Buried cable calibration-free path reconstruction method based on Topo-NeRF and active perception

Abstract

This invention provides a calibration-free path reconstruction method for buried cables based on Topo-NeRF and active sensing. Addressing the issues of traditional magnetic field inversion relying on calibration and being prone to mismatch in environments with strong interference such as reinforced concrete, the method preprocesses raw data to obtain a spatiotemporal feature matrix. This matrix undergoes feature extraction, spatial alignment, and drift compensation to eliminate extrinsic parameter calibration, resulting in multi-source fused data. This multi-source fused data is combined to characterize the cable's magnetic field using a continuous three-dimensional topological manifold. An implicit neural radiation field is constructed and coupled with differentiable electromagnetic rendering. The cable body and branch nodes are separated within a persistently cohomologically constrained topological bottleneck layer. The initial reconstruction results are combined with conditional diffusion and ground-penetrating radar dielectric priors to enhance low signal-to-noise ratio weak fields, ensuring consistency between the reconstruction results and the underground physical structure. Based on reconstruction uncertainties, topological entropy is calculated, and online acquisition trajectories are planned to form a closed-loop active sensing system. Finally, a three-dimensional path model is output, enabling rapid detection of underground cables.

Description

Technical Field

[0001] This invention relates to the field of underground cable detection technology, and in particular to a method for reconstructing the calibration-free path of buried cables based on Topo-NeRF and active sensing. Background Technology

[0002] With the increasing density of urban underground space utilization, underground cables, as key channels for power transmission, require accurate path reconstruction for operation and maintenance safety, fault location, and engineering planning. Traditional cable path detection methods mainly rely on magnetic field inversion and ground-penetrating radar imaging to infer the location of underground cables by measuring the surface magnetic field or electromagnetic wave echo. However, these methods usually require prior calibration of sensor extrinsic parameters, and in environments with multiple parallel cables and strong interference from reinforced concrete, path mismatch and artifacts are easily caused by electromagnetic coupling and multipath effects.

[0003] Traditional magnetic field inversion methods are based on dipole models or boundary element methods, which require prior knowledge of parameters such as cable current and burial depth. They are also sensitive to sensor pose calibration errors. In actual engineering, it is difficult to maintain the sensor installation pose accurately. Differences between batches of equipment further introduce scale and rotation deviations, resulting in systematic shifts in the reconstruction path. In addition, although ground-penetrating radar can provide dielectric information, its resolution is limited by antenna frequency and underground medium inhomogeneity, making it difficult to effectively separate cable targets from background clutter under low signal-to-noise ratio conditions.

[0004] Existing path reconstruction methods mostly use fixed sampling paths and lack proactive responses to reconstruction uncertainties, resulting in insufficient sampling in complex topological regions and low reconstruction integrity and efficiency. Although some studies have introduced SLAM technology for trajectory optimization, it relies on accurate extrinsic parameter calibration and initial position, and is easily affected by sensor drift during long-term operation.

[0005] In recent years, Neural Radiation Field (NeRF) technology has demonstrated powerful capabilities in 3D reconstruction, enabling the recovery of continuous scenes from sparse observations. However, traditional NeRF lacks explicit constraints on topology, making it prone to pseudo-connectivity or breaks in cable path reconstruction. Furthermore, calibration dependencies and alignment difficulties in multi-source data fusion remain major bottlenecks in practical deployment. Summary of the Invention

[0006] In view of this, the present invention proposes a calibration-free path reconstruction method for buried cables based on Topo-NeRF and active sensing, which can realize high-precision reconstruction of the three-dimensional continuous path of buried cables and extraction of topological relationships.

[0007] The technical solution of this invention is implemented as follows: The method for reconstructing the calibration-free path of buried cables based on Topo-NeRF and active sensing includes the following steps: Step S1: Collect raw data generated by a characteristic frequency current flowing through a cable using a sensor array, and obtain a spatiotemporal feature matrix after preprocessing the raw data. Step S2: After performing feature extraction, spatial alignment, and drift compensation on the spatiotemporal feature matrix, multi-source fused data is obtained; Step S3: Based on multi-source fusion data, the electromagnetic field of the cable is modeled as a continuous three-dimensional topological manifold, an implicit neural radiation field coupled with differentiable electromagnetic rendering is constructed, and the main body of the cable and the branch nodes are separated by a topological bottleneck layer with persistent cohomology constraints to obtain the first round of reconstruction results. Step S4: Based on the first round of reconstruction results, a diffusion model with multi-source information is introduced to sample, denoise and enhance the signal in the weak field region under low signal-to-noise ratio and strong interference. After applying dielectric uniformity constraints, the enhanced high-precision reconstruction results are obtained. Step S5: Calculate the reconstruction uncertainty based on the high-precision reconstruction results and obtain the local topological entropy. Fuse the local topological entropy and multi-source fusion data to obtain the information gain index. Based on the information gain index, determine whether there are areas with high information gain that need to be supplemented for data collection. Step S6: When it is determined that additional data collection is needed, the sensor movement trajectory is dynamically planned based on the information gain index, and steps S1-S5 are repeated; when it is determined that no additional data collection is needed, the high-precision reconstruction results are linked with the geographic information system through a standardized interface to output a three-dimensional path model.

[0008] Preferably, step S1 includes the following steps: A multimodal sensor array is deployed above the cable path, and a characteristic frequency current is passed through the cable to collect magnetic field signals, ground-penetrating radar echoes, odometer and inertial information, and environmental background quantities as raw data. The magnetic field signal was decomposed into six levels using the db8 wavelet basis function and reconstructed after soft thresholding. All original data were then de-DC and trend term denoising were performed. The outlier is removed from the denoised original data based on the 3σ principle, and min-max normalization is used to normalize the original data after outlier removal. Time alignment is performed on the normalized raw data based on GPS / BeiDou synchronization signals to obtain a spatiotemporal feature matrix.

[0009] Preferably, the specific steps of feature extraction in step S2 include: Establish a mathematical framework for the special Euclidean group SE(3), and define its group action as:

[0010] in This represents a transformation operation determined by a group element g, where g represents the group element. Indicates the object being transformed. Let t be a three-dimensional rotation matrix and t be a translation vector. A standard equivariant feature extraction network Φ:X→Z is constructed, wherein the standard equivariant feature extraction network satisfies the core equivariant constraint condition:

[0011] in Let X be a set of input data; The spatiotemporal feature matrix is ​​input into the normalized equivariant feature extraction network. Normalized equivariant features are extracted through equivariant convolutional layers, and an equivariant feature set is output. The feature transformation formula is as follows:

[0012] Where k is the equivariant convolution kernel. Here, is the Haar measure, and is the learnable weight matrix. Represents coordinate position in space. This represents the feature map of the l-th layer.

[0013] Preferably, the specific steps of spatial alignment in step S2 include: Using an equivariant feature set as input, the alignment problem is transformed into a weighted Protodyakonov analysis problem:

[0014] in Let be the weight coefficient of the i-th corresponding point, s be the scale factor, and N be the number of corresponding points. and For the corresponding feature points of different sensors, R represents the rotation matrix and t represents the translation vector; The weighting coefficient Calculation based on feature similarity:

[0015] in , denoted as Euclidean distances between different sensors at corresponding feature points i and j in the feature space. For bandwidth parameters; The weighted centroid is calculated using SVD decomposition:

[0016] in and The weighted centroids of feature points from different sensors; Calculate the covariance matrix: ; After performing SVD decomposition on the covariance matrix, the optimal rotation matrix, optimal translation vector, and optimal scale factor are obtained, and spatially aligned data is output. The SVD decomposition is as follows: ,in , It is an orthogonal matrix. It is a singular value matrix; Optimal rotation matrix Optimal translation vector , , in is the trace of the singular value matrix.

[0017] Preferably, the specific steps of drift compensation in step S2 are as follows: Online drift compensation is performed using an extended Kalman filter, defining the state vector as including position, velocity, attitude, and sensor bias:

[0018] in For three-dimensional position coordinates, For three-dimensional velocity components, For attitude quaternions, For accelerometer deviation, This is due to gyroscope bias. After updating the drift compensation amount using the Kalman gain, the drift-compensated data is output. The drift compensation update formula is as follows:

[0019] in This represents the drift compensation amount at time k. Here is the Kalman gain matrix. For the observation vector, For the observation function, This is the predicted state value. Forgetting factor; After integrating the drift-compensated data, the magnetic field gradient, relative permittivity, and GPR echo characteristics are extracted as multi-source fusion data.

[0020] Preferably, the specific steps of step S3 are as follows: Based on multi-source fusion data, a topology graph structure describing the topological characteristics of a cable network is defined. , where V is the set of spatial sampling points and E is the set of topological connection relationships; For each sampling point i, define its feature vector. ,in The three-axis magnetic field strength, The relative permittivity, For the current intensity, define its eigenvector for each edge (i,j)∈E(i,j). ,in For spatial distance, It is the direction angle. For electromagnetic field gradient, For connection confidence; Spatial features are extracted using a topological graph convolutional layer, and the calculation formula is as follows:

[0021] in It is an adjacency matrix with self-connections. For degree matrix, This represents the node features of the l-th layer. For learnable weight matrix, For activation functions; Three-dimensional coordinates based on multi-source fusion data Position features are generated by using a multi-frequency sine function for position encoding.

[0022] in L is the coding frequency; By fusing location features with spatial topological features, an implicit neural radiation field coupled with differentiable electromagnetic rendering is constructed, and the field strength and topological features of the neural radiation field are output. The network output is as follows:

[0023] in The magnetic field vector, For bulk density, For topological feature vectors, The observation direction vector; A topological bottleneck layer is set at layer 6 of the implicit neural radiation field network. A persistent cohomology constraint is introduced to construct a topological loss function, and the field strength and topological characteristics after topological constraint are obtained. The topological loss function is:

[0024] in Here, (b, d) represents the weighting coefficients, and (b, d) represents the birth-death pairs in the persistent graph. For a one-dimensional Betti number, The target value; and These are the topological feature vectors of adjacent nodes; The topologically constrained field strength and topological features are mapped to the probability space through a fully connected layer, outputting the first-round reconstruction results containing the cable path probability distribution and topological connectivity:

[0025]

[0026] in For the probability distribution of cable paths, This is the final hidden state. and For path prediction parameters, This represents the topological connection relationship. and Predict parameters for connectivity relationships. This is the activation function.

[0027] Preferably, step S4 includes the following specific steps: Based on the results of the first round of reconstruction, a conditional diffusion model is constructed by integrating the relative permittivity and GPR echo characteristics from multi-source fusion data, and the conditional vector is defined as follows: ; in To reconstruct the uncertainty graph, The relative permittivity, Code for geological type, This is a characteristic of GPR echo; Based on the conditional diffusion model, a sampling denoising formula for the back diffusion process is defined:

[0028] in Let t be the diffusion state at step t. Here, T is the noise variance parameter, and T is the total number of diffusion steps. For variance, The mean value is the parameterized value from the denoising network. The weak field region data with low signal-to-noise ratio and strong interference in the first round of reconstruction results are input into the conditional diffusion model for sampling, denoising and signal enhancement, and the denoised and enhanced data is output. Using the denoised and enhanced data as input, a weighted loss function is constructed by introducing dielectric consistency constraints, and the constrained optimized data is output. The expression of the weighted loss function is as follows:

[0029] in , , These are the weighting coefficients. To rebuild the losses, To smooth the constraints, This is based on the physical rationality constraints of the relative permittivity; After integrating the constrained optimization data, the probability distribution of cable paths, topological connection relationships and corresponding confidence levels are extracted, and the results are output as enhanced high-precision reconstruction results.

[0030] Preferably, the specific steps of step S5 are as follows: Based on the volume density and topological feature vectors in the high-precision reconstruction results, ensemble learning is used to estimate the reconstruction uncertainty at each location in space:

[0031] in For spatial reconstruction of uncertainty distribution, M is the number of models in the ensemble. This is the volume density output for the m-th model. The topological features output for the m-th model are... and The mean volume density and mean topological features output by the ensemble model; Calculate the local topological entropy by combining the spatial reconstruction uncertainty distribution with the cable path probability distribution in the high-precision reconstruction results:

[0032] in Let x be the probability that position x belongs to the k-th cable, and K be the number of cables. For uncertainty weighting coefficients, The gradient is the logarithmic probability gradient. The information gain index is calculated based on local topological entropy, and the spatial information gain distribution is output:

[0033] in For spatial information gain distribution, , , , These are the weighting coefficients. The magnitude of the magnetic field gradient. For sampling interval indicators, This represents the global maximum value of the magnetic field gradient magnitude; Set an information gain threshold, compare the spatial information gain distribution with the information gain threshold, and determine whether there are areas that need to be supplemented by sampling that exceed the threshold.

[0034] Preferably, the specific steps for determining in step S6 that supplementary sampling is required are as follows: Based on spatial information gain distribution, a model predictive control framework is used to construct the trajectory optimization objective function: st

[0035] in H represents the prediction time domain, serving as the control input. As a discount factor, R is the control weight matrix. For the safe zone, , A feasible control set; After solving the objective function for trajectory optimization, the optimized sensor movement trajectory is obtained. Steps S1-S5 are then executed again according to the sensor movement trajectory.

[0036] Preferably, step S6, when it is determined that no further sampling is needed, includes the following steps: After the high-precision reconstruction results are linked with the geographic information system through a standardized interface, a three-dimensional path model containing path geometry information, topology connection information, and cable attribute information is output. The path geometry information is as follows: The topology connection information is The cable attribute information is ; in As coordinates, Cable radius, For confidence level, For connection weights, For connection type, Cable type For voltage level, The date of burial.

[0037] Compared with the prior art, the beneficial effects of the present invention are: This invention presents a calibration-free path reconstruction method for buried cables based on Topo-NeRF and active sensing. It collects raw data using a multimodal sensor array, preprocesses it to obtain a spatiotemporal feature matrix, and then automatically aligns the matrix based on a normalized isovariant feature representation. This achieves consistent fusion across devices and batches without external parameter calibration, enabling online compensation for sensor drift and maintaining long-term stability. Next, the cable magnetic field is modeled as a continuous three-dimensional topological manifold using a topological neural radiation field, coupled with differentiable electromagnetic rendering. By introducing persistent cohomology constraints into the network to maintain topological correctness, the cable body and branch nodes can be accurately separated, yielding the first-round reconstruction result. For low signal-to-noise ratio regions in the first-round reconstruction result, uncertainty graphs and energy-saving parameters are introduced. The conditional diffusion model, with the number as a condition, enhances weak field signals through backsampling and applies dielectric consistency constraints to ensure that the reconstruction results are consistent with the underground physical structure, thereby obtaining high-precision reconstruction results. To improve reconstruction efficiency, an active sensing mechanism based on local topological entropy is set up. When the local uncertainty is high, the sensor movement path is automatically adjusted to achieve supplementary sampling, realizing closed-loop optimization. Finally, a three-dimensional path model containing path geometry information, topological connection information, and cable attribute information can be output, visualized, and archived. Without the need for external parameter calibration and manual intervention, high-precision reconstruction of the three-dimensional continuous path of buried cables and extraction of topological relationships can be achieved. The active sensing improves sampling efficiency and maintains robustness in low signal-to-noise ratio environments, making it suitable for rapid mapping and long-term operation and maintenance of urban underground cables. Attached Figure Description

[0038] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only preferred embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0039] Figure 1 This is a flowchart of the method for reconstructing the calibration-free path of buried cables based on Topo-NeRF and active sensing according to the present invention. Detailed Implementation

[0040] To better understand the technical content of this invention, a specific embodiment is provided below, and the invention will be further described in conjunction with the accompanying drawings.

[0041] See Figure 1 The method for reconstructing the calibration-free path of buried cables based on Topo-NeRF and active sensing provided by this invention includes the following steps: Step S1: Acquire raw data generated by a characteristic frequency current flowing through a cable using a sensor array, and preprocess the raw data to obtain a spatiotemporal feature matrix. Specific steps include: A multi-mode sensor array, including a triaxial magnetic field sensor, a ground-penetrating radar antenna, an odometer, and an IMU, is deployed above the cable path. The sampling frequency is preferably 10kHz and the GPR spacing is 5cm. Anti-aliasing filtering is configured at the front end to ensure that the measurement range is not saturated. After a characteristic frequency current is passed into the cable, magnetic field signals, ground-penetrating radar echoes, odometer and inertial information, and environmental background quantities are collected as raw data. Geomagnetic compensation and trend term removal are performed on the magnetic field signal to establish a geomagnetic field model:

[0042] in The compensated magnetic field signal, This is the original magnetic field reading. , The coefficient for the trend term. , This is the power frequency harmonic compensation coefficient. By removing the geomagnetic field background and power frequency interference, a clean cable magnetic field signal is provided for subsequent processing. For the compensated magnetic field signal A 6-level decomposition was performed using the db8 wavelet basis function. After decomposing to the J-th level, approximate coefficients were obtained. With detail coefficient , , For scaling function, Using wavelet basis, this decomposition will transform the signal The components are separated into different splicing points to facilitate subsequent noise suppression and feature extraction. Then, soft thresholding is applied to the detail coefficients obtained from the decomposition.

[0043] in Let the threshold be the value of the j-th layer. Let N be the standard deviation of the noise at layer j, and N be the signal length. A soft thresholding process is applied to the detail coefficients. This thresholding process suppresses noise while preserving the edge features of the cable's magnetic field, ensuring the accuracy of subsequent feature extraction.

[0044] The unthresholded approximation coefficients and the soft-thresholded detail coefficients are then reconstructed using wavelet reconstruction to obtain the reconstructed denoised magnetic field signal:

[0045] in The reconstructed denoised magnetic field signal, The approximation coefficients for the Jth layer are... These are the detail coefficients after thresholding at each layer. J This represents the wavelet decomposition level.

[0046] After obtaining the reconstructed signal, all raw data are subjected to DC removal and trend term denoising. At the same time, outliers are removed from the denoised raw data based on the 3σ principle. Min-max normalization is used to normalize the raw data after outlier removal. The outlier removal threshold is set to mean ± 3 times standard deviation, and the normalization range is set to the [0,1] interval. The time alignment accuracy reaches the millisecond level to ensure that multi-source data are comparable under a unified spatiotemporal framework.

[0047] To achieve precise spatiotemporal alignment of multi-source data, a time synchronization model is established, and a unified time benchmark is set up to ensure precise spatiotemporal alignment of multi-source data, providing a foundation for subsequent data fusion. Based on GPS / BeiDou synchronization signals, the normalized raw data is time-aligned to obtain a spatiotemporal feature matrix.

[0048] The time synchronization model is as follows:

[0049] in The standard timestamp after synchronization For the local data acquisition time of each sensor, This is the system clock offset. For clock drift correction, For the i-th GPS time reference point, after time synchronization is completed, a data quality assessment system is established to ensure that the data entering subsequent processing has reliable quality.

[0050] Preprocessing may introduce new errors, requiring a system-wide quality assessment to filter out qualified data and ensure the accuracy of subsequent modeling.

[0051]

[0052]

[0053] in, This is a comprehensive quality score, ranging from [0,1], used for data filtering. The signal-to-noise ratio (SNR) is used to evaluate signal purity. Waveform distortion, used to detect the degree of signal distortion. These are the weighting coefficients. , These are signal power and noise power, respectively. After the qualified data are screened through quality assessment, they need to be integrated into a unified feature representation.

[0054] To support subsequent topological neural radiation field modeling, it is necessary to integrate multi-source heterogeneous data into a unified matrix. This is to facilitate neural network processing:

[0055] Where F is the spatiotemporal feature matrix, which integrates all sensor data. Let M be the feature value of the i-th sensor at time j, M be the number of sensor types, and T be the time series length. After the feature matrix is ​​constructed, final data standardization is required to eliminate the influence of dimensions.

[0056] To achieve automatic alignment and fusion of multi-sensor data without external parameter calibration, in step S2, feature extraction, spatial alignment, and drift compensation are performed on the spatiotemporal feature matrix to obtain multi-source fused data, ensuring the stability of the system during long-term operation. Feature extraction: Establish a mathematical framework for the special Euclidean group SE(3), and define its group action as:

[0057] in This represents a transformation operation determined by a group element g, where g represents the group element. Indicates the object being transformed. Let t be a three-dimensional rotation matrix and t be a translation vector. A standard equivariant feature extraction network Φ:X→Z is constructed, wherein the standard equivariant feature extraction network satisfies the core equivariant constraint condition:

[0058] in Let X be a set of input data; The spatiotemporal feature matrix is ​​input into the normalized equivariant feature extraction network. Normalized equivariant features are extracted through equivariant convolutional layers, and an equivariant feature set is output. The feature transformation formula is as follows:

[0059] Where k is the equivariant convolution kernel. Here, is the Haar measure, and is the learnable weight matrix. Represents coordinate position in space. Let represent the feature map of the l-th layer, which is a function.

[0060] To ensure the network meets the equivariance requirement, an equivariant loss function is defined as a constraint:

[0061] in For sampling transform group, For decoder networks, Using the Frobenius norm, this loss function forces the network to maintain transformation equivariance during learning, providing geometrically consistent feature representations for subsequent alignment.

[0062] Spatial alignment: Using an equivariant feature set as input, the alignment problem is transformed into a weighted Protodyakonov analysis problem:

[0063] in Let be the weight coefficient of the i-th corresponding point, s be the scale factor, and N be the number of corresponding points. and For the corresponding feature points of different sensors, R represents the rotation matrix and t represents the translation vector; The weighting coefficient Calculation based on feature similarity:

[0064] in , denoted as Euclidean distances between different sensors at corresponding feature points i and j in the feature space. The bandwidth parameter is set to 0.1. This weighting mechanism ensures that high-quality corresponding points play a greater role in the alignment process. The weighted centroid is calculated using SVD decomposition:

[0065] in and The weighted centroids of feature points from different sensors; Calculate the covariance matrix: ; After performing SVD decomposition on the covariance matrix, the optimal rotation matrix, optimal translation vector, and optimal scale factor are obtained, and spatially aligned data is output. The SVD decomposition is as follows: ,in , It is an orthogonal matrix. It is a singular value matrix; Optimal rotation matrix Optimal translation vector , , in is the trace of the singular value matrix.

[0066] After completing the spatial alignment of multi-sensor data, in order to solve the attitude drift problem caused by the accumulation of sensor deviations such as the inertial measurement unit during long-term operation, an online drift compensation mechanism needs to be introduced: Online drift compensation is performed using an extended Kalman filter, defining the state vector as including position, velocity, attitude, and sensor bias:

[0067] in For three-dimensional position coordinates, For three-dimensional velocity components, For attitude quaternions, For accelerometer deviation, This is due to gyroscope bias. After updating the drift compensation amount using the Kalman gain, the drift-compensated data is output. The drift compensation update formula is as follows:

[0068] in This represents the drift compensation amount at time k. Here is the Kalman gain matrix. For the observation vector, For the observation function, This is the predicted state value. Forgetting factor; After integrating the drift-compensated data, the magnetic field gradient, relative permittivity, and GPR echo characteristics are extracted as multi-source fusion data.

[0069] Through the standardized isotropic alignment and drift compensation mechanism established in this step, the system achieves automatic and accurate fusion of multi-source sensor data in both spatiotemporal dimensions. Spatially, it eliminates the dependence on external parameter calibration, and temporally, it suppresses sensor deviation drift. Together, they ensure measurement stability during long-term operation and provide a reliable data foundation for high-quality cable path reconstruction.

[0070] Step S3: Based on multi-source fusion data, the cable electromagnetic field is modeled as a continuous three-dimensional topological manifold, an implicit neural radiation field coupled with differentiable electromagnetic rendering is constructed, and the cable body and branch nodes are separated through a topological bottleneck layer with persistent cohomology constraints to obtain the first round of reconstruction results. The specific steps are as follows: Based on multi-source fusion data, a topology graph structure describing the topological characteristics of a cable network is defined. , where V is the set of spatial sampling points and E is the set of topological connection relationships; For each sampling point i, define its feature vector. ,in The three-axis magnetic field strength, The relative permittivity, For the current intensity, define its eigenvector for each edge (i,j)∈E(i,j). ,in For spatial distance, It is the direction angle. For electromagnetic field gradient, For connection confidence; Based on the constructed graph structure, to extract spatial dependencies between nodes, a topological graph convolutional layer is used to aggregate neighborhood information. Feature propagation is achieved through graph convolution operations, gradually extracting higher-level spatial topological features. The spatial features extracted through the topological graph convolutional layer are calculated using the following formula:

[0071] in It is an adjacency matrix with self-connections. For degree matrix, This represents the node features of the l-th layer. For learnable weight matrix, For activation functions; Three-dimensional coordinates based on multi-source fusion data Position features are generated by using a multi-frequency sine function for position encoding.

[0072] in L=10 is the encoding frequency, generating 60-dimensional position features. The periodic combination of sine and cosine functions can effectively characterize the spatial variation features at different resolutions. Based on the obtained positional encoding, positional features are fused with spatial topological features to construct an implicit neural radiation field coupled with differentiable electromagnetic rendering. The field strength and topological features of the neural radiation field are then output. The network output is:

[0073] in The magnetic field vector, For bulk density, For topological feature vectors, The observation direction vector; A topological bottleneck layer is set at layer 6 of the implicit neural radiation field network. A persistent cohomology constraint is introduced to construct a topological loss function, and the field strength and topological characteristics after topological constraint are obtained. The topological loss function is:

[0074] in Here, (b, d) represents the weighting coefficients, and (b, d) represents the birth-death pairs in the persistent graph. For a one-dimensional Betti number, The target value; and The topological feature vectors of adjacent nodes are represented by the first term in the topological loss function, which is a persistence constraint. The stability of the topological features is constrained by the persistence of birth-death pairs in the persistent graph. The second term is a one-dimensional Betti number constraint, which ensures that the reconstruction result does not contain non-physical loop structures. The third term is a topological feature consistency constraint, which guarantees the spatial continuity of the topological features of adjacent nodes.

[0075] After training the topologically constrained neural network, the topologically constrained field strength and topological features are mapped to the probability space through a fully connected layer, outputting the first-round reconstruction results containing the cable path probability distribution and topological connectivity:

[0076]

[0077] in For the probability distribution of cable paths, This is the final hidden state. and For path prediction parameters, This represents the topological connection relationship. and Predict parameters for connectivity relationships. This is the activation function.

[0078] This step outputs the initial reconstruction results, accurately describing the main cable path, branch node locations, and their connection confidence. These reconstruction results provide foundational data for topology entropy-based active sensing and trajectory planning, supporting subsequent path optimization decisions.

[0079] Step S4: Based on the first-round reconstruction results, a diffusion model conditioned on multi-source information is introduced to sample, denoise, and enhance the signal in the weak-field region under low signal-to-noise ratio and strong interference. After applying dielectric uniformity constraints, the enhanced high-precision reconstruction result is obtained. The specific steps include: Based on the results of the first round of reconstruction, a conditional diffusion model is constructed by integrating the relative permittivity and GPR echo characteristics from multi-source fusion data, and a conditional vector is defined. : The conditional vector integrates multi-source prior information from the reconstruction process and physical measurements.

[0080] in To reconstruct the uncertainty graph, The relative permittivity, Code for geological type, This is a characteristic of GPR echo; Based on the conditional diffusion model, a sampling denoising formula for the back diffusion process is defined, the core of which lies in learning the conditional probability distribution:

[0081] in Let t be the diffusion state at step t. Here, T is the noise variance parameter, and T is the total number of diffusion steps. For variance, The mean value is the parameterized value from the denoising network. The weak field region data with low signal-to-noise ratio and strong interference in the first round of reconstruction results are input into the conditional diffusion model for sampling, denoising and signal enhancement, and the denoised and enhanced data is output. To ensure that the reconstructed cable path is consistent with the underground physical structure, a weighted loss function is constructed using the denoised and enhanced data as input, incorporating dielectric consistency constraints, and outputting the constrained and optimized data. The expression for the weighted loss function is as follows:

[0082] in , , These are the weighting coefficients. To rebuild the losses, To smooth the constraints, This is based on the physical rationality constraints of the relative permittivity; After integrating the constrained optimization data, the probability distribution of cable paths, topological connection relationships and corresponding confidence levels are extracted, and the results are output as enhanced high-precision reconstruction results.

[0083] Step S5: Calculate the reconstruction uncertainty based on the high-precision reconstruction results and obtain the local topological entropy. Fuse the local topological entropy and multi-source fusion data to obtain the information gain index. Based on the information gain index, determine whether there are high-information-gain areas to be supplemented. The specific steps are as follows: Based on the volume density and topological feature vectors in the high-precision reconstruction results, ensemble learning is used to estimate the reconstruction uncertainty at various spatial locations, reflecting the prediction confidence of the model at different spatial locations:

[0084] in To reconstruct the uncertainty distribution in space, M=10 represents the number of models in the ensemble. This is the volume density output for the m-th model. The topological features output for the m-th model are... and The higher the uncertainty U(x) of the integrated model output, the less reliable the reconstruction results in this region are, and the more likely it is to be sampled first.

[0085] Calculate the local topological entropy by combining the spatial reconstruction uncertainty distribution with the cable path probability distribution in the high-precision reconstruction results:

[0086] in Let x be the probability that position x belongs to the k-th cable, and K be the number of cables. For uncertainty weighting coefficients, The logarithmic probability gradient and the local topological entropy The higher the value, the more complex the topology of the region or the greater the uncertainty, and the higher the potential for information gain.

[0087] The information gain index is calculated based on local topological entropy. By integrating topological entropy, field gradient, sampling gap, and platform reachability, a comprehensive sampling value function is formed, and the spatial information gain distribution is output.

[0088] in For spatial information gain distribution, , , , These are the weighting coefficients. The magnitude of the magnetic field gradient. The sampling gap index is calculated based on the nearest neighbor distance, and its expression is: , For the set of sampled points, This represents the global maximum value of the magnetic field gradient magnitude; Set an information gain threshold, compare the spatial information gain distribution with the information gain threshold, and determine whether there are areas that need to be supplemented by sampling that exceed the threshold.

[0089] Based on the reconstruction of the topological neural radiation field, an active sensing mechanism based on topological entropy is introduced to improve sampling efficiency and reconstruction quality. This mechanism quantifies the uncertainty of local reconstruction, calculates the local topological entropy, and then calculates the information gain index to determine whether there is a region to be sampled, so as to facilitate the subsequent dynamic planning of the sensor's movement trajectory and achieve closed-loop optimization with information gain as the goal.

[0090] Step S6: When it is determined that additional data collection is needed, the sensor movement trajectory is dynamically planned based on the information gain index, and steps S1-S5 are repeated; when it is determined that no additional data collection is needed, the high-precision reconstruction results are linked with the geographic information system through a standardized interface to output a three-dimensional path model. The specific steps for when supplementary sampling is required are as follows: Based on spatial information gain distribution, a model predictive control framework is used to construct a trajectory optimization objective function. The optimization objective is to maximize the cumulative information gain and minimize the control cost. st

[0091] in H represents the prediction time domain, serving as the control input. As a discount factor, R is the control weight matrix. For the safe zone, , A feasible control set; After solving the objective function for trajectory optimization, the optimized sensor movement trajectory is obtained. Steps S1-S5 are then executed again according to the sensor movement trajectory.

[0092] Trajectory planner every The system updates once, recalculating the information gain g(x) based on the current reconstruction results and entropy map, generating a locally optimal trajectory. Through closed-loop feedback, the system automatically increases the sampling density in regions of high uncertainty, thereby improving reconstruction efficiency and completeness. The optimized sensor trajectory sequence is then output. The corresponding control commands enable proactive sensing. This trajectory serves as the input for the next round of data acquisition, forming a closed loop of reconstruction-planning-acquisition, and gradually optimizing the cable path and topology.

[0093] The specific steps when no additional sampling is required are as follows: After the high-precision reconstruction results are linked with the geographic information system through a standardized interface, a three-dimensional path model containing path geometry information, topology connection information, and cable attribute information is output. The path geometry information is as follows: The topology connection information is The cable attribute information is ; in As coordinates, Cable radius, For confidence level, For connection weights, For connection type, Cable type, For voltage level, The date of burial.

[0094] To ensure system performance and data integrity, a rigorous quality control system must be established. This system requires high accuracy in path reconstruction, excellent accuracy in branch identification, and sufficient efficiency for each scan. Appropriate confidence levels must be set to guarantee the reliability of the results. All data changes must be fully tracked through version control to ensure data consistency and traceability. Specifically, the quality control system requires path reconstruction error to be no more than 0.25 meters, a branch identification rate of over 99.2%, a single scan time of no more than 83 seconds, a confidence threshold of 0.85, and the recording of data changes through a version control system.

[0095] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for reconstructing the calibration-free path of buried cables based on Topo-NeRF and active sensing, characterized in that, Includes the following steps: Step S1: Collect raw data generated by a characteristic frequency current flowing through a cable using a sensor array, and obtain a spatiotemporal feature matrix after preprocessing the raw data. Step S2: After performing feature extraction, spatial alignment, and drift compensation on the spatiotemporal feature matrix, multi-source fused data is obtained; Step S3: Based on multi-source fusion data, the electromagnetic field of the cable is modeled as a continuous three-dimensional topological manifold, an implicit neural radiation field coupled with differentiable electromagnetic rendering is constructed, and the main body of the cable and the branch nodes are separated by a topological bottleneck layer with persistent cohomology constraints to obtain the first round of reconstruction results. Step S4: Based on the first round of reconstruction results, a diffusion model with multi-source information is introduced to sample, denoise and enhance the signal in the weak field region under low signal-to-noise ratio and strong interference. After applying dielectric uniformity constraints, the enhanced high-precision reconstruction results are obtained. Step S5: Calculate the reconstruction uncertainty based on the high-precision reconstruction results and obtain the local topological entropy. Fuse the local topological entropy and multi-source fusion data to obtain the information gain index. Based on the information gain index, determine whether there are areas with high information gain that need to be supplemented for data collection. Step S6: When it is determined that additional data collection is needed, the sensor movement trajectory is dynamically planned based on the information gain index, and steps S1-S5 are repeated; when it is determined that no additional data collection is needed, the high-precision reconstruction results are linked with the geographic information system through a standardized interface to output a three-dimensional path model.

2. The method for reconstructing the calibration-free path of buried cables based on Topo-NeRF and active sensing according to claim 1, characterized in that, The specific steps of step S1 include: A multimodal sensor array is deployed above the cable path, and a characteristic frequency current is passed through the cable to collect magnetic field signals, ground-penetrating radar echoes, odometer and inertial information, and environmental background quantities as raw data. The magnetic field signal was decomposed into six levels using the db8 wavelet basis function and reconstructed after soft thresholding. All original data were then de-DC and trend term denoising were performed. The outlier is removed from the denoised original data based on the 3σ principle, and min-max normalization is used to normalize the original data after outlier removal. Time alignment is performed on the normalized raw data based on GPS / BeiDou synchronization signals to obtain a spatiotemporal feature matrix.

3. The method for reconstructing the calibration-free path of buried cables based on Topo-NeRF and active sensing according to claim 1, characterized in that, The specific steps of feature extraction in step S2 include: Establish a mathematical framework for the special Euclidean group SE(3), and define its group action as: in This represents a transformation operation determined by a group element g, where g represents the group element. Indicates the object being transformed. Let t be a three-dimensional rotation matrix and t be a translation vector. A standard equivariant feature extraction network Φ:X→Z is constructed, wherein the standard equivariant feature extraction network satisfies the core equivariant constraint condition: in Let X be a set of input data; The spatiotemporal feature matrix is ​​input into the normalized equivariant feature extraction network. Normalized equivariant features are extracted through equivariant convolutional layers, and an equivariant feature set is output. The feature transformation formula is as follows: Where k is the equivariant convolution kernel. Here, is the Haar measure, and is the learnable weight matrix. Represents coordinate position in space. This represents the feature map of the l-th layer.

4. The method for reconstructing the calibration-free path of buried cables based on Topo-NeRF and active sensing according to claim 3, characterized in that, The specific steps of spatial alignment in step S2 include: Using an equivariant feature set as input, the alignment problem is transformed into a weighted Protodyakonov analysis problem: in Let be the weight coefficient of the i-th corresponding point, s be the scale factor, and N be the number of corresponding points. and For the corresponding feature points of different sensors, R represents the rotation matrix and t represents the translation vector; The weighting coefficient Calculation based on feature similarity: in , denoted as Euclidean distances between different sensors at corresponding feature points i and j in the feature space. For bandwidth parameters; The weighted centroid is calculated using SVD decomposition: in and The weighted centroids of feature points from different sensors; Calculate the covariance matrix: ; After performing SVD decomposition on the covariance matrix, the optimal rotation matrix, optimal translation vector, and optimal scale factor are obtained, and spatially aligned data is output. The SVD decomposition is as follows: ,in , It is an orthogonal matrix. It is a singular value matrix; Optimal rotation matrix Optimal translation vector , , in is the trace of the singular value matrix.

5. The method for reconstructing the calibration-free path of buried cables based on Topo-NeRF and active sensing according to claim 4, characterized in that, The specific steps for drift compensation in step S2 are as follows: Online drift compensation is performed using an extended Kalman filter, defining the state vector as including position, velocity, attitude, and sensor bias: in For three-dimensional position coordinates, For three-dimensional velocity components, For attitude quaternions, For accelerometer deviation, This is due to gyroscope bias. After updating the drift compensation amount using the Kalman gain, the drift-compensated data is output. The drift compensation update formula is as follows: in This represents the drift compensation amount at time k. Here is the Kalman gain matrix. For the observation vector, For the observation function, This is the predicted state value. Forgetting factor; After integrating the drift-compensated data, the magnetic field gradient, relative permittivity, and GPR echo characteristics are extracted as multi-source fusion data.

6. The method for reconstructing the calibration-free path of buried cables based on Topo-NeRF and active sensing according to claim 1, characterized in that, The specific steps of step S3 are as follows: Based on multi-source fusion data, a topology graph structure describing the topological characteristics of a cable network is defined. , where V is the set of spatial sampling points and E is the set of topological connection relationships; For each sampling point i, define its feature vector. ,in The three-axis magnetic field strength, The relative permittivity, For the current intensity, define its eigenvector for each edge (i,j)∈E(i,j). ,in For spatial distance, It is the direction angle. For electromagnetic field gradient, For connection confidence; Spatial features are extracted using a topological graph convolutional layer, and the calculation formula is as follows: in It is an adjacency matrix with self-connections. For degree matrix, This represents the node features of the l-th layer. For learnable weight matrix, For activation functions; Three-dimensional coordinates based on multi-source fusion data Position features are generated by using a multi-frequency sine function for position encoding. in L is the coding frequency; By fusing location features with spatial topological features, an implicit neural radiation field coupled with differentiable electromagnetic rendering is constructed, and the field strength and topological features of the neural radiation field are output. The network output is as follows: in The magnetic field vector, For bulk density, For topological feature vectors, The observation direction vector; A topological bottleneck layer is set at layer 6 of the implicit neural radiation field network. A persistent cohomology constraint is introduced to construct a topological loss function, and the field strength and topological characteristics after topological constraint are obtained. The topological loss function is: in Here, (b, d) represents the weighting coefficients, and (b, d) represents the birth-death pairs in the persistent graph. For a one-dimensional Betti number, The target value; and These are the topological feature vectors of adjacent nodes; The topologically constrained field strength and topological features are mapped to the probability space through a fully connected layer, outputting the first-round reconstruction results containing the cable path probability distribution and topological connectivity: in For the probability distribution of cable paths, This is the final hidden state. and For path prediction parameters, This represents the topological connection relationship. and Predict parameters for connectivity relationships. This is the activation function.

7. The method for reconstructing the calibration-free path of buried cables based on Topo-NeRF and active sensing according to claim 1, characterized in that, The specific steps of step S4 include: Based on the results of the first round of reconstruction, a conditional diffusion model is constructed by integrating the relative permittivity and GPR echo characteristics from multi-source fusion data, and the conditional vector is defined as follows: ; in To reconstruct the uncertainty graph, The relative permittivity, Code for geological type, This is a characteristic of GPR echo; Based on the conditional diffusion model, a sampling denoising formula for the back diffusion process is defined: in Let t be the diffusion state at step t. Here, T is the noise variance parameter, and T is the total number of diffusion steps. For variance, The mean value is the parameterized value from the denoising network. The weak field region data with low signal-to-noise ratio and strong interference in the first round of reconstruction results are input into the conditional diffusion model for sampling, denoising and signal enhancement, and the denoised and enhanced data is output. Using the denoised and enhanced data as input, a weighted loss function is constructed by introducing dielectric consistency constraints, and the constrained optimized data is output. The expression of the weighted loss function is as follows: in , , These are the weighting coefficients. To rebuild the losses, To smooth the constraints, This is based on the physical rationality constraints of the relative permittivity; After integrating the constrained optimization data, the probability distribution of cable paths, topological connection relationships and corresponding confidence levels are extracted, and the results are output as enhanced high-precision reconstruction results.

8. The method for reconstructing the calibration-free path of buried cables based on Topo-NeRF and active sensing according to claim 1, characterized in that, The specific steps of step S5 are as follows: Based on the volume density and topological feature vectors in the high-precision reconstruction results, ensemble learning is used to estimate the reconstruction uncertainty at each location in space: in For spatial reconstruction of uncertainty distribution, M is the number of models in the ensemble. This is the volume density output for the m-th model. The topological features output for the m-th model are... and The mean volume density and mean topological features output by the ensemble model; Calculate the local topological entropy by combining the spatial reconstruction uncertainty distribution with the cable path probability distribution in the high-precision reconstruction results: in Let x be the probability that position x belongs to the k-th cable, and K be the number of cables. For uncertainty weighting coefficients, The gradient is the logarithmic probability gradient. The information gain index is calculated based on local topological entropy, and the spatial information gain distribution is output: in For spatial information gain distribution, , , , These are the weighting coefficients. The magnitude of the magnetic field gradient. For sampling interval indicators, This represents the global maximum value of the magnetic field gradient magnitude; Set an information gain threshold, compare the spatial information gain distribution with the information gain threshold, and determine whether there are areas that need to be supplemented by sampling that exceed the threshold.

9. The method for reconstructing the calibration-free path of buried cables based on Topo-NeRF and active sensing according to claim 8, characterized in that, The specific steps for determining in step S6 that supplementary sampling is required are as follows: Based on spatial information gain distribution, a model predictive control framework is used to construct the trajectory optimization objective function: ,s.t. in H represents the prediction time domain, serving as the control input. As a discount factor, R is the control weight matrix. For the safe zone, , A feasible control set; After solving the objective function for trajectory optimization, the optimized sensor movement trajectory is obtained. Steps S1-S5 are then executed again according to the sensor movement trajectory.

10. The method for reconstructing the calibration-free path of buried cables based on Topo-NeRF and active sensing according to claim 1, characterized in that, The specific steps in step S6 when it is determined that no further sampling is needed are as follows: After the high-precision reconstruction results are linked with the geographic information system through a standardized interface, a three-dimensional path model containing path geometry information, topology connection information, and cable attribute information is output. The path geometry information is as follows: The topology connection information is The cable attribute information is ; in As coordinates, Cable radius, For confidence level, For connection weights, For connection type, Cable type For voltage level, The date of burial.

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