Urban road underground target parameterization efficient inversion method
By combining parameterized target inversion and the CMA-ES method with cost function and stepwise inversion, the problems of noise sensitivity and low accuracy of ground penetrating radar in the inversion of underground targets in urban roads are solved, and efficient and accurate underground target detection is achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- FUDAN UNIVERSITY
- Filing Date
- 2026-05-15
- Publication Date
- 2026-07-31
AI Technical Summary
Existing ground-penetrating radar inversion methods suffer from problems such as noise sensitivity, poor real-time performance, and low inversion accuracy when dealing with underground targets on urban roads, making it difficult to meet complex detection requirements.
A parametric subsurface target inversion method is adopted, combined with a two-stage CMA-ES inversion method. By defining multiple cost functions and performing step-by-step inversion, accurate inversion of subsurface targets is achieved, including optimization of discrete types and continuous locations/sizes. B-scan images are used for efficient inversion.
It achieves non-destructive testing of underground targets, with the pixel value error between the B-scan image and the simulated image being less than 5.0%, meeting the requirements for smaller granularity inversion and providing reliable technical support for underground target inversion and disaster assessment.
Smart Images
Figure CN122488071A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of radar detection technology, specifically, it relates to a parameterized and efficient inversion method for underground targets in urban roads. Background Technology
[0002] Ground penetrating radar (GPR) is a non-destructive testing technology based on high-frequency electromagnetic waves (typically 10MHz to 3GHz), widely used in fields such as engineering geology, road inspection, underground pipeline location, archaeology, and environmental monitoring. The core of GPR inversion is to quantitatively infer the electromagnetic parameters (dielectric constant, conductivity, and magnetic permeability) and geometric structure of the underground medium from the received electromagnetic response.
[0003] GPR inversion is a typical nonlinear ill-posed inverse problem. Let the observed data vector be... The model parameter vector is , forward operator A mapping from parameters to data was established. Inversion is essentially solving an optimization problem.
[0004]
[0005] In the formula As a weighting factor, As a regularization term, prior constraints can be introduced; the essence of parametric inversion is to map the geometric features of arbitrary shapes to a finite-dimensional parameter space, making the target parameters... The number of discrete degrees of freedom is much smaller than that of the grid, thus improving the well-posedness of the problem. Parametric inversion, through the strategy of "dimensionality reduction + prior embedding", effectively alleviates the non-uniqueness and computational burden of GPR inversion, and is a key bridge connecting the original radar waveform and engineering quantitative parameters.
[0006] Current GPR inversion methods mainly include physical model-based methods, imaging-driven methods, and machine learning methods. Physical model-based inversion methods, such as full-waveform inversion, update subsurface model parameters by minimizing the error between observed data and forward simulation data. This method utilizes all information of the waveform (including amplitude and phase), offering advantages such as high accuracy and the ability to recover continuous medium parameters. However, it is computationally expensive, sensitive to the initial model, and prone to getting trapped in local optima. Imaging-driven methods use the integral form of the wave equation for imaging, often used for rapid reconstruction of subsurface structures. They can handle complex structures and multiple waves well, but their imaging accuracy is often insufficient. Machine learning methods take GPR data (usually B-scan images) as input and directly output the distribution or structure map of subsurface medium parameters. Through training with a large number of data samples, they learn complex nonlinear physical processes, enabling rapid prediction of subsurface scenes and targets based on observed data. They offer advantages such as high real-time performance and ease of operation, and by providing a good initial solution, they greatly alleviate the problems of traditional methods getting trapped in local solutions or failing to converge. However, the effectiveness of this method depends on the training samples, has poor generalization ability, and has not yet become a technically usable method in engineering. Although the above methods have achieved good results in handling certain special scenarios, they generally suffer from problems such as noise sensitivity, poor real-time performance, and low inversion accuracy, and cannot meet the increasingly complex engineering application requirements of ground penetrating radar. Summary of the Invention
[0007] To address the problems existing in the prior art, the present invention aims to provide an efficient inversion method for underground target parameters in urban roads. This invention, targeting the formation and distribution characteristics of underground targets in urban roads, parameterizes underground cavities or metal structures and combines a two-level CMA-ES (Covariance Matrix Adaptation Evolution Strategy) inversion method to achieve accurate inversion of discrete types / materials and continuous locations / sizes. This enables non-destructive testing of underground targets. The relative error of pixel values between the Bscan image obtained using the inversion parameters and the simulated image is less than 5.0%, providing more accurate input for underground target inversion and meeting the needs of smaller-granularity underground target inversion. This provides reliable technical support for underground target inversion detection and disaster assessment.
[0008] The technical solution of the present invention is described in detail below.
[0009] This invention provides a parameterized and efficient inversion method for underground targets in urban roads. It utilizes parameterized underground targets to achieve efficient inversion based on B-scan echoes. The underground target shapes include ellipses and rectangles, the target material is air or metal, and the spatial location and geometric dimensions are continuously adjustable optimization parameters. The specific steps are as follows:
[0010] Step 1: Set the distribution of formation geometry and physical parameters, place the excitation source and scanning parameters, and obtain B-scan images of the layered medium background and B-scan images containing different targets. Subtract the background B-scan image from the target B-scan image to obtain a B-scan image with strong target response correlation, defined as... ;
[0011] Step 2: Define the target optimization parameters, which include position, size, type, and material. The type can be either discrete ellipse or rectangle; the material can be either metal or air; and the position and size are continuous optimization parameters.
[0012] Step 3: Define the cost function to provide guidance for parameter optimization. The cost function includes Hilbert-based envelope matching, scan energy profile-based position matching, symbol scan profile-based type matching, and scan centroid-based spatial position matching. The overall cost function is a weighted sum of the different cost functions.
[0013] Step 4: The CMA-ES method is used to optimize the target parameters (i.e., target location, target type, geometry, and material) in stages. First, the target response strongly correlated images obtained in Step 1 are analyzed. Downsampling on the scan axis yields a new image defined as follows: Then, using the observed image as the target, target inversion is performed to obtain the target parameters. Finally, this parameter is used as the initial value for refined inversion, with the image... To achieve the goal, fine-tune the previously obtained target parameters. To obtain more accurate target parameters This enables the accurate inversion of underground targets.
[0014] In this invention, in step 1, the radar operating parameters are set according to the simulation requirements, and the scattered echo of the target is simulated using the Richer wavelet as the excitation source to form a B-scan image; the time-domain expression of the Richer wavelet is:
[0015]
[0016] In the formula, For operating frequency, As a delay time factor, this invention adopts , The sampling time of the signal.
[0017] In this invention, in step 1, when simulating the scattered echo of the target using a Richer wavelet as the excitation source, the simulation scene mesh is... The B-scan image records 800 time steps on the time axis and 80 radar echo data points horizontally; the forward modeling method uses the FDTD method, with a 15-layer CPML truncation boundary and a spatial grid spacing of [missing information]. The observation point and the excitation source are located at the same position to record the scattered echo.
[0018] In this invention, in step 2, the target shape parameters are defined in two ways:
[0019]
[0020] In the formula, For rectangular elements in Minimum and maximum dimensions of the direction, For rectangular elements in Minimum and maximum dimensions of the direction. The center position of the elliptical target. Let be the major and minor axes of the ellipse. There are two target materials: [metal, void]. During optimization, each target has only four continuous parameters and two material type parameters. For multiple targets, the optimization parameter space increases fourfold.
[0021] In this invention, in step 3, variables are defined: ; In the formula, Indicates the Hilbert transform; superscript ' 'Indicates the average value of the parameter; subscript Indicates the removal of the sign; 1 for values > 0, 0 otherwise; subscript Indicates pixel energy; This is the overall envelope information of the Bscan image, used to describe the instantaneous amplitude of the Bscan image; Represents the Bscan image's first... The energy profiles corresponding to each column are used to locate the target position; Indicates the row number of the Bscan image; Indicates the first The normalized sequence of the energy distribution of the column; Indicates the centroid location of the Bscan image; Indicates the first The sign function, with the superscript '-' indicating the average of all classes; Represents the relative change in sign between different classes; The cost function for the normalized time-domain scattering field is defined as follows: ; In the formula This represents the electric field distribution of the target's B-scan image after removing background echoes during the optimization process. The cost function for each channel envelope is defined as follows: ; In the formula, for The envelope distribution; The energy partitioning cost of the scanning surface is defined as: ; In the formula, for Energy distribution; Define the centroid offset cost as: ; In the formula, for The center of mass; position. This represents the number of horizontal scan points. The overall cost function is defined as: .
[0022] In this invention, in step 4, considering that CMA-ES is suitable for continuous optimization but lacks gradient information in discrete optimization, a method is adopted that uses continuous optimization of geometric position / size and discrete optimization of target shape / material. In the first traversal, for each set of optimization parameters, optimization is first performed with equal probability in the combination of discrete parameters (i.e., target shape type and material) to obtain the optimal result of each set of initial parameters in each discrete combination state. Then, the probability of the discrete combination corresponding to the optimal parameter is increased, and the probability of other combinations is decreased, which is used as the initial value for the next geometric iteration. This process is repeated until the convergence condition is met.
[0023] In this invention, step 4 addresses the shortcomings of low efficiency and long simulation time in forward modeling by employing a step-by-step inversion method. First, coarse sampling is performed on the transverse echoes. Target inversion is then carried out on the coarsely sampled observation echoes, significantly reducing the simulation time for generating B-scans during the forward modeling process. Then, the optimized parameters are used as initial values for the inversion of the original fine observation echoes to improve inversion accuracy.
[0024] In this invention, step 4 employs a two-stage CMA-ES iterative method. First, a 5-fold downsampling is performed along the scanning dimension to obtain a set of results. Due to the consistency of the target parameter space before and after FBscan downsampling of the observed image, the optimization results of the coarse grid can be directly used as the initial values for the fine grid iteration. After secondary optimization, the inversion results corresponding to the fine grid can be obtained efficiently.
[0025] In this invention, in step 4, the image strongly correlated with the target response obtained in step 1 is... Downsample by 5 times on the scan axis.
[0026] The present invention relates to the hybrid use of multiple cost functions, parameterized design combining continuous space with discrete distribution, and two-stage combinatorial optimization based on CMA-ES, etc. Compared with the prior art, the beneficial effects of the present invention are as follows:
[0027] (1) The method of the present invention takes into full consideration the distribution of B-scan scattered echoes and combines waveform envelope, energy distribution, centroid position and other factors to define a cost function to achieve inversion with higher efficiency.
[0028] (2) The method of the present invention utilizes the inversion method of discrete parameter space combined with continuous geometric position, and adjusts the weight of discrete combination during the iteration process, which has better applicability. Attached Figure Description
[0029] Figure 1 Flowchart of the method of this invention.
[0030] Figure 2 A simulation scene with a single void.
[0031] Figure 3 Comparison of B-scan results for the inversion parameters of a single void target.
[0032] Figure 4 A simulation scenario for two metallic targets.
[0033] Figure 5 Comparison of B-scan results for the inversion parameters of two metallic targets. Detailed Implementation
[0034] The present invention will be further described below with reference to specific embodiments and accompanying drawings. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.
[0035] like Figure 1 As shown, this invention provides a parameterized and efficient inversion method for underground targets in urban roads, combining background elimination, cost function definition, CMA-ES inversion, and other processes. The specific steps are as follows:
[0036] Step 1: Set the distribution of formation geometry and physical parameters, place the excitation source and probe path, and obtain the B-scan image.
[0037] The radar's operating electromagnetic waves were configured with observation parameters such as center frequency, bandwidth, and polarization according to simulation requirements. Then, gprMax software was used to simulate the scattered echoes from different geological strata, with the signal receiving and transmitting positions being identical. The simulated echo signals received at each location formed A-scan echoes, and multiple A-scan images formed along the observation direction were synthesized into a B-scan image of the current target. The transmitted signal was a Richter wavelet with a center frequency of 0.5 GHz. There were 80 A-scan channels, and each A-scan image was scanned for 800 time steps.
[0038] Step 2: Define the target optimization parameters, including location, size, type, and material. The type can be either discrete (elliptical or rectangular); the material can be either metal or air; and the location and size are continuous optimization parameters. Considering the characteristics of underground targets in urban roads, this invention considers two materials (metal / cavity) and two geometric shapes (elliptical / rectangular), resulting in four possible combinations.
[0039] Step 3: Define the cost function to provide guidance for parameter optimization. The cost function includes Hilbert-based envelope matching, position matching based on scan energy profile, type matching based on symbol scan profile, and spatial position matching based on scan centroid, etc. The overall cost function is a weighted sum of different cost functions. Through extensive result analysis, the cost loss weight combination with better performance adopted in this invention is: [0.25, 0.25, 0.1, 0.26, 0.14].
[0040] Step 4: Optimize the target parameters in stages using the CMA-ES method. First, optimize the target response strongly correlated images obtained in Step 1. Downsampling by a factor of 5 on the scan axis yields a new image defined as follows: Then, using the observed image as the target, target inversion is performed to obtain the target parameters. Finally, this parameter is used as the initial value for refined inversion, with the image... To achieve the goal, fine-tune the previously obtained target parameters. To obtain more accurate target parameters This achieves accurate inversion of underground targets. In coarse-grid optimization, CMA-ES uses 20 parameters per scan, iterates 100 times, and the cost function convergence threshold is 0.003. In fine-grid refinement inversion, the number of parameters per scan is 15, iterates 20 times, and the cost function convergence threshold is 0.001.
[0041] The following are specific examples.
[0042] Example 1
[0043] The radar operates at a frequency of 500MHz, and the spatial grid discrete size is... The simulation area is 2.2m × 1.6m (the upper boundary of the simulation area is 0.22m above the ground). There are 15 absorbing boundary layers, and each radar echo is collected over 800 time steps, totaling 80 locations. The radar transmitter is located at 0.01m above the ground, and the receiver is located at 0.03m above the ground. The target is a single cavity with an elliptical shape, centered at (1.1m, 0.71m), with a major axis of 0.22m and a minor axis of 0.12m. The dielectric constant distribution of the discrete grid points after partitioning is shown below. Figure 2 As shown, the relative permittivity of the air layer is 1.0, and the relative permittivity of the soil is 9.0. The parameters retrieved from the target using the method of this invention are: center position (1.1m, 0.71m), major axis 0.219m, minor axis 0.12m, and a relative error of 0.45% for the major axis. The B-scan image simulated using the retrieved parameters matches the observation results well, as shown... Figure 3 As shown, the maximum pixel deviation value of the Bscan image is 0.0001 (the number of CMA iterations in this embodiment is 100), and the relative error is 3.33%.
[0044] Example 2
[0045] The basic parameters (frequency, discrete size, simulation region size, absorbing boundary layer, etc.) are set as in Example 1. The targets are two cylindrical metal tubes. The center of the first metal tube is located at (0.055m, 0.056m), with a radius of 0.006m; the center of the second metal tube is located at (0.12m, 0.081m), with a radius of 0.009m. The relative permittivity of the soil is 9.0. The permittivity distribution of the discrete grid points after partitioning is shown below. Figure 4 As shown. During the simulation, the conductivity of the metal region is infinite, and the relative permittivity is given as 1.0. When encountering a metal mesh during the simulation, the phase is directly reversed, while the amplitudes of the electric and magnetic fields remain unchanged. Using the method of this invention, the center positions of the first cylinder (0.0549m, 0.0582m) are inverted. The geometric major axis of the elliptical inversion is 0.0066m, and the minor axis is 0.0082m. The center positions of the second cylinder are (0.12m, 0.102m), and the geometric major axis of the elliptical inversion is 0.014m, and the minor axis is 0.03m. In this embodiment, due to the limitation of the mesh discrete size, the forward modeling accuracy is relatively low. The relative deviation of the target geometric center position is less than 25%, and the relative deviation of the radius is less than 10%. The B-scan image simulated using the inversion parameters and the observation results are shown below. Figure 5 As shown, the maximum relative error between the two is 0.0004 (the number of CMA simulation iterations in this embodiment is 100).
Claims
1. A parameterized and efficient inversion method for underground targets in urban roads, characterized in that, Efficient inversion based on B-scan echoes is achieved using parameterized underground targets. The underground targets have shapes including elliptical and rectangular, and their materials are either cavities or metal. Their spatial location and geometric dimensions are continuously adjustable optimization parameters. The specific steps are as follows: Step 1: Set the distribution of formation geometry and physical parameters, place the excitation source and scanning parameters, and obtain B-scan images of the layered medium background and B-scan images containing different targets. Subtract the background B-scan image from the target B-scan image to obtain a B-scan image with strong target response correlation, defined as... ; Step 2: Define the target optimization parameters, which include position, size, type, and material. The type can be either discrete ellipse or rectangle; the material can be either metal or air; and the position and size are continuous optimization parameters. Step 3: Define the cost function to provide guidance for parameter optimization. The cost function includes Hilbert-based envelope matching, scan energy profile-based position matching, symbol scan profile-based type matching, and scan centroid-based spatial position matching. The overall cost function is a weighted sum of the different cost functions. Step 4: The CMA-ES method is used to invert target parameters in stages, namely target location, target type, geometric dimensions, and material. First, the target response strongly correlated images obtained in Step 1 are analyzed. Downsampling on the scan axis yields a new image defined as follows: Then, using the observed image as the target, target inversion is performed to obtain the target parameters. Finally, this parameter is used as the initial value for refined inversion, with the image... To achieve the goal, fine-tune the previously obtained target parameters. To obtain more accurate target parameters This enables the accurate inversion of underground targets.
2. The efficient inversion method for parameterized inversion of underground targets in urban roads according to claim 1, characterized in that, In step 1, the radar operating parameters are set according to the simulation requirements, and the scattered echo of the target is simulated using Richer wavelet as the excitation source to form a B-scan image.
3. The efficient inversion method for parameterized inversion of underground targets in urban roads according to claim 2, characterized in that, When simulating the scattered echo of a target using a Richer wavelet as the excitation source, the simulation scene mesh is as follows: The B-scan image records 800 time steps on the time axis and 80 radar echo data points horizontally; the forward modeling method uses the FDTD method, with a 15-layer CPML truncation boundary and a spatial grid spacing of [missing information]. The observation point and the excitation source are located at the same position to record the scattered echo.
4. The efficient inversion method for parameterized inversion of underground targets in urban roads according to claim 1, characterized in that, Define variables in step 3: ； In the formula, Indicates the Hilbert transform; superscript ' ' indicates the average value of the parameter; subscript Indicates the removal of the sign; 1 for values > 0, 0 otherwise; subscript Indicates pixel energy; This is the overall envelope information of the Bscan image, used to describe the instantaneous amplitude of the Bscan image; Represents the Bscan image's first... The energy profiles corresponding to each column are used to locate the target position; Indicates the row number of the Bscan image; Indicates the first The normalized sequence of the energy distribution of the column; Indicates the centroid location of the Bscan image; Indicates the first The sign function, with the superscript '-' indicating the average of all classes; Represents the relative change in sign between different classes; The cost function for the normalized time-domain scattering field is defined as follows: ； In the formula This represents the electric field distribution of the target's B-scan image after removing background echoes during the optimization process. The cost function for each channel envelope is defined as follows: ； In the formula, for The envelope distribution; The energy partitioning cost of the scanning surface is defined as: ； In the formula, for Energy distribution; Define the centroid offset cost as: ； In the formula, for The center of mass; Location, This represents the number of horizontal scan points. The overall cost function is defined as: 。 5. The efficient inversion method for parameterized inversion of underground targets in urban roads according to claim 1, characterized in that, In step 4, a step-by-step inversion method is adopted. First, coarse sampling is performed on the transverse echo, and target inversion is carried out on the coarsely sampled observation echo, which greatly reduces the simulation time for generating B-scan during the forward modeling process. Then, the optimized parameters are used as the initial values for the inversion of the original fine observation echo to improve the inversion accuracy.
6. The efficient inversion method for parameterized inversion of underground targets in urban roads according to claim 1, characterized in that, In step 4, an optimization method is adopted that continuously optimizes the geometric position / size while discretizing the target shape / material. In the first traversal, for each set of optimization parameters, the discrete parameters, namely the combination of target shape type and material, are first optimized with equal probability to obtain the optimal result of each set of initial parameters in each discrete combination state; then the discrete combination probability corresponding to the optimal parameter is increased and the probability of other combinations is decreased, which is used as the initial value for the next geometric iteration; this process is repeated until the convergence condition is met.
7. The efficient inversion method for parameterized inversion of underground targets in urban roads according to claim 1, characterized in that, In step 4, the images strongly correlated with the target response obtained in step 1 are analyzed. Downsampling by 5 times on the scan axis.