Three-dimensional visualization and reconstruction method based on residual stress layered measurement

Abstract

The invention relates to the technical field of advanced manufacturing and material testing, in particular to a three-dimensional visualization and reconstruction method based on residual stress layering measurement, and the method comprises the steps: obtaining component surface dense measurement data, and reconstructing a surface two-dimensional stress field matrix; establishing a depth direction stress attenuation model based on a stress relaxation mechanism and self-balancing constraint, and deducing a stress distribution reference value of each depth layer; obtaining internal sparse verification data, fusing multi-source data by adopting a sequential Bayesian updating framework, and dynamically updating posterior stress field distribution and an uncertainty quantification result; generating a three-dimensional virtual point cloud and calculating a deduced stress value; and credibility grades are distinguished through color mapping and transparency, so that residual stress three-dimensional visualization is realized. According to the method, the problems that in the prior art, three-dimensional interpolation depends on dense internal measuring points, and sparse data reconstruction confidence is low are solved, internal deduction is driven by surface data, and optimal balance between cost and precision is achieved.

Description

Technical Field

[0001] This invention relates to the field of advanced manufacturing and materials testing technology, and in particular to a three-dimensional visualization and reconstruction method based on residual stress layer measurement. Background Technology

[0002] In high-end equipment manufacturing fields such as aerospace, nuclear power, and rail transportation, the residual stress state of key components directly affects their service safety and fatigue life. Residual stress is a self-balancing internal stress caused by uneven plastic deformation, thermal cycling, or phase transformation during the manufacturing process (such as welding, casting, heat treatment, and machining). Its magnitude, distribution, and gradient changes along the depth direction play a decisive role in the deformation, cracking, and failure behavior of components. Therefore, achieving accurate three-dimensional characterization and visualization of residual stress is of great significance for optimizing manufacturing processes, assessing component integrity, and predicting service performance.

[0003] In existing technologies, residual stress measurement methods are mainly divided into two categories: destructive methods and non-destructive methods. Destructive methods include blind hole methods, profilometry, and layer-by-layer drilling methods, which release stress by removing material and measuring strain changes to invert stress distribution. Non-destructive methods include X-ray diffraction, neutron diffraction, and ultrasonic critical refraction longitudinal wave methods, which directly detect lattice distortion or sound velocity changes caused by stress using physical principles. However, all of the above methods have obvious limitations: destructive methods destroy the integrity of the component and are difficult to reconstruct in three dimensions; X-ray diffraction can only measure stress on the surface and near the surface (usually less than 0.05 mm); although neutron diffraction can penetrate deep layers, the equipment is expensive, the measurement points are sparse, and the spatial resolution is low; ultrasonic methods are affected by the sound attenuation of the material, and the uncertainty of deep layer measurements increases exponentially with depth.

[0004] In terms of data reconstruction, existing technologies mainly rely on two-dimensional interpolation methods (such as griddata and kriging interpolation) to reconstruct discrete measurement points into a continuous stress field. However, these methods are only applicable to surface planes and cannot characterize stress changes in the depth direction (Z-axis). Traditional three-dimensional interpolation methods (such as three-dimensional kriging and radial basis functions) suffer from low confidence and large errors when faced with extremely sparse internal data, and cannot effectively integrate the complementary information between dense surface data and sparse internal data. In engineering practice, due to cost and accessibility constraints, the number of measurement points inside components is usually far less than that on the surface (e.g., 50-500 points on the surface, 5-20 points inside). This asymmetric data characteristic of "dense surface - sparse internal" makes it difficult for existing three-dimensional reconstruction methods to achieve a balance between accuracy and cost.

[0005] Therefore, there is an urgent need for a new method that can reasonably infer and reconstruct the three-dimensional stress field inside the component based on rich surface measurement data, achieve the optimal balance between cost and accuracy, and possess uncertainty quantification and credibility classification visualization. Summary of the Invention

[0006] Therefore, the present invention provides a three-dimensional visualization and reconstruction method based on residual stress layer measurement to solve the aforementioned problems existing in the prior art.

[0007] To achieve the above objectives, this invention provides a three-dimensional visualization and reconstruction method based on residual stress layer measurement, comprising:

[0008] Step S1: Obtain a discrete measurement point dataset, which includes the two-dimensional spatial coordinates of surface measurement points and their corresponding residual stress values; Based on the spatial coordinate distribution of the surface measurement points, generate a uniform or adaptively refined two-dimensional grid node matrix in the area to be reconstructed, and use a spatial interpolation algorithm to calculate the stress values ​​of the grid nodes to obtain the surface two-dimensional stress field matrix.

[0009] Step S2: Establish a stress attenuation model based on stress relaxation mechanism and self-balancing constraint. The stress attenuation model takes the two-dimensional stress field matrix of the surface as the boundary condition and derives the stress distribution benchmark value of each depth layer by solving the self-balancing equation that satisfies the zero volume integral stress.

[0010] Step S3: Obtain internal sparse verification data at different depths at key locations of the component. Using the stress distribution benchmark value as a priori, the internal sparse verification data is fused using a sequential Bayesian update framework to dynamically update the posterior stress field distribution and uncertainty quantification results.

[0011] Step S4: Generate virtual point cloud coordinates within the three-dimensional spatial envelope of the component. For each virtual point, interpolate the corresponding surface stress reference value through the surface two-dimensional stress field matrix. Combine the depth information of the virtual point and the posterior stress field distribution to calculate the inferred stress value of the virtual point.

[0012] Step S5: Combine the virtual point cloud coordinates with the inferred stress value, and visually display the spatial distribution of residual stress in a three-dimensional graphic form through at least one of color mapping, isosurface drawing, or volume drawing; the visualization distinguishes high-confidence areas from inferred areas through transparency or color difference mapping.

[0013] Furthermore, the discrete measurement point dataset is obtained through layer-by-layer material removal and measurement techniques, which are selected from blind hole method, contour method, layer-by-layer drilling method, X-ray diffraction method, ultrasonic critical refraction longitudinal wave method or neutron diffraction method; the number of surface measurement points is significantly greater than the number of internal sparse verification data.

[0014] Furthermore, the spatial interpolation algorithm employs Kriging interpolation, inverse distance weighted interpolation, radial basis function interpolation, or cubic spline interpolation; the adaptive densification dynamically adjusts the node density based on the stress gradient, automatically subdividing the mesh in regions where the gradient value exceeds a preset threshold.

[0015] Furthermore, the depth-direction stress attenuation model is expressed as:

[0016] ;

[0017] in, This represents the stress value at the corresponding position in the two-dimensional stress field matrix of the surface. This is the inherent depth decay kernel function of the material. The stress relaxation correction term caused by material removal is satisfied through iterative solution. The self-equilibrium conditions are determined.

[0018] Furthermore, the process of iteratively solving for the stress relaxation correction term to satisfy the self-equilibrium condition includes:

[0019] Based on the current layer geometry, the stress release caused by material removal is calculated using elastic or elastoplastic constitutive methods.

[0020] The relaxed stress field is projected onto the self-balancing constraint space, and the force balance constraint and torque balance constraint are satisfied by least squares correction.

[0021] The local relaxation step and the global projection step are executed alternately until the stress field change norm of two adjacent iterations is less than a preset threshold.

[0022] Furthermore, the process of using a sequential Bayesian update framework to fuse the internal sparse validation data and dynamically update the posterior stress field distribution and uncertainty quantification results includes:

[0023] Based on the posterior distribution of the stress field in the current layer, the prior distribution of stress in the next depth layer is predicted by a state transition model; the state transition model is determined based on the stress relaxation mechanism caused by material removal and the self-balancing constraint.

[0024] Obtain the internal sparse validation data of the next depth layer, calculate the residual between the prior distribution and the internal sparse validation data, and use the Kalman gain matrix to weighted fuse the prior prediction and measured information to obtain the posterior mean and covariance matrix of the next layer.

[0025] Determine whether the residual exceeds a preset anomaly threshold: if it does not exceed it, maintain the current uncertainty bandwidth and proceed to the next layer of prediction; if it exceeds it, trigger an anomaly flag, expand the current layer uncertainty bandwidth, and calculate the optimal measurement position for the next layer based on the information gain criterion.

[0026] Furthermore, the uncertainty bandwidth is dynamically adjusted according to the characteristics of the measurement technology: the surface measurement data is allocated a fixed low variance, while the internal ultrasonic data is allocated a depth-correlated exponentially increasing variance.

[0027] Furthermore, the process of step S4 includes:

[0028] Within the three-dimensional spatial envelope of the component, a regular grid point cloud or a randomly distributed point cloud is generated according to a preset resolution as virtual point cloud coordinates; the virtual point cloud coordinates include the two-dimensional planar coordinates and depth coordinates of the virtual points;

[0029] For each virtual point, based on its two-dimensional plane coordinates, spatial interpolation is performed using the surface two-dimensional stress field matrix to obtain the surface stress reference value corresponding to the virtual point.

[0030] Based on the depth coordinates of the virtual point, the depth direction stress attenuation relationship of the corresponding depth layer is extracted from the posterior stress field distribution. The surface stress reference value is substituted into the depth direction stress attenuation relationship to calculate the depth direction extrapolated stress value of the virtual point.

[0031] The uncertainty bandwidth of the corresponding depth layer is extracted from the uncertainty quantification result of the posterior stress field distribution. The inferred stress value in the depth direction is randomly perturbed with the uncertainty bandwidth as the amplitude to obtain the inferred stress value with uncertainty label.

[0032] The three-dimensional spatial coordinates of all virtual points and their corresponding inferred stress values ​​are summarized to generate three-dimensional volume data with uncertainty indicators.

[0033] Furthermore, the process of applying a random perturbation to the inferred stress value along the depth direction with the uncertainty bandwidth as the amplitude to obtain the inferred stress value with an uncertainty label includes:

[0034] The relative uncertainty is obtained by calculating the ratio of the uncertainty bandwidth to the estimated stress value in the depth direction;

[0035] Determine whether the relative uncertainty exceeds a preset proportional threshold: if it does not exceed the threshold, apply a first-amplitude random perturbation to the depth-direction inferred stress value; if it exceeds the threshold, apply a second-amplitude random perturbation to the depth-direction inferred stress value and mark the virtual point as a low-confidence point; the second amplitude is greater than the first amplitude.

[0036] The stress value after applying random perturbation is used as the inferred stress value, and the relative uncertainty or the low confidence point is marked as the uncertainty identifier.

[0037] Furthermore, the process of step S5 includes:

[0038] The inferred stress value is mapped to a color value according to a preset color spectrum. In the color spectrum, tensile stress and compressive stress are distinguished by contrasting colors, and the absolute value of stress is represented by color saturation or brightness gradient.

[0039] The confidence level of each virtual point is determined based on the uncertainty identifier. High confidence areas are rendered with a first transparency, and low confidence areas are rendered with a second transparency, where the second transparency is greater than the first transparency.

[0040] Based on the virtual point cloud coordinates, the color value, and the transparency, a three-dimensional stress surface map is generated through surface rendering, or a three-dimensional stress volume map is generated through volume drawing, or an isosurface map with a specific stress level is generated through isosurface extraction.

[0041] It provides a human-computer interaction interface that supports rotation, scaling, and translation of the three-dimensional graphics, supports interactive display of stress distribution on any cut surface, and supports dynamic playback of two-dimensional slices at different depths in depth order to demonstrate the stress field evolution process.

[0042] Compared with existing technologies, the advantages of this invention are as follows: This invention establishes a depth-direction stress attenuation model by heterogeneously fusing dense surface measurement data and sparse internal verification data, using stress relaxation mechanisms and self-balancing constraints. The surface stress field is used as a boundary condition to deduce the internal stress distribution. The prior model is corrected by dynamically fusing measured data using a sequential Bayesian update framework, so that the uncertainty quantification result of the posterior stress field distribution is adaptively adjusted with the measurement data density. Thus, under asymmetric sampling conditions where the number of surface measurement points is significantly greater than the number of internal verification points, the optimal balance between the accuracy of three-dimensional stress field reconstruction and measurement cost is achieved, avoiding the accumulation of interpolation errors caused by the sparsity of internal data. At the same time, the high uncertainty region is transparently identified through credibility classification visualization, providing a technical solution that takes into account both economy and reliability for the assessment of residual stress in engineering components. Attached Figure Description

[0043] Figure 1 A flowchart illustrating the three-dimensional visualization and reconstruction method based on residual stress layer measurement provided by this invention;

[0044] Figure 2 This is a flowchart illustrating step S4 in the three-dimensional visualization and reconstruction method based on residual stress layer measurement provided by the present invention. Detailed Implementation

[0045] To make the objectives and advantages of the present invention clearer, the present invention will be further described below with reference to embodiments; it should be understood that the specific embodiments described herein are merely for explaining the present invention and are not intended to limit the present invention.

[0046] Preferred embodiments of the present invention will now be described with reference to the accompanying drawings. Those skilled in the art should understand that these embodiments are merely illustrative of the technical principles of the present invention and are not intended to limit the scope of protection of the present invention.

[0047] It should be noted that in the description of this invention, the terms "upper", "lower", "left", "right", "inner", "outer", etc., which indicate directions or positional relationships, are based on the directions or positional relationships shown in the accompanying drawings. This is only for the convenience of description and is not intended to indicate or imply that the device or element must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, it should not be construed as a limitation of this invention.

[0048] Furthermore, it should be noted that, in the description of this invention, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0049] Please see Figure 1 As shown, this invention provides a three-dimensional visualization and reconstruction method based on residual stress layer measurement, including:

[0050] Step S1: Obtain a discrete measurement point dataset, which includes the two-dimensional spatial coordinates of surface measurement points and their corresponding residual stress values; Based on the spatial coordinate distribution of the surface measurement points, generate a uniform or adaptively refined two-dimensional grid node matrix in the area to be reconstructed, and use a spatial interpolation algorithm to calculate the stress values ​​of the grid nodes to obtain the surface two-dimensional stress field matrix.

[0051] Specifically, the discrete measurement point dataset is obtained through layer-by-layer material removal and measurement techniques, which are selected from blind hole method, contour method, layer-by-layer drilling method, X-ray diffraction method, ultrasonic critical refraction longitudinal wave method or neutron diffraction method; the number of surface measurement points is significantly greater than the number of internal sparse verification data.

[0052] Specifically, the spatial interpolation algorithm employs Kriging interpolation, inverse distance weighted interpolation, radial basis function interpolation, or cubic spline interpolation; the adaptive densification dynamically adjusts the node density based on the stress gradient, automatically subdividing the mesh in regions where the gradient value exceeds a preset threshold.

[0053] Specifically, a measurement point array is planned on the surface of the component to be tested. This array uses a uniform grid or an adaptive grid based on geometric features. For flat components, M×N surface measurement points are planned at equal intervals Δx and Δy along the length direction X and width direction Y, where Δx and Δy are determined based on the component size and required spatial resolution, typically ranging from 1mm to 10mm. The two-dimensional spatial coordinates (x_i, y_i) and corresponding residual stress value σ_i of each surface measurement point are recorded, where i = 1, 2, ..., M×N, forming a surface measurement point dataset S_surface = {(x_i, y_i, σ_i)}. The number of surface measurement points M×N is typically 50-500 to ensure the spatial resolution of the surface stress field. The surface measurement point dataset is preprocessed, including outlier removal, data smoothing, and coordinate alignment. Based on the preprocessed spatial coordinate distribution of the surface measurement points, the numerical range of the region to be reconstructed is determined.

[0054] X-direction range: [x_min, x_max], where x_min = min(x_i), x_max = max(x_i);

[0055] Y-direction range: [y_min, y_max], where y_min = min(y_i), y_max = max(y_i);

[0056] A two-dimensional mesh node matrix is ​​generated within the region to be reconstructed, including two modes:

[0057] Uniform grid mode: User-defined resolution P×Q generates uniformly distributed grid node coordinates (Xq, Yq), where Xq are P vectors linearly interpolated in the interval [x_min, x_max], and Yq are Q vectors linearly interpolated in the interval [y_min, y_max]. Typical resolutions are 100×100 or 200×200.

[0058] Adaptive encryption mode: First, a basic uniform grid is generated, and the stress gradient ‖∇σ‖ within each grid cell is calculated; for grid cells ‖∇σ‖>ε_th, quadtree subdivision is performed until the maximum subdivision level L_max is reached or the cell size is smaller than the minimum size d_min; the threshold ε_th is determined according to the stress field variation characteristics, usually taken as 1-2 times the mean square error of the entire field, L_max is usually taken as 3-5 layers, and d_min is usually taken as 0.5mm-1mm.

[0059] Step S2: Establish a stress attenuation model based on stress relaxation mechanism and self-balancing constraint. The stress attenuation model takes the two-dimensional stress field matrix of the surface as the boundary condition and derives the stress distribution benchmark value of each depth layer by solving the self-balancing equation that satisfies the zero volume integral stress.

[0060] Specifically, the depth-direction stress attenuation model is expressed as:

[0061] ;

[0062] in, This represents the stress value at the corresponding position in the two-dimensional stress field matrix of the surface. This is the inherent depth decay kernel function of the material. The stress relaxation correction term caused by material removal is satisfied through iterative solution. The self-equilibrium conditions are determined.

[0063] Specifically, the process of iteratively solving for the stress relaxation correction term to satisfy the self-equilibrium condition includes:

[0064] Based on the current layer geometry, the stress release caused by material removal is calculated using elastic or elastoplastic constitutive methods.

[0065] Specifically, those skilled in the art can use finite element software (such as ABAQUS, ANSYS) or a self-developed finite element program to establish a finite element model of the current layer, apply the two-dimensional stress field matrix of the surface as the initial stress field, simulate the material removal process through the kill element technique, and calculate the relaxation stress field after stress redistribution.

[0066] The relaxed stress field is projected onto the self-balancing constraint space, and the force balance constraint and torque balance constraint are satisfied by least squares correction.

[0067] Specifically, force balance constraints: That is, the integral of the stress field within the volume of the component is equal to zero;

[0068] Torque balance constraint: That is, the integral of the torque of the stress field about any axis is equal to zero, where This is the distance to the axis.

[0069] The least squares correction is achieved by superimposing a uniform stress field and a linear stress field on the relaxed stress field. The coefficients of the uniform stress field and the linear stress field are determined by solving the constraint equations. This is a conventional technique in computational mechanics and will not be elaborated further.

[0070] The local relaxation step and the global projection step are executed alternately until the stress field change norm of two adjacent iterations is less than a preset threshold.

[0071] Specifically, the local relaxation step and the global projection step are executed alternately to calculate... Stress field variation norm between two adjacent iterations The iteration terminates when the variation norm is less than a preset threshold ϵ (usually 1 MPa or 1% relative error), and the stress relaxation correction term is output; otherwise, iteration continues until the maximum number of iterations Nmax (usually 10-50) is reached. Based on the depth-direction stress attenuation model, the stress attenuation at each depth layer is calculated. (Stress distribution baseline values ​​for k=1,2,...,K, where K is the depth layer number, typically taken as 10-50 layers): Output the stress distribution reference values ​​for each depth layer. As a priori input for step S3.

[0072] Step S3: Obtain internal sparse verification data at different depths at key locations of the component. Using the stress distribution benchmark value as a priori, the internal sparse verification data is fused using a sequential Bayesian update framework to dynamically update the posterior stress field distribution and uncertainty quantification results.

[0073] Specifically, internal sparse verification data at different depths are obtained at key locations on the component. These key locations include stress concentration areas (such as geometric abrupt changes and weld joints) and uniform areas (such as the center of a plate) to verify the accuracy of the stress distribution benchmark value. The number of internal sparse verification data points is significantly less than the number of surface measurement points, typically 5-20, distributed along the depth direction at different depth layers. The internal sparse verification data are obtained using the same measurement techniques or complementary techniques as in step S1. For deep stress measurement, the profilometry method or neutron diffraction method is preferred. The three-dimensional coordinates of each verification point are recorded. and measured stress values To form an internal validation dataset ; Calculate the baseline value of stress distribution at the corresponding position (x,y) of each verification point. Establish a mapping relationship between the benchmark value and the measured value.

[0074] Specifically, the process of using a sequential Bayesian update framework to fuse the internal sparse validation data and dynamically update the posterior stress field distribution and uncertainty quantification results includes:

[0075] Based on the posterior distribution of the stress field in the current layer, the prior distribution of stress in the next depth layer is predicted by a state transition model; the state transition model is determined based on the stress relaxation mechanism caused by material removal and the self-balancing constraint.

[0076] Specifically, the stress distribution reference value As the initial prior distribution, let the initial state vector and its covariance matrix of the first depth layer (surface layer, z=0) be defined:

[0077] Initial mean vector ;

[0078] Initial covariance matrix ,in, The variance of the surface measurement uncertainty is determined based on the accuracy of the measurement technique; for X-ray diffraction, it is typically taken as 10-100 MPa. 2 , where I is the identity matrix.

[0079] For the k-th depth layer (k=1,2,...,K), based on the posterior distribution of the (k-1)-th layer, the prior stress distribution of the k-th layer is predicted using a state transition model:

[0080]

[0081]

[0082] in, The transition matrix is ​​determined based on the stress relaxation mechanism caused by material removal and the self-balancing constraints, for elastic relaxation. The decay form is approximated as an identity matrix for elastoplastic relaxation. Determined through finite element sensitivity analysis; The process noise covariance matrix characterizes the uncertainty of the state transition model and is determined based on the iterative convergence residual of the stress relaxation correction term. Let be the prior mean and prior covariance of the k-th layer, respectively.

[0083] Obtain the internal sparse validation data of the next depth layer, calculate the residual between the prior distribution and the internal sparse validation data, and use the Kalman gain matrix to weighted fuse the prior prediction and measured information to obtain the posterior mean and covariance matrix of the next layer.

[0084] Specifically, to determine whether there is sparse validation data in the k-th depth layer: if validation points exist, obtain the measured values. Calculate the new information residual: ,in The observation matrix maps the state vector to the measurement space; for point measurements... For interpolation operators; calculate the Kalman gain matrix. , of which The noise covariance is measured and determined based on the measurement technology characteristics of the validation data; the posterior distribution is then updated. , If no validation points exist, the prior distribution is retained as the posterior distribution: , .

[0085] Determine whether the residual exceeds a preset anomaly threshold: if it does not exceed it, maintain the current uncertainty bandwidth and proceed to the next layer of prediction; if it exceeds it, trigger an anomaly flag, expand the current layer uncertainty bandwidth, and calculate the optimal measurement position for the next layer based on the information gain criterion.

[0086] Specifically, the new information residual is determined. Whether the preset anomaly threshold τ is exceeded: The anomaly threshold τ is determined based on the prior uncertainty, and is usually taken as... That is, 3 times the standard deviation; if It is determined to be a normal residual, and the current uncertainty bandwidth is maintained (i.e., , where γ is the amplification factor, usually taken as 4-10;

[0087] Calculate the optimal measurement location for the next layer based on the information gain criterion: Calculate the candidate location set. Prediction variance Information gain is defined as the expected reduction in entropy after measurement. Select the location with the maximum information gain that is also reachable. As the optimal measurement location for the next layer, output sampling suggestions. Let k = k + 1, and repeat S3-3 to S3-5 until all depth layers are updated; output the posterior stress field distribution of each depth layer. (i.e., posterior mean) and uncertainty quantification results (i.e., the posterior covariance matrix), which serves as the input for step S4.

[0088] Specifically, the uncertainty bandwidth is dynamically adjusted according to the characteristics of the measurement technology: surface measurement data is allocated a fixed low variance, while internal ultrasonic data is allocated a depth-correlated exponentially increasing variance.

[0089] Specifically, surface measurement data were acquired using X-ray diffraction with a fixed low variance. ,in, The measurement uncertainty variance of the instrument is determined according to the calibration certificate of the X-ray stress analyzer, and is usually taken as 100-400 MPa. 2 (Corresponding standard deviation 10-20 MPa); The variance of the measurement point positioning uncertainty is determined based on the accuracy of the positioning device, and is typically taken as 25-100 MPa. 2 (Corresponding standard deviation 5-10 MPa); Total variance of surface measurement data Typically, 125-500 MPa² is used as the initial covariance matrix. The diagonal elements. Internal sparse validation data were acquired using the ultrasonic critical refraction longitudinal wave method (LCR wave), and the depth-related exponentially growing variance was assigned: ,in The initial variance of the surface is equal to the variance of the surface measurement data. The magnitudes are comparable, typically ranging from 100 to 400 MPa²; α is the material's acoustic attenuation coefficient, determined based on the material's ultrasonic properties, and for steel, it is typically taken as 0.5 to 2.0 mm². -1 For aluminum alloys, a thickness of 0.3-1.5 mm is typically used. -1 z represents the detection depth in mm, with the positive direction being from the surface inwards. The physical basis for the depth-related exponentially growing variance is that the ultrasonic signal attenuates with increasing propagation depth, leading to a decrease in the signal-to-noise ratio and an increase in measurement uncertainty. The exponential growth model is an empirical model in the field of ultrasonic testing, and the parameter α can be determined through ultrasonic calibration experiments on standard test blocks.

[0090] Specifically, the observation noise covariance matrix The type of measurement technique used to determine the k-th layer verification data is used. If the k-th layer verification data comes from surface measurements or near-surface measurements (z≤0.1mm), then... If the verification data for the k-th layer comes from internal ultrasonic measurements (z>0.1mm), then take... For cases where there are multiple verification points at the same depth layer, This is a diagonal matrix, with each diagonal element calculated based on the measurement technique and depth of the corresponding verification point. The uncertainty bandwidth is sequentially passed through the posterior covariance matrix of the Kalman filter:

[0091] High confidence region: The posterior standard deviation is less than the preset threshold (e.g., 30 MPa), corresponding to high confidence stress estimation;

[0092] Low confidence region: The posterior standard deviation is greater than the preset threshold, which corresponds to the region that needs further verification or supplementary measurement.

[0093] The dynamic adjustment of the uncertainty bandwidth ensures that surface-dense measurement data has a higher weight in the fusion process, the uncertainty of deep sparse verification data is reasonably amplified, and overconfident posterior estimation is avoided.

[0094] Step S4: Generate virtual point cloud coordinates within the three-dimensional spatial envelope of the component. For each virtual point, interpolate the corresponding surface stress reference value through the surface two-dimensional stress field matrix. Combine the depth information of the virtual point and the posterior stress field distribution to calculate the inferred stress value of the virtual point.

[0095] Specifically, such as Figure 2 As shown, the process of step S4 includes:

[0096] Step S41: Within the three-dimensional spatial envelope of the component, generate a regular grid point cloud or a randomly distributed point cloud as virtual point cloud coordinates according to a preset resolution; the virtual point cloud coordinates include the two-dimensional planar coordinates and depth coordinates of the virtual points.

[0097] Specifically, within the three-dimensional spatial envelope of the component, virtual point cloud coordinates are generated according to a preset resolution. The three-dimensional spatial envelope is defined by the maximum external dimensions of the component in the X, Y, and Z directions. The virtual point cloud generation includes two modes:

[0098] Regular mesh point cloud: Regular mesh nodes are generated in the X, Y, and Z directions at equal intervals Δx, Δy, and Δz, respectively, to form a structured point cloud; the intervals are determined according to the required spatial resolution, typically Δx=Δy=0.1-1mm (consistent with or refined to the surface reconstruction mesh resolution), Δz=0.05-0.5mm (refined along the depth direction).

[0099] Randomly distributed point cloud: An unstructured point cloud is generated within a three-dimensional spatial envelope by uniform random distribution or importance sampling; the importance sampling adjusts the sampling density according to stress gradient or geometric features, and increases the number of sampling points in areas of high stress concentration;

[0100] The virtual point cloud coordinates are represented as ( ), where v = 1, 2, ..., Nv, and Nv is the total number of virtual points, usually taken as 10,000-100,000; each virtual point contains two-dimensional planar coordinates. and depth coordinates .

[0101] Step S42: For each virtual point, based on its two-dimensional plane coordinates, spatial interpolation is performed using the surface two-dimensional stress field matrix to obtain the surface stress reference value corresponding to the virtual point.

[0102] Specifically, for each virtual point v, based on its two-dimensional plane coordinates By spatial interpolating the two-dimensional stress field matrix of the surface, the reference value of the surface stress corresponding to the virtual point is obtained. For regular grid point clouds, if their planar coordinates coincide with the reconstructed grid nodes on the surface, the corresponding matrix element values ​​are directly extracted.

[0103] Step S43: Based on the depth coordinates of the virtual point, extract the depth direction stress attenuation relationship of the corresponding depth layer from the posterior stress field distribution, substitute the surface stress reference value into the depth direction stress attenuation relationship, and calculate the depth direction extrapolated stress value of the virtual point.

[0104] Specifically, based on the depth coordinates of the virtual point Extract the corresponding depth layer k (satisfied with) from the posterior stress field distribution. The depth-direction stress attenuation relationship is calculated by substituting the surface stress reference value into the depth-direction stress attenuation relationship, and then calculating the depth-direction extrapolated stress value for the virtual point.

[0105]

[0106] in The posterior mean of the k-th layer is Interpolation at a given location, where ϕ(z) is the depth decay kernel function; or spatial interpolation using the posterior mean can be directly employed. As the stress value extrapolated in the depth direction.

[0107] Step S44: Extract the uncertainty bandwidth of the corresponding depth layer from the uncertainty quantification result of the posterior stress field distribution, and apply random perturbation to the inferred stress value in the depth direction with the uncertainty bandwidth as the amplitude to obtain the inferred stress value with uncertainty label.

[0108] Specifically, the process of applying a random perturbation to the inferred stress value in the depth direction with the uncertainty bandwidth as the amplitude to obtain the inferred stress value with uncertainty label includes:

[0109] The relative uncertainty is obtained by calculating the ratio of the uncertainty bandwidth to the estimated stress value in the depth direction;

[0110] Specifically, the formula for calculating relative uncertainty is: The relative uncertainty is a dimensionless quantity that characterizes the relative reliability of the stress estimate.

[0111] Determine whether the relative uncertainty exceeds a preset proportional threshold: if it does not exceed the threshold, apply a first-amplitude random perturbation to the depth-direction inferred stress value; if it exceeds the threshold, apply a second-amplitude random perturbation to the depth-direction inferred stress value and mark the virtual point as a low-confidence point; the second amplitude is greater than the first amplitude.

[0112] Specifically, the relative uncertainty is determined. Does it exceed the preset ratio threshold? (Typically, a relative error of 0.1-0.3 is taken, i.e., 10%-30%)

[0113] like The virtual point is determined to be a high-confidence point, and a first-amplitude random perturbation is applied to the inferred stress value in the depth direction: ,in, The first amplitude is the uncertainty bandwidth itself, which is a random number taken from the standard normal distribution N(0,1).

[0114] like The virtual point is determined to be a low-confidence point, and a second amplitude random perturbation is applied to the inferred stress value in the depth direction: ,in, These are random numbers drawn from the standard normal distribution N(0,1). The amplitude is the amplification factor (usually 2-5), the second amplitude is the amplified uncertainty bandwidth, and the second amplitude is greater than the first amplitude; at the same time, the virtual point is marked as a low confidence point.

[0115] The stress value after applying random perturbation is used as the inferred stress value, and the relative uncertainty or the low confidence point is marked as the uncertainty identifier.

[0116] Specifically, the stress value after applying random perturbation As the inferred stress value; the relative uncertainty is used as... Alternatively, the low-confidence point markers can be used as uncertainty identifiers and stored as tag data corresponding to the inferred stress values.

[0117] Step S45: Summarize the three-dimensional spatial coordinates of all virtual points and their corresponding inferred stress values ​​to generate three-dimensional volume data with uncertainty indicators.

[0118] Specifically, the three-dimensional volume data is stored in a structured mesh format (such as VTK, HDF5) or an unstructured point cloud format (such as PLY, LAS), and includes the following data channels: geometric channel: virtual point three-dimensional coordinates; stress channel: inferred stress value; uncertainty channel: relative uncertainty or uncertainty bandwidth; confidence label channel: high confidence point / low confidence point markers.

[0119] Step S5: Combine the virtual point cloud coordinates with the inferred stress value, and visually display the spatial distribution of residual stress in a three-dimensional graphic form through at least one of color mapping, isosurface drawing, or volume drawing; the visualization distinguishes high-confidence areas from inferred areas through transparency or color difference mapping.

[0120] Specifically, step S5 includes the following process:

[0121] The inferred stress value is mapped to a color value according to a preset color spectrum. In the color spectrum, tensile stress and compressive stress are distinguished by contrasting colors, and the absolute value of stress is represented by color saturation or brightness gradient.

[0122] Specifically, the inferred stress value is mapped to a color value according to a preset color spectrum; the color spectrum adopts a bipolar color scheme, with tensile stress mapped to warm colors (such as reds) and compressive stress mapped to cool colors (such as blues), and neutral colors (such as white or green) used for transition in the area near zero stress; the magnitude of the absolute stress value is represented by color saturation or brightness gradient, with high absolute stress value corresponding to high saturation or high brightness.

[0123] The confidence level of each virtual point is determined based on the uncertainty identifier. High confidence areas are rendered with a first transparency, and low confidence areas are rendered with a second transparency, where the second transparency is greater than the first transparency.

[0124] Specifically, the confidence level of each virtual point is determined based on the uncertainty identifier obtained in step S4:

[0125] High confidence region (relative uncertainty) Or no non-low confidence point markers): Rendered with first transparency (low transparency, opaque, or semi-transparent);

[0126] Low confidence region (relative uncertainty) (Possibly with low-confidence markers): Rendered with second transparency (high transparency, significantly transparent);

[0127] The second transparency is greater than the first transparency, which makes the low confidence area appear blurred or transparent, creating a visual distinction from the surrounding high confidence area.

[0128] Based on the virtual point cloud coordinates, the color value, and the transparency, a three-dimensional stress surface map is generated through surface rendering, or a three-dimensional stress volume map is generated through volume drawing, or an isosurface map with a specific stress level is generated through isosurface extraction.

[0129] Specifically, based on the virtual point cloud coordinates, the color values, and the transparency, a graphics rendering algorithm is used to generate a 3D visualization graphic:

[0130] 3D stress surface plot: Extract virtual point cloud at a specific depth layer and generate a colored stress surface through surface rendering (such as triangular mesh or NURBS surface);

[0131] 3D stress volume diagram: Using a volume rendering ray casting algorithm, color and transparency are accumulated along the line of sight to generate a semi-transparent volume visualization of the overall 3D stress field;

[0132] Isosurface plot: The moving cube algorithm is used to extract the isosurface of specific stress values ​​(such as zero stress surface or maximum principal stress surface).

[0133] It provides a human-computer interaction interface that supports rotation, scaling, and translation of the three-dimensional graphics, supports interactive display of stress distribution on any cut surface, and supports dynamic playback of two-dimensional slices at different depths in depth order to demonstrate the stress field evolution process.

[0134] Specifically, users can rotate, scale, and translate 3D graphics using a mouse or touch gestures; obtain 2D cross-sectional stress cloud maps at any location using an interactive cutting plane; and dynamically play a sequence of 2D slices in depth order using a timeline control to demonstrate the evolution of the stress field along the depth direction.

[0135] Specifically, this invention heterogeneously fuses dense surface measurement data with sparse internal verification data, establishes a depth-direction stress attenuation model using stress relaxation mechanisms and self-balancing constraints, uses the surface stress field as a boundary condition to deduce the internal stress distribution, and dynamically fuses measured data using a sequential Bayesian update framework to correct the prior model. This allows the uncertainty quantification result of the posterior stress field distribution to adaptively adjust with the measurement data density, thereby achieving an optimal balance between the accuracy of three-dimensional stress field reconstruction and measurement cost under asymmetric sampling conditions where the number of surface measurement points is significantly greater than the number of internal verification points. This avoids the accumulation of interpolation errors caused by the sparsity of internal data. At the same time, it achieves transparent identification of high uncertainty areas through credibility-level visualization, providing a technical solution that balances economy and reliability for the assessment of residual stress in engineering components.

[0136] The technical solution of the present invention has been described above with reference to the preferred embodiments shown in the accompanying drawings. However, it will be readily understood by those skilled in the art that the scope of protection of the present invention is obviously not limited to these specific embodiments. Without departing from the principles of the present invention, those skilled in the art can make equivalent changes or substitutions to the relevant technical features, and the technical solutions after these changes or substitutions will all fall within the scope of protection of the present invention.

[0137] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A three-dimensional visualization and reconstruction method based on residual stress layer measurement, characterized in that, include: Step S1: Obtain a discrete measurement point dataset, which includes the two-dimensional spatial coordinates of surface measurement points and their corresponding residual stress values. Based on the spatial coordinate distribution of the surface measurement points, a uniform or adaptively refined two-dimensional mesh node matrix is ​​generated in the area to be reconstructed. The stress values ​​of the mesh nodes are calculated using a spatial interpolation algorithm to obtain the two-dimensional stress field matrix of the surface. Step S2: Establish a stress attenuation model based on stress relaxation mechanism and self-balancing constraint. The stress attenuation model takes the two-dimensional stress field matrix of the surface as the boundary condition and derives the stress distribution benchmark value of each depth layer by solving the self-balancing equation that satisfies the zero volume integral stress. Step S3: Obtain internal sparse verification data at different depths at key locations of the component. Using the stress distribution benchmark value as a priori, the internal sparse verification data is fused using a sequential Bayesian update framework to dynamically update the posterior stress field distribution and uncertainty quantification results. Step S4: Generate virtual point cloud coordinates within the three-dimensional spatial envelope of the component. For each virtual point, interpolate the corresponding surface stress reference value through the surface two-dimensional stress field matrix. Combine the depth information of the virtual point and the posterior stress field distribution to calculate the inferred stress value of the virtual point. Step S5: Combine the virtual point cloud coordinates with the inferred stress value, and visually display the spatial distribution of residual stress in a three-dimensional graphic form through at least one of color mapping, isosurface drawing, or volume drawing; the visualization distinguishes high-confidence areas from inferred areas through transparency or color difference mapping.

2. The three-dimensional visualization and reconstruction method based on residual stress layer measurement according to claim 1, characterized in that, The discrete measurement point dataset is obtained through layer-by-layer material removal and measurement techniques, which are selected from blind hole method, contour method, layer-by-layer drilling method, X-ray diffraction method, ultrasonic critical refraction longitudinal wave method or neutron diffraction method; the number of surface measurement points is significantly greater than the number of internal sparse verification data.

3. The three-dimensional visualization and reconstruction method based on residual stress layer measurement according to claim 2, characterized in that, The spatial interpolation algorithm employs Kriging interpolation, inverse distance weighted interpolation, radial basis function interpolation, or cubic spline interpolation; the adaptive densification dynamically adjusts the node density based on the stress gradient, automatically subdividing the mesh in regions where the gradient value exceeds a preset threshold.

4. The three-dimensional visualization and reconstruction method based on residual stress layer measurement according to claim 3, characterized in that, The depth-direction stress attenuation model is expressed as follows: ； in, This represents the stress value at the corresponding position in the two-dimensional stress field matrix of the surface. This is the inherent depth decay kernel function of the material. The stress relaxation correction term caused by material removal is satisfied through iterative solution. The self-equilibrium conditions are determined.

5. The three-dimensional visualization and reconstruction method based on residual stress layer measurement according to claim 4, characterized in that, The process of iteratively solving for the stress relaxation correction term to satisfy the self-equilibrium condition includes: Based on the current layer geometry, the stress release caused by material removal is calculated using elastic or elastoplastic constitutive methods. The relaxed stress field is projected onto the self-balancing constraint space, and the force balance constraint and torque balance constraint are satisfied by least squares correction. The local relaxation step and the global projection step are executed alternately until the stress field change norm of two adjacent iterations is less than a preset threshold.

6. The three-dimensional visualization and reconstruction method based on residual stress layer measurement according to claim 5, characterized in that, The process of using a sequential Bayesian update framework to fuse the internal sparse validation data and dynamically update the posterior stress field distribution and uncertainty quantification results includes: Based on the posterior distribution of the stress field in the current layer, the prior distribution of stress in the next depth layer is predicted by a state transition model; the state transition model is determined based on the stress relaxation mechanism caused by material removal and the self-balancing constraint. Obtain the internal sparse validation data of the next depth layer, calculate the residual between the prior distribution and the internal sparse validation data, and use the Kalman gain matrix to weighted fuse the prior prediction and measured information to obtain the posterior mean and covariance matrix of the next layer. Determine whether the residual exceeds a preset anomaly threshold: if it does not exceed it, maintain the current uncertainty bandwidth and proceed to the next layer of prediction; if it exceeds it, trigger an anomaly flag, expand the current layer uncertainty bandwidth, and calculate the optimal measurement position for the next layer based on the information gain criterion.

7. The three-dimensional visualization and reconstruction method based on residual stress layer measurement according to claim 6, characterized in that, The uncertainty bandwidth is dynamically adjusted according to the characteristics of the measurement technology: surface measurement data are allocated a fixed low variance, while internal ultrasonic data are allocated a depth-correlated exponentially increasing variance.

8. The three-dimensional visualization and reconstruction method based on residual stress layer measurement according to claim 7, characterized in that, The process of step S4 includes: Within the three-dimensional spatial envelope of the component, a regular grid point cloud or a randomly distributed point cloud is generated according to a preset resolution as virtual point cloud coordinates; the virtual point cloud coordinates include the two-dimensional planar coordinates and depth coordinates of the virtual points; For each virtual point, based on its two-dimensional plane coordinates, spatial interpolation is performed using the surface two-dimensional stress field matrix to obtain the surface stress reference value corresponding to the virtual point. Based on the depth coordinates of the virtual point, the depth direction stress attenuation relationship of the corresponding depth layer is extracted from the posterior stress field distribution. The surface stress reference value is substituted into the depth direction stress attenuation relationship to calculate the depth direction extrapolated stress value of the virtual point. The uncertainty bandwidth of the corresponding depth layer is extracted from the uncertainty quantification result of the posterior stress field distribution. The inferred stress value in the depth direction is randomly perturbed with the uncertainty bandwidth as the amplitude to obtain the inferred stress value with uncertainty label. The three-dimensional spatial coordinates of all virtual points and their corresponding inferred stress values ​​are summarized to generate three-dimensional volume data with uncertainty indicators.

9. The three-dimensional visualization and reconstruction method based on residual stress layer measurement according to claim 8, characterized in that, The process of applying a random perturbation to the inferred stress value along the depth direction with the uncertainty bandwidth as the amplitude to obtain the inferred stress value with an uncertainty label includes: The relative uncertainty is obtained by calculating the ratio of the uncertainty bandwidth to the estimated stress value in the depth direction; Determine whether the relative uncertainty exceeds a preset proportional threshold: if it does not exceed the threshold, apply a first-amplitude random perturbation to the depth-direction inferred stress value; if it exceeds the threshold, apply a second-amplitude random perturbation to the depth-direction inferred stress value and mark the virtual point as a low-confidence point; the second amplitude is greater than the first amplitude. The stress value after applying random perturbation is used as the inferred stress value, and the relative uncertainty or the low confidence point is marked as the uncertainty identifier.

10. The three-dimensional visualization and reconstruction method based on residual stress layer measurement according to claim 9, characterized in that, The process of step S5 includes: The inferred stress value is mapped to a color value according to a preset color spectrum. In the color spectrum, tensile stress and compressive stress are distinguished by contrasting colors, and the absolute value of stress is represented by color saturation or brightness gradient. The confidence level of each virtual point is determined based on the uncertainty identifier. High confidence areas are rendered with a first transparency, and low confidence areas are rendered with a second transparency, where the second transparency is greater than the first transparency. Based on the virtual point cloud coordinates, the color value, and the transparency, a three-dimensional stress surface map is generated through surface rendering, or a three-dimensional stress volume map is generated through volume drawing, or an isosurface map with a specific stress level is generated through isosurface extraction. It provides a human-computer interaction interface that supports rotation, scaling, and translation of the three-dimensional graphics, supports interactive display of stress distribution on any cut surface, and supports dynamic playback of two-dimensional slices at different depths in depth order to demonstrate the stress field evolution process.

Images