculated to extract the radial distance; the azimuth angle of the coordinate point on the projection plane perpendicular to the central axis is calculated to extract the phase angle; the physical coordinates of the coordinate point along the central axis are directly preserved or translated to extract the axial displacement. Through this step, the complex spatial spiral point cloud is normalized into structured data containing polar radius, polar angle, and height.

[0048] For example, the nominal lead of a lead screw nut to be tested is read as 10 mm. For a specific coordinate point in the sparse cross-section point cloud, its lateral coordinate in a three-dimensional rectangular coordinate system is 3 mm, its axial coordinate is 4 mm, and its depth coordinate is 5 mm. Using the Pythagorean theorem, the square root of the sum of the squares of 3 and 4 is used to obtain the radial distance of 5 mm; the ratio of the ordinate to the lateral coordinate is calculated using the arctangent function, yielding a phase angle of 53.1 degrees; simultaneously, the depth coordinate is directly extracted, resulting in an axial displacement of 5 mm.

[0049] A linear mapping operator between the phase angle and the axial displacement is constructed based on the nominal lead parameters, and the linear mapping operator is combined to generate a spiral space decoupling transformation matrix; Based on the physical kinematics of an ideal helix, a dimension-reduced mapping benchmark is established. Using nominal lead parameters, a linear mapping operator for phase angle and axial displacement is constructed. The core physical basis of this linear mapping operator originates from the helical surface flattening formula: , in, This represents the theoretical axial displacement corresponding to a certain phase angle under ideal conditions. Represents the phase angle in three-dimensional cylindrical coordinates; Represents the nominal lead parameter; This represents the constant pi. The linear mapping operator is embedded into a high-dimensional transformation matrix, which is then combined to generate a spiral space decoupling transformation matrix. This matrix, while preserving the radial error characteristics of the cross-section, mathematically dissects and flattens the three-dimensional spiral surface by offsetting the axial height change caused by the theoretical helix angle.

[0050] For example, when processing data with a nominal lead of 10 mm, a linear mapping operator is constructed based on the helical surface flattening formula. When encountering a phase angle of 180 degrees, i.e., π radians, the theoretical axial displacement is calculated to be equal to π radians multiplied by 10 mm and then divided by twice the π constant, resulting in 5 mm. This proportionally scaled relationship between angle and displacement is encapsulated in the form of an algebraic matrix, thereby generating a helical space decoupling transformation matrix specifically for this type of lead screw nut.

[0051] Substitute the radial distance, the phase angle, and the axial displacement into the spiral space decoupling transformation matrix to perform spatial dimensionality reduction calculation, calculate the two-dimensional plane unfolded coordinates, and output a plane sparse coordinate array.

[0052] A spiral spatial decoupling transformation mechanism is constructed, using the extracted radial distance, phase angle, and axial displacement as input column vectors, which are then substituted into the spiral spatial decoupling transformation matrix to perform matrix multiplication. During the multiplication process, the linear mapping operator within the matrix compares the actual axial displacement of each node with its theoretical axial displacement based on the kinematic relationship between the nominal lead and the phase angle, stripping away the macroscopic depth information generated by the spiral winding and retaining only the microscopic fluctuation characteristics reflecting processing errors. Through this spatial dimensionality reduction calculation, the 3D spiral point cloud originally distributed on the 3D cylindrical surface is accurately mapped to a set of nodes on a 2D plane, achieving a dimensionality reduction representation of complex spatial structures. The horizontal and vertical coordinate values ​​of each node on this 2D plane are calculated and recorded, ultimately outputting a planar sparse coordinate array. This process successfully transforms the originally highly nonlinear 3D point cloud reconstruction problem into a more easily processed 2D sparse data completion problem.

[0053] For example, the measured radial distance of a node is extracted to be 5.02 mm, the phase angle is π radians, and the actual axial displacement is 5.01 mm. These values ​​are then substituted into the spiral space decoupling transformation matrix for computation. The matrix operation subtracts the theoretical axial displacement of 5 mm corresponding to the phase angle from the actual axial displacement of 5.01 mm, yielding a micro-fluctuation feature of 0.01 mm. Subsequently, the arc length of the unfolded spiral is used as the abscissa, and the micro-feature containing radial and axial fluctuations is used as the ordinate to calculate the two-dimensional planar coordinates of the point on the unfolded plane. Finally, the two-dimensional coordinates of all nodes are summarized and output as a planar sparse coordinate array, whose data structure resembles a two-dimensional map with sparse effective pixels, awaiting dense filling by the neural network.

[0054] Optionally, the output planar dense prediction coordinate array includes: The dense point cloud reconstruction model is invoked to receive the planar sparse coordinate array, and the planar sparse coordinate array is used to construct a topological node relationship graph. Information aggregation operation of neighboring nodes is performed to generate spatial correlation features. A dense point cloud reconstruction model with fixed parameters is loaded, and the resulting sparse planar coordinate array is read into the computer's video memory as the initial input tensor for inference. To capture the geometric coherence between discrete nodes, all two-dimensional coordinate points in the sparse planar coordinate array are traversed. Based on the two-dimensional Euclidean distance, the nearest neighbor nodes in physical space for each specific node are searched, thus establishing directed connections between discrete coordinate points and constructing a topological node relationship graph. In this topological node relationship graph, each coordinate point acts as a vertex. Subsequently, information aggregation operations on neighbor nodes are performed on the constructed topological node relationship graph. The underlying mechanism of this information aggregation operation relies on graph convolution operations, and its core mathematical formula is defined as: , in, This represents the spatial correlation feature vector output after a single neighborhood aggregation is completed. The activation function represents the ability to introduce nonlinear mapping. This represents a aggregation operation that mathematically sums the characteristics of all known neighboring nodes. The convolution weight matrix represents the convolution weight matrix that has been fixed during the training phase of the dense point cloud reconstruction model. Its physical meaning is the contribution weight of the relative positions of different neighborhoods to the inference of the current node's shape. The initial two-dimensional coordinate feature vectors representing each neighboring node; This represents the initial two-dimensional coordinate feature vector of the current central node. Through this matrix multiplication and summation mechanism, isolated two-dimensional coordinate points are transformed into a high-dimensional representation that incorporates the trend patterns of the surrounding curved surfaces, ultimately outputting spatial correlation features.

[0055] For example, a sparse planar coordinate array containing two hundred two-dimensional coordinate points is input into the dense point cloud reconstruction model. For a center point with an x-coordinate of 5 mm and a y-coordinate of 10 mm, the Euclidean distance is calculated, and the sixteen nearest neighbor points are identified as neighbor nodes. These seventeen points are connected by mathematical edges to form a local topological node relationship graph. Subsequently, a fixed convolution weight matrix is ​​retrieved, and the coordinate vectors of these sixteen neighbor nodes are multiplied by the convolution weight matrix and summed. Finally, the feature vector of the center point itself is added, and after mapping with a nonlinear activation function, a spatial correlation feature vector of length sixty-four dimensions is output. This feature vector no longer represents only a single physical location but also highly condenses the local curvature and orientation of the unfolded surface of the region.

[0056] The spatial correlation features are substituted into the dense point cloud reconstruction model, and nonlinear matrix mapping and dense coordinate interpolation calculations are performed on the feature dimensions to output a planar dense prediction coordinate array.

[0057] After extracting and encoding the local geometric patterns, the spatial correlation features are substituted into the decoding network layer of the dense point cloud reconstruction model. During the decoding stage, nonlinear matrix mapping and dense coordinate interpolation calculations are performed on the feature dimensions to achieve the transition from sparse features to high-density physical coordinates. First, the feature replication operator is used to augment the tensor dimension of the spatial correlation features according to a preset upsampling rate. Then, a multilayer perceptron is used to perform nonlinear matrix mapping on the augmented features, forcibly projecting them back into a two-dimensional physical coordinate space. The core algebraic formula for this dense coordinate interpolation calculation is: , in, This represents a completely new two-dimensional coordinate vector generated after interpolation. This represents the upsampling mapping weight matrix of the decoding layer in a dense point cloud reconstruction model. This represents the spatial correlation feature matrix after tensor amplification. This represents the bias parameter vector corresponding to the decoding layer. The values ​​of both the weight matrix and the bias parameter vector originate from the convergence parameters fixed during model training. Through these multi-level matrix multiplication and addition operations, a large number of unknown coordinate nodes conforming to the original curvature trend are automatically generated from the original sparse coordinate points, ultimately outputting a planar dense prediction coordinate array. This planar dense prediction coordinate array achieves an order-of-magnitude leap in data scale, accurately completing the two-dimensional contour details of the inner roller track unfolding plane.

[0058] For example, spatial correlation features containing two hundred 64-dimensional feature vectors are received. Based on a set upsampling factor of eight, these two hundred feature vectors are first amplified to 1600 feature vectors in the computer's video memory. Then, these 1600 feature vectors are substituted into the upsampling mapping weight matrix to perform denser coordinate interpolation calculations. After matrix multiplication and addition of bias parameters, the originally abstract 64-dimensional high-dimensional features are precisely decoded into 1600 specific 2D coordinate nodes. These newly generated 1600 2D coordinate points tightly fill the spaces between the original two hundred sparse coordinate points, collectively forming a planar dense predictive coordinate array with extremely smooth contours, laying a complete data foundation for subsequent inverse rollback into a 3D spiral space.

[0059] Optionally, the output three-dimensional dense point cloud includes: The inverse matrix is ​​generated by performing an algebraic inversion operation on the spiral space decoupling transformation matrix. The plane dense prediction coordinate array is multiplied by the inverse matrix to perform dimension restoration calculation, and the dense radial distance, dense phase angle and dense axial displacement in the three-dimensional cylindrical coordinate system are calculated. The two-dimensional coordinate array output by deep learning networks lacks the three-dimensional topological properties of the physical world, thus requiring a dimensionality-up transformation. The spiral space decoupling transformation matrix cached in computer memory is extracted, and a linear algebra function is used to perform an algebraic inversion operation on this matrix, generating an inverse matrix with inverse mapping capabilities. Subsequently, all two-dimensional coordinate nodes in the planar dense prediction coordinate array are extracted, transformed into homogeneous coordinate column vectors, and the planar dense prediction coordinate array is multiplied by the generated inverse matrix to perform dimension reduction calculation. The core algebraic formula for this dimension reduction calculation is: , Among them, superscript This represents the transpose operation of a matrix; This represents the inverse matrix generated by algebraic inversion. and These represent the horizontal and vertical physical coordinate components of a single interpolation node in a planar dense prediction coordinate array on a two-dimensional unfolded plane, respectively. This represents the dense radial distance in the three-dimensional cylindrical coordinate system calculated after dimension reduction. This represents the calculated dense phase angle; This represents the calculated dense axial displacement. Through this inverse matrix multiplication operation, the independent high-density pixels on the plane are given a new helical curling physical property, completing the basic mapping from a two-dimensional manifold to a three-dimensional helical cylinder.

[0060] For example, processing is performed on a specific high-density interpolation node in a planar dense predictive coordinate array. The horizontal physical coordinate component of this node on the two-dimensional unfolded plane is read as 50 mm, and the vertical physical coordinate component is 0.01 mm. These two values, along with a constant, are combined into a homogeneous column vector, and matrix multiplication is performed between the generated inverse matrix and this homogeneous column vector. After multiplication and accumulation operations, the dense radial distance corresponding to this interpolation node is calculated to be 15 mm, the dense phase angle is π radians, and the dense axial displacement is 2.51 mm. These three values ​​accurately determine the absolute polar coordinate position of this node inside the three-dimensional cylindrical space of the inner raceway.

[0061] Based on the transformation relationship between the three-dimensional cylindrical coordinate system and the three-dimensional rectangular coordinate system, the dense radial distance, the dense phase angle and the dense axial displacement are mapped to the three-dimensional rectangular coordinate system to perform spatial inverse calculation and splice to generate a three-dimensional dense point cloud.

[0062] After obtaining the cylindrical coordinate system features, in order to meet the general data format requirements of subsequent 3D deviation evaluation software, the data must be further unified to the Cartesian coordinate system. Based on the transformation relationship between the 3D cylindrical coordinate system and the 3D rectangular coordinate system, each 3D cylindrical coordinate node, composed of dense radial distances, dense phase angles, and dense axial displacements, is mapped to the 3D rectangular coordinate system for spatial inverse calculation. The underlying trigonometric function transformation formula for this spatial inverse calculation is: , , , in, This represents the horizontal spatial coordinates in a three-dimensional Cartesian coordinate system after transformation. This represents the vertical spatial coordinates in a three-dimensional Cartesian coordinate system after the transformation; This represents the depth space coordinates in a three-dimensional Cartesian coordinate system after the transformation. These depth space coordinates directly inherit the calculated dense axial displacements. and These represent cosine and sine trigonometric functions, respectively. By iterating through all cylindrical coordinate nodes and executing the above combined formula, tens of thousands of three-dimensional rectangular coordinate points are obtained. Finally, these massive rectangular coordinate points are matrix-concatenated in global space to generate a dense three-dimensional point cloud that fully reflects the true microscopic and macroscopic physical morphology of the raceway inside the lead screw nut.

[0063] For example, the calculated high-density interpolation node is processed. The node's dense radial distance of 15 mm, dense phase angle of π radians, and dense axial displacement of 2.51 mm are extracted. These values ​​are substituted into a trigonometric function transformation formula to calculate the cosine of 15 mm multiplied by π radians as -1, yielding a horizontal spatial coordinate of -15 mm; the sine of 15 mm multiplied by π radians as zero, yielding a vertical spatial coordinate of zero millimeters; and the depth spatial coordinate is directly assigned as 2.51 mm. Through this purely geometric and physical formula calculation, the absolute coordinates of the node in 3D space are precisely locked as -15, zero, and 2.51. Tens of thousands of similar coordinate points are then stitched together to finally output an extremely dense 3D point cloud that can be directly imported into 3D modeling and inspection software for visualization.

[0064] Optionally, the output surface deviation dataset includes: The nominal geometric parameters are extracted using the lead screw nut to be tested, and a theoretical surface point cloud array is constructed in a three-dimensional coordinate system based on the nominal geometric parameters. To establish a comparison benchmark, nominal geometric parameters were extracted from the technical specifications of the lead screw nut under test. These nominal geometric parameters cover the nominal diameter, ball diameter, and nominal lead. Using a parametric surface modeling algorithm, an error-free ideal raceway surface was derived in a three-dimensional Cartesian coordinate system and discretized to construct a theoretical surface point cloud array. The core of generating the theoretical geometric features relies on the parametric equations of the helix: , , , in, , and These represent the horizontal theoretical coordinates, vertical theoretical coordinates, and depth theoretical coordinates of discrete nodes in a theoretical surface point cloud array, respectively. This represents the theoretical pitch circle radius calculated from the nominal diameter; Represents the extracted nominal lead; Represents the theoretical phase angle variable during the spatial discretization process; This represents the constant pi. By setting an extremely small theoretical phase angle variable step size, a massive number of reference coordinate nodes are generated iteratively, thus forming a theoretical surface point cloud array with absolutely ideal geometric shape.

[0065] For example, the technical specification document of the lead screw nut to be tested is read, and the nominal lead is extracted to be 10 mm and the nominal diameter to be 30 mm. The theoretical pitch circle radius is calculated to be 15 mm. The parametric surface modeling algorithm is started. When the theoretical phase angle variable steps to 180 degrees, i.e., π radians, it is substituted into the parametric equation of the helix. The cosine value of 15 mm multiplied by π radians is calculated to be -1, resulting in a theoretical horizontal coordinate of -15 mm; the sine value of 15 mm multiplied by π radians is calculated to be zero, resulting in a theoretical vertical coordinate of zero mm; the theoretical depth coordinate of 10 mm multiplied by π radians and divided by twice the π constant is calculated to be 5 mm. Through this iterative calculation, millions of reference coordinate nodes are densely distributed in three-dimensional space, forming a flawless theoretical surface point cloud array.

[0066] The three-dimensional dense point cloud is registered with the theoretical surface point cloud array, the three-dimensional Euclidean distance between the registered nodes is calculated, and the aggregated result is output as a surface deviation dataset.

[0067] After generating an ideal alignment benchmark, geometric alignment of the physical data and theoretical data is performed. Since translational and rotational deviations are inevitably introduced during physical measurement and clamping, an iterative nearest-point algorithm is used to perform spatial node registration between the 3D dense point cloud and the theoretical surface point cloud array. This spatial node registration iteratively searches for the optimal rigid transformation matrix, ensuring that the overall spatial pose of the 3D dense point cloud conforms to the theoretical surface point cloud array, eliminating pose deviations caused by non-manufacturing factors. After spatial alignment, for each reconstructed node in the 3D dense point cloud, the nearest target matching node is retrieved in the theoretical surface point cloud array, and the 3D spatial Euclidean distance between the registered nodes is calculated. This distance calculation relies on the classic spatial distance formula: , in, Represents the three-dimensional Euclidean distance reflecting processing defects; , and The horizontal, vertical, and depth reconstruction coordinates of the nodes in the 3D dense point cloud after spatial node registration are represented. , and This represents the horizontal, vertical, and depth theoretical coordinates of the corresponding matching nodes in the theoretical surface point cloud array. The calculated 3D Euclidean distances of all nodes are aggregated in an array and associated with the corresponding 3D coordinate nodes, ultimately outputting a structured surface deviation dataset. This surface deviation dataset quantifies the manufacturing tolerance deviation of each surface with micron-level precision.

[0068] For example, the 3D dense point cloud was successfully translated and rotated to perfectly coincide with the central axis of the theoretical surface point cloud array. A specific node in the 3D dense point cloud was selected, with a lateral reconstruction coordinate of -15.01 mm, a lateral reconstruction coordinate of 0.02 mm, and a depth reconstruction coordinate of 5.01 mm. The corresponding matching node was retrieved in the theoretical surface point cloud array, with a lateral theoretical coordinate of -15 mm, a lateral theoretical coordinate of 0 mm, and a depth theoretical coordinate of 5 mm. Substituting these values ​​into the spatial distance formula, the sum of the squares of the lateral deviation, the longitudinal deviation, and the depth deviation was calculated to be 0.0006. Taking the square root of this sum yielded a 3D Euclidean distance of approximately 0.024 mm, or 24 micrometers. This absolute value of the 24-micrometer error was bound to its spatial coordinates and written into the surface deviation dataset to represent the micro-machining protrusions on the inner raceway surface at that location. Figure 3As shown, compared to traditional interpolation methods and ordinary deep learning models, the absolute values ​​of the deviations in cross-sectional geometry and spatial coordinates of the output reconstructed point cloud are significantly reduced. Meanwhile, the interquartile range distribution of the box plot indicates that the error distribution is highly concentrated, with very few extreme distortion outliers, achieving high reconstruction accuracy and algorithm stability at the micrometer level.

[0069] Based on the same inventive concept, this application also provides a deep learning-based sparse reconstruction system for the inner raceway profile of a lead screw nut, such as... Figure 4 As shown, the system includes: The sparse sample construction module is used to acquire the full point cloud samples, extract the cross-sectional contour spatial coordinates along the helical axis of the inner raceway of the lead screw nut at fixed phase angle intervals, construct a sparse sample set, and input the sparse sample set into a preset sparse point cloud reconstruction model to output the predicted point cloud. The reconstruction model training module is used to calculate the Euclidean distance, cross-sectional radius difference, axial mapping difference, and normal gradient difference between the predicted point cloud and the full point cloud sample, and generate a loss function by weighted summation, perform parameter updates, and output a dense point cloud reconstruction model. The inner surface point cloud acquisition module is used to locate the lead screw nut to be tested. The lead screw nut to be tested drives the endoscopic rotating laser sensor to perform scanning, extract and aggregate the spatial coordinate points of the inner surface reflection, and construct the point cloud of the sparse section to be tested. The spiral space decoupling mapping module is used to obtain the nominal lead parameters using the lead screw nut to be tested, establish a linear mapping relationship between the phase angle and the axial displacement based on the nominal lead parameters, generate a spiral space decoupling transformation matrix, input the sparse cross-section point cloud to be tested into the spiral space decoupling transformation matrix, perform the mapping calculation from the three-dimensional cylindrical coordinate system to the two-dimensional plane, and output a planar sparse coordinate array. The dense point cloud prediction module is used to input the planar sparse coordinate array into the dense point cloud reconstruction model, construct a topological node relationship graph using the planar sparse coordinate array, perform information aggregation operation of neighboring nodes to extract spatial correlation features, and perform coordinate interpolation mapping to output a planar dense prediction coordinate array. The three-dimensional space inverse reconstruction module is used to obtain the inverse matrix using the spiral space decoupling transformation matrix, multiply the planar dense prediction coordinate array by the inverse matrix to perform three-dimensional space inverse calculation, and output a three-dimensional dense point cloud; The surface deviation calculation module is used to calculate the three-dimensional Euclidean distance between the three-dimensional dense point cloud and the lead screw nut to be measured, and output the surface deviation dataset.

[0070] It should be noted that the functional division and information interaction between the various modules described above are logical, but in terms of physical implementation, they can be integrated on the same software platform or deployed in a distributed manner. The connections between them represent data flow and control flow, aiming to collaboratively achieve the objectives of this application. The above description is merely an exemplary embodiment of this application and should not be construed as limiting the scope of protection of this application.

Claims

1. A sparse reconstruction method for the inner raceway profile of a lead screw nut based on deep learning, characterized in that, The method includes: Obtain full point cloud samples, extract cross-sectional contour spatial coordinates along the helical axis of the inner raceway of the lead screw nut at fixed phase angle intervals, construct a sparse sample set, and input the sparse sample set into a preset sparse point cloud reconstruction model to output the predicted point cloud. The Euclidean distance, cross-sectional radius difference, axial mapping difference, and normal gradient difference are calculated between the predicted point cloud and the full point cloud sample, and a loss function is generated by weighted summation. Parameter updates are performed, and a dense point cloud reconstruction model is output. Position the lead screw nut to be tested, and drive the endoscopic rotary laser sensor to perform scanning through the lead screw nut to extract and aggregate the spatial coordinate points of the inner surface reflection to construct a cloud of points of the sparse cross section to be tested. The nominal lead parameter is obtained using the lead screw nut to be tested. A linear mapping relationship between the phase angle and the axial displacement is established based on the nominal lead parameter to generate a helical space decoupling transformation matrix. The cloud of sparse cross-section points to be tested is input into the helical space decoupling transformation matrix to perform a mapping calculation from a three-dimensional cylindrical coordinate system to a two-dimensional plane and output a planar sparse coordinate array. The planar sparse coordinate array is input into the dense point cloud reconstruction model. A topological node relationship graph is constructed using the planar sparse coordinate array. Information aggregation operation of neighboring nodes is performed to extract spatial correlation features. Coordinate interpolation mapping is performed to output a planar dense prediction coordinate array. The inverse matrix is ​​obtained by using the spiral space decoupling transformation matrix. The planar dense prediction coordinate array is multiplied by the inverse matrix to perform three-dimensional space inverse calculation and output a three-dimensional dense point cloud. The three-dimensional Euclidean distance is calculated using the three-dimensional dense point cloud and the lead screw nut to be tested, and the surface deviation dataset is output.

2. The method for sparse reconstruction of the inner raceway profile of a lead screw nut based on deep learning according to claim 1, characterized in that, The step of inputting the sparse sample set into a preset sparse point cloud reconstruction model and outputting a predicted point cloud includes: Extract full scan data of lead screws and nuts from historical processing batches, construct full point cloud samples, extract cross-sectional profile spatial coordinates at fixed phase angle intervals along the helix axis, and construct a sparse sample set; The sparse sample set is input into the sparse point cloud reconstruction model, and correlation feature extraction and interpolation operations are performed on the sparse sample set to output the predicted point cloud.

3. The method for sparse reconstruction of the inner raceway profile of a lead screw nut based on deep learning according to claim 1, characterized in that, The preset sparse point cloud reconstruction model includes: The spatial coordinate node dimension is extracted using the sparse sample set, and the dense coordinate tensor dimension is extracted using the full point cloud sample set. Based on the spatial coordinate node dimension and the dense coordinate tensor dimension, an input network layer, a graph neural network layer, and an output network layer are constructed to generate an initial generator network topology. Numerical initialization is performed on the neuron connection matrix and bias parameters of the initial generator network topology to generate a sparse point cloud reconstruction model.

4. The method for sparse reconstruction of the inner raceway profile of a lead screw nut based on deep learning according to claim 1, characterized in that, The output dense point cloud reconstruction model includes: The coordinate vector norm is calculated based on the predicted point cloud and the full point cloud sample to generate the Euclidean distance. The radial deviation distance is calculated based on the predicted point cloud in the local normal section coordinate system to generate the section radius difference. The linear mapping deviation of the axial displacement and phase of the predicted point cloud in cylindrical coordinates is calculated to generate the axial mapping difference. The directional difference between the predicted point cloud and the surface normal vector and the theoretical contact angle vector is calculated to generate the normal gradient difference. The weighted sum is used to generate the loss function and backpropagation is performed to output the dense point cloud reconstruction model.

5. The method for sparse reconstruction of the inner raceway profile of a lead screw nut based on deep learning according to claim 1, characterized in that, The construction of the sparse cross-sectional point cloud set to be tested includes: The endoscopic rotary laser sensor is controlled to perform axial feed along the inner raceway helix of the lead screw nut to be tested, and cross-sectional profile sampling is triggered at the helix phase angle interval to extract the spatial coordinate points of the inner surface reflection. Based on the spiral phase angle interval and the axial feed, a three-dimensional spatial coordinate system splicing operation is performed on the reflection spatial coordinate points of the inner surface to construct a cloud of sparse cross-section points to be measured.

6. The method for sparse reconstruction of the inner raceway profile of a lead screw nut based on deep learning according to claim 1, characterized in that, The output plane sparse coordinate array includes: The nominal lead parameters are extracted using the lead screw nut to be tested, and the three-dimensional rectangular coordinates of the sparse cross-section point set to be tested are transformed into radial distance, phase angle and axial displacement in a three-dimensional cylindrical coordinate system. A linear mapping operator between the phase angle and the axial displacement is constructed based on the nominal lead parameters, and the linear mapping operator is combined to generate a spiral space decoupling transformation matrix; Substitute the radial distance, the phase angle, and the axial displacement into the spiral space decoupling transformation matrix to perform spatial dimensionality reduction calculation, calculate the two-dimensional plane unfolded coordinates, and output a plane sparse coordinate array.

7. The method for sparse reconstruction of the inner raceway profile of a lead screw nut based on deep learning according to claim 1, characterized in that, The output plane dense prediction coordinate array includes: The dense point cloud reconstruction model is invoked to receive the planar sparse coordinate array, and the planar sparse coordinate array is used to construct a topological node relationship graph. Information aggregation operation of neighboring nodes is performed to generate spatial correlation features. The spatial correlation features are substituted into the dense point cloud reconstruction model, and nonlinear matrix mapping and dense coordinate interpolation calculations are performed on the feature dimensions to output a planar dense prediction coordinate array.

8. The method for sparse reconstruction of the inner raceway profile of a lead screw nut based on deep learning according to claim 1, characterized in that, The output three-dimensional dense point cloud includes: The inverse matrix is ​​generated by performing an algebraic inversion operation on the spiral space decoupling transformation matrix. The plane dense prediction coordinate array is multiplied by the inverse matrix to perform dimension restoration calculation, and the dense radial distance, dense phase angle and dense axial displacement in the three-dimensional cylindrical coordinate system are calculated. Based on the transformation relationship between the three-dimensional cylindrical coordinate system and the three-dimensional rectangular coordinate system, the dense radial distance, the dense phase angle and the dense axial displacement are mapped to the three-dimensional rectangular coordinate system to perform spatial inverse calculation and splice to generate a three-dimensional dense point cloud.

9. The sparse reconstruction method for the inner raceway profile of a lead screw nut based on deep learning according to claim 1, characterized in that, The output surface deviation dataset includes: The nominal geometric parameters are extracted using the lead screw nut to be tested, and a theoretical surface point cloud array is constructed in a three-dimensional coordinate system based on the nominal geometric parameters. The three-dimensional dense point cloud is registered with the theoretical surface point cloud array, the three-dimensional Euclidean distance between the registered nodes is calculated, and the aggregated result is output as a surface deviation dataset.

10. A deep learning-based sparse reconstruction system for the inner raceway profile of a lead screw nut, applied to the deep learning-based sparse reconstruction method for the inner raceway profile of a lead screw nut as described in any one of claims 1-9, characterized in that, The system includes: The sparse sample construction module is used to acquire the full point cloud samples, extract the cross-sectional contour spatial coordinates along the helical axis of the inner raceway of the lead screw nut at fixed phase angle intervals, construct a sparse sample set, and input the sparse sample set into a preset sparse point cloud reconstruction model to output the predicted point cloud. The reconstruction model training module is used to calculate the Euclidean distance, cross-sectional radius difference, axial mapping difference, and normal gradient difference between the predicted point cloud and the full point cloud sample, and generate a loss function by weighted summation, perform parameter updates, and output a dense point cloud reconstruction model. The inner surface point cloud acquisition module is used to locate the lead screw nut to be tested. The lead screw nut to be tested drives the endoscopic rotating laser sensor to perform scanning, extract and aggregate the spatial coordinate points of the inner surface reflection, and construct the point cloud of the sparse section to be tested. The spiral space decoupling mapping module is used to obtain the nominal lead parameters using the lead screw nut to be tested, establish a linear mapping relationship between the phase angle and the axial displacement based on the nominal lead parameters, generate a spiral space decoupling transformation matrix, input the sparse cross-section point cloud to be tested into the spiral space decoupling transformation matrix, perform the mapping calculation from the three-dimensional cylindrical coordinate system to the two-dimensional plane, and output a planar sparse coordinate array. The dense point cloud prediction module is used to input the planar sparse coordinate array into the dense point cloud reconstruction model, construct a topological node relationship graph using the planar sparse coordinate array, perform information aggregation operation of neighboring nodes to extract spatial correlation features, and perform coordinate interpolation mapping to output a planar dense prediction coordinate array. The three-dimensional space inverse reconstruction module is used to obtain the inverse matrix using the spiral space decoupling transformation matrix, multiply the planar dense prediction coordinate array by the inverse matrix to perform three-dimensional space inverse calculation, and output a three-dimensional dense point cloud; The surface deviation calculation module is used to calculate the three-dimensional Euclidean distance between the three-dimensional dense point cloud and the lead screw nut to be tested, and output the surface deviation dataset.

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