A structural damage assessment method fusing point cloud information and mean square curvature

Abstract

The application discloses a kind of fusion point cloud information and structure damage assessment method of mean square curvature, it is related to building structure monitoring technical field;The method comprises the following steps: obtaining undamaged image before structure damage and damaged image with damage area after structure damage;Image data is reconstructed into three-dimensional point cloud data by applying SFM algorithm;The overall coordinate system of three-dimensional point cloud data of undamaged image and the overall coordinate system of fitting plane are aligned by applying RANSAC algorithm to obtain the best fitting plane of structure whole;Three-dimensional point cloud data of damaged image is registered with the three-dimensional point cloud data of undamaged image after alignment;Local adaptive gradient method is used to carry out quadratic surface fitting to damage area point cloud, and local best fitting surface is obtained;The mean square curvature of local best fitting surface is calculated;The mapping relationship between mean square curvature and structure stiffness is obtained by applying elasticity mechanics, and the stiffness of damage area is quantified.The application solves the technical problems of low efficiency and large error of traditional stiffness calculation method.

Description

Technical Field

[0001] This invention belongs to the field of building structure monitoring technology, and in particular relates to a structural damage assessment method that integrates point cloud information and mean square curvature. Background Technology

[0002] With the continuous development of modern buildings and bridges, ensuring their safety and stability has become a core task in design and maintenance. Traditional methods for calculating structural stiffness mainly rely on theoretical models and manual calculations. While these methods can provide a certain degree of accuracy, in complex structures and large-scale projects, relying on manual calculations and experience is often inefficient and prone to errors.

[0003] In recent years, with the advancement of computer science and data acquisition technology, the acquisition of 3D point cloud data of objects through photographs or 3D scanning technology can accurately describe the shape and details of structures. However, such point cloud data itself contains a large amount of information. How to effectively extract the local deformation information of the object's surface, establish a direct mapping relationship between deformation information and structural stiffness, and then evaluate the degree of damage to the structure is an urgent problem to be solved.

[0004] To address the problems of existing structural stiffness quantification methods and the characteristics of point cloud data, this invention provides a structural damage assessment method that integrates point cloud information and mean square curvature. This method utilizes local point cloud data of the damaged region, fits the optimal surface within the neighborhood of the damaged point cloud using a local adaptive gradient method, calculates the mean square curvature of the best-fit surface of the damaged region, and combines this with elasticity mechanics to obtain the mapping relationship between the mean square curvature and stiffness of the damaged region, thereby evaluating the degree of structural damage. This solves the technical problems of low efficiency and large errors in the traditional stiffness calculation methods mentioned above. Summary of the Invention

[0005] The purpose of this invention is to provide a structural damage assessment method that integrates point cloud information and mean square curvature, so as to solve the problems of low efficiency and large error of traditional stiffness calculation methods mentioned in the background art.

[0006] To achieve the above objectives, the present invention employs the following technical solution:

[0007] This invention proposes a structural damage assessment method that integrates point cloud information and mean square curvature, comprising the following steps:

[0008] S1. Acquire image data: Obtain undamaged images of the structure before damage and damaged images of the structure with damaged areas after damage.

[0009] S2, 3D point cloud reconstruction: The SFM algorithm is applied to reconstruct 3D point cloud data from image data;

[0010] S3, Coordinate Alignment: The RANSAC algorithm is applied to obtain the overall best fitting plane of the structure, and the three-dimensional point cloud data of the lossless image is aligned with the overall coordinate system of the fitting plane.

[0011] S4. Point cloud registration: The KD-tree-based ICP algorithm is applied to register the 3D point cloud data of the lossy image with the 3D point cloud data of the aligned lossless image.

[0012] S5. Damage Surface Fitting: The local adaptive gradient method is used to perform quadratic surface fitting on the point cloud of the damaged area to obtain the local best-fitting surface.

[0013] S6. Mean Square Curvature Calculation: Calculate the mean square curvature of the local best-fit surface;

[0014] S7. Structural stiffness quantification: Applying elasticity mechanics to obtain the mapping relationship between mean square curvature and structural stiffness, the stiffness of the damaged area is quantified.

[0015] Preferably, S1 is specifically as follows:

[0016] When acquiring damaged images of structurally damaged areas, the camera's internal parameters are calibrated, and the camera's movement trajectory is planned in advance.

[0017] Preferably, step S2 specifically includes the following steps:

[0018] S201. Use the SFM algorithm to detect key feature points in the image, and use the feature matching algorithm to match the same feature points between different images;

[0019] S202. Calculate the intrinsic and extrinsic parameters of the camera by matching feature points, and solve the camera pose by using the essential matrix and epipolar geometry.

[0020] S203. Using the camera's intrinsic and extrinsic parameters and matched feature points, the three-dimensional coordinates of each feature point are calculated through triangulation to generate sparse point cloud data.

[0021] S204. Based on sparse point clouds, multi-view stereo matching algorithm is applied in combination with camera pose to obtain structurally dense point cloud data.

[0022] Furthermore, the SOR algorithm is applied to denoise the point cloud data, and the quadratic sampling algorithm is applied to downsample the denoised point cloud data.

[0023] Preferably, step S3 is as follows:

[0024] The RANSAC algorithm is applied to obtain the best-fit plane for the overall structure. The coordinate transformation matrix of the fitting plane is extracted, and the inverse of the coordinate transformation matrix is ​​used to align the 3D point cloud data of the lossless image with the overall coordinate system.

[0025] Preferably, step S4 specifically includes the following steps:

[0026] S401. Set the initial transformation matrix and coarsely align the damaged 3D point cloud data with the undamaged 3D point cloud data.

[0027] S402. For each point in the damaged 3D point cloud data, find the point closest to it in the undamaged 3D point cloud data to form a point pair;

[0028] S403. Solve the rigid transformation of each pair of points using the least squares method, and use the rigid transformation to project the damaged 3D point cloud data onto the corresponding position of the undamaged 3D point cloud data.

[0029] Furthermore, S403 is specifically as follows:

[0030] The KD-tree ICP algorithm is used for searching, and the optimal rigid transformation is calculated based on the point pairs. The rigid transformation includes rotation matrix and translation vector. The rigid transformation is achieved by minimizing the error between the source point and the target point.

[0031] A rigid transformation is applied to the damaged point cloud to obtain the transformed point cloud, and the error between the damaged point cloud and the undamaged point cloud is calculated.

[0032] If the error is less than the preset threshold or the maximum number of iterations is reached, the registration ends; otherwise, repeat S402-S403 until the error converges or the termination condition is met.

[0033] Preferably, step S5 is as follows:

[0034] By setting the neighborhood range of each point in the point cloud of the damaged region, the local adaptive gradient method is used to fit the surface in the neighborhood of that point.

[0035] Furthermore, for the neighborhood of each point in the damaged region, assume that the coordinates of each point in the neighborhood are p(x) i ,y i ,z i ), i∈[1,n], where i represents the i-th point in the neighborhood;

[0036] Construct a local data matrix A and the corresponding vector b:

[0037]

[0038] b = (z1, z2, ..., z n ) T

[0039] The surface of the damaged region is fitted using a quadratic surface. The fitting model of the surface is as follows:

[0040] z = ax 2 +bxy+cy 2

[0041] In the formula, a, b, and c are the coefficients of the quadratic surface equation;

[0042] The parameters of the fitted model are solved using the adaptive gradient method; the optimization objective of the adaptive gradient method is to minimize the squared error between the fitted surface and the point cloud data points.

[0043]

[0044] First, initialize the parameters to constants randomly:

[0045] a = c1

[0046] b = c2

[0047] c = c3

[0048] Then calculate the gradient of the objective function.

[0049] By updating the first and second moments of a, b, and c:

[0050] The first moment is updated as follows:

[0051]

[0052] In the formula, β1 is the attenuation factor, and m t Let m be the first moment at time t. t-1 The first moment at time t-1;

[0053] The second moment is updated as follows:

[0054]

[0055] In the formula, β2 is the attenuation factor, v t Let v be the second moment at time t. t-1 Let be the second moment at time t-1;

[0056] Deviation correction:

[0057]

[0058] Update parameters a, b, and c as follows:

[0059]

[0060] In the formula, ε is a small constant, usually taking a value in the range of 10. -8 Up to 10 -4 between;

[0061] Repeat the above steps until the gradient is less than the set value;

[0062] For the solved quadratic surface, the root mean square error is used to measure the fitting effect:

[0063]

[0064] If the error is large, a new neighborhood is selected for fitting until the error is less than the specified value.

[0065] Preferably, step S6 is as follows:

[0066] First, obtain the first and second fundamental forms of the locally best-fitting surface through differential geometry. Then, use the ratio of the second fundamental form of the surface to the first fundamental form of the surface to obtain the normal curvature of any point on the surface. Calculate the maximum and minimum values ​​of the normal curvature at that point, and the square mean is the mean square curvature of that point.

[0067] Furthermore, the locally best-fit surface can be written in the form of parametric equations:

[0068]

[0069] The first and second fundamental forms of surfaces are obtained through differential geometry:

[0070] The first basic form is as follows:

[0071] I = E(du) 2 +2Fdudv+G(dv) 2

[0072] In the formula, E = r u ·r u F = r u ·r v G = r v ·r v , where r u r v Let r be the first-order partial derivative;

[0073] The second basic form is as follows:

[0074] II = L(du) 2 +2Mdudv+N(dv) 2

[0075] In the formula, L = r uu ·n, M=r uv ·n, G=r vv ·n, where r uu r uv r vv Let r be the second-order partial derivative of r, and n be the unit normal vector of the surface;

[0076] The normal curvature at any point on the surface can be obtained by using the ratio of the second fundamental form of the surface to the first fundamental form of the surface:

[0077]

[0078] Where, k n Let be the normal curvature at any point;

[0079] Calculate the maximum and minimum values ​​of the normal curvature at this point, and their squared mean is the mean square curvature at that point:

[0080]

[0081] Where k is the mean square curvature at any point.

[0082] Preferably, step S7 is as follows:

[0083] Based on the principles of elasticity, a negative correlation is found between mean square curvature and structural stiffness; high curvature regions correspond to low stiffness, and low curvature regions correspond to high stiffness.

[0084] Compared with the prior art, the beneficial effects of the present invention are:

[0085] The method in this invention acquires photos using a camera, generates three-dimensional point clouds of the structure before and after damage using motion structure recovery technology, and projects the damaged point cloud onto the undamaged point cloud using the ICP algorithm, thus realizing a comparative evaluation of the structure before and after damage. At the same time, by calculating the mean square curvature of the point cloud in the damaged area and combining it with the principles of elasticity, the mapping relationship between the mean square curvature and stiffness of the damaged area is obtained, realizing the quantification of the stiffness of the damaged area and providing a strong basis for efficiently evaluating the current load-bearing capacity of the structure. Attached Figure Description

[0086] Figure 1 This is a flowchart of the structural damage assessment method that integrates point cloud information and mean square curvature in this invention.

[0087] Figure 2 This is a non-destructive point cloud image from Embodiment 1 of the present invention;

[0088] Figure 3 The damage point cloud diagram is shown in Embodiment 1 of the present invention;

[0089] Figure 4 This is the registered point cloud image in Embodiment 1 of the present invention;

[0090] Figure 5 This is a damage assessment diagram from Embodiment 1 of the present invention. Detailed Implementation

[0091] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0092] Example 1:

[0093] This embodiment uses a square thin-plate structure as an example to illustrate the structural damage assessment method proposed in this invention, which integrates point cloud information and mean square curvature. Figure 1 As shown, in order to quantify the stiffness of the damaged area of ​​the square thin plate, the present invention mainly includes the following steps:

[0094] Step 1: Take photos of the structure before and after the damage;

[0095] In specific implementation, in step 1, a non-damaging photograph refers to a photograph of the target structure surface without any damage, while a damaged photograph is a photograph of the structure surface with cracks, dents, defects, or other damage. The photographs must meet the following conditions:

[0096] The photos should cover different perspectives of the object, and ensure that there is an overlapping area of ​​the same scene or object in at least two photos, with the overlap being 60% or more.

[0097] Feature points (such as corners, textures, etc.) in the photo should be evenly distributed, avoiding areas that are too concentrated or lack features.

[0098] During the shooting process, try to use the same focal length. Using a higher resolution camera provides more detail, which helps to extract more feature points, thereby improving the accuracy of the reconstruction results.

[0099] Avoid overexposure or low-light conditions. Ensure image sharpness and contrast by shooting in natural light whenever possible, and using appropriate artificial light sources when necessary.

[0100] Step 2: Perform 3D reconstruction;

[0101] First, based on the undamaged and damaged photos obtained in step 1, the SFM algorithm is used to detect key feature points in the images.

[0102] Then, using a feature matching algorithm, the same feature points are matched between different images.

[0103] Subsequently, the camera's intrinsic and extrinsic parameters, namely its position, orientation, and focal length, are calculated using the matched feature points. The camera's pose is then solved using the essential matrix and epipolar geometry. Using the camera's intrinsic and extrinsic parameters and the matched feature points, the 3D coordinates of each feature point are calculated via triangulation, generating a sparse point cloud.

[0104] Finally, bundle adjustment is used to globally optimize the 3D point cloud and camera pose to reduce errors and improve accuracy. Based on the sparse point cloud, dense point cloud reconstruction is further performed using multi-view stereo vision technology.

[0105] The reconstructed non-destructive point cloud is as follows Figure 2 As shown, the reconstructed damaged point cloud is as follows: Figure 3 As shown.

[0106] Step 3: Align coordinates;

[0107] In terms of specific implementation, the RANSAC algorithm is applied to fit the best plane of the structure, the coordinate transformation matrix of the fitted plane is extracted, and the inverse matrix of the coordinate transformation matrix is ​​used to align the 3D point cloud data before damage with the overall coordinate system.

[0108] Specifically, first select a set of reference planes in the point cloud generated in step 2, use the RANSAC algorithm to fit the planes to obtain the coordinate transformation matrix of the planes, obtain the inverse matrix of the coordinate transformation matrix, and then apply the obtained inverse matrix to the point cloud data before damage to align the point cloud data before damage with the overall coordinate axis.

[0109] Step 4: Register the damaged point cloud with the non-damaged point cloud;

[0110] In practice, step 4 involves registering the undamaged point cloud and the damaged point cloud to align them in the same coordinate system. Specifically, the damaged point cloud is aligned with the undamaged point cloud through a transformation.

[0111] First, coarse registration is performed between the non-destructive point cloud and the damaged point cloud.

[0112] Then, for each point in the damaged point cloud, the nearest point in the undamaged point cloud is found, and a KD-tree is used to accelerate the search of the spatial data structure. Based on the corresponding points between the damaged and undamaged point clouds, the optimal rigid transformation, including the rotation matrix and translation vector, is calculated by minimizing the error between the source and target points. This transformation matrix is ​​applied to the damaged point cloud to obtain the transformed point cloud, and the error between the damaged and undamaged point clouds is calculated.

[0113] Finally, if the error is less than a preset threshold or the maximum number of iterations is reached, the registration ends. Otherwise, repeat the above steps until the error converges or the termination condition is met.

[0114] The registered point cloud is as follows Figure 4 As shown.

[0115] Step 5: Local surface fitting;

[0116] In specific implementation, in step 5, local surface fitting is performed on the registered damage point cloud data. For the neighborhood of each point in the damage region, it is assumed that the coordinates of each point in the neighborhood are p(x) i ,y i ,z i ), i∈[1,n], where i represents the i-th point in the neighborhood.

[0117] Construct a local data matrix A and the corresponding vector b:

[0118]

[0119] b = (z1, z2, ..., z n ) T

[0120] The damaged region is fitted with a quadratic surface, which takes the following form:

[0121] z = ax 2 +bxy+cy 2

[0122] In the formula, a, b, and c are the coefficients of the quadratic surface equation;

[0123] The adaptive gradient method is used to solve for the parameters of the fitted model. The optimization objective of the adaptive gradient method is to minimize the squared error between the fitted surface and the point cloud data points.

[0124]

[0125] First, initialize the parameters to constants randomly:

[0126] a = c1

[0127] b = c2

[0128] c = c3

[0129] Calculate the gradient of the objective function

[0130] By updating the first and second moments of a, b, and c:

[0131] The first moment is updated as follows:

[0132]

[0133] In the formula, β1 is the attenuation factor, and m t Let m be the first moment at time t.t-1 The first moment at time t-1;

[0134] The second moment is updated as follows:

[0135]

[0136] In the formula, β2 is the attenuation factor, v t Let v be the second moment at time t. t-1 Let be the second moment at time t-1;

[0137] Deviation correction:

[0138]

[0139] Update parameters a, b, and c as follows:

[0140]

[0141] In the formula, ε is a small constant, usually taking a value in the range of 10. -8 Up to 10 -4 between;

[0142] Repeat the above steps until the gradient is less than the set value.

[0143] For the solved quadratic surface, the root mean square error (RMSE) is used to measure the fitting effect:

[0144]

[0145] If the error is large, a new neighborhood is selected for fitting until the error is less than the specified value.

[0146] Step 6: Calculate the mean square curvature;

[0147] In specific implementation, in step 6, the surface from step 5 is written in the form of parametric equations:

[0148]

[0149] The first and second fundamental forms of the surface in step 5 are obtained through differential geometry:

[0150] The first basic form is as follows:

[0151] I = E(du) 2 +2Fdudv+G(dv) 2

[0152] In the formula, E = r u ·r u F = r u ·r v G = r v·r v , where r u r v Let r be the first-order partial derivative;

[0153] The second basic form is as follows:

[0154] II = L(du) 2 +2Mdudv+N(dv) 2

[0155] In the formula, L = r uu ·n, M=r uv ·n, G=r vv ·n, where r uu r uv r vv Let r be the second-order partial derivative of r, and n be the unit normal vector of the surface;

[0156] The normal curvature at any point on the surface can be obtained by using the ratio of the second fundamental form of the surface to the first fundamental form of the surface:

[0157]

[0158] Then calculate the maximum and minimum values ​​of the normal curvature at that point, and their squared mean is the mean square curvature at that point:

[0159]

[0160] Step 7: Rigid quantization;

[0161] In specific implementation, in step 7, the surface stiffness of the object is further quantified based on the mean square curvature calculated in step 6.

[0162] Based on the principles of elasticity, a negative correlation exists between curvature and stiffness; high curvature regions correspond to lower stiffness, while low curvature regions correspond to higher stiffness. By analyzing the distribution of the mean square curvature of the damaged region, the stiffness characteristics of the damaged region can be evaluated, thereby obtaining the overall load-bearing capacity of the structure. Finally, the structural damage obtained using the method of this invention is as follows: Figure 5 As shown.

[0163] The above description is only for the purpose of helping to understand the method and core essence of the present invention, but the scope of protection of the present invention is not limited thereto. For those skilled in the art, any equivalent substitutions or modifications made to the technical solution and inventive concept disclosed in the present invention within the scope of the technology disclosed in the present invention should be covered within the scope of protection of the present invention. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A structural damage assessment method integrating point cloud information and mean square curvature, characterized in that, Includes the following steps: S1. Acquire image data: Obtain undamaged images of the structure before damage and damaged images of the structure with damaged areas after damage. S2, 3D point cloud reconstruction: The SFM algorithm is applied to reconstruct 3D point cloud data from image data; S3, Coordinate Alignment: The RANSAC algorithm is applied to obtain the overall best fitting plane of the structure, and the three-dimensional point cloud data of the lossless image is aligned with the overall coordinate system of the fitting plane. S4. Point cloud registration: The KD-tree-based ICP algorithm is applied to register the 3D point cloud data of the lossy image with the 3D point cloud data of the aligned lossless image. S5. Damage Surface Fitting: The local adaptive gradient method is used to perform quadratic surface fitting on the point cloud of the damaged area to obtain the local best-fitting surface. S6. Mean Square Curvature Calculation: Calculate the mean square curvature of the local best-fit surface; S7. Structural stiffness quantification: Applying elasticity mechanics to obtain the mapping relationship between mean square curvature and structural stiffness, the stiffness of the damaged area is quantified.

2. The structural damage assessment method integrating point cloud information and mean square curvature according to claim 1, characterized in that, S1 is specifically as follows: When acquiring damaged images of structurally damaged areas, the camera's internal parameters are calibrated, and the camera's movement trajectory is planned in advance.

3. The structural damage assessment method integrating point cloud information and mean square curvature according to claim 2, characterized in that, S2 specifically includes the following steps: S201. Use the SFM algorithm to detect key feature points in the image, and use the feature matching algorithm to match the same feature points between different images; S202. Calculate the intrinsic and extrinsic parameters of the camera by matching feature points, and solve the camera pose by using the essential matrix and epipolar geometry. S203. Using the camera's intrinsic and extrinsic parameters and matched feature points, the three-dimensional coordinates of each feature point are calculated through triangulation to generate sparse point cloud data. S204. Based on sparse point clouds, multi-view stereo matching algorithm is applied in combination with camera pose to obtain structurally dense point cloud data.

4. The structural damage assessment method integrating point cloud information and mean square curvature according to claim 3, characterized in that, S3 is specifically as follows: The RANSAC algorithm is applied to obtain the best-fit plane for the overall structure. The coordinate transformation matrix of the fitting plane is extracted, and the inverse of the coordinate transformation matrix is ​​used to align the 3D point cloud data of the lossless image with the overall coordinate system.

5. The structural damage assessment method integrating point cloud information and mean square curvature according to claim 4, characterized in that, S4 specifically includes the following steps: S401. Set the initial transformation matrix and coarsely align the damaged 3D point cloud data with the undamaged 3D point cloud data. S402. For each point in the damaged 3D point cloud data, find the point closest to it in the undamaged 3D point cloud data to form a point pair; S403. Solve the rigid transformation of each pair of points using the least squares method, and use the rigid transformation to project the damaged 3D point cloud data onto the corresponding position of the undamaged 3D point cloud data.

6. The structural damage assessment method integrating point cloud information and mean square curvature according to claim 5, characterized in that, S403 is specifically as follows: The KD-tree ICP algorithm is used for searching, and the optimal rigid transformation is calculated based on the point pairs. The rigid transformation includes rotation matrix and translation vector. The rigid transformation is achieved by minimizing the error between the source point and the target point. A rigid transformation is applied to the damaged point cloud to obtain the transformed point cloud, and the error between the damaged point cloud and the undamaged point cloud is calculated. If the error is less than the preset threshold or the maximum number of iterations is reached, the registration ends. Otherwise, repeat S402-S403 until the error converges or the termination condition is met.

7. A structural damage assessment method that integrates point cloud information and mean square curvature according to claim 1 or 6, characterized in that, S5 is specifically as follows: By setting the neighborhood range of each point in the point cloud of the damaged region, the local adaptive gradient method is used to fit the surface in the neighborhood of that point.

8. The structural damage assessment method fusing point cloud information and mean square curvature according to claim 7, characterized in that, For the neighborhood of each point in the damaged region, assume the coordinates of each point in the neighborhood are p(x) i ,y i ,z i ), i∈[1,n], where i represents the i-th point in the neighborhood; Construct a local data matrix A and the corresponding vector b: b=(z1,z2,…,z n ) T The surface of the damaged region is fitted using a quadratic surface. The fitting model of the surface is as follows: z=ax 2 +bxy+cy 2 In the formula, a, b, and c are the coefficients of the quadratic surface equation; The parameters of the fitted model are solved using the adaptive gradient method; the optimization objective of the adaptive gradient method is to minimize the squared error between the fitted surface and the point cloud data points. First, initialize the parameters to constants randomly: a = c1 b = c2 c = c3 Then calculate the gradient of the objective function. By updating the first and second moments of a, b, and c: The first moment is updated as follows: In the formula, β1 is the attenuation factor, and m t Let m be the first moment at time t. t-1 The first moment at time t-1; The second moment is updated as follows: In the formula, β2 is the attenuation factor, v t Let v be the second moment at time t. t-1 Let be the second moment at time t-1; Deviation correction: Update parameters a, b, and c as follows: In the formula, ε is a small constant with a value between 10 and 10. -8 Up to 10 -4 between; Repeat the above steps until the gradient is less than the set value; For the solved quadratic surface, the root mean square error is used to measure the fitting effect: If the error is large, a new neighborhood is selected for fitting until the error is less than the specified value.

9. The structural damage assessment method integrating point cloud information and mean square curvature according to claim 8, characterized in that, S6 is specifically as follows: First, obtain the first and second fundamental forms of the locally best-fitting surface through differential geometry. Then, use the ratio of the second fundamental form of the surface to the first fundamental form of the surface to obtain the normal curvature of any point on the surface. Calculate the maximum and minimum values ​​of the normal curvature at that point, and the square mean is the mean square curvature of that point.

10. The structural damage assessment method integrating point cloud information and mean square curvature according to claim 9, characterized in that, The local best-fit surface can be expressed in the form of parametric equations: The first and second fundamental forms of surfaces are obtained through differential geometry: The first basic form is as follows: I=E(you) 2 +2Fdudv+G(dv) 2 In the formula, E = r u ·r u F = r u ·r v G = r v ·r v , where r u r v Let r be the first-order partial derivative; The second basic form is as follows: II=L(black) 2 +2Mdudv+N(dv) 2 In the formula, L = r uu ·n, M=r uv ·n, G=r vv ·n, where r uu r uv r vv Let r be the second-order partial derivative of r, and n be the unit normal vector of the surface; The normal curvature at any point on the surface can be obtained by using the ratio of the second fundamental form of the surface to the first fundamental form of the surface: Where, k n Let be the normal curvature at any point; Calculate the maximum and minimum values ​​of the normal curvature at this point, and their squared mean is the mean square curvature at that point: Where k is the mean square curvature at any point.

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