A method for constructing a post-explosion point cloud residual deformation field of a bridge pier

Abstract

The present application belongs to the field of bridge pier explosion damage, and particularly relates to a method for constructing a point cloud residual deformation field after bridge pier explosion. The method comprises the following steps: calculating the analysis point spacing, normal vector and local shape descriptor of the point cloud before and after the bridge pier explosion; constructing the residual abnormal quantity, residual barrier passing coefficient and stable continuous domain for each point after the explosion; establishing a candidate reference set to obtain a candidate displacement; constructing a non-equilibrium probability transmission cost matrix to solve a probability transmission matrix; performing soft correction on the candidate reference point contribution of the probability transmission matrix to obtain a candidate displacement probability, and obtaining a UOT probability displacement trend of the point to be analyzed; generating a trend confidence degree for each point after the explosion, locally continuous the UOT probability displacement trend to obtain a continuous probability displacement trend field; fitting a displacement gradient in the local tangent plane of the reference configuration point; and calculating the minimum and maximum principal strain to obtain an effective strain domain. The present application reduces the amplification influence of point-to-point hard matching error in a non-uniform deformation scene on the strain result.

Description

Technical Field

[0001] This invention belongs to the field of bridge pier explosion damage, specifically relating to a method for constructing the residual deformation field of point cloud after a bridge pier explosion. Background Technology

[0002] Techniques such as 3D laser scanning, photogrammetry, and structured light can acquire 3D point clouds of bridge pier surfaces. For point clouds before and after an explosion, engineering analysis typically needs to determine where spalling or loss occurred on the bridge pier surface, where the continuous shape was maintained, and how the residual displacement and strain trends are distributed within the continuous areas.

[0003] Existing methods for detecting changes in nearest neighbor distance, point-to-surface distance, and fixed thresholds primarily rely on geometric distance. While these methods can generate distance difference maps or change zones, they are prone to misinterpreting erroneous correspondences as true sources of displacement when bridge piers are damaged by explosions, occluded, partially exposed, or have uneven point density.

[0004] ICP (Iterative Closest Point) and its variants are primarily used for rigid registration of point clouds from two phases, aiming to obtain the overall rotation and translation. When there is real residual deformation or damage in local areas, if all points are included in the registration, the exploded damage area will cause the overall transformation; if only manual thresholding is used to remove the changed areas, peeling edges, damaged rough areas, or slowly deformed areas may be mistakenly identified as stable supports. The resulting displacement difference often contains registration errors and missing values.

[0005] Voxel similarity, local feature similarity, and stable region screening methods can improve registration stability, but their main goal is still to find stable regions and complete rigid registration. They usually cannot directly generate displacement trend fields with probability confidence, nor can they pass on the uncertainty of candidate correspondences to the subsequent strain recovery process.

[0006] Strain recovery methods based on grids or regular nodes typically require explicit node correspondences or the existence of a continuous grid. However, actual bridge pier point clouds are usually unstructured scattered points, and the surface after an explosion may contain holes, spalling boundaries, noise, and non-uniform sampling. Directly differentiating the nearest neighbor displacement difference of the scattered points can easily amplify hole boundaries, fracture edges, or mismatches into abnormal strain. Summary of the Invention

[0007] The purpose of this invention is to provide a method for constructing the residual deformation field of point clouds after a bridge pier explosion. A candidate displacement probability distribution is established based on the concept of non-equilibrium optimal transport, without forcing each point to find a unique corresponding point or performing point-to-point hard matching. The candidate displacement probabilities are weighted and fused to obtain the UOT (Usage-Oriented Displacement) probabilistic displacement trend. The discrete trend is extended into a continuous probabilistic displacement trend field using stable continuous domain and connected domain constraints. Then, the reference configuration is inferred from the continuous probabilistic displacement trend field, and the principal strain is calculated in the local tangent plane using the Green-Lagrange formula from continuum mechanics. This achieves a unified recovery of the residual deformation field and principal strain field from the point clouds before and after the bridge pier explosion.

[0008] The technical solution to achieve the purpose of this invention is: a method for constructing the residual deformation field of point cloud after bridge pier explosion, comprising the following steps:

[0009] S1: Obtain the first point cloud before the bridge pier explosion. and the second point cloud after the explosion Voxel downsampling was performed on the two point clouds, the X coordinate system was transformed to the Y coordinate system, weighted rigid correction was performed using stable points, and the analysis point spacing, normal vector and local morphological descriptor of the two point clouds were calculated.

[0010] S2: Based on the missing relationships, distance differences, normal differences, point density differences, roughness changes, and feature entropy changes between the two point clouds, residual anomalies are constructed for each point in the second point cloud. Residual barrier passability coefficient and stable continuous domain ;

[0011] S3: Within a stable continuous domain, with For the point to be analyzed, a stable candidate reference point is searched in the first point cloud Y. Establish a candidate reference set and through By obtaining candidate displacements, the object of displacement inversion is expanded from a single point correspondence to a set of candidate displacements;

[0012] S4: Construct an unbalanced probability transmission cost matrix C based on the spatial topological proximity and local morphological descriptor similarity between the local neighborhood of the point to be analyzed and the candidate reference set, and solve the probability transmission matrix P using the unbalanced entropy regular probability transmission model.

[0013] S5: Utilizing the first phase of point clouds The residual barrier passage coefficients at each point are softly corrected for their contribution to the candidate reference point of the probability transfer matrix P, thus obtaining the candidate displacement probability. The candidate displacements are then subjected to probability-weighted fusion to obtain the UOT probability displacement trend of the point to be analyzed. ;

[0014] S6: Based on the effective transmission quality rate, candidate displacement probability entropy, peak probability, candidate displacement dispersion, and residual barrier passage coefficient, assess the confidence level of the generation trend of each point in the second-phase point cloud X. Furthermore, the probability displacement trend of UOT is locally continuous within the same stable continuous domain and the same connected domain to obtain the continuous probability displacement trend field. ;

[0015] S7: Using the continuous probability displacement trend field, the points in the second phase point cloud X are inversely derived as reference configuration points. And fit the displacement gradient in the local tangent plane of the reference configuration point. ;

[0016] S8: Based on the reference configuration points and displacement gradient, calculate the local principal strain according to the Green-Lagrange strain definition to obtain the minimum and maximum principal strains. The reference configuration points that satisfy the strain fitting validity criterion constitute the effective strain domain. ;

[0017] S9: Outputs the residual deformation field of the point cloud after the pier explosion, including the UOT probabilistic displacement trend, continuous probabilistic displacement trend field, trend confidence, stable continuous domain, effective strain domain, minimum principal strain, and maximum principal strain.

[0018] Compared with the prior art, the significant advantages of this invention are:

[0019] First, this invention transforms the single-corresponding-point matching in the point cloud change analysis before and after the bridge pier explosion into candidate displacement probability distribution modeling. Multiple candidate reference points are constructed in the point cloud before the explosion, and the probability contribution of each candidate displacement is obtained through non-equilibrium probability transmission, forming a probabilistic displacement trend. This reduces hard matching errors caused by local peeling, occlusion, missing points, or uneven point density.

[0020] Second, this invention introduces effective mass and candidate displacement stability constraints into the probabilistic displacement trend. When there are insufficient candidate reference points, the displacement direction and amplitude are scattered, or the displacement is located near the residual failure boundary, the effective mass decreases, the probability distribution becomes discrete, and the trend confidence is weakened accordingly. This mechanism is applicable to the edge of the bridge pier explosion damage zone, near holes, and in areas with incomplete local observations, and can avoid forcibly generating high-confidence displacements in locations lacking reliable geometric support.

[0021] Third, this invention introduces a probability concentration coefficient and a displacement dispersion suppression factor. These two factors respectively measure whether the candidate displacement probabilities are concentrated and whether the candidate displacement directions and amplitudes are consistent, so that the probability displacement trend considers not only the distance between candidate points but also the stability of the candidate displacement distribution itself.

[0022] Fourth, this invention utilizes the residual barrier passage coefficient and the co-domain propagation constraint to limit displacement propagation and strain differentiation. The residual barrier passage coefficient weakens the influence of low continuity, low reliability, and neighboring points of the damaged boundary, while the co-domain propagation constraint limits the probabilistic displacement trend to propagate only within the same stable continuous domain, thereby avoiding interpolation across spalling, hole, or damaged boundaries.

[0023] Fifth, this invention first derives the reference configuration from the continuous probability displacement trend field, then fits the local displacement gradient by combining the trend confidence and residual barrier weights, and recovers the minimum principal strain and maximum principal strain based on the Green-Lagrange strain tensor. Compared with directly differentiating the nearest neighbor displacement difference of the scattered points, this method is more in line with the strain recovery idea of ​​continuous medium, suitable for expressing the principal strain trend of the residual structure surface, and can reduce the interference of scattered point noise, mismatch and failure boundary on strain differentiation. Attached Figure Description

[0024] Figure 1 This is a flowchart of the point cloud residual deformation field construction method of the present invention.

[0025] Figure 2 This is a schematic diagram of the weighted fusion of candidate displacement probabilities.

[0026] Figure 3 This is a schematic diagram of Green-Lagrange principal strain recovery.

[0027] Figure 4 This is a schematic diagram of the output of a continuous probability displacement trend field.

[0028] Figure 5 This diagram illustrates the residual barrier passability coefficient, the stable continuous domain, and the effective strain domain.

[0029] Figure 6 The diagram shows the actual output of the residual barrier passage coefficient; where (a) is the blast-facing side and (b) is the blast-back side.

[0030] Figure 7 The actual output diagram of the continuous probability displacement trend field is shown; where (a) is the blast-facing surface and (b) is the blast-back surface.

[0031] Figure 8 The actual output diagram of trend confidence is shown; where (a) is the frontal blast face and (b) is the back blast face.

[0032] Figure 9 The actual output diagram of the main strain field is shown; where (a) is the blast-facing surface and (b) is the blast-back surface. Detailed Implementation

[0033] The present invention will now be described in further detail with reference to the accompanying drawings.

[0034] A method for constructing the residual deformation field of point cloud after a bridge pier explosion includes the following steps:

[0035] I. Point cloud input, unified coordinates and local description

[0036] Let Y be the first phase point cloud before the bridge pier explosion, and X be the second phase point cloud after the bridge pier explosion:

[0037] ,

[0038] ,

[0039] Voxel downsampling was performed on the two point clouds to transform the second point cloud to the coordinate system of the first point cloud, ensuring that both point clouds were under a unified spatial reference. To refine the registration results, points with residual damage probabilities within the 35th percentile of all point clouds, registration residual distances within the 60th percentile, and normal vector consistency above the 45th percentile were used as stable supports. A small rigid transformation matrix was calculated using weighted singular value decomposition, and this transformation was applied to the second point cloud to compensate for the traction error of the explosion damage zone on the registration. At the same time, rotation angle thresholds and translation thresholds were set to constrain the correction amplitude.

[0040] The registered point clouds from both periods are downsampled using voxels at a preset multiple of the analysis point spacing s. The analysis point spacing is then recalculated based on the downsampled point clouds to provide a unified scale basis for subsequent candidate search, residual boundary protection, displacement continuity, and strain recovery.

[0041]

[0042] Among them, NN X ( ) and NN Y ( ) represent the nearest neighbor points that are different from the corresponding points within the same point cloud. The s obtained in the above way is used to unify the candidate search radius, residual boundary protection distance, displacement continuity radius and strain neighborhood radius to the point cloud density scale, so that point clouds of different densities can use the same set of relative scale parameters.

[0043] Local geometric constraints are introduced in the candidate reference point selection and probability transfer calculation. For each point p, a neighborhood N(p) is constructed in the radius neighborhood or within the k nearest neighbors. The neighborhood covariance matrix Σ(p) is calculated, and its eigenvalues ​​are obtained. ≥ ≥ ≥0:

[0044] ,

[0045] ,

[0046] ,

[0047] ,

[0048] in, ; For local morphological descriptors, Indicates linearity, Indicates flatness, The discreteness is represented by the same definition as roughness in this invention, namely the ratio of the smallest eigenvalue of the covariance matrix to the trace. Represents feature entropy, Indicates verticality. Let p be the normal vector of point p. It is a unit vector in the vertical direction. It is a constant, with a value of 10. -12 This descriptor determines whether the local morphology of the two point clouds is similar in subsequent candidate reference point selection and UOT probability transmission, avoiding the reliance on spatial distance alone to form candidate displacements.

[0049] II. Residual Barrier Passage Coefficient and Stable Continuous Domain Construction

[0050] Points in the second phase of the point cloud after the explosion Calculate the distance anomalies relative to the first phase point cloud. Normal anomaly Point density anomaly Roughness anomaly and the probability of peeling Each outlier was normalized using percentiles to reduce the interference of point cloud noise and outliers on the estimation of residual outliers. Specifically, the 5th and 95th percentiles of each indicator were used as the lower and upper bounds of the mapping, respectively, to linearly map the median value to the [0,1] interval, and truncate any values ​​exceeding this range. The residual outlier was obtained through weighted fusion. :

[0051]

[0052] in, , , , , and The non-negative fusion weights satisfy the following conditions: + =1, The peeling probability is obtained from the missing relationship between the first phase point cloud and the second phase point cloud. The larger the value, the more likely the point is located in a peeling, damaged, occluded boundary, or discontinuous region.

[0053] This invention will reduce residual anomalies. Further converted into residual barrier passage coefficient The residual anomalies are transformed from hard-discrimination results into continuous soft weights that can be used in subsequent calculations:

[0054] ,

[0055] in, A value close to 1 indicates that the local area is more suitable as a support for continuous displacement and strain analysis; A value close to 0 indicates that the point should be weakened or eliminated. This differs from simply classifying a point as changed or unchanged. It can provide a unified continuous weight for subsequent UOT probabilistic displacement trend calculation and Green-Lagrange strain recovery.

[0056] To limit the probabilistic displacement trend to propagation only within the stable, continuous surface after the explosion, this invention is based on the peeling core region in the second-phase point cloud. Residual anomalies and residual boundary protection distance Establishing a stable continuous domain in the second phase point cloud :

[0057]

[0058] in, This represents the core area of ​​the peeling in the second phase of the point cloud. This refers to the boundary protection distance relative to the peeling core area. The residual damage threshold, This serves as the lower bound for the passability factor. This stable continuum is used to prevent displacement trends from propagating across spalling zones, void boundaries, or residual damage barriers, and serves as the effective analytical range for constructing probabilistic displacement trends and recovering principal strains. When using the lower bound for the passability factor, points within the stable continuum should also satisfy… Not less than .

[0059] Connectivity analysis is performed on both the peeling core region and the stable continuous region. Isolated connected regions with fewer than a preset threshold of points are removed to avoid a small number of outliers or noise points from damaging the integrity of the stable continuous region.

[0060] III. Construction of Candidate Displacement Sets

[0061] For stable continuous domains Any point to be analyzed within Candidate reference points are searched in the first point cloud Y to form a candidate reference set. :

[0062]

[0063]

[0064] in, As a candidate reference radius, This represents the missing probability of the first phase of candidate reference points. To stabilize the candidate threshold, These are candidate displacements. If the number of candidate reference points is insufficient, the candidate reference radius is adaptively expanded according to a preset multi-scale factor η∈{1.0,1.5,2.0,2.5,...}. This ensures that each point to be analyzed can form a valid set of candidate displacements, and the probability distribution of candidate displacements is still used as the object of displacement inversion.

[0065] Through the aforementioned candidate set, this invention transforms the "single corresponding point matching" in the two-phase point cloud change analysis into "candidate displacement set modeling," allowing each point to be analyzed to retain multiple possible reference positions, thus laying the foundation for subsequent non-equilibrium probability transmission calculation of candidate displacement probabilities.

[0066] IV. Non-equilibrium probability transport and candidate displacement probability

[0067] Treatment of analysis points and candidate reference points Construct an unbalanced probability transport cost matrix C. This cost matrix comprehensively considers local morphological descriptor similarity and spatial topological proximity.

[0068] ,

[0069] in, and These are the local morphological descriptors for the local neighborhood points of the second phase point cloud and the candidate reference points of the first phase, respectively. It is a constant, with a value of 10. -12 , and These represent the weights for local morphological descriptor similarity and spatial topological proximity, respectively. Local morphological descriptors undergo joint standardization before constructing the cost matrix. This involves merging the local morphological descriptors from the two point clouds, uniformly calculating their mean and standard deviation, and then performing zero-mean unit variance standardization on both descriptors separately to eliminate the influence of dimensional differences on the similarity measure.

[0070] This cost matrix allows candidate reference points with more similar morphology and more reasonable spatial relationships to obtain lower transmission costs. The residual barrier passage coefficient is not used as a hard threshold to forcibly delete candidates, but is used as a soft weight in probability normalization and confidence calculation to weaken the contribution of candidate points with low continuity.

[0071] The probability transfer matrix P is solved using a non-equilibrium entropy regular probability transfer model on the cost matrix C:

[0072]

[0073] Where P is the probability transfer matrix. For probability smoothing parameters, , Let be the quality relaxation parameter, and a and b be the analysis quality vectors. The purpose of quality relaxation is to allow the transmission quality to decrease when a point under analysis lacks a reliable candidate reference point, the candidate point distribution is unstable, or the candidate point is affected by residual damage, without having to forcibly match it to a certain reference point. Here, <C,P> represents the matrix inner product, KL represents the Kullback-Leibler divergence, and 1 represents a vector with all elements equal to 1.

[0074] The above unbalanced probability transfer model can be solved iteratively in the following form:

[0075]

[0076]

[0077] in, It is a constant, with a value of 10. -12 The row vectors of the unbalanced transfer matrix P need to be normalized to a probability distribution first, and then weighted normalized again by the barrier coefficient to ensure that the sum of probabilities is 1. K is the kernel matrix, and u and v are scaling vectors. The iterative solution terminates when one of the following stopping conditions is met: (1) the preset maximum number of iterations is reached; (2) the maximum change of the scaling vector in two adjacent iterations is less than the preset convergence threshold.

[0078] The probability transfer matrix P allows us to simultaneously obtain the probability contribution and transfer quality of candidate reference points, providing a basis for subsequent trend confidence calculations. `diag(·)` represents constructing a diagonal matrix using vector elements as diagonal components.

[0079] V. Weighted fusion of candidate displacement probabilities to form the UOT probabilistic displacement trend

[0080] The probability transfer matrix P is set according to the first phase candidate reference point. Residual barrier passability coefficient After correction and normalization, the candidate displacement probabilities are obtained. :

[0081]

[0082] in, These are the probability weights used for candidate displacement fusion. As the first phase of candidate reference points The residual barrier passage coefficient, It is a constant, with a value of 10. -12 , , This will weaken the contribution of residual destruction candidate points, making it less likely that candidate points with low continuity will dominate the UOT probability displacement trend, even if they are close to each other.

[0083] The probabilistic displacement trend and the effective quality rate of transmission are obtained by the following formulas:

[0084]

[0085]

[0086] in, It is not the displacement given by a single reference point, but is obtained by fusion of multiple candidate displacements in a probability-weighted manner; The lower the value, the weaker the effective candidate support for the point to be analyzed. To analyze the mass vector a and the point to be analyzed The corresponding components, It is a constant, with a value of 10. -12 .

[0087] VI. Trend Confidence and Continuous Probability Displacement Trend Field

[0088] To avoid propagating dispersed and unstable candidate displacements into the continuous field, this invention calculates probability concentration coefficients. Peak contribution coefficient and displacement discrepancy suppression factor :

[0089]

[0090]

[0091]

[0092] in, This is a newly introduced probability concentration coefficient in this invention, indicating whether the probabilities of candidate displacements are concentrated. Contribute to the largest candidate displacement; This indicates the degree of dispersion of candidate displacements around the probabilistic displacement trend of the UOT, used to suppress candidate displacement sets with excessively large differences in direction or amplitude. Based on this, the present invention integrates trend effective quality, probability concentration, peak contribution, displacement dispersion, and residual barrier into a trend confidence score. : in, The displacement discrete scale. It is a constant, with a value of 10. -12 .

[0093]

[0094] in, , , and The weight is used when the effective quality is insufficient, the candidate probability distribution is not concentrated, the candidate displacement is discrete, or the point is located in a region with strong residual barriers. The corresponding reduction is to avoid the unreliability trend being amplified in subsequent continuum and strain differentiation.

[0095] By locally continuumizing the discrete UOT probability displacement trend, we obtain the continuous probability displacement trend field u(X):

[0096]

[0097]

[0098] in, For local continuous scale; and These are points in the second phase of the point cloud. and its neighboring points The residual barrier passage coefficient, Indicates the position to be interpolated The local neighborhood within the stable continuous domain, This represents the corresponding spatial kernel weight. It is a constant, with a value of 10. -12 . This invention introduces a new continuous domain propagation indicator factor when... and The value is 1 when the data are within the same stable continuous domain and the same connected domain; otherwise, it is 0. This indicator factor ensures that the UOT probabilistic displacement trend does not cross the spalling zone, the boundary of the hole, or the residual damage barrier, and that the continuous probabilistic displacement trend field only propagates within a reliable and continuous local surface.

[0099] VII. Reference Configuration Regression and Green-Lagrange Principal Strain Recovery

[0100] The post-explosion point is extrapolated back to the reference configuration using a continuous probability displacement trend field:

[0101]

[0102] in, This is the reference configuration point derived from the continuous probability displacement trend field. This reference configuration is not directly determined through single-point correspondence, but rather derived from the UOT probability displacement trend field, and is used for subsequent strain recovery in the continuous medium.

[0103] At the reference configuration point At that point, according to the point normal direction Construct two tangential bases The normal vector at the reference configuration point is preferentially obtained by re-estimation from the inversely derived reference configuration; if estimation fails, the original normal vector from the second-phase point cloud is used. For neighborhood points k∈ Project the reference configuration coordinate difference and probability displacement difference onto the tangent plane:

[0104]

[0105]

[0106] in, and Post-explosion point and neighboring points The reference configuration point, and Post-explosion point and neighboring points The probability shift trend, Tangential projection of the reference configuration coordinate difference, This represents the tangential projection of the probability displacement difference. Differentiation within the local tangential plane avoids the instability caused by directly calculating the displacement gradient in the 3D scattered points, making it easier to stabilize and recover the tensile and compressive tendencies of the residual surface deformation. and These are mutually orthogonal unit tangent vectors.

[0107] Fitting local displacement gradients using weighted regular least squares :

[0108]

[0109]

[0110] in, = The strain fitting weights are formed by spatial distance, trend confidence, and residual barrier passage coefficient. For the weighted reference coordinate covariance matrix, The strain gradient canonical coefficient is... For two-dimensional tangential displacement gradient, Reference configuration point The strain fitting neighborhood. and Together, we ensure that low-confidence points, residual failure points, and cross-domain points do not dominate strain differentiation.

[0111] Calculate the local deformation gradient and strain tensor based on the Green-Lagrange strain definition in continuum mechanics:

[0112]

[0113]

[0114]

[0115] in, It is a two-dimensional identity matrix. The deformation gradient within the local tangent plane. For the Green-Lagrange strain tensor, and These are the minimum principal strain and the maximum principal strain, respectively. This invention outputs principal strain results to express the residual tensile or compressive trend obtained by inversely extrapolating from the UOT probability displacement trend field within a stable continuous domain. A positive maximum principal strain indicates a local tensile trend, while a negative maximum principal strain indicates a local compressive trend. Similarly, a positive minimum principal strain indicates a local tensile trend, while a negative minimum principal strain indicates a local compressive trend.

[0116] The effective strain domain consists of reference configuration points that meet the strain fitting validity criteria (the number of local neighborhood points is not less than a preset threshold, the effective fitting weight is greater than a preset threshold, and the condition number of the local weighted covariance matrix is ​​less than a preset threshold). Points that do not meet the above conditions will not have their principal strain calculation results output. The effective strain domain is the result of further filtering of the stable continuous domain, ensuring that the final output principal strain is reliable in a region with sufficient geometric support and numerical stability.

[0117] Example

[0118] This embodiment takes a reinforced concrete bridge pier explosion test as the object, and uses two sets of three-dimensional reconstructed point cloud data before and after the explosion to fully verify the effectiveness of the bridge pier residual deformation field construction method of the present invention under real explosion damage conditions.

[0119] The test bridge pier was constructed using C40 concrete, with internal reinforcement uniformly using HRB400 grade steel bars with a diameter of 8mm. The pier's cross-section was an elliptical composite shape, with an outer diameter of 105mm for the arc segment and a long side of 200mm for the straight segment. The total height of the pier was 2100mm. The explosion was an unprotected direct contact explosion, with a 1kg explosive charge applied directly to the pier surface without any buffer or protective plate. After 3D reconstruction, the original point cloud of the intact pier before the explosion contained approximately 3.93 million points, while the point cloud of the damaged pier after the explosion contained approximately 8.26 million points. This embodiment fully runs the complete algorithm flow of this invention, intuitively demonstrating the application effect of this invention in real bridge pier scenarios with spalling, holes, occlusion, non-uniform residual deformation, and differences in point cloud density.

[0120] Read the two point clouds and unify their coordinates. Input the point cloud Y before deformation and the point cloud X after deformation. Calculate the median nearest neighbor distance within the two point clouds respectively, and take the average as the analysis point spacing s. If the coordinate systems of the two point clouds are inconsistent, use FPFH-RANSAC global coarse registration, weighted SVD fine-tuning, and point-to-surface ICP fine registration to transform the second point cloud to the coordinate system of the first point cloud. In this embodiment, the FPFH voxel size can be 0.02, the FPFH feature radius can be 0.10, and the normal estimation radius can be 0.05; the number of RANSAC runs can be 3, the maximum number of iterations can be 200,000, the confidence level can be 0.999, the maximum corresponding distance can be 0.2, and the distance threshold can be 0.1; the weighted SVD coarse sampling voxel coefficient can be 2.5, the distance weight scale can be 0.02, the normal weight exponent can be 0.5, the minimum number of corresponding points can be 100; and the maximum number of ICP iterations can be 80. After registration, downsampling can be performed at 4.5s, and the distance between analysis points can be recalculated based on the downsampled point cloud. Alternatively, stable points with low residual damage probability can be used to calculate small rigid transformations through weighted SVD to compensate for the traction error of the explosion damage zone on registration.

[0121] Calculate the normal vector and local morphological descriptor. The normal estimation radius can be set to 12s, and the maximum number of nearest neighbors can be set to 80. The local morphological descriptor is constructed using 20 nearest neighbors, including discreteness, feature entropy, linearity, planarity, and perpendicularity. The two point cloud descriptors are jointly normalized to ensure that the features before and after deformation are at the same scale.

[0122] Calculate the residual anomaly. First, calculate the first-stage peeling probability based on the missing distance from the point before deformation to the point after deformation. The missing search radius can be set to 5s, the basic threshold for peeling probability can be set to 0.80, and the adaptive threshold bin number can be set to 128. Then, construct the residual anomaly based on the distance anomalies, normal anomalies, density anomalies, roughness anomalies, feature entropy anomalies, and the first-stage peeling probability of the point after deformation relative to the first-stage point cloud. The weights can be set to 0.30, 0.18, 0.12, 0.12, 0.08, and 0.20, respectively. The residual damage threshold can be set to 0.55 by default, the adaptive search range can be set to 0.35 to 0.75, and isolated noise is removed by connected component cleaning.

[0123] Generate the spalling core region, boundary protection zone, residual barrier access coefficient, and stable continuous domain. The spalling core region is jointly determined by missing support, post-explosion anomaly support, and geometric anomaly, and connected component cleanup is performed using a radius of 2.8s, with a minimum of 50 connected component points. The spalling context region is generated by expanding the spalling core region, with an expansion radius of 1.5s. The boundary protection distance can be set to 1.8s. The stable continuous domain consists of points from the non-spalling context region, the non-boundary protection zone, and points with low residual damage that belong to the effective connected domain, with a connection radius of 3.0s and a minimum of 50 connected component points. Output the residual barrier access coefficient and the stable continuous domain, whose composition relationship is as follows: Figure 5 As shown, the actual output result of the residual barrier passage coefficient is as follows: Figure 6 (a) and Figure 6 As shown in (b) of the diagram.

[0124] Construct a set of candidate displacements. For the points to be analyzed within the stable continuous domain... Search for candidate reference points from the first phase of stable candidate point cloud points. and form candidate displacements The candidate reference radius can be set to 16s; if there are insufficient candidate points, the search radius is expanded using multi-scale factors of 1.0, 1.5, 2.0, and 2.5, with a minimum target number of candidate points of 10. The first-phase stable candidate threshold can be set to 0.45. This step retains the candidate displacement set but does not output a unique corresponding point.

[0125] Solving for the unbalanced probability transfer. A cost matrix C is constructed from the local neighborhood of the point to be analyzed and the candidate reference set. The cost matrix is ​​composed of morphological descriptor similarity and spatial topological proximity. The unbalanced probability transfer matrix P is solved using an unbalanced Sinkhorn iteration. In this embodiment, the kernel matrix... and with the quality relaxation index Update the scaling vector. The probability smoothing parameter ε can be set to 0.06, the quality relaxation parameter τ can be set to 0.6, and the maximum number of iterations can be set to 25. The computation can be performed using a GPU, and the data type can be float32. In this embodiment, both the mass vector a of the point to be analyzed and the mass vector b of the candidate reference point are set to all 1s, indicating that all points to be analyzed and candidate reference points have the same initial transmission quality weights. In practical applications, this weight can be adaptively adjusted according to the point cloud density.

[0126] Calculate the probability of candidate displacements and UOT probability displacement trend For the transmission row vector corresponding to the point to be analyzed in the probability transmission matrix P, the residual barrier passage coefficient of the candidate reference point is used. After correction and normalization, the candidate displacement probabilities are obtained. Then, for the candidate displacements... Weighted summation yields the probability displacement trend of UOT. Soft weighting of candidate point barriers before the explosion. Can be limited to 1 e-6 Between 1 and 4s, the displacement variance scale can be taken as (4s). 2 . Figure 2 This is the core implementation step of forming a probabilistic displacement trend from a set of candidate displacements.

[0127] Calculate the trend confidence level The UOT layer matching confidence score is obtained by combining transmission quality, probability entropy, peak probability, and displacement variance, with weights of 0.20, 0.25, 0.25, and 0.30, respectively; transmission quality can be normalized by its ratio to 0.7. Subsequently, the UOT layer matching confidence score, local topological stability, and structural stability are fused, with weights of 0.60, 0.25, and 0.15, respectively, and the trend confidence score is obtained by combining it with the residual barrier passage coefficient of the second-phase point cloud points. Subsequently, a continuous probability displacement trend field is constructed only within the same stable continuous domain and the same connected domain. The local continuity radius can be 6s, the maximum adaptive scaling factor can be 2.0, and the minimum number of interpolation seeds can be 3. When there are insufficient seeds within the radius, 16 nearest neighbors can be used as backoff candidates within the same connected domain. The interpolation weights are composed of spatial distance weights, trend confidence, and residual barrier passage coefficients, where the spatial distance weights are in Gaussian form and the scale is half of the continuity radius. The construction process of the continuous probability displacement trend field is as follows: Figure 4 As shown, its actual output is as follows Figure 7 (a) and Figure 7 As shown in (b) above; the trend confidence output results are as follows: Figure 8 (a) and Figure 8 As shown in (b) of the diagram.

[0128] Reverse the reference configuration. According to... = The deformed points are then used to derive the reference configuration points. This reference configuration is derived from the continuous probability displacement trend field. It does not require each deformed point to have a unique historical corresponding point, thus reducing the impact of hard-matching errors on strain recovery. The process of reference configuration back-deriving and principal strain recovery is as follows: Figure 3 As shown.

[0129] Fit the local tangential displacement gradient. The strain neighborhood radius can be 10s, and the minimum number of neighborhood points can be 24. The local tangential plane normal is preferentially re-estimated from the back-reasoned reference configuration; if estimation fails, the normal of the deformed point is used. The fitting weights consist of spatial distance weights, the geometric mean of the trend confidence of the center point and neighboring points, the geometric mean of the residual barrier passage coefficient, and constraints of the same connected region. Among them, the spatial distance weights can be... Both the trend confidence level and the lower bound of the residual barrier soft weights can be set to 1. e-6 The displacement gradient regularization coefficient can be taken as 0.25. This is possible if the number of neighborhood points is insufficient, the effective weights are too small, or the local matrix condition number is greater than 1. e-8 If the strain is not found at a given point, then no principal strain will be output at that point. Reference configuration points that satisfy the above strain fitting validity criteria constitute the effective strain domain.

[0130] Calculate the Green-Lagrange principal strains. Within the local tangent plane of the reference configuration, based on the two-dimensional displacement gradient... Constructing local deformation gradient And calculate according to the aforementioned Green-Lagrange strain formula The Green-Lagrange strain tensor was obtained, and then... Find the feature values and .in, Indicates the local maximum stretching trend. This represents the local maximum compression trend. The output includes the UOT probability displacement trend, continuous probability displacement trend field, trend confidence level, exfoliation core region, boundary protection zone, stable continuous domain, effective strain domain, minimum principal strain, and maximum principal strain. The actual output of the principal strain field is as follows: Figure 9 (a) and Figure 9 As shown in (b) of the example. This embodiment also outputs the residual barrier passage coefficient, displacement amplitude, and a CSV result table containing all intermediate variables, so that engineers can perform secondary analysis.

[0131] This invention can also be implemented as a system for constructing the residual deformation field of point clouds after a bridge pier explosion. The system includes a point cloud preprocessing module, a residual barrier and stable continuum construction module, a candidate displacement set generation module, a non-equilibrium probability transmission module, a candidate displacement probability correction module, a probability displacement trend fusion module, a trend confidence calculation module, a continuous probability displacement trend field generation module, a reference configuration backpropagation module, a local tangent plane displacement gradient fitting module, a principal strain recovery module, and a result output module. Each module can be implemented using computer programs, GPU parallel computing programs, or instructions executed by a general-purpose processor.

[0132] The specific parameters of this invention can be adjusted according to point cloud density, pier scale, scanning noise, and the degree of explosion damage. For example, the candidate reference radius can be set to several times the analysis point spacing s, and the local continuity scale and strain neighborhood radius can also be proportionally set according to s; the residual damage threshold, spalling probability threshold, and lower limit of the passability coefficient can be determined using Otsu, adaptive quantiles, or engineering experience thresholds. The above parameter adjustments do not change the technical essence of this invention, which constructs the residual deformation field of the point cloud after the pier explosion through candidate displacement probability fusion, stable continuous domain constraints, and Green-Lagrange principal strain recovery.

Claims

1. A method for constructing the residual deformation field of point cloud after a bridge pier explosion, characterized in that, Includes the following steps: S1: Obtain the first point cloud before the bridge pier explosion. and the second point cloud after the explosion Voxel downsampling was performed on the two point clouds, the X coordinate system was transformed to the Y coordinate system, weighted rigid correction was performed using stable points, and the analysis point spacing, normal vector and local morphological descriptor of the two point clouds were calculated. S2: Based on the missing relationships, distance differences, normal differences, point density differences, roughness changes, and feature entropy changes between the two point clouds, residual anomalies are constructed for each point in the second point cloud. Residual barrier passability coefficient and stable continuous domain ; S3: Within a stable continuous domain, with For the point to be analyzed, a stable candidate reference point is searched in the first point cloud Y. Establish a candidate reference set and through By obtaining candidate displacements, the object of displacement inversion is expanded from a single point correspondence to a set of candidate displacements; S4: Construct an unbalanced probability transmission cost matrix C based on the spatial topological proximity and local morphological descriptor similarity between the local neighborhood of the point to be analyzed and the candidate reference set, and solve the probability transmission matrix P using the unbalanced entropy regular probability transmission model. S5: Utilizing the first phase of point clouds The residual barrier passage coefficients at each point are softly corrected for their contribution to the candidate reference point of the probability transfer matrix P, thus obtaining the candidate displacement probability. The candidate displacements are then subjected to probability-weighted fusion to obtain the UOT probability displacement trend of the point to be analyzed. ; S6: Based on the effective transmission quality rate, candidate displacement probability entropy, peak probability, candidate displacement dispersion, and residual barrier passage coefficient, assess the confidence level of the generation trend of each point in the second-phase point cloud X. Furthermore, the probability displacement trend of UOT is locally continuous within the same stable continuous domain and the same connected domain to obtain the continuous probability displacement trend field. ; S7: Using the continuous probability displacement trend field, the points in the second phase point cloud X are inversely derived as reference configuration points. And fit the displacement gradient in the local tangent plane of the reference configuration point. ; S8: Based on the reference configuration points and displacement gradient, calculate the local principal strain according to the Green-Lagrange strain definition to obtain the minimum and maximum principal strains. The reference configuration points that satisfy the strain fitting validity criterion constitute the effective strain domain. ; S9: Outputs the residual deformation field of the point cloud after the pier explosion, including the UOT probabilistic displacement trend, continuous probabilistic displacement trend field, trend confidence, stable continuous domain, effective strain domain, minimum principal strain, and maximum principal strain.

2. The method according to claim 1, characterized in that, Step S2 is as follows: For the points in the second phase of point cloud The residual anomaly quantity is obtained by weighted fusion of distance anomaly, normal anomaly, point density anomaly, roughness anomaly, feature entropy change, and peeling probability. : ， in, , , , , These are distance anomalies, normal anomalies, density anomalies, roughness anomalies, and feature entropy anomalies, respectively. This represents the points in the second phase of the point cloud. The probability of peeling off in the vicinity of the first phase point cloud is obtained by mapping the missing data relationship from the first phase point cloud to the second phase point cloud. , , , and To integrate weights, satisfy ; Residual barrier passability coefficient To follow the residual anomaly Continuous soft weights that increase and decrease, satisfying The expression is as follows: ， This indicates that the calculation result will be truncated to 0 to 1; Stable continuous domain satisfy: ， in, This represents the core area of ​​the peeling in the second phase of the point cloud. For boundary protection distance, The residual damage threshold, This is the lower limit of the passability coefficient; both the peeled core region and the stable continuous region are processed by connected component analysis, and isolated connected components with fewer than the preset threshold are removed.

3. The method according to claim 2, characterized in that, The candidate reference set established in step S3 as follows: ， in, As a candidate reference radius, This represents the missing probability of the first phase of candidate reference points. To stabilize the candidate threshold, when the number of candidate reference points is insufficient, the candidate reference radius is adaptively expanded according to the preset multi-scale factor, and the candidate displacement probability distribution is still used as the displacement inversion object.

4. The method according to claim 3, characterized in that, The unbalanced probability transport cost matrix C in step S4 is determined by at least the local morphological similarity cost and the spatial topological proximity cost, satisfying: ， in, and These are the local morphological descriptors for the local neighborhood points of the second phase point cloud and the candidate reference points of the first phase, respectively. and These are the weights for local morphological descriptor similarity and spatial topological proximity, respectively. It is a constant, with a value of 10. -12 .

5. The method according to claim 4, characterized in that, Candidate displacement probability in step S5 The row vectors in the probability transfer matrix P corresponding to the point to be analyzed and residual barrier mobility coefficient of candidate reference points Together, we determine that the following conditions must be met: ， The probability displacement trend of UOT can be obtained from the following formula: ， in and As the first phase of candidate reference points and The residual barrier passage coefficient, It is a constant, with a value of 10. -12 .

6. The method according to claim 5, characterized in that, Trend confidence in step S6 Effective quality rate based on trends Concentration coefficient Peak contribution coefficient and displacement discrepancy suppression factor The result of joint integration: ， ， ， in, The displacement discrete scale. It is a constant, with a value of 10. -12 ; ， in, , , and For weights.

7. The method according to claim 6, characterized in that, Continuous probability displacement trend field in step S6 Trend of discrete UOT probability displacement Trend confidence Residual barrier passability coefficient and co-domain propagation indicator Together, we determine that the following conditions must be met: ， ， Where k is the post-explosion point. The index of neighboring points within the local neighborhood is obtained by traversing all points in the neighborhood set that participate in the weighted calculation. For neighborhood points The discrete UOT probability displacement trend. For local continuous scale, and These are points in the second phase of the point cloud. and its neighboring points The residual barrier passage coefficient, To indicate the position to be interpolated The local neighborhood within the stable continuous domain, This represents the corresponding spatial kernel weights; It is a constant, with a value of 10. -12 Indicator of co-domain propagation exist and The value is 1 if the elements are in the same stable continuous domain and the same connected domain, otherwise it is 0.

8. The method according to claim 7, characterized in that, Fitting the displacement gradient in the local tangent plane in step S7 We obtain it from the following formula: At the reference configuration point Construct tangent basis vectors based on normal vectors: ， in Reference configuration point A set of mutually orthogonal unit tangential basis vectors in the tangential plane, both perpendicular to the plane. Surface normal vector; And order: ， ， in and Post-explosion point and neighboring points The reference configuration point, and Post-explosion point and neighboring points The probability shift trend, Tangential projection of the reference configuration coordinate difference, This is the tangential projection of the probability displacement difference; The reference configuration point is obtained by soft-weighted regularized least squares fitting. Two-dimensional tangential displacement gradient : ， in It is jointly formed by spatial distance, trend confidence, residual barrier traffic coefficient, and co-domain propagation constraints. The strain gradient canonical coefficient is... Reference configuration point The strain fitting neighborhood is given by B, which is the matrix of variables to be calculated for the two-dimensional tangential displacement gradient during the calculation process.

9. The method according to claim 8, characterized in that, The minimum and maximum principal strains of the pair in step S8 are calculated using the following formula: ， ， in The deformation gradient within the local tangent plane. For the Green-Lagrange strain tensor, It is a two-dimensional identity matrix; The minimum principal strain and the maximum principal strain are respectively The smaller and larger values ​​of the two eigenvalues.

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