A method and system for progressive expansion modeling of internal road cracks based on single-trajectory guidance

Abstract

This invention provides a method and system for progressively expanding road internal cracks based on single-trajectory guidance, relating to the field of road engineering technology. Within a predefined three-dimensional road space, a crack curve A is generated based on a constrained randomization method. Based on key points on curve A, and combined with the top and bottom boundaries of the road, a crack curve B is generated. Using curves A and B as boundaries, a bicubic B-spline surface algorithm is employed to perform surface patching operations between them, generating a three-dimensional crack surface model. The three-dimensional crack surface model undergoes morphological refinement to simulate the surface irregularities and branching expansion behavior of real cracks. This achieves the technical effect of rapidly generating realistic three-dimensional crack models that conform to physical laws.

Description

Technical Field

[0001] This application relates to the field of road engineering technology, and in particular to a method and system for progressive expansion modeling of internal road cracks based on single-trajectory guidance. Background Technology

[0002] With the rapid development of transportation infrastructure, the importance of road maintenance and inspection technologies is becoming increasingly prominent. Road cracks, as the most common type of pavement distress, require accurate modeling for significant purposes in road condition assessment and maintenance decision-making. Currently, road crack modeling primarily utilizes manual measurement and simplified geometric modeling methods, which suffer from low efficiency and poor realism. In existing technological systems, image recognition-based crack detection methods can only acquire two-dimensional surface information, lacking three-dimensional depth features; while traditional three-dimensional modeling methods often use regular geometric shapes to simulate cracks, failing to reflect the irregularity and complexity of real cracks. In practical applications of road maintenance, there is an urgent need for a method that can quickly generate realistic three-dimensional crack models that conform to physical laws. Summary of the Invention

[0003] To quickly generate realistic 3D crack models that conform to physical laws, this application provides a method and system for progressive expansion modeling of internal road cracks based on single-trajectory guidance.

[0004] Firstly, the method for progressive expansion modeling of internal road cracks based on single-trajectory guidance provided in this application adopts the following technical solution:

[0005] A method for progressive expansion modeling of internal road cracks based on single-trajectory guidance includes:

[0006] Within a predefined three-dimensional road space, a smooth and continuous A-curve representing the crack surface path is generated based on a constrained randomization method.

[0007] Based on the key points on the A curve, and combined with the top and bottom boundaries of the road, a smooth and continuous B curve representing the path of the crack in the depth direction is generated.

[0008] Using curves A and B as boundaries, a bicubic B-spline surface algorithm is used to perform surface patching operations between them to generate a three-dimensional crack surface model.

[0009] The three-dimensional crack surface model is subjected to morphological refinement to simulate the surface irregularities and branching behavior of real cracks.

[0010] Optionally, the step of generating a smooth, continuous A-curve representing the crack surface path based on a constrained randomization method includes:

[0011] Within the three-dimensional space of the road, an initial point M and an end point N are randomly selected, wherein the distance between point M and point N satisfies a preset minimum relative distance threshold and a preset maximum relative distance threshold.

[0012] Divide the straight line connecting point M and point N into segments to obtain multiple segmentation points;

[0013] For each segment point, a key point is randomly selected within a spherical neighborhood with a preset radius.

[0014] Using the initial point M, the endpoint N, and all randomly selected key points as control points, the smooth and continuous A curve is generated using the B-spline interpolation algorithm.

[0015] Optionally, the step of generating a smooth, continuous B-curve representing the path of the crack in the depth direction based on key points on the A-curve and in combination with the top and bottom boundaries of the road includes:

[0016] For each key point on curve A, its extended coordinates in the Z-axis direction are calculated based on its Z-coordinate, the top boundary of the road, the bottom boundary of the road, and the preset extension distance, to obtain a temporary key point.

[0017] Using the X and Y coordinates of each temporary key point as the center, randomly select a point within the neighborhood of the disk with a preset radius as the key point of the B curve;

[0018] Using all key points of the B-curve as control points, the smooth and continuous B-curve is generated using the B-spline interpolation algorithm.

[0019] Optionally, the B-spline interpolation algorithm includes:

[0020] The input keypoint sequence is parameterized by cumulative chord length to obtain the parameter value corresponding to each keypoint.

[0021] For each component of the three-dimensional coordinates, construct a piecewise cubic spline function that passes through the coordinates of all corresponding key points;

[0022] For each piecewise cubic spline function, apply interpolation conditions, function values ​​at the piecewise connection points, continuity conditions for the first and second derivatives, and natural boundary conditions.

[0023] Solve the system of linear equations formed by the above conditions to obtain spline coefficients, thereby generating a smooth three-dimensional parametric curve.

[0024] Optionally, the bicubic B-spline surface algorithm includes:

[0025] Parameterize and resample curves A and B respectively to obtain two smooth parameterized boundary curves;

[0026] Define a two-dimensional parameter space, where the first parameter Along the direction of the boundary curve, the second parameter This represents the interpolation weights between the two boundary curves;

[0027] Using the bilinear interpolation formula, based on the parameters Calculate the coordinates of a point on the surface;

[0028] The parameter space is uniformly discretized and sampled to generate regular mesh vertices;

[0029] Connect the vertices of the mesh to form triangular patches, creating a continuous triangular mesh surface.

[0030] Optionally, the fractal noise propagation in the morphology refinement process includes:

[0031] Calculate the normal vectors at the vertices of the surface and generate the fractal displacement field using a three-dimensional Perlin noise function;

[0032] The vertex position is adjusted using the vertex position update formula.

[0033] Optionally, the method further includes a result verification step:

[0034] The generated 3D crack model was compared and analyzed with the real crack point cloud data;

[0035] Calculate the Hausdorff distance and surface deviation values, and determine whether the model is qualified based on the calculation results;

[0036] Output an inspection report containing statistical information on crack length, width, and depth.

[0037] Secondly, this application provides a progressive expansion modeling system for internal road cracks based on single-trajectory guidance, comprising:

[0038] The A-curve generation module is used to generate a smooth and continuous A-curve representing the crack surface path within a predefined three-dimensional road space based on a constrained randomization method.

[0039] The B-curve generation module is used to generate a smooth and continuous B-curve representing the path of the crack in the depth direction based on the key points on the A-curve and the top and bottom boundaries of the road.

[0040] The three-dimensional surface generation module is used to generate a three-dimensional crack surface model by using the A curve and the B curve as boundaries and employing a bicubic B-spline surface algorithm to perform surface patching operations between the two curves.

[0041] The output module is used to refine the morphology of the three-dimensional crack surface model to simulate the surface irregularities and branching behavior of real cracks.

[0042] Thirdly, this application provides a computer device, the device comprising: a memory and a processor, wherein the processor, when executing computer instructions stored in the memory, performs the method described above.

[0043] Fourthly, this application provides a computer-readable storage medium including instructions that, when executed on a computer, cause the computer to perform the method described above.

[0044] In summary, this application generates a crack curve A within a predefined three-dimensional road space based on a constrained randomization method; based on key points on curve A, combined with the top and bottom boundaries of the road, a crack curve B is generated; using curves A and B as boundaries, a bicubic B-spline surface algorithm is employed to perform surface patching operations between them, generating a three-dimensional crack surface model; the three-dimensional crack surface model undergoes morphological refinement to simulate the surface irregularities and branching behavior of real cracks. This achieves the technical effect of rapidly generating realistic three-dimensional crack models that conform to physical laws. Attached Figure Description

[0045] Figure 1 This is a schematic diagram of the computer device structure of the hardware operating environment involved in the embodiments of this application;

[0046] Figure 2 This is a flowchart illustrating the first embodiment of the single-trajectory-guided progressive expansion modeling method for internal road cracks in this application;

[0047] Figure 3 This is a surface rendering of the first embodiment of the single-track guided progressive expansion modeling method for internal road cracks in this application;

[0048] Figure 4 This is a diagram illustrating the natural expansion behavior of cracks in the first embodiment of the single-track guided progressive expansion modeling method for internal road cracks in this application.

[0049] Figure 5 This is a structural block diagram of the first embodiment of the single-track guided progressive expansion modeling system for internal road cracks in this application. Detailed Implementation

[0050] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0051] Reference Figure 1 , Figure 1 This is a schematic diagram of the computer device structure of the hardware operating environment involved in the embodiments of this application.

[0052] like Figure 1 As shown, the computer device may include: a processor 1001, such as a central processing unit (CPU), a communication bus 1002, a user interface 1003, a network interface 1004, and a memory 1005. The communication bus 1002 is used to enable communication between these components. The user interface 1003 may include a display screen or an input unit such as a keyboard; optionally, the user interface 1003 may also include a standard wired interface or a wireless interface. The network interface 1004 may optionally include a standard wired interface or a wireless interface (such as a Wireless-Fidelity (Wi-Fi) interface). The memory 1005 may be high-speed random access memory (RAM) or stable non-volatile memory (NVM), such as a disk drive. The memory 1005 may also optionally be a storage device independent of the aforementioned processor 1001.

[0053] Those skilled in the art will understand that Figure 1 The structure shown does not constitute a limitation on the computer device and may include more or fewer components than shown, or combine certain components, or have different component arrangements.

[0054] like Figure 1 As shown, the memory 1005, which serves as a storage medium, may include an operating system, a network communication module, a user interface module, and a progressive expansion modeling program for internal road cracks based on single-track guidance.

[0055] exist Figure 1 In the computer device shown, the network interface 1004 is mainly used for data communication with the network server; the user interface 1003 is mainly used for data interaction with the user; the processor 1001 and the memory 1005 in this application can be set in the computer device. The computer device calls the road internal crack progressive expansion modeling program based on single trajectory guidance stored in the memory 1005 through the processor 1001, and executes the road internal crack progressive expansion modeling method based on single trajectory guidance provided in the embodiment of this application.

[0056] This application provides a method for progressive expansion modeling of internal road cracks based on single-trajectory guidance, referring to... Figure 2 , Figure 2 This is a flowchart illustrating the first embodiment of the single-trajectory-guided progressive expansion modeling method for internal road cracks in this application.

[0057] In this embodiment, the method for progressively expanding road internal cracks based on single-trajectory guidance includes the following steps:

[0058] Step S10: In the predefined three-dimensional space of the road, generate a smooth and continuous A curve representing the crack surface path based on the constraint randomization method.

[0059] It should be noted that the terminology used in this embodiment includes:

[0060] B-spline interpolation is a mathematical method that uses a smooth curve to precisely pass through a series of given control points. It generates the curve in segments, each controlled by only a few nearby points. Therefore, adjusting a single point only affects a local area of ​​the curve without altering its overall shape. This method produces very smooth and controllable curves.

[0061] Bicubic B-spline surface algorithm: a method that uses a control point mesh to generate an extremely smooth surface.

[0062] Bicubic refers to its two parameter directions ( and On the surface, each small section is determined by an array of local control points, and each direction is blended using a cubic (third-order) B-spline function. The cubic nature ensures the smoothness of the surface. (Continuity, i.e., curvature continuity); the final surface is a complete surface formed by the smooth splicing of these local small pieces.

[0063] Bilinear interpolation surfaces: This is a simple method for generating surfaces on a regular quadrilateral mesh. Given four corner points, it calculates the value or position of any point inside the mesh by performing two linear interpolations. The result is a smoothly transitioning saddle-shaped surface. Linear interpolation is an estimation method that makes a "straight line connection" between two known points. Surface discretization is the process of converting a continuous mathematical surface (such as the bilinear interpolation surface above) into a mesh composed of a large number of simple geometric elements (usually triangles or quadrilaterals). This process is like tiling a smooth mural with many small mosaic tiles. The discretized polygonal mesh is a standard format that computer graphics hardware can directly understand and render.

[0064] It should be noted that, within the three-dimensional space of the road, an initial point M and an end point N are randomly selected, wherein the distance between point M and point N satisfies the preset minimum relative distance threshold and maximum relative distance threshold; the straight line connecting point M and point N is segmented to obtain multiple segment points; a key point is randomly selected in a spherical neighborhood with a preset radius centered on each segment point; the initial point M, the end point N, and all randomly selected key points are used as control points, and the smooth and continuous A curve is generated using the B-spline interpolation algorithm.

[0065] It is understood that the step of generating a smooth and continuous B-curve representing the path of the crack in the depth direction based on the key points on the A-curve and the top and bottom boundaries of the road includes: for each key point on the A-curve, calculating its extension coordinates in the Z-axis direction based on its Z-coordinate, the top boundary of the road, the bottom boundary of the road, and a preset extension distance to obtain a temporary key point; randomly selecting a point in the neighborhood of a disk with a preset radius centered on the X and Y coordinates of each temporary key point as the key point of the B-curve; and using all the key points of the B-curve as control points, generating the smooth and continuous B-curve using the B-spline interpolation algorithm.

[0066] It is understandable that the B-spline interpolation algorithm includes:

[0067] The input keypoint sequence is parameterized by cumulative chord length to obtain the parameter value corresponding to each keypoint. For each component of the 3D coordinates, a piecewise cubic spline function passing through the coordinates of all corresponding keypoints is constructed. Interpolation conditions, function values ​​at the piecewise connection points, continuity conditions of the first and second derivatives, and natural boundary conditions are applied to each piecewise cubic spline function. The linear equation system composed of the above conditions is solved to obtain the spline coefficients, thereby generating a smooth 3D parametric curve.

[0068] In practical implementation, the road itself is assumed to be a three-dimensional space. ,in ;

[0069] Randomly select an initial point within the constructed three-dimensional space of the road body. Then, select a destination N. The generation of destination N must satisfy the following distance constraints:

[0070]

[0071] Minimum relative distance threshold: =10cm

[0072] Maximum relative distance threshold: =30cm

[0073] : Represents the absolute value of the distance between points M and N along each axis.

[0074] Calculate the value in only one direction based on the coordinates of two points, for example... and The absolute value of the magnitude represents the distance between two points in the X direction. For example... The value is 30cm, then The range of values ​​is (30-30, 30-10)∪(30+10, 30+30), which is (0cm, 20cm)∪(40cm, 60cm); the same applies to the Y and Z directions.

[0075] This gives us a spatial domain as the selection range for point N, and point N will be randomly selected within this range.

[0076] Determine line L based on connection points M and N, divide line L into P equal segments, generating P+1 segmentation points (including endpoints M and N), and use each segmentation point... Define a spherical neighborhood centered on [the point]. :

[0077]

[0078] =3cm keypoint neighborhood radius;

[0079] : is a variable that represents any point that may be located within the spherical neighborhood;

[0080] :express It is a point in three-dimensional real space with three coordinate components. ;

[0081] : Represents the absolute value of the distance between the random point and the segment point;

[0082] Within each spherical neighborhood, a point is randomly selected as the key point;

[0083] The initial and final points, along with all key points, are used as nodes and connected to form a smooth and continuous A-curve using the B-spline interpolation algorithm.

[0084] The B-spline interpolation algorithm includes: given a set of 3D key points: .

[0085] Objective: To provide input data for the algorithm, namely a series of three-dimensional spatial points. These points represent the key locations through which the curve should pass.

[0086] This lays the groundwork for the next step: these control points are fundamental to the entire interpolation process. Without these points, parameterization or interpolation is impossible. The next step will use these points to calculate the parameter values.

[0087] The steps of parameterization include:

[0088] Define cumulative chord length parameter :

[0089]

[0090] in, Indicates the first The parameter values ​​corresponding to each key point; express , , The first With the Spatial distance between key points.

[0091] Objective: To map control points to parameter space and calculate the parameter value for each point using the cumulative chord length method. This ensures that the parameter value is proportional to the geometric distance between points, thus avoiding curve distortion caused by uneven parameter distribution.

[0092] Preparing for the next step: a sequence of parameter values ​​(such as...) This will serve as the independent variable (i.e., the parameter domain) for spline interpolation, providing the foundation for the next step of constructing the spline function. Without parameterization, the spline function cannot be defined on a unified parameter domain.

[0093] Parametric cubic spline interpolation includes:

[0094] Establish a cubic spline function for each coordinate component:

[0095] Coordinate component splines:

[0096]

[0097] Each segment is a cubic polynomial:

[0098]

[0099] in, : No. Within each interval Component spline functions;

[0100] , , , The polynomial coefficients of this segment (to be solved);

[0101] Starting from the interval Local parameters are used as a reference.

[0102] Coordinate component splines:

[0103]

[0104] Each segment is a cubic polynomial:

[0105]

[0106] Coordinate component splines:

[0107]

[0108] Each segment is a cubic polynomial:

[0109]

[0110] Objective: To decompose the three-dimensional curve interpolation problem into three independent one-dimensional problems. Each component is represented using a piecewise cubic polynomial. This simplifies the computation because each component can be processed individually.

[0111] This lays the groundwork for the next step: the form of the spline function (piecewise cubic polynomial) is defined, and the framework for the interpolation conditions (S3.4) is set. The expression for the spline function (e.g.) This will be used to substitute the interpolation conditions.

[0112] Interpolation conditions include:

[0113] Each component spline must pass through its corresponding coordinate values:

[0114]

[0115]

[0116]

[0117] Objective: To ensure that the spline function passes precisely through all control points; that is, the curve must pass through the given input points. This sets the basic requirements for interpolation.

[0118] This lays the groundwork for the next step: the interpolation conditions generate a set of equations that will be used to solve for the spline coefficients. However, the number of equations is insufficient with just the interpolation conditions, and continuity conditions are needed to supplement them.

[0119] Continuity conditions include:

[0120] For each component spline, the following must be satisfied:

[0121] Function values ​​are continuous:

[0122]

[0123] The first derivative is continuous:

[0124]

[0125] The second derivative is continuous:

[0126]

[0127] Objective: To ensure a smooth transition of the spline function at the control point connections. Function value continuity avoids breaks, first derivative continuity ensures smooth tangent direction, and second derivative continuity ensures smooth curvature. This gives the curve... Continuity (i.e., continuity of the second derivative).

[0128] This lays the groundwork for the next step: the continuity condition provides additional equations that, combined with the interpolation condition, form a complete system of linear equations. Without the continuity condition, splines may exhibit cusps or breaks at connection points, compromising smoothness.

[0129] Boundary conditions include:

[0130] Natural boundary conditions:

[0131]

[0132] Objective: To specify the behavior at the endpoints of a curve. Natural boundary conditions (second derivative is zero) cause the curve to bend "naturally" at the endpoints, i.e., with zero curvature. This ensures the stability of the curve endpoints.

[0133] This lays the groundwork for the next step: the boundary conditions provide the final two equations, making the system of linear equations closed (the number of equations equals the number of unknowns). Thus, the system of equations is solvable, preparing for the determination of the coefficients.

[0134] The coefficients are solved, including:

[0135] Let the interval length be:

[0136] From the interpolation conditions, we can obtain:

[0137] Relationship between coefficients:

[0138] Objective: To combine interpolation conditions, continuity conditions, and boundary conditions into a system of linear equations and solve for the spline coefficients (a, b, c, d). These coefficients completely define each piecewise cubic polynomial.

[0139] This lays the groundwork for the next step: once the coefficients are known, the spline function is completely determined and can be used to calculate the coordinates corresponding to any parameter value. The next step will be to specify the solution method for the system of equations.

[0140] The tridiagonal linear system of equations includes:

[0141] Unknown quantity The following system of linear equations is satisfied:

[0142]

[0143] for ,

[0144] The equations corresponding to the boundary conditions are:

[0145]

[0146] Matrix form:

[0147] The system of linear equations can be written as:

[0148]

[0149] in:

[0150] It is a (n+1)×(n+1) tridiagonal matrix;

[0151]

[0152] It is the right-hand vector;

[0153] Components and The methods for solving the components are completely similar.

[0154] Objective: To transform the problem of finding coefficients into solving a system of tridiagonal linear equations. Tridiagonal matrices have efficient algorithms with low computational complexity.

[0155] This lays the groundwork for the next step: solving this system of equations yields the coefficients, which can then be used to derive the other coefficients through the relationships. In this way, the spline function becomes fully usable, providing the foundation for curve generation.

[0156] Smooth curve generation includes:

[0157] Parameter range sampling, within the parameter range Take evenly from the top Points:

[0158]

[0159] Objective: To generate a dense series of parameter values ​​by uniformly sampling over a parameter range. These parameter values ​​will be used to calculate points on the curve, thus approximating a continuous and smooth curve.

[0160] This lays the groundwork for the next step: sampling points are the input for coordinate calculation. Without sampling, discrete curve points cannot be obtained.

[0161] Coordinate calculation, including:

[0162] For each sampling point Calculate the three-dimensional coordinates:

[0163]

[0164] Objective: For each sampled parameter value, calculate the corresponding... , , Coordinates. This is actually evaluating the spline function.

[0165] This lays the groundwork for the next step: coordinate calculations generate the final sequence of 3D points, which represent a smooth curve. This is the direct source of the output.

[0166] The final result includes: a three-dimensional smooth curve can be represented by parametric equations:

[0167]

[0168] This parameterization method ensures the smoothness of the curve in three-dimensional space and can handle three-dimensional curves in any direction.

[0169] Step S20: Based on the key points on the A curve, and combined with the top and bottom boundaries of the road, generate a smooth and continuous B curve representing the path of the crack in the depth direction.

[0170] In practical implementation, key points on curve A are obtained by passing through... Method for obtaining temporary key points on curve B by extending along the axis:

[0171] Basic parameter definitions:

[0172] Top boundary: (Road surface area) = 78cm;

[0173] Bottom boundary: (Road bottom layer) = 0cm;

[0174] Total road thickness: =78cm.

[0175] Input data:

[0176] Key points of the original curve:

[0177] Curve A: Composed of n+1 key points, denoted as... ;

[0178] No. Coordinates of key points: ,in ;

[0179] Extended parameters:

[0180] Extended distance The value ranges from 13 cm to 20 cm;

[0181] Extension direction: Randomly select to extend upwards or downwards;

[0182] Distance calculation:

[0183] For each key point Calculate its vertical distance to the road boundary:

[0184] Distance to top: ;

[0185] Distance to bottom: .

[0186] The upward extension algorithm includes:

[0187] Conditional judgment: Check if at least one key point satisfies: .

[0188] Extended rules:

[0189] Scenario 1: A key point exists that exceeds the top;

[0190] When there is at least one key point hour:

[0191] Extended distance: The actual distance each point extends to the top;

[0192] new coordinate: ;

[0193] Scenario 2: All points have sufficient room to extend;

[0194] When all key points are satisfied hour:

[0195] Extension distance: All points are extended uniformly. distance;

[0196] new coordinate: .

[0197] Downward extension algorithm:

[0198] Conditional judgment: Check if at least one key point is satisfied: ;

[0199] Extended rules include:

[0200] Scenario 1: There are key points that are too close to the bottom;

[0201] When there is at least one key point hour;

[0202] Extended distance: The actual distance each point extends to the bottom;

[0203] new coordinate: .

[0204] Scenario 2: All points have sufficient room for extension:

[0205] When all key points are satisfied hour;

[0206] Extension distance: All points are extended uniformly. distance;

[0207] New Z coordinates: ;

[0208] A set of key points obtained by extending the key points of curve A is used as the temporary key points of curve B. .

[0209] For each temporary critical point Let its centered neighborhood perpendicular to the Z-axis be a disk on the XY plane. This neighborhood is defined as... Centered on the XY coordinates, with a radius R = 3cm.

[0210] In three-dimensional space, the corresponding neighborhood is: , It is a radius of The disk is located on the horizontal plane. Above, and the center of the circle is at Then, a point is randomly selected from each neighborhood as the key point of the B curve. Finally, all key points are connected as nodes using the B-spline interpolation algorithm to form a smooth and continuous B curve.

[0211] Step S30: Using the A curve and B curve as boundaries, perform surface patching operation between them using the bicubic B-spline surface algorithm to generate a three-dimensional crack surface model.

[0212] In practical implementation, it should be noted that the bicubic B-spline surface algorithm includes: parameterizing and resampling the A and B curves respectively to obtain two smooth parameterized boundary curves; defining a two-dimensional parameter space, where the first parameter... Along the direction of the boundary curve, the second parameter This represents the interpolation weights between the two boundary curves; using the bilinear interpolation formula, based on the parameters... Calculate the coordinates of points on the surface; perform uniform discretization sampling on the parameter space to generate regular mesh vertices; connect the mesh vertices to form triangular patches, forming a continuous triangular mesh surface.

[0213] The bicubic B-spline surface algorithm includes:

[0214] Given two three-dimensional curves as the boundaries of the surface:

[0215] Curve A:

[0216] Curve B:

[0217] Objective: To provide the basic input data for the algorithm.

[0218] This lays the groundwork for the next step: the two curves will serve as boundary conditions for surface generation, determining the basic shape and extent of the surface.

[0219] Curve parameterization and smoothing include:

[0220] Cumulative chord length parameterization calculates the cumulative chord length parameter for each curve:

[0221] For curve A:

[0222]

[0223]

[0224] For curve B:

[0225]

[0226]

[0227] Cubic spline interpolation performs cubic spline interpolation on each of the three coordinate components of the curve:

[0228] For curve A:

[0229]

[0230]

[0231]

[0232] The same applies to curve B.

[0233] Smooth curve generation involves uniform sampling over the parameter range to obtain a smooth curve: For curve A:

[0234]

[0235]

[0236] in This represents the number of sampling points.

[0237] The same applies to curve B.

[0238] Objective: To transform discrete boundary curve points into continuous, smooth, parameterized curves.

[0239] This lays the groundwork for the next step: cumulative chord length parameterization provides the basis for defining the surface parameter space; cubic spline interpolation ensures the boundary curves... Continuity lays the foundation for surface smoothness, and the generation of smooth curves provides high-quality boundary conditions for subsequent surface interpolation.

[0240] Surface generation algorithm:

[0241] Parameter space definition: Define the surface parameter space.

[0242] : Parameters along the curve direction (corresponding to the original curve parameters);

[0243] : Parameters used for interpolation between two curves.

[0244] Objective: To establish a two-dimensional parametric coordinate system for a curved surface.

[0245] This lays the groundwork for the next step: The direction parameter corresponds to the curve direction, maintaining consistency with the boundary curve; The direction parameter defines how the surface transitions between two boundaries, providing a parametric framework for bilinear interpolation.

[0246] Bilinear interpolation surfaces include:

[0247] Points on the surface are obtained by bilinear interpolation:

[0248]

[0249] Expand into coordinate component form:

[0250]

[0251]

[0252]

[0253] Objective: To construct a continuous surface between two boundary curves.

[0254] This lays the groundwork for the next step: providing a continuous mathematical expression for the points on the surface, thus providing a theoretical basis for discretization and ensuring that the continuity constraints of the surface at the boundary are satisfied.

[0255] Discretization: Discretizing the parameter space into a grid.

[0256]

[0257]

[0258] in The number of samples along the curve direction. The number of samples in the interpolation direction.

[0259] The coordinates of the points on the curved surface mesh are:

[0260]

[0261] Objective: To convert continuous surfaces into discrete mesh representations.

[0262] This lays the groundwork for the next step: generating structured mesh points with rules provides vertex data for triangular mesh generation;

[0263] Establish a discrete mapping from parameter space to geometric space.

[0264] Triangular mesh generation includes:

[0265] Vertex index mapping:

[0266] Mapping 2D mesh vertices to 1D indices:

[0267]

[0268] Triangle division:

[0269] For each grid cell This generates two triangles:

[0270] The first triangle:

[0271]

[0272] The second triangle:

[0273]

[0274] Objective: To connect discrete mesh points into triangular patches, laying the groundwork for the next step: defining the topological connectivity of the surface, providing basic units for the triangular mesh set, and establishing the geometric integrity of the surface in the discrete case.

[0275] The triangular mesh set includes:

[0276] The triangular mesh of the entire surface is the union of all mesh element triangles:

[0277]

[0278] Objective: To integrate all triangular facets to form a complete surface mesh. Algorithm endpoint: To output a 3D surface model that can be used for visualization, analysis, and further processing.

[0279] Step S40: Perform morphological refinement processing on the three-dimensional crack surface model to simulate the surface irregularity and branching behavior of real cracks.

[0280] It should be noted that the fractal noise expansion in the morphological refinement process includes: calculating the normal vector of the surface vertex, generating the fractal displacement field using the three-dimensional Perlin noise function, and adjusting the vertex position through the vertex position update formula.

[0281] It is understood that the method also includes a result verification step: comparing and analyzing the generated three-dimensional crack model with real crack point cloud data; calculating the Hausdorff distance and surface deviation value, and determining whether the model is qualified based on the calculation results; and outputting a detection report containing statistical information on crack length, width, and depth.

[0282] It's important to note that the Hausdorff distance is a metric for measuring the maximum mismatch between two point sets. It answers the question, "What is the maximum distance from any point in the model to the ground truth point cloud?" Surface bias typically refers to the average distance or the standard deviation (root mean square error, RMSE) between two point sets. It reflects the overall average fitting accuracy.

[0283] In the evaluation phase, determining whether a model is qualified requires setting tolerance thresholds for the two indicators mentioned above. These thresholds need to be adjusted according to actual needs.

[0284] The test report includes the following core statistical information:

[0285] Validation Result Summary:

[0286] Model ID, generation time, and verification time.

[0287] Overall conclusion: Pass / Fail.

[0288] Explanation of the main indicators that exceed the standard (if they are not up to standard).

[0289] Accuracy Specifications Details:

[0290] Hausdorff distance: final value, and values ​​of one-way distances H1 and H2.

[0291] Surface deviation statistics: average deviation, root mean square error (RMSE), standard deviation of distance, maximum positive deviation, maximum negative deviation, etc.

[0292] Crack critical dimension statistics:

[0293] Length: The unfolded length of the main crack path calculated based on the qualified model;

[0294] Average width: The average width value calculated from multiple samples along the crack length direction;

[0295] Maximum width: The value at the widest point of the crack;

[0296] Average depth: The average depth of the crack relative to the road surface;

[0297] Maximum depth: The deepest point of the crack;

[0298] Volume: The total volume occupied by the crack model is of great significance for evaluating the amount of material filling.

[0299] In practical implementation, the surface obtained from curves A and B is further expanded to obtain cracks, specifically including:

[0300] Basic surface definition:

[0301] A continuous parametric surface generated by two given boundary curves:

[0302]

[0303] in and It is a smooth boundary curve.

[0304] Objective: To establish a continuous mathematical surface model.

[0305] This lays the groundwork for the next step: providing a continuous mathematical description of the surface, thus establishing the foundation for discretized sampling;

[0306] Surface discretization:

[0307] Parameter space sampling, uniform discretization over the parameter domain:

[0308]

[0309]

[0310] Vertex coordinate calculation: ;

[0311] Triangular mesh generation: Two triangles are generated for each mesh cell.

[0312]

[0313]

[0314] Objective: To convert continuous surfaces into discrete meshes that can be processed by computers.

[0315] This lays the groundwork for the next step: generating a regular structured mesh, providing a topological foundation for normal vector calculation and subsequent expansion;

[0316] Vertex normal vector calculation:

[0317] Calculating the surface normal vector for a triangle vertex :

[0318]

[0319] Vertex normal vector weighted average:

[0320]

[0321] in It contains vertices A set of triangles, It is the weighting coefficient.

[0322] Objective: Calculate the direction of the normal vector for each vertex.

[0323] This lays the groundwork for the next step: providing information on the direction of expansion, as both fractal expansion and branching generation depend on the direction of the normal vector;

[0324] Fractal noise spread:

[0325] 3D Perlin noise function:

[0326]

[0327] Parameter description:

[0328] : Quantity (number of fractal layers);

[0329] Persistence;

[0330] : Scaling vector;

[0331] 3D Perlin noise function fractal displacement

[0332]

[0333] in It is a roughness control parameter.

[0334] Vertex position update:

[0335]

[0336] Objective: To simulate the irregularity of a real crack surface by applying fractal perturbations in the normal direction of the surface.

[0337] This lays the groundwork for the next step: generating preliminary crack surface features to provide the geometric basis for branch generation.

[0338] Crack branch generation:

[0339] The branch point selection probability is to randomly select the branch starting point from the vertices of the main crack:

[0340]

[0341] in:

[0342] Basic branch density;

[0343] :vertex Curvature at that point;

[0344] Curvature-related functions (branches are more likely to occur at locations with high curvature).

[0345] Branch direction generation:

[0346]

[0347] This formula calculates the unit direction vector of the branch crack. It determines the direction in which the branch extends from the main crack.

[0348] in:

[0349] A random vector that follows a three-dimensional standard normal distribution (mean 0, covariance matrix is ​​identity matrix) is used to introduce randomness and allow the branch direction to change naturally.

[0350] : The tangent direction vector of the main crack, representing the local orientation of the main crack;

[0351] : The normal vector of the main crack, representing the perpendicular direction of the main crack surface;

[0352] : A scalar parameter that controls the perpendicularity of the branch to the main crack. When When the fracture is larger, the branches tend to be perpendicular to the main fracture; when... When the value is small, the branch direction is more influenced by the random vector. Influence;

[0353] The cross product of the normal vector and the tangent vector generates a vector perpendicular to both, which is used to define the reference direction of the branch.

[0354] In the denominator This represents the magnitude of the vector, used for normalization, so that... It becomes a unit vector.

[0355] Branch geometry generates branch endpoint coordinates:

[0356]

[0357] in It is the branch length. It is a curvature-related length adjustment function.

[0358] Branch triangulation generates connection triangles for each branch:

[0359]

[0360] in:

[0361] A starting point on the main crack from which branches begin to form;

[0362] : The unit direction vector obtained from Formula 1;

[0363] The length of the branch is a scalar value;

[0364] : A with curvature Related functions are used to adjust branch length. Curvature This indicates that the main crack is at point [point]. The degree of curvature at the point; typically, branches in areas of high curvature may be shorter to enhance realism;

[0365] A triangle is composed of the indices of its three vertices.

[0366] and : Index of adjacent points on the main crack, representing a segment of the main crack;

[0367] : Total number of points in the main crack mesh;

[0368] The index of the branch, used to uniquely identify each branch;

[0369] The index of the branch endpoints is used to avoid index conflicts by offsetting the number of main crack points.

[0370] This indicates that the main crack point , The branches are connected to the endpoints to form a triangle, thus creating the geometry of the branches in the grid.

[0371] The entire expression represents starting from the beginning. Along direction distance traveled Obtain the branch endpoints.

[0372] Objective: To generate secondary branches based on the main crack to increase realism and lay the groundwork for the next step: to refine the crack morphology and form a complete crack network.

[0373] A complete crack surface model, including:

[0374] The integrated deformation field combines various extended effects:

[0375]

[0376] Final surface representation:

[0377]

[0378] Discrete form:

[0379]

[0380] A point on a curved surface;

[0381] Fractal deformation fields, typically generated based on fractal noise (such as Perrlin noise), are used to increase the roughness and irregularity of the crack surface, making it more natural.

[0382] Branch deformation field: representing the displacement caused by branch cracks, usually calculated based on branch geometry;

[0383] The total deformation field is the vector sum of fractal and branching deformations, applied to a point. ;

[0384] : Original surface parameterization, where and These are parameters that define the initial shape of the surface;

[0385] The total deformation field at the point on the surface The value at that point is a displacement vector;

[0386] The final crack surface is the result of adding a deformation field to the original surface, revealing the details of the cracks and branches.

[0387] It should be noted that this embodiment differs from existing technologies in the following ways: Constrained randomization generation mechanism: By using neighborhood constraints and physical parameter range limitations, the randomness of the generated results is ensured while maintaining their rationality, solving the problem of overly regular or completely unreasonable crack morphologies in traditional methods. Layered depth model: Depth parameters are automatically determined based on crack type, and the natural expansion behavior of cracks is simulated, significantly improving the physical realism and type adaptability of the crack model. Hyperbolic constraint surface construction: Surface generation is achieved by using A and B hyperbolas to jointly constrain the surface, ensuring the fit between crack geometry and the road body, avoiding the problem of the model deviating from the actual environment. Fully parametric design: All key parameters (neighborhood range, depth value, etc.) can be adjusted according to actual needs, making the method widely applicable and flexible.

[0388] In specific implementation, such as Figure 3 The diagram illustrates the effect of curves A and B, and the surface between them derived using a bicubic B-spline surface algorithm. Curve A represents curve A, and Curve B represents curve B.

[0389] like Figure 4 As shown in the figure, the portion depicted is a crack that expands from a curved surface, simulating the natural expansion behavior of a crack.

[0390] This embodiment generates a crack curve A within a predefined three-dimensional road space based on a constrained randomization method. Based on key points on curve A, and combined with the top and bottom boundaries of the road, a crack curve B is generated. Using curves A and B as boundaries, a bicubic B-spline surface algorithm is employed to perform surface patching operations between them, generating a three-dimensional crack surface model. The three-dimensional crack surface model undergoes morphological refinement to simulate the surface irregularities and branching behavior of real cracks. This achieves the technical effect of rapidly generating realistic three-dimensional crack models that conform to physical laws.

[0391] Furthermore, embodiments of this application also propose a computer-readable storage medium storing a program for progressive expansion modeling of internal road cracks based on a single trajectory, wherein when the program for progressive expansion modeling of internal road cracks based on a single trajectory is executed by a processor, the program implements the steps of the method for progressive expansion modeling of internal road cracks based on a single trajectory as described above.

[0392] Reference Figure 5 , Figure 5 This is a structural block diagram of the first embodiment of the single-track guided progressive expansion modeling system for internal road cracks in this application.

[0393] like Figure 5 As shown in the embodiments of this application, the progressive expansion modeling system for internal road cracks based on single-trajectory guidance includes:

[0394] The A-curve generation module 10 is used to generate a smooth and continuous A-curve representing the crack surface path in a predefined three-dimensional road space based on a constrained randomization method.

[0395] B-curve generation module 20 is used to generate a smooth and continuous B-curve representing the path of the crack in the depth direction based on the key points on the A-curve and in combination with the top and bottom boundaries of the road.

[0396] The three-dimensional surface generation module 30 is used to generate a three-dimensional crack surface model by using the A curve and the B curve as boundaries and employing a bicubic B-spline surface algorithm to perform surface patching operations between the two curves.

[0397] Output module 40 is used to refine the morphology of the three-dimensional crack surface model in order to simulate the surface irregularity and branching behavior of real cracks.

[0398] It should be understood that the above are merely illustrative examples and do not constitute any limitation on the technical solution of this application. In specific applications, those skilled in the art can make settings as needed, and this application does not impose any restrictions on this.

[0399] This embodiment generates a crack curve A within a predefined three-dimensional road space based on a constrained randomization method. Based on key points on curve A, and combined with the top and bottom boundaries of the road, a crack curve B is generated. Using curves A and B as boundaries, a bicubic B-spline surface algorithm is employed to perform surface patching operations between them, generating a three-dimensional crack surface model. The three-dimensional crack surface model undergoes morphological refinement to simulate the surface irregularities and branching behavior of real cracks. This achieves the technical effect of rapidly generating realistic three-dimensional crack models that conform to physical laws.

[0400] It should be noted that the workflow described above is merely illustrative and does not limit the scope of protection of this application. In practical applications, those skilled in the art can select some or all of it to achieve the purpose of this embodiment according to actual needs, and no restrictions are imposed here.

[0401] In addition, for technical details not described in detail in this embodiment, please refer to the method for progressive expansion modeling of internal road cracks based on single-trajectory guidance provided in any embodiment of this application, which will not be repeated here.

[0402] Furthermore, it should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or system that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or system. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or system that includes that element.

[0403] The sequence numbers of the embodiments in this application are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0404] Through the above description of the embodiments, those skilled in the art can clearly understand that the methods of the above embodiments can be implemented by means of software plus necessary general-purpose hardware platforms. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium (such as read-only memory (ROM) / RAM, magnetic disk, optical disk), and includes several instructions to cause a terminal device (which may be a mobile phone, computer, server, or network device, etc.) to execute the methods of the various embodiments of this application. The above are only preferred embodiments of this application and do not limit the patent scope of this application. All equivalent structural or procedural transformations made using the content of this application's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of this application.

Claims

1. A method for progressive expansion modeling of internal road cracks based on single-trajectory guidance, characterized in that, include: Within a predefined three-dimensional road space, a smooth and continuous A-curve representing the crack surface path is generated based on a constrained randomization method. Based on the key points on the A curve, and combined with the top and bottom boundaries of the road, a smooth and continuous B curve representing the path of the crack in the depth direction is generated. Using curves A and B as boundaries, a bilinear interpolation algorithm is used to perform surface patching between them to generate a three-dimensional crack surface model. The three-dimensional crack surface model is subjected to morphological refinement to simulate the surface irregularity and branching behavior of real cracks; The step of generating a smooth, continuous A-curve representing the crack surface path based on the constrained randomization method includes: Within the three-dimensional space of the road, an initial point M and an end point N are randomly selected, wherein the distance between point M and point N satisfies a preset minimum relative distance threshold and a preset maximum relative distance threshold. Divide the straight line connecting point M and point N into segments to obtain multiple segmentation points; For each segment point, a key point is randomly selected within a spherical neighborhood with a preset radius. Using the initial point M, the endpoint N, and all randomly selected key points as control points, the smooth and continuous A curve is generated using the B-spline interpolation algorithm. The step of generating a smooth, continuous curve B representing the path of the crack in the depth direction based on key points on curve A and the top and bottom boundaries of the road includes: For each key point on curve A, its extended coordinates in the Z-axis direction are calculated based on its Z-coordinate, the top boundary of the road, the bottom boundary of the road, and the preset extension distance, to obtain a temporary key point. Using the X and Y coordinates of each temporary key point as the center, randomly select a point within the neighborhood of the disk with a preset radius as the key point of the B curve; Using all the key points of the B-curve as control points, the smooth and continuous B-curve is generated using the B-spline interpolation algorithm. The B-spline interpolation algorithm includes: The input keypoint sequence is parameterized by cumulative chord length to obtain the parameter value corresponding to each keypoint. For each component of the three-dimensional coordinates, construct a piecewise cubic spline function that passes through the coordinates of all corresponding key points; For each piecewise cubic spline function, apply interpolation conditions, function values ​​at the piecewise connection points, continuity conditions for the first and second derivatives, and natural boundary conditions. Solve the system of linear equations formed by the above conditions to obtain spline coefficients, thereby generating a smooth three-dimensional parametric curve.

2. The method according to claim 1, characterized in that, Bilinear interpolation algorithms include: Parameterize and resample curves A and B respectively to obtain two smooth parameterized boundary curves; Define a two-dimensional parameter space, where the first parameter Along the direction of the boundary curve, the second parameter This represents the interpolation weights between the two boundary curves; Using the bilinear interpolation formula, based on the parameters Calculate the coordinates of a point on the surface; The parameter space is uniformly discretized and sampled to generate regular mesh vertices; Connect the vertices of the mesh to form triangular patches, creating a continuous triangular mesh surface.

3. The method as described in claim 1, characterized in that, Fractal noise propagation in morphological refinement includes: Calculate the normal vectors at the vertices of the surface and generate the fractal displacement field using a three-dimensional Perlin noise function; The vertex position is adjusted using the vertex position update formula.

4. The method as described in claim 1, characterized in that, The method also includes a result verification step: The generated 3D crack model was compared and analyzed with the real crack point cloud data; Calculate the Hausdorff distance and surface deviation values, and determine whether the model is qualified based on the calculation results; Output an inspection report containing statistical information on crack length, width, and depth.

5. A progressive expansion modeling system for internal road cracks based on single-trajectory guidance, characterized in that, Performing the method as described in claim 1 includes: The A-curve generation module is used to generate a smooth and continuous A-curve representing the crack surface path within a predefined three-dimensional road space based on a constrained randomization method. The B-curve generation module is used to generate a smooth and continuous B-curve representing the path of the crack in the depth direction based on the key points on the A-curve and the top and bottom boundaries of the road. The three-dimensional surface generation module is used to generate a three-dimensional crack surface model by using curves A and B as boundaries and performing surface patching operations between them using a bilinear interpolation algorithm. The output module is used to refine the morphology of the three-dimensional crack surface model to simulate the surface irregularities and branching behavior of real cracks.

6. A computer device, characterized in that, The device includes a memory and a processor, wherein the processor, when executing computer instructions stored in the memory, performs the method as described in any one of claims 1 to 4.

7. A computer-readable storage medium, characterized in that, Includes instructions that, when executed on a computer, cause the computer to perform the method as described in any one of claims 1 to 4.

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