A method and system for determining residual stress of a steel box girder

Abstract

The present application provides a kind of steel box girder residual stress determination method and system, it is related to box girder stress calculation technical field, the present application is grided to steel box girder, steel box girder is divided into several categories, in each category, select equal number of several grid units, and obtain the actual and simulated alternating disturbance characteristics of each grid unit;The actual residual stress of the grid unit selected in each clustering category is respectively space interpolation inversion, to obtain the corresponding residual stress distribution field, based on the simulated alternating disturbance characteristics of each grid unit, actual alternating disturbance characteristics, to determine the weight coefficient of each residual stress distribution field;Combining the residual stress distribution field of each clustering category and the corresponding weight coefficient to obtain the final residual stress of each grid unit;Through positive and negative pressure alternating disturbance response analysis to steel box girder surface grid unit, and combining regional clustering, kriging inversion and the associated influence between grids, the accurate determination of steel box girder residual stress is realized.

Description

Technical Field

[0001] This invention relates to the field of box girder stress calculation technology, specifically to a method and system for determining the residual stress of a steel box girder. Background Technology

[0002] Methods for determining the residual stress of steel box girders typically rely on interpolation or inversion using a small number of measured points to obtain the overall residual stress distribution. However, the surface structure of steel box girders is complex, with weld boundaries, U-rib boundaries, diaphragm boundaries, and junctions between different plates. The residual stress variation patterns differ in different regions. If only ordinary interpolation is performed based on the spatial location of a small number of measured points, it is easy to erroneously extend the residual stress variation pattern of one region to other regions, resulting in significant deviations in the determination of residual stress near welds, at regional boundaries, or in areas with strong local constraints.

[0003] Furthermore, in actual testing operations, due to limitations in testing conditions and site conditions, it is impossible to conduct residual stress and disturbance response measurements on all grid cells; only a small number of typical cells can be selected for fixed-point testing. Inversion solutions can be obtained by using a small number of measured cells from different categories of regions to obtain the corresponding full-area residual stress distribution results. However, due to differences in the regional attributes and data characteristics of the measured points, the fitting reliability of different inversion results varies significantly at each unmeasured grid location. Existing technologies struggle to distinguish the residual stress distribution obtained from inversions of different measured samples, and the optimal reliable result at the unmeasured grid location cannot reasonably extrapolate and propagate the verification error at the measured points to the entire unmeasured grid, ultimately limiting the accuracy of the full-field residual stress distribution calculation. The information disclosed in the background section is only for enhancing the understanding of the background of this disclosure and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0004] The purpose of this invention is to provide a method and system for determining the residual stress of steel box girders, so as to solve the problems mentioned in the background art.

[0005] To achieve the above objectives, the present invention provides the following technical solution: A method for determining the residual stress of a steel box girder, comprising the following steps: Step 1: Divide the outer surface of the steel box girder into multiple grid units, and apply alternating positive and negative pressure perturbations to the outer surface of the steel box girder to perform finite element numerical simulation. Based on the simulation results, extract the alternating perturbation characteristics simulated by each grid unit. Step 2: Extract the boundary of the outer surface of the steel box girder based on the edge extraction algorithm, and divide the steel box girder into several regions based on the boundary. Cluster all regions to obtain several cluster categories. Select a number of grid cells of equal quantity in each cluster category, measure the actual residual stress of each grid cell, and apply alternating positive and negative pressure perturbation to the outer surface of the steel box girder to obtain the actual alternating perturbation characteristics of each grid cell. Step 3: Perform spatial interpolation inversion on the actual residual stress of the selected grid cells in each cluster category to obtain the corresponding residual stress distribution field. The residual stress of any grid cell is characterized as the weighted sum of the residual stress of the corresponding grid cells in the residual stress distribution field of each cluster category. Step 4: For each residual stress distribution field corresponding to each cluster category, traverse all grid cells within it. Based on the simulated alternating perturbation characteristics and actual alternating perturbation characteristics of each grid cell, determine the stress correlation influence coefficient of each grid cell relative to the selected grid cells within the cluster category. Combine the actual residual stress and the inverted residual stress to determine the weight coefficient of the residual stress distribution field at the corresponding grid cell. Step 5: Combine the residual stress distribution field of each cluster category with the corresponding weight coefficients to obtain the final residual stress of each grid element.

[0006] Furthermore, the logic for applying alternating positive and negative pressure disturbances to the outer surface of the steel box girder for finite element numerical simulation is as follows: preset the pressure amplitude and single-segment loading duration; The load is applied to each grid cell in four time segments. A complete loading cycle consists of four equal-duration phases: the first phase is to apply a pressure load with a preset pressure amplitude along the direction perpendicular to the plane of the grid cell; the second phase is to keep the load unloaded; the third phase is to apply a tensile load with the same amplitude along the direction perpendicular to the plane of the grid cell; and the fourth phase is to keep the load unloaded again, thus forming a periodic positive and negative pressure alternating disturbance loading mode.

[0007] Furthermore, the alternating disturbance characteristics include compressive springback stiffness and compressive-tensile deformation symmetry deviation; The simulation results include the deformation of each mesh element under each loading stage, and define the inward concave deformation of the mesh element as positive and the outward convex deformation as negative. The logic for obtaining the compressive rebound deformation stiffness is as follows: calculate the sum of the deformation in the first stage and the deformation in the fourth stage, and divide the sum by the preset pressure amplitude to obtain the compressive rebound deformation stiffness. The logic for obtaining the symmetrical deviation of compression and tension deformation is as follows: calculate the square of the difference in deformation between the first stage and the fourth stage, and divide the calculation result by the square of the preset pressure amplitude to obtain the symmetrical deviation of compression and tension deformation.

[0008] Furthermore, based on the simulated alternating perturbation characteristics and the actual alternating perturbation characteristics of each grid element, the stress correlation influence coefficient of each grid element relative to the selected grid elements within the category is determined. The specific logic is as follows: Calculate the square of the norm of the actual alternating perturbation vector and the simulated alternating perturbation vector for each grid cell, and divide it by a preset alternating norm scaling factor. Construct an exponential expression with the natural constant as the base and the negative of the ratio as the power. Use the result as the alternation term. Calculate the spatial distance between each grid cell and the selected grid cells within the category. Ratio the distance value with a preset distance scaling factor. Construct an exponential term with the natural constant as the base and the negative of the ratio as the power. Use this as the distance feature term. Multiply the alternation term and the distance feature term to obtain the stress correlation influence coefficient of each grid cell relative to the selected grid cells within the category.

[0009] Furthermore, by combining the actual residual stress and the inverted residual stress, the logic for determining the weighting coefficients of the residual stress distribution at the corresponding mesh element is as follows: For any cluster category corresponding to the residual stress distribution field, the selected grid cells within that cluster category used to invert the residual stress distribution are called confidence grid cells, and the remaining grid cells within the same category that do not participate in the inversion are defined as unconfidence grid cells. Confidence grid cells are paired with any unconfidence grid cell to form an unconfidence group. For any unconfidence group, the verification residual stress error of the unconfidence grid cells is multiplied by a preset scaling factor, and then the alternation error is added. The calculation result is multiplied by the stress correlation influence coefficient corresponding to the confidence grid in that group to obtain the verification error of a single group. Furthermore, for any grid cell within the current cluster category, the validation errors of all nonconfidence groups containing that grid cell are summarized to obtain the validation error accumulation term; The stress correlation influence coefficients within the corresponding non-confidence groups are summarized synchronously to obtain the error propagation amount; the ratio of the verification error accumulation term to the error propagation amount is used to solve for the non-confidence level of the current mesh element. An exponential expression is constructed with the natural constant as the base and the negative of the confidence level as the power, to obtain the confidence term of the grid cell under the residual stress distribution field of the current cluster category; Furthermore, for any grid cell, the non-confidence terms corresponding to all cluster categories are summed and solved. The non-confidence terms corresponding to a single cluster category are compared with the sum of the non-confidence terms of all cluster categories. After normalization, the weight coefficient of the residual stress distribution field of that cluster category at the current grid cell is obtained. Specifically, the difference between the actual residual stress and the inverted residual stress of all selected mesh elements is calculated and defined as the verification residual stress error. The norm between the actual alternating perturbation vector and the simulated alternating perturbation vector of all selected mesh elements is calculated and defined as the alternation error.

[0010] Furthermore, by combining the residual stress distribution field of each cluster category and the corresponding weighting coefficients, the logic for obtaining the final residual stress of each mesh element is as follows: For any grid cell, obtain its residual stress in the residual stress distribution field corresponding to each cluster category, multiply the residual stress under each cluster category by the corresponding weight coefficient, and then perform a weighted summation. The summation result is the final residual stress of the grid cell.

[0011] This invention further provides a system for determining the residual stress of a steel box girder, the system being used to implement the aforementioned method for determining the residual stress of a steel box girder, specifically including: The alternating simulation module is used to divide the outer surface of the steel box girder into multiple grid units and apply alternating positive and negative pressure perturbations to the outer surface of the steel box girder to perform finite element numerical simulation. Based on the simulation results, the alternating perturbation characteristics simulated by each grid unit are extracted. The category analysis module is used to extract the boundary of the outer surface of the steel box girder based on the edge extraction algorithm, divide the steel box girder into several regions based on the boundary, cluster all regions to obtain several cluster categories, select a number of grid cells of equal quantity in each cluster category, measure the actual residual stress of each grid cell, and apply alternating positive and negative pressure perturbation to the outer surface of the steel box girder to obtain the actual alternating perturbation characteristics of each grid cell. The inversion representation module is used to perform spatial interpolation inversion on the actual residual stress of the selected grid cells in each cluster category to obtain the corresponding residual stress distribution field. The residual stress of any grid cell is represented as the weighted sum of the residual stress of the corresponding grid cells in the residual stress distribution field of each cluster category. The weight determination module is used to traverse all grid cells for each residual stress distribution field corresponding to each cluster category. Based on the simulated alternating perturbation characteristics and actual alternating perturbation characteristics of each grid cell, it determines the stress correlation influence coefficient of each grid cell relative to the selected grid cells within the cluster category. Combining the actual residual stress and the inverted residual stress, it determines the weight coefficient of the residual stress distribution field at the corresponding grid cell. The stress determination module combines the residual stress distribution field of each cluster category with the corresponding weighting coefficients to obtain the final residual stress of each grid cell.

[0012] Compared with the prior art, the beneficial effects of the present invention are: This invention meshes the surface of a steel box girder and combines it with finite element simulation of alternating positive and negative pressure disturbances to extract the simulated alternating disturbance characteristics of each mesh element. This allows even mesh elements that have not been actually measured to obtain characteristic information to characterize their local mechanical response. Compared to interpolating residual stress solely based on geometric distance, this invention can utilize the response differences of mesh elements under alternating positive and negative pressure disturbances to reflect their local structural characteristics, thereby providing a basis for subsequently judging the credibility of different residual stress distributions at each mesh element.

[0013] This invention also identifies the structural boundaries on the surface of the steel box girder based on an edge extraction algorithm, and then divides the steel box girder into several regions based on the boundaries and performs clustering. In each cluster region, a small number of units are selected for actual residual stress measurement and actual alternating disturbance feature acquisition. By using the measured units of each cluster region to invert the corresponding full-area residual stress distribution, the problem of insufficient coverage of local area features when inverting the whole field with only a single set of measuring points can be avoided, so that the residual stress variation law of different cluster categories can all participate in the final residual stress determination.

[0014] This invention traverses all grid cells within each residual stress distribution field corresponding to each cluster category. Based on the simulated alternating perturbation characteristics and actual alternating perturbation characteristics of each grid cell, it determines the stress correlation influence coefficient of each grid cell relative to the selected grid cells within the cluster category. Combining the actual residual stress and the inverted residual stress, it determines the weight coefficient of the residual stress distribution field at the corresponding grid cell. Therefore, the final residual stress is not simply the average of each inverted distribution, but a weighted fusion based on the local correlation influence of each inverted distribution at the corresponding grid cell. This improves the accuracy of the residual stress determination results for unmeasured grid cells and reduces the impact of cross-regional false propagation and local anomaly interpolation on the final result. Attached Figure Description

[0015] Figure 1 This is a schematic diagram of the overall method flow of the present invention; Figure 2 This is a schematic diagram of the overall system structure of the present invention. Detailed Implementation

[0016] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments.

[0017] It should be noted that, unless otherwise defined, the technical or scientific terms used in this invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0018] Example: Please see Figure 1 The present invention provides a technical solution: A method for determining the residual stress of a steel box girder, comprising the following steps: Step 1: Divide the outer surface of the steel box girder into multiple grid units, and apply alternating positive and negative pressure perturbations to the outer surface of the steel box girder to perform finite element numerical simulation. Based on the simulation results, extract the alternating perturbation characteristics simulated by each grid unit. The finite element model is an existing technology. The specific construction logic is as follows: A three-dimensional geometric model is established based on the actual structural dimensions of the steel box girder. This geometric model includes at least a top plate, bottom plate, web, diaphragms, U-ribs, and welded connection areas. The steel box girder plates are meshed, and the outer surface of the steel box girder is discretized into multiple mesh elements. Steel material parameters, including elastic modulus, Poisson's ratio, and yield strength, are assigned to the model, and corresponding displacement constraint boundary conditions are set according to the actual support state of the steel box girder. Subsequently, using the normal direction of each mesh element surface as the load direction, a periodic alternating loading condition is established for each mesh element. One loading cycle includes four consecutive stages: positive pressure loading, no-load unloading, reverse tensile loading, and another no-load unloading. The positive pressure and reverse tensile forces have the same pressure amplitude but opposite directions, and the duration of each stage is consistent. The transient finite element method is used to calculate the displacement, deformation, strain, and stress response of each mesh element under each loading stage, and the corresponding time-series response results are output as data input for subsequent alternating disturbance feature extraction and residual stress analysis.

[0019] Furthermore, the logic for applying alternating positive and negative pressure disturbances to the outer surface of the steel box girder for finite element numerical simulation is as follows: preset the pressure amplitude and single-segment loading duration; The magnitude of the pressure amplitude and the duration of single-segment loading are set according to the specific situation. Specifically, different combinations of pressure amplitude and single-segment loading duration are set and loaded. When selecting the combination of pressure amplitude and single-segment loading duration, it is necessary to ensure that the mesh elements generate obvious elastic strain so as to capture the true response characteristics of the structure in the finite element simulation. If the pressure amplitude is too small or the loading time is too short, the deformation generated is insufficient to reflect the local stiffness difference of the material and structure, resulting in the alternating disturbance characteristics not being obvious. Therefore, the combination of pressure amplitude and single-segment loading time that can generate elastic strain is selected, and the combination of pressure amplitude and single-segment loading time corresponding to the mode or upper quartile of elastic strain is selected as the control parameter for applying alternating positive and negative pressure disturbance to the outer surface of the steel box girder. The load is applied to each grid cell in four time segments. A complete loading cycle consists of four equal-duration phases: the first phase is to apply a pressure load with a preset pressure amplitude along the direction perpendicular to the plane of the grid cell; the second phase is to keep the load unloaded; the third phase is to apply a tensile load with the same amplitude along the direction perpendicular to the plane of the grid cell; and the fourth phase is to keep the load unloaded again, thus forming a periodic positive and negative pressure alternating disturbance loading mode.

[0020] The first stage of positive pressure loading is used to excite the compressive deformation characteristics of the mesh elements; the second stage of no-load state is used to reflect the rebound ability after unloading, thereby characterizing the local stiffness and energy release characteristics; the third stage applies equal amplitude reverse tensile force to obtain the tensile response corresponding to the compressive state, enabling the model to identify the asymmetric response of the structure under positive load; the fourth stage is no-load again to observe the recovery behavior after tensile unloading. The symmetrical periodic loading method of "compression-no-load-tension-no-load" can, on the one hand, eliminate the response bias caused by single-direction loading, so that the extracted features simultaneously include compressive characteristics, tensile characteristics and rebound characteristics; on the other hand, since the positive load amplitude is the same and the direction is opposite, it enhances the comparability of response differences in different residual stress regions, thereby improving the accuracy of subsequent alternating perturbation feature extraction, stress correlation analysis and residual stress inversion.

[0021] Furthermore, the alternating disturbance features include compressive rebound stiffness and compressive-tensile deformation symmetry deviation; the alternating disturbance features are used to characterize the local mechanical response capability and positive load response consistency of each grid element on the outer surface of the steel box girder under periodic alternating positive and negative pressure loading conditions.

[0022] Specifically, the finite element simulation results include deformation data of each mesh element at each loading stage. The deformation is the displacement change of the mesh element along its own surface normal direction. To unify the response characterization direction, when the mesh element undergoes concave deformation towards the inside of the steel box girder, its deformation is defined as positive; when the mesh element undergoes convex deformation away from the inside of the steel box girder, its deformation is defined as negative.

[0023] The compressive rebound stiffness is used to characterize the comprehensive recovery capability of the mesh element after pressure application and the end of a complete alternating cycle. The acquisition logic is as follows: extract the mesh element deformation at the end of the first stage of positive pressure loading and the mesh element deformation at the end of the fourth stage of no-load recovery, sum the deformation of the first stage and the deformation of the fourth stage to obtain the periodic compressive rebound deformation value; then normalize the periodic compressive rebound deformation value with the preset pressure amplitude, that is, divide it by the preset pressure amplitude to obtain the compressive rebound stiffness of the corresponding mesh element.

[0024] The reason for adopting the above calculation method is that the deformation of the first stage reflects the instantaneous deformation capacity of the mesh element under compression, while the deformation of the fourth stage reflects the final recovery state after experiencing positive pressure, unloading, reverse tension and unloading again. Considering the two together, it reflects the compression response characteristics and rebound recovery capacity of the local area. By introducing pressure amplitude normalization processing, the influence of different loading intensity conditions on the dimension and numerical range of the results is eliminated, and the comparability between different mesh elements is improved.

[0025] Furthermore, the compressive-tensile deformation symmetry deviation is used to characterize the degree of consistency of the response of mesh elements under positive pressure and in the complete cycle recovery state, and is used to identify asymmetric mechanical behavior caused by local residual stress, boundary constraints or structural inhomogeneity.

[0026] The acquisition logic is as follows: extract the mesh element deformation corresponding to the first stage and the mesh element deformation corresponding to the fourth stage, and calculate the difference between the two; then, perform a square operation on the difference to eliminate the positive and negative influences and enhance the response contribution of larger differences; finally, normalize the squared result by dividing it by the square of the preset pressure amplitude to obtain the compressive and tensile deformation symmetry deviation.

[0027] The reason for using the above calculation method is that when the mesh element exhibits a strong elastic symmetry response during the periodic alternating loading process, the difference in deformation between the first and fourth stages is small, corresponding to a low value for the symmetry deviation of compressive and tensile deformation. However, when there is residual stress concentration, differences in weld boundary constraints, or local stiffness inhomogeneity in a local area, the response of the mesh element in the positive and negative loading cycles often shows obvious asymmetry. In this case, the difference in deformation between the first and fourth stages increases, corresponding to an increase in the symmetry deviation of compressive and tensile deformation. By squaring, the regions with a greater degree of asymmetric response can be highlighted, making the obtained features more capable of identifying local abnormal mechanical states.

[0028] Therefore, by jointly constructing two alternating perturbation features—compression rebound stiffness and compressive-tensile deformation symmetry deviation—the mechanical behavior of the mesh element is characterized from two dimensions: local deformation recovery capability and positive load response consistency. This provides a basic input for subsequent correlation analysis between simulated alternating perturbation features and actual alternating perturbation features, as well as residual stress distribution inversion.

[0029] Step 2: Extract the boundary of the outer surface of the steel box girder based on the edge extraction algorithm, and divide the steel box girder into several regions based on the boundary. Cluster all regions to obtain several cluster categories. Select a number of grid cells of equal quantity in each cluster category, measure the actual residual stress of each grid cell, and apply alternating positive and negative pressure perturbation to the outer surface of the steel box girder to obtain the actual alternating perturbation characteristics of each grid cell. The surface image of the steel box girder is acquired, and the boundary of the surface image is extracted using the Sobel operator. Based on the boundary of the surface image, the steel box girder is divided into the background and several connected regions. The gray-level average, gray-level co-occurrence matrix contrast, homogeneity, and inverse moment entropy of the background and several connected regions are calculated. The K-Means algorithm is used to cluster the gray-level average, gray-level co-occurrence matrix contrast, homogeneity, and inverse moment entropy of the background and several connected regions to obtain the categories of the background and several connected regions.

[0030] Specifically, two-dimensional image data of the outer surface of the steel box girder is acquired using an industrial camera, line scan camera, or other image acquisition equipment, and the acquired steel box girder surface image is preprocessed. The preprocessing includes grayscale processing, noise filtering processing, and brightness normalization processing to reduce the impact of ambient light, surface reflection, and random noise on the accuracy of boundary recognition. Among them, grayscale processing is used to convert the color image into a single-channel grayscale image, noise filtering processing is used to reduce high-frequency noise interference, and brightness normalization processing is used to unify the grayscale distribution range of different areas.

[0031] After image preprocessing, the Sobel operator is used to extract edge features from the surface image of the steel box girder. First, horizontal and vertical gradient convolution kernels are constructed and convolution operations are performed on the preprocessed steel box girder surface image to accurately solve the gray-level gradient changes in the horizontal and vertical directions, obtaining the gradient components in both directions. Then, the horizontal and vertical gradient components are fused and synthesized, and the edge response intensity at each pixel position is calculated to accurately identify the edge features of the steel box girder surface image.

[0032] Since the weld areas, plate junction areas, U-rib boundary areas, and diaphragm connection areas on the surface of steel box girders typically exhibit significant abrupt changes in grayscale and texture variations, the high-gradient regions extracted using the Sobel operator are used as representation information of the steel box girder structural boundaries. Based on the edge response results, boundary segmentation processing is performed on the steel box girder surface image, defining the area outside the boundary as the background area, and identifying the continuously connected image areas inside the boundary as several connected regions.

[0033] The connected regions are continuous sets of pixels enclosed by boundaries, and each connected region corresponds to a local structural region, welding region, or construction feature region on the surface of the steel box girder. Grayscale features and texture features are extracted for the background region and each connected region, respectively.

[0034] Specifically, the average gray level of each region is calculated to characterize the overall brightness distribution characteristics of the region; at the same time, the gray-level co-occurrence matrix corresponding to each region is constructed, and texture statistical features are extracted based on the gray-level co-occurrence matrix.

[0035] The gray-level co-occurrence matrix is ​​used to describe the joint distribution relationship of image gray values ​​in the spatial neighborhood to reflect the texture change pattern within the region; based on the gray-level co-occurrence matrix, contrast, homogeneity, and inverse moment entropy are further calculated.

[0036] Subsequently, the K-Means clustering algorithm is used to cluster the feature vectors of the background region and each connected region. Specifically, the number of clusters is determined based on the elbow rule. The feature vectors of the background region and each connected region are used as clustering input samples. The distance relationship between each region feature vector and the cluster center is calculated iteratively, and the region with the closest distance is assigned to the corresponding category. After completing one category division, the cluster center corresponding to each category is recalculated, and the region classification and cluster center update operation is continued until the change in cluster center meets the convergence condition or reaches the preset number of iterations.

[0037] Finally, based on the clustering results, the category labels corresponding to the background region and each connected region are obtained, thereby completing the classification of different structural regions on the surface of the steel box girder.

[0038] The reason for adopting the above method is that different structural regions on the surface of steel box girders usually have different texture distributions, grayscale variations, and boundary features. For example, the weld area, base material area, reinforcing member area, and structural junction area have differences in grayscale statistical features and texture features. By combining boundary extraction, grayscale statistical feature analysis, and texture feature clustering, regions with different mechanical behavior characteristics can be effectively distinguished, thus providing a regional division basis for selecting mesh elements in each category, conducting residual stress measurement, and constructing a classified residual stress distribution field.

[0039] Step 3: Perform spatial interpolation inversion on the actual residual stress of the selected grid cells in each cluster category to obtain the corresponding residual stress distribution field. The residual stress of any grid cell is characterized as the weighted sum of the residual stress of the corresponding grid cells in the residual stress distribution field of each cluster category. For the residual stress obtained from all selected mesh elements under each category, Kriging interpolation is used to invert the residual stress of all mesh elements on the entire steel box girder surface to obtain the residual stress distribution under that category. For the actual residual stress obtained from the selected grid cells under each cluster category, spatial interpolation inversion is performed using the Kriging interpolation method to generate the residual stress distribution field covering the entire surface of the steel box girder under the corresponding category.

[0040] Specifically, for any cluster category, the corresponding actual residual stress measurement value is obtained from multiple grid cells selected within that category, and the spatial position coordinates of each selected grid cell in the steel box girder surface coordinate system are recorded. The spatial position coordinates of each selected grid cell and the corresponding residual stress value together constitute the interpolation sample set of that cluster category.

[0041] Subsequently, a spatial random field model of residual stress is established based on the interpolated sample set. Specifically, the spatial distance between grid cells is used as the independent variable, and the corresponding difference in residual stress values ​​is used as the statistical object. The semivariance function of residual stress under different spatial distance conditions is calculated to characterize the correlation law of residual stress with spatial location.

[0042] The semivariance function is used to describe the relationship between spatial location interval and residual stress fluctuation. As the spatial distance between grid cells increases, the correlation of residual stress gradually weakens, and the corresponding semivariance value gradually increases.

[0043] After obtaining the experimental semivariance distribution, a theoretical variogram model is constructed to fit the experimental semivariance function. The theoretical variogram model can be a spherical model, an exponential model, a Gaussian model, or other variogram models suitable for spatial correlation analysis, in order to obtain the correlation parameters of the spatial distribution of residual stress under the corresponding cluster category.

[0044] After completing the variogram modeling, the residual stress of all grid elements on the surface of the steel box girder is estimated using the Kriging interpolation method. Specifically, for any grid element on the surface of the steel box girder to be estimated, the spatial distance between it and each selected grid element in the current cluster category is first calculated, and the spatial correlation between the grid element to be estimated and each interpolation sample is calculated based on the established theoretical variogram model; then, the Kriging interpolation equation system is established, and the interpolation weight coefficients corresponding to each selected grid element are solved.

[0045] The interpolation weight coefficients are not directly determined by geometric distance, but are jointly determined by the spatial correlation between grid cells, so that sample cells that are closer and more correlated have a higher contribution weight to the grid cells to be estimated.

[0046] After obtaining the interpolation weight coefficients, the actual residual stress corresponding to each selected grid cell is linearly weighted and summed according to its corresponding weight to calculate the residual stress value of the grid cell to be estimated; the above calculation process is repeated for all grid cells to be estimated on the surface of the steel box girder to obtain the full surface residual stress distribution field corresponding to the current cluster category.

[0047] The formula for calculating the residual stress corresponding to each cluster category is: in, Indicates the first The first cluster category Residual stress obtained by inversion of individual grid elements; Indicates the first Within the cluster category, the first The actual residual stress of a selected mesh element; This represents the corresponding Kriging interpolation weight coefficient; Indicates the first The number of grid cells selected for interpolation calculations within each cluster category. For the index of cluster categories, , The total number of cluster categories. For the index of the grid cell, , The total number of grid cells. To select the index of the grid cell, .

[0048] The reason for using Kriging interpolation for residual stress inversion is that the residual stress on the surface of steel box girders usually exhibits significant spatial continuity and regional correlation, and the residual stress distributions in adjacent areas often show statistical correlations. Compared to ordinary distance-weighted interpolation or simple polynomial fitting methods, Kriging interpolation can not only utilize the spatial positional relationships of measurement points but also explicitly characterize the spatial correlation characteristics of residual stress through the variogram, thereby improving the accuracy of residual stress estimation results in unmeasured grid areas. Simultaneously, establishing independent residual stress distribution fields for different cluster categories avoids the cross-regional mispropagation problem caused by insufficient coverage of local features by a single set of measurement points, providing a foundation for subsequent weighted fusion of multi-category residual stress distribution fields.

[0049] For each grid cell, its residual stress is expressed as the weighted sum of the residual stresses of the corresponding grid cells in each category of residual stress distribution field.

[0050] Step 4: For each residual stress distribution field corresponding to each cluster category, traverse all grid cells within it. Based on the simulated alternating perturbation characteristics and actual alternating perturbation characteristics of each grid cell, determine the stress correlation influence coefficient of each grid cell relative to the selected grid cells within the cluster category. Combine the actual residual stress and the inverted residual stress to determine the weight coefficient of the residual stress distribution field at the corresponding grid cell. Furthermore, based on the simulated alternating perturbation characteristics and the actual alternating perturbation characteristics of each grid element, the stress correlation influence coefficient of each grid element relative to the selected grid elements within the category is determined. The specific logic is as follows: Furthermore, the compressive springback stiffness and compressive-tensile deformation symmetry deviation of each mesh element are combined to form an alternating perturbation vector; for the th The actual alternating perturbation vector of each grid cell is represented as follows: Its simulated alternating perturbation vector is expressed as: in, Indicates the first The actual alternating perturbation vector of each grid cell; Indicates the first Simulated alternating perturbation vectors for each grid cell; Indicates the first The actual compressive springback stiffness of each grid cell; Indicates the first The actual compressive and tensile deformation symmetry deviation of each grid cell; Indicates the first The compressive springback deformation stiffness simulated by a single mesh element; Indicates the first Symmetrical deviation of compressive and tensile deformation simulated by individual mesh elements.

[0051] Subsequently, the degree of deviation between the actual alternating perturbation vector and the simulated alternating perturbation vector is calculated to obtain the alternation term: in, Indicates the first Alternating terms corresponding to each grid cell; The Euclidean norm represents the difference between the actual alternating perturbation vector and the simulated alternating perturbation vector, and is used to characterize the overall degree of difference between the two. The squared value of the Euclidean norm is used to amplify the effect of large differences in response. This represents the preset alternation norm scaling factor, used to adjust the effect of alternation perturbation differences on the decay rate of alternation terms.

[0052] The preset alternation norm scaling factor The settings can be adaptively configured based on sample data. Specifically, after acquiring the actual alternating perturbation features of several grid cells and extracting the alternating perturbation features from the finite element simulation, the norm square between the actual alternating perturbation vector and the simulated alternating perturbation vector of each sample grid cell is calculated to obtain a set of alternating difference sample values. The alternating difference sample values ​​are statistically sorted, and the median or upper quartile is selected as the preset alternating norm scaling factor. The reason for adopting this setting is that the median can reflect the level of difference in the conventional alternating response of most grid cells, while the upper quartile can retain the tolerance for larger response differences. This can avoid individual abnormal grid cells causing the alternating term to decay too fast or too slow, so that the alternating term can stably characterize the consistency between the actual response and the simulated response.

[0053] The alternation term is used to characterize the consistency of the perturbation response of the grid cell. When the actual alternating perturbation characteristics are closer to the simulated alternating perturbation characteristics, the value of the alternation term is larger, indicating that the response characteristics of the grid cell are more stable and reliable. When the difference between the two is greater, the value of the alternation term is smaller, indicating that the grid cell has a large response deviation.

[0054] Further, calculate the first The grid cell and the first Within the cluster category, the first By selecting the spatial distance of each grid cell, the distance feature term is obtained: in, Indicates the first The grid cell and the first Within the cluster category, the first Select the distance feature term between grid cells; Indicates the first The grid cell and the first Within the cluster category, the first Spatial distance between selected grid cells; This represents a preset distance scale factor, used to control the effect of spatial distance on the rate of attenuation of correlation strength.

[0055] The distance feature term is used to characterize the law that the influence of residual stress decreases with increasing spatial distance. That is, the closer the spatial distance, the larger the distance feature term and the stronger the spatial correlation; the farther the spatial distance, the smaller the distance feature term and the weaker the spatial correlation.

[0056] Finally, multiplying the alternation term by the distance characteristic term yields the stress correlation influence coefficient: in, Indicates the first The grid cell relative to the first Within the cluster category, the first The stress correlation influence coefficient of each selected grid element is used. The larger the value, the closer the alternating perturbation responses of the two elements are and the stronger the spatial correlation. The smaller the value, the greater the difference in the responses of the two elements or the greater the spatial distance between them.

[0057] In this way, the stress correlation influence coefficient takes into account both the similarity of the disturbance response and the spatial proximity, so that grid cells with actual and simulated responses that are close in space have a higher degree of correlation influence, thus providing a basis for subsequent error propagation, confidence level calculation and determination of residual stress distribution weights.

[0058] The first Within a cluster category, the selected grid cells used for Kriging inversion of the residual stress distribution field are defined as confidence grid cells, and the grid cells within the same cluster category that do not participate in the inversion of the residual stress distribution field are defined as non-confidence grid cells.

[0059] For any unconfidence group consisting of confident and unconfidence mesh elements, first calculate the verification residual stress error of the unconfidence mesh elements: in, Indicates the first The residual stress distribution field corresponding to the cluster category is in the _th ... Verification residual stress error at one unbelievable mesh element; Indicates the first The actual residual stress of an unbelievable mesh element; Indicates the first The residual stress distribution field corresponding to the cluster category is in the _th ... Residual stress obtained by inversion at an unbelievable mesh element; For the index of unconfident grid cells, , To calculate the alternation error of the unconfidence grid cells, given the total number of unconfidence grid cells: in, Indicates the first Alternating errors of an unbelievable grid cell; Indicates the first The actual alternating perturbation vector of an unbelievable grid cell; Indicates the first Simulated alternating perturbation vectors for an unbelieved grid cell.

[0060] The single-group validation error corresponding to the non-confidence group is: in, Indicates the first Each cluster category consists of unbelief grid cells With confidence grid cells The single-group verification error of the nonconfidence group; This represents a preset scaling factor, used to adjust the dimensions and contribution ratio between the verification residual stress error and the alternation error. Indicates the first The unbelievable grid cell relative to the first Within the cluster category, the first The stress correlation influence coefficient of each confidence grid element. It should be noted that in this invention, the selected grid element is defined as a confidence grid element, and both share the same index.

[0061] The preset scaling factor The setting can be done using dimensional normalization, specifically by first obtaining the verification residual stress error corresponding to all mesh elements participating in the verification. and alternating error Calculate the average value of the residual stress error samples for verification. and the average value of alternating error samples Then set the preset scaling factor to: in, Indicates the preset scaling factor; This represents the average value of the alternating error samples; This represents the average value of the residual stress error samples used for verification. This represents the smallest positive number that prevents the denominator from being zero. By using the above settings, and By keeping the values ​​close to each other, the residual stress error or alternation error is avoided from having too much weight in a single set of verification errors due to differences in dimensions, thereby improving the stability of the calculation of a single set of verification errors.

[0062] The reason for constructing a single set of verification errors using the above method is that the verification residual stress error can characterize the degree of deviation between the inversion result and the actual residual stress, the alternation error can reflect the consistency between the actual mechanical response and the simulated mechanical response of the grid element, and the stress correlation influence coefficient can characterize the local mechanical similarity and spatial propagation correlation between grid elements. Therefore, by coupling the verification residual stress error, the alternation error, and the stress correlation influence coefficient, the error propagation process can simultaneously consider the inversion accuracy, the degree of response matching, and the spatial correlation law. This allows the verification information from the high-confidence region to be reasonably propagated to regions with similar mechanical behavior and strong spatial correlation, thereby improving the accuracy of subsequent confidence evaluation and determination of residual stress distribution weights.

[0063] For any grid cell within the current cluster category Summarize the individual verification errors of all nonconfidence groups containing the grid cell to obtain the verification error accumulation term: in, Indicates the first The grid cell in the first... Validation error accumulation term under each cluster category; Indicates the first All clusters containing the first cluster category The set of unbelief groups for each grid cell.

[0064] Simultaneously summarize the stress correlation influence coefficients within the corresponding unconfidence groups to obtain the error propagation amount: in, Indicates the first The grid cell in the first... Error propagation amount under each cluster category.

[0065] The ratio of the verification error accumulation term to the error propagation amount is used to obtain the first... The grid cell in the first... Confidence level of residual stress distribution in each cluster category: in, Indicates the first The grid cell in the first... Unconfidence level of residual stress distribution in each cluster category.

[0066] Furthermore, construct a nonconfidence term based on the nonconfidence level: in, Indicates the first The grid cell in the first... The uncertainty term under the residual stress distribution field of each cluster category; the smaller the uncertainty, the better. The larger the value, the more reliable the residual stress distribution field of that category is at that mesh element; the larger the degree of disbelief, the more reliable the value. The smaller the value, the lower the reliability of the residual stress distribution field of that category at that grid cell.

[0067] Finally, the nonconfidence terms corresponding to all cluster categories are normalized to obtain the first... The residual stress distribution field of the cluster category in the th... Weighting coefficients at each grid cell: in, Indicates the first The residual stress distribution field of the cluster category in the th... Weighting coefficients at each grid cell.

[0068] The technical advantages of the above approach are twofold: First, the stress correlation influence coefficient incorporates both alternating disturbance response differences and spatial distance attenuation relationships, enabling error propagation to no longer rely solely on geometric distance but to be judged in conjunction with the similarity of local mechanical responses of grid cells. Second, by constructing a confidence level using actual residual stress errors and alternating errors, the reliability of the residual stress distribution fields obtained from different clustering categories at each grid cell can be reflected. Therefore, during the final weighted fusion, residual stress distribution fields with higher confidence levels receive greater weights, while those with lower confidence levels receive smaller weights. This reduces the impact of cross-regional error propagation and local anomaly interpolation on the overall residual stress determination results, improving the accuracy and stability of the residual stress inversion results for the steel box girder surface.

[0069] Step 5: Combine the residual stress distribution field of each cluster category with the corresponding weight coefficients to obtain the final residual stress of each grid element.

[0070] Furthermore, by combining the residual stress distribution field of each cluster category and the corresponding weighting coefficients, the logic for obtaining the final residual stress of each mesh element is as follows: For any grid cell, obtain its residual stress in the residual stress distribution field corresponding to each cluster category, multiply the residual stress under each cluster category by the corresponding weight coefficient, and then perform a weighted summation. The summation result is the final residual stress of the grid cell.

[0071] This invention further provides a system for determining the residual stress of a steel box girder, the system being used to implement the aforementioned method for determining the residual stress of a steel box girder, specifically including: The alternating simulation module is used to divide the outer surface of the steel box girder into multiple grid units and apply alternating positive and negative pressure perturbations to the outer surface of the steel box girder to perform finite element numerical simulation. Based on the simulation results, the alternating perturbation characteristics simulated by each grid unit are extracted. The category analysis module is used to extract the boundary of the outer surface of the steel box girder based on the edge extraction algorithm, divide the steel box girder into several regions based on the boundary, cluster all regions to obtain several cluster categories, select a number of grid cells of equal quantity in each cluster category, measure the actual residual stress of each grid cell, and apply alternating positive and negative pressure perturbation to the outer surface of the steel box girder to obtain the actual alternating perturbation characteristics of each grid cell. The inversion representation module is used to perform spatial interpolation inversion on the actual residual stress of the selected grid cells in each cluster category to obtain the corresponding residual stress distribution field. The residual stress of any grid cell is represented as the weighted sum of the residual stress of the corresponding grid cells in the residual stress distribution field of each cluster category. The weight determination module is used to traverse all grid cells for each residual stress distribution field corresponding to each cluster category. Based on the simulated alternating perturbation characteristics and actual alternating perturbation characteristics of each grid cell, it determines the stress correlation influence coefficient of each grid cell relative to the selected grid cells within the cluster category. Combining the actual residual stress and the inverted residual stress, it determines the weight coefficient of the residual stress distribution field at the corresponding grid cell. The stress determination module combines the residual stress distribution field of each cluster category with the corresponding weighting coefficients to obtain the final residual stress of each grid cell.

[0072] The above formulas are all dimensionless calculations. The formulas are derived from software simulations based on a large amount of collected data to obtain the most recent real-world results. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.

[0073] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented in software, the above embodiments can be implemented, in whole or in part, as a computer program product. Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution.

[0074] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment, depending on actual needs.

[0075] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions that cannot be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.

Claims

1. A method for determining the residual stress of a steel box girder, characterized in that, The specific steps include: Step 1: Divide the outer surface of the steel box girder into multiple grid units, and apply alternating positive and negative pressure perturbations to the outer surface of the steel box girder to perform finite element numerical simulation. Based on the simulation results, extract the alternating perturbation characteristics simulated by each grid unit. Step 2: Extract the boundary of the outer surface of the steel box girder based on the edge extraction algorithm, and divide the steel box girder into several regions based on the boundary. Cluster all regions to obtain several cluster categories. Select a number of grid cells of equal quantity in each cluster category, measure the actual residual stress of each grid cell, and apply alternating positive and negative pressure perturbation to the outer surface of the steel box girder to obtain the actual alternating perturbation characteristics of each grid cell. Step 3: Perform spatial interpolation inversion on the actual residual stress of the selected grid cells in each cluster category to obtain the corresponding residual stress distribution field. The residual stress of any grid cell is characterized as the weighted sum of the residual stress of the corresponding grid cells in the residual stress distribution field of each cluster category. Step 4: For each residual stress distribution field corresponding to each cluster category, traverse all grid cells within it. Based on the simulated alternating perturbation characteristics and actual alternating perturbation characteristics of each grid cell, determine the stress correlation influence coefficient of each grid cell relative to the selected grid cells within the cluster category. Combine the actual residual stress and the inverted residual stress to determine the weight coefficient of the residual stress distribution field at the corresponding grid cell. Step 5: Combine the residual stress distribution field of each cluster category with the corresponding weight coefficients to obtain the final residual stress of each grid element.

2. The method for determining residual stress in a steel box girder according to claim 1, characterized in that: The logic for applying alternating positive and negative pressure disturbances to the outer surface of the steel box girder for finite element numerical simulation is as follows: preset the pressure amplitude and single-segment loading duration; The load is applied to each grid cell in four time segments. A complete loading cycle consists of four equal-duration phases: the first phase is to apply a pressure load with a preset pressure amplitude along the direction perpendicular to the plane of the grid cell; the second phase is to keep the load unloaded; the third phase is to apply a tensile load with the same amplitude along the direction perpendicular to the plane of the grid cell; and the fourth phase is to keep the load unloaded again, thus forming a periodic positive and negative pressure alternating disturbance loading mode.

3. The method for determining the residual stress of a steel box girder according to claim 2, characterized in that: The alternating disturbance characteristics include compressive rebound stiffness and compressive-tensile deformation symmetry deviation; The simulation results include the deformation of each mesh element under each loading stage, and define the inward concave deformation of the mesh element as positive and the outward convex deformation as negative. The logic for obtaining the compressive rebound deformation stiffness is as follows: calculate the sum of the deformation in the first stage and the deformation in the fourth stage, and divide the sum by the preset pressure amplitude to obtain the compressive rebound deformation stiffness. The logic for obtaining the symmetrical deviation of compression and tension deformation is as follows: calculate the square of the difference in deformation between the first stage and the fourth stage, and divide the calculation result by the square of the preset pressure amplitude to obtain the symmetrical deviation of compression and tension deformation.

4. The method for determining the residual stress of a steel box girder according to claim 3, characterized in that: Based on the simulated alternating perturbation characteristics and the actual alternating perturbation characteristics of each grid element, the stress correlation influence coefficient of each grid element relative to the selected grid elements within the category is determined. The specific logic is as follows: Calculate the square of the norm of the actual alternating perturbation vector and the simulated alternating perturbation vector for each grid cell, and divide it by a preset alternating norm scaling factor. Construct an exponential expression with the natural constant as the base and the negative of the ratio as the power. Use the result as the alternation term. Calculate the spatial distance between each grid cell and the selected grid cells within the category. Ratio the distance value with a preset distance scaling factor. Construct an exponential term with the natural constant as the base and the negative of the ratio as the power. Use this as the distance feature term. Multiply the alternation term and the distance feature term to obtain the stress correlation influence coefficient of each grid cell relative to the selected grid cells within the category.

5. The method for determining the residual stress of a steel box girder according to claim 4, characterized in that: The logic for determining the weighting coefficients of the residual stress distribution at the corresponding mesh element by combining the actual residual stress and the inverted residual stress is as follows: For any cluster category corresponding to the residual stress distribution field, the selected grid cells within that cluster category used to invert the residual stress distribution are called confident grid cells, and the remaining grid cells within the same category that did not participate in the inversion are defined as unconfident grid cells. Confident grid cells are paired with any unconfident grid cell to form an unconfident group. For any unconfident group, the verification residual stress error of the unconfident grid cells is multiplied by a preset scaling factor, and then the alternation error is added. The calculation result is then multiplied by the stress correlation influence coefficient corresponding to the confident grid cell in that group to obtain the verification error of a single group.

6. The method for determining the residual stress of a steel box girder according to claim 5, characterized in that: For any grid cell within the current cluster category, the validation errors of all nonconfidence groups containing that grid cell are summarized to obtain the validation error accumulation term; The stress correlation influence coefficients within the corresponding unconfidence groups are summarized synchronously to obtain the error propagation amount; The confidence level of the current grid cell is obtained by calculating the ratio of the verification error accumulation term to the error propagation amount. An exponential expression is constructed using the natural constant as the base and the negative of the confidence level as the power, to obtain the confidence term of the grid cell under the residual stress distribution field of the current cluster category.

7. The method for determining the residual stress of a steel box girder according to claim 6, characterized in that: For any given grid cell, the non-confidence terms corresponding to all cluster categories are summed. The non-confidence terms corresponding to a single cluster category are compared with the sum of the non-confidence terms of all cluster categories. After normalization, the weight coefficient of the residual stress distribution field of that cluster category at the current grid cell is obtained. Specifically, the difference between the actual residual stress and the inverted residual stress of all selected mesh elements is calculated and defined as the verification residual stress error. The norm between the actual alternating perturbation vector and the simulated alternating perturbation vector of all selected mesh elements is calculated and defined as the alternation error.

8. The method for determining residual stress in a steel box girder according to claim 1, characterized in that: The logic for obtaining the final residual stress of each mesh element by combining the residual stress distribution field of each cluster category and the corresponding weight coefficient is as follows: For any grid cell, obtain its residual stress in the residual stress distribution field corresponding to each cluster category, multiply the residual stress under each cluster category by the corresponding weight coefficient, and then perform a weighted summation. The summation result is the final residual stress of the grid cell.

9. A system for determining residual stress in steel box girders, characterized in that: The system is used to implement the method for determining the residual stress of a steel box girder as described in any one of claims 1-8, specifically including: The alternating simulation module is used to divide the outer surface of the steel box girder into multiple grid units and apply alternating positive and negative pressure perturbations to the outer surface of the steel box girder to perform finite element numerical simulation. Based on the simulation results, the alternating perturbation characteristics simulated by each grid unit are extracted. The category analysis module is used to extract the boundary of the outer surface of the steel box girder based on the edge extraction algorithm, divide the steel box girder into several regions based on the boundary, cluster all regions to obtain several cluster categories, select a number of grid cells of equal quantity in each cluster category, measure the actual residual stress of each grid cell, and apply alternating positive and negative pressure perturbation to the outer surface of the steel box girder to obtain the actual alternating perturbation characteristics of each grid cell. The inversion representation module is used to perform spatial interpolation inversion on the actual residual stress of the selected grid cells in each cluster category to obtain the corresponding residual stress distribution field. The residual stress of any grid cell is represented as the weighted sum of the residual stress of the corresponding grid cells in the residual stress distribution field of each cluster category. The weight determination module is used to traverse all grid cells for each residual stress distribution field corresponding to each cluster category. Based on the simulated alternating perturbation characteristics and actual alternating perturbation characteristics of each grid cell, it determines the stress correlation influence coefficient of each grid cell relative to the selected grid cells within the cluster category. Combining the actual residual stress and the inverted residual stress, it determines the weight coefficient of the residual stress distribution field at the corresponding grid cell. The stress determination module combines the residual stress distribution field of each cluster category with the corresponding weight coefficients to obtain the final residual stress of each grid cell.

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