A direct-buried cable non-calibration positioning method based on quantum heuristic field and topology perception

Abstract

The application relates to the technical field of cable positioning, and discloses a direct-buried cable non-calibration positioning method based on a quantum heuristic field and topological perception. The method obtains an observation set Y representing the characteristics of a plurality of physical fields of an underground cable, defines a complex probability amplitude field as a unified field and converts the unified field into an implicit neural network to establish a parameterized Schrodinger equation. The observation set is mapped to the unified field and iteratively fitted to obtain initial values of the unified field and a gauge field under the constraint of the equation. A joint loss function containing a physical and data consistency term is constructed, and the unified field reconstruction is completed by alternately updating. Based on the reconstructed unified field, the three-dimensional path of the cable, the depth curve, the branch and joint node positioning results and the confidence evaluation information are output. The method has high robustness in a strong scattering and low signal-to-noise ratio scene such as reinforced concrete, can realize centimeter-level continuous path reconstruction, is suitable for cable survey, construction early warning and dynamic fault diagnosis, and has the advantages of high precision, non-calibration and engineering feasibility.

Description

Technical Field

[0001] This invention relates to the field of cable positioning technology, and in particular to a calibration-free positioning method for directly buried cables based on quantum heuristic fields and topological sensing. Background Technology

[0002] With the increasing utilization of urban underground space, the density of power cable laying is rapidly rising, and the complexity, deep burial, and multi-layered intersection of power lines are becoming increasingly common. Traditional positioning methods relying on manual detection, cable identification instruments, or single physical field measurements are no longer sufficient to meet the requirements of continuity, accuracy, and anti-interference in modern urban power operation and maintenance. Multimodal geophysical measurement methods, including ground-penetrating radar, low-frequency electromagnetic response, and distributed fiber optic vibration and temperature sensing, can reflect the underground medium structure, cable conductor current coupling characteristics, and disturbance information along the line, providing new information sources for cable path tracing and condition identification. However, in real-world scenarios, these signals are affected by multiple factors such as soil moisture, reinforced concrete reflection, road machinery vibration, and temperature noise, exhibiting characteristics such as weak amplitude, strong interference, and inconsistent time references, significantly increasing the difficulty of direct positioning.

[0003] Existing research commonly employs methods such as ground-penetrating radar (GPR) feature enhancement, low-frequency electromagnetic inversion, and vibration signal envelope analysis for cable detection. While these single-mode algorithms are effective in specific scenarios, inherent contradictions exist between multi-mode signals, including differences in sampling frequency, propagation physical mechanisms, and temporal asynchrony. Traditional methods often struggle to effectively fuse different signal sources. Furthermore, GPR is sensitive to densely metal areas and prone to strong scattering artifacts; low-frequency electromagnetic signals attenuate rapidly in high-conductivity soils; and distributed fiber optic responses are significantly affected by background noise and temperature drift. Faced with complex environments, the various modal signals often exhibit nonlinear superposition and unstable spatiotemporal distribution, making it difficult for traditional rule-based, filtering, or static model-based processing methods to obtain stable and interpretable representations of underground targets.

[0004] To address these issues, recent years have seen the emergence of methods that incorporate deep learning, attention mechanisms, and multimodal fusion networks to automatically learn the correlation structures of different signals from data. However, these models still face challenges when processing non-stationary data across physical modes, such as underground electromagnetic, radar, and fiber optic data, including insufficient generalization, weak dependence on physical constraints, and difficulty in ensuring spatial continuity. Especially in densely packed reinforced concrete urban environments, local distortions caused by strong scattering are difficult to correct using purely data-driven methods. Therefore, there is an urgent need for a unified modeling method that can simultaneously consider multimodal physical mechanisms, possess automatic cross-modal alignment capabilities, and maintain stability in noisy environments. This would enable high-precision, calibration-free positioning of underground cable paths, burial depths, and branch structures, providing reliable technical support for cable surveys, construction avoidance, and emergency maintenance. Summary of the Invention

[0005] In view of the above-mentioned prior art, the present invention provides a calibration-free positioning method for direct-buried cables based on quantum heuristic fields and topological sensing, which mainly solves the technical problems existing in the background art.

[0006] To achieve the above objectives, the technical solution of this invention is implemented as follows: This invention discloses a calibration-free positioning method for directly buried cables based on quantum heuristic fields and topological sensing. The aforementioned method includes the following steps: Obtain an observation set Y characterizing the multi-physics field properties of underground cables, wherein the observation set Y contains multi-modal observation data; We define the complex-valued probability amplitude field as a unified field, transform the complex-valued probability amplitude field into an implicit neural network, and establish a parameterized Schrödinger-type equation. The observation set Y is mapped to a complex probability amplitude field, and the implicit neural network is iteratively fitted to obtain the initial solution of the unified field and the initial value of the gauge field under the constraint of the parameterized Schrödinger type equation. Based on the initial solution of the unified field, a joint loss function containing physical consistency terms and data consistency terms is constructed. The unified field and the gauge field are alternately updated through the joint loss function during the iteration process to complete the reconstruction of the unified field. Based on the reconstructed three-dimensional path, burial depth curve, and location results of branches and joint nodes of the unified field output cable, confidence assessment information of the corresponding location results is generated.

[0007] Optionally, an observation set Y characterizing the multiphysics properties of underground cables is obtained, specifically including: Multimodal sensors are deployed along the surface within the corridor of the underground cable. The multimodal sensors include at least a triaxial magnetic field sensor or a triaxial electric field sensor for acquiring low-frequency current injection response data, a ground-penetrating radar antenna for acquiring underground medium scattering echo data, and distributed optical fibers for vibration and temperature response along the line. Set the deployment parameters and sampling parameters for each sensor, and use a loosely coupled time base to record the timestamps and clock drift parameters of each channel's data; Multimodal data acquisition is performed based on multimodal sensors to obtain low-frequency electromagnetic three-component sequences, ground-penetrating radar echo sequences, and distributed optical fiber vibration and temperature sequences, thereby obtaining raw multimodal observation data. After performing denoising, outlier removal and correction preprocessing on the original multimodal observation data, it is unified to a common spatiotemporal reference to generate an observation set Y with a unified spatiotemporal index.

[0008] Optionally, define the complex-valued probability amplitude field in the spatiotemporal domain. As a unified field, where x represents the spatial coordinates of the lateral survey line on the ground surface, z represents the subsurface depth coordinates, and t represents the time dimension, the complex-valued probability amplitude field... It is a complex-valued function that is square-integrable.

[0009] Optional, implicit neural network Using spacetime coordinate triples As input, the real part of the complex-valued probability amplitude field. With the imaginary part As a dual-output, it realizes a continuously differentiable representation of the complex-valued probability amplitude field in the spatiotemporal domain. It is the set of all parameters in a neural network.

[0010] Optionally, the constructed parameterized Schrödinger-type equation can be expressed as follows:

[0011] Where α represents the diffusion or equivalent migration coefficient of the field. For equivalent electromagnetic potential, This is the thermo-stress coupling potential. For equivalent source terms, Here, i is the Laplace operator, and i is the imaginary unit. The decoherence intensity coefficient, For complex-valued probability amplitude fields, Represents the time evolution operator of the field; When constructing parameterized Schrödinger-type equations, a covariant derivative is introduced to replace the Laplace operator to characterize the relative phase and equivalent gauge transformation between different modes. The covariant derivative is expressed as follows: ,in To standardize the field.

[0012] Optionally, the observation set Y is mapped to a complex-valued probability amplitude field, and the implicit neural network is iteratively fitted to obtain the initial solution of the unified field and the initial value of the gauge field under the constraint of the parameterized Schrödinger-type equation. Specifically, this includes: Define a complex-valued probability amplitude field for each observation mode. Corresponding observation operator The implicit neural network generates the prediction sequence for the m-th mode. Its calculation expression is: ; With multimodal data consistency as the core, an initial solution fitting loss function containing robust loss terms and parameter regularization terms is constructed. Based on backpropagation and gradient descent algorithms, under the constraint of parameterized Schrödinger-type equations, the unified field and the gauge field are alternately and iteratively updated to obtain the initial solution of the unified field and the initial value of the gauge field.

[0013] Optionally, based on backpropagation and gradient descent algorithms, the unified field and gauge field are alternately and iteratively updated under the constraint of the parameterized Schrödinger-type equation. To obtain the initial solution for the unified field and the initial values ​​for the normalized field, the process includes: using the Adam adaptive optimizer to minimize the loss function fitting the initial solution through backpropagation, and iteratively updating... All parameters in the output are used to converge. All parameters in the trained implicit neural network As the initial solution for the unified field, the comprehensive robustness index is calculated within a sliding time window. If the comprehensive robustness index decreases within a continuous time window and the decrease exceeds a preset threshold, the Adam adaptive optimizer is used to adaptively update the gauge field A. Through the above alternating updates, the initial solution for the unified field and the initial value of the gauge field are obtained.

[0014] Optionally, the overall robustness index is calculated within the sliding time window, specifically including: dividing the data into multiple time windows and traversing the full time series data; for the m-th observation mode within a single sliding time window, extracting the actual observation sequence within the window. Predicted observation sequences generated by the unified field observation operator Mean of the observed sequence within the window The coefficient of determination, root mean square error, and observation variance are calculated based on the number of sample points n. A comprehensive robustness index is obtained based on the calculation results. This index is used to uniformly measure the fit and robustness of different modes.

[0015] Optionally, the initial solution of the unified field is used as the object to be estimated, and physical constraints such as electromagnetic and thermal conduction are introduced as soft constraints. These constraints, together with the observation consistency terms of each observation mode, drive the optimization. A sliding window and multi-resolution strategy are adopted to refine the field distribution and boundary / source term descriptions at coarse to fine spatial and temporal scales, thereby completing the reconstruction of the unified field.

[0016] Optionally, the energy field is calculated based on the reconstructed unified field, and the energy field is weighted and accumulated in the time dimension to form a saliency map; the saliency map is then used for ridge tracing and combined with directional consistency constraints to obtain a continuous and smooth three-dimensional cable path centerline; At each lateral position along the three-dimensional path of the cable, the peak value of the significance curve in the depth direction is searched to obtain the initial value of the burial depth. The initial value of the burial depth is fine-tuned and de-biased by combining phase continuity and group delay consistency, and the fine burial depth curve distributed along the path is output. In the candidate region of the saliency map, a closed loop is constructed, and the complex-valued probability amplitude field phase winding number, i.e. the topological charge, is calculated. When the phase winding number is non-zero and simultaneously satisfies the characteristics of local energy maxima and direction field bifurcation, it is determined to be a real cable branch and joint node. The identified branch and joint nodes are skeletonized and connected and then pruned with low saliency to obtain the structured information of branch and joint nodes with spatial location and connection relationship.

[0017] The beneficial effects of this invention are as follows: Addressing the challenges of multimodal observations involving heterogeneous sources, time asynchrony, and difficulties in localization under strong interference, this invention proposes unifying low-frequency current injection, ground-penetrating radar, and distributed fiber optic vibration and temperature observations into a complex-valued probability amplitude field. A parameterized Schrödinger-type spatiotemporal neural field is constructed, and a covariant derivative is introduced into the gauge field to achieve gauge-invariant alignment across modes, eliminating the need for hardware synchronization or absolute calibration. By injecting Maxwell's electromagnetic laws and thermal conduction laws into the physical consistency loss in the form of residuals, the complex-valued probability amplitude field and medium / gauge parameters are reconstructed through training with a joint data consistency term. Furthermore, decoherence suppression and topological charge detection are utilized to stably extract cable paths, burial depth profiles, and branch nodes from the spatial ridges and phase windings of the energy field. This method maintains high robustness even in scenarios with strong scattering and low signal-to-noise ratios, such as reinforced concrete, enabling centimeter-level continuous path reconstruction. It supports edge-cloud collaborative deployment and is suitable for cable surveys, construction early warning, and dynamic fault diagnosis, offering advantages such as high precision, calibration-free operation, and engineering feasibility. Attached Figure Description

[0018] 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.

[0019] Figure 1 This is a flowchart illustrating the calibration-free positioning method for direct-buried cables based on quantum heuristic fields and topological sensing in an embodiment of this application. Detailed Implementation

[0020] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to limit the invention. In the following description, the expression "some embodiments" refers to a subset of all possible embodiments; however, it should be understood that "some embodiments" can be the same subset or different subsets of all possible embodiments and can be combined with each other without conflict.

[0021] In the following description, numerous specific details are set forth in order to provide a more thorough understanding of the invention. However, it will be apparent to those skilled in the art that the invention can be practiced without one or more of these details. In other instances, certain technical features well-known in the art have not been described in order to avoid obscuring the invention.

[0022] It should be understood that the present invention can be embodied in various forms and should not be construed as being limited to the embodiments set forth herein. Rather, providing these embodiments will make the disclosure thorough and complete, and will fully convey the scope of the invention to those skilled in the art. Furthermore, the terminology used herein is intended only to describe particular embodiments and is not intended to limit the invention. When used herein, the singular forms “a,” “an,” and “the” are also intended to include the plural forms unless the context clearly indicates otherwise. It should also be understood that the terms “compose” and / or “comprising,” when used in this specification, identify the presence of the stated features, integers, steps, operations, elements, and / or components, but do not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups. When used herein, the term “and / or” includes any and all combinations of the associated listed items.

[0023] It should also be noted that when an element is referred to as being "fixed to" another element, it can be directly attached to the other element or there may be an intervening element. When an element is referred to as being "connected to" another element, it can be directly connected to the other element or there may be an intervening element. The terms "vertical," "horizontal," "inner," "outer," "left," "right," and similar expressions used herein are for illustrative purposes only and do not represent the only possible implementation.

[0024] To fully understand this invention, a detailed structure will be presented in the following description to illustrate the technical solution proposed by this invention. Optional embodiments of the invention are described in detail below; however, in addition to these detailed descriptions, the invention may have other embodiments.

[0025] Please refer to the attached document. Figure 1 This application provides a calibration-free positioning method for directly buried cables based on quantum heuristic fields and topological sensing. The method includes the following steps: S1. Obtain an observation set Y characterizing the multi-physics field properties of underground cables, wherein the observation set Y contains multi-modal observation data; In some embodiments of this application, step S1 involves obtaining an observation set Y characterizing the multiphysics properties of the underground cable, specifically including: Multimodal sensors are deployed along the surface within the corridor of the underground cable. The multimodal sensors include at least a triaxial magnetic field sensor or a triaxial electric field sensor for acquiring low-frequency current injection response data, a ground-penetrating radar antenna for acquiring underground medium scattering echo data, and distributed optical fibers for vibration and temperature response along the line. Set the deployment parameters and sampling parameters for each sensor, and use a loosely coupled time base to record the timestamps and clock drift parameters of each channel's data; Multimodal data acquisition is performed based on multimodal sensors to obtain low-frequency electromagnetic three-component sequences, ground-penetrating radar echo sequences, and distributed optical fiber vibration and temperature sequences, thereby obtaining raw multimodal observation data. After performing denoising, outlier removal and correction preprocessing on the original multimodal observation data, it is unified to a common spatiotemporal reference to generate an observation set Y with a unified spatiotemporal index.

[0026] Specifically, to obtain high-quality raw observation data characterizing the multi-physics field properties around the cable, low-frequency electromagnetic sensors, ground-penetrating radar antennas, and distributed fiber optic survey lines were deployed within the target corridor to simultaneously acquire surface electromagnetic disturbances, underground scattered echoes, and vibration and temperature signals along the cable. The low-frequency channel measured the three components of the magnetic or electric field, respectively. (or ) It is used to characterize the time-varying response of cable conductor current at the ground surface; Ground-penetrating radar output A-scan echo sequence It reflects the scattering characteristics of the interface between the underground medium structure and the cable sheath; distributed optical fibers provide vibration signals along the line. With temperature signal It is used to capture information about external disturbances, mechanical actions, and heat diffusion. During data acquisition, each channel records timestamps, local clock drift, and survey line spatial indexes according to its own sampling mode, providing necessary spatiotemporal references for subsequent unified field modeling. To reduce the impact of environmental interference and equipment drift on observations, the raw signals undergo on-site preprocessing, including: The acquired raw signals undergo bandpass filtering, DC drift removal, amplitude self-checking, and anomaly removal sequentially to suppress power frequency interference, low-frequency drift, and high-frequency noise. Dedicated preprocessing, including dewow, zero-time correction, and gain compensation, is performed on the radar channel, while wavelet denoising and optical path correction are applied to the fiber optic channel to ensure amplitude stability and temporal continuity of each mode signal. Subsequently, all observation sequences are uniformly mapped to a common time grid using resampling. Furthermore, the measurement point numbers, fiber optic distances, and radar locations are uniformly mapped to the geographic coordinate system, forming a multi-channel observation block with a consistent spatiotemporal reference. Its structure is represented as: .

[0027] S2. Define the complex-valued probability amplitude field as a unified field, convert the complex-valued probability amplitude field into an implicit neural network, and establish a parameterized Schrödinger-type equation. In this embodiment, to address the issues of heterogeneous physical mechanisms, asynchronous time bases, and difficulty in direct fusion of multimodal observation data, this invention first constructs a unified field capable of uniformly characterizing the comprehensive physical state around underground cables. Specifically, this unified field adopts a complex-valued probability amplitude field. As a mathematical expression, the unified field refers to a field variable that maps previously independent heterogeneous data such as low-frequency electromagnetic responses, ground-penetrating radar echoes, distributed optical fiber vibrations, and temperature signals onto the same spatiotemporally continuous mathematical framework, achieving unified carrying and collaborative representation of multimodal physical information. The complex-valued probability amplitude field... It is a square-integrable complex-valued function defined in a two-dimensional spatial domain (x is the coordinate of the horizontal survey line on the ground surface, z is the coordinate of the underground depth) and a time domain t. It belongs to the complex-valued Hilbert space, and its core characteristic is that it includes amplitude. With phase The two dimensions—amplitude and phase—can uniformly characterize the energy / intensity features of each modality's data, while phase can accurately capture the spatiotemporal evolution characteristics of different modes. The synergistic effect of the two allows a single field variable to be compatible with multiple physical processes such as electromagnetic propagation, medium scattering, and thermal diffusion.

[0028] To achieve optimizable and continuous representation of complex-valued probability amplitude fields in engineering, this invention converts them into an implicit neural network representation, i.e. ,That The implicit neural network, consisting of all the parameters to be trained in the neural network, including the weight matrices and bias vectors of each layer, is a type of neural network based on spatiotemporal coordinate triples. As input, the real part of the complex-valued probability amplitude field. With the imaginary part As a dual-output parameterized model that realizes the continuous differentiable representation of complex-valued probability amplitude fields in the spatiotemporal domain, its core advantage lies in its ability to implicitly express infinite-dimensional spatiotemporal continuous fields with finite network parameters, without the need for dense discrete sampling in the spatiotemporal domain. This ensures both the continuity and differentiability of the field while significantly reducing computational complexity. Choosing an implicit neural network as the parameterization carrier essentially transforms the optimization problem of complex-valued probability amplitude fields from an infinite-dimensional function space into a numerical optimization problem in a finite-dimensional parameter space. This enables the subsequent gradient descent algorithm based on backpropagation to be executed effectively, providing an engineering-feasible technical path for cross-modal alignment and physical constraint reconstruction.

[0029] Furthermore, based on the implicit neural representation of the complex-valued probability amplitude field described above, this invention further establishes a parameterized Schrödinger-type equation as the core rule for the spatiotemporal evolution of the field. The expression of the constructed parameterized Schrödinger-type equation is as follows:

[0030] The parameterized Schrödinger equation refers to a generalized partial differential equation inspired by the quantum mechanical Schrödinger equation. By introducing adaptively optimizable physical parameters, it can be adapted to multi-physics coupling scenarios in underground cable detection. Here, α represents the field diffusion or equivalent migration coefficient. For equivalent electromagnetic potential, This is the thermo-stress coupling potential. For equivalent source terms, Here, i is the Laplace operator, and i is the imaginary unit. The decoherence intensity coefficient, For complex-valued probability amplitude fields, Represents the time evolution operator of the field; Furthermore, to address the issues of time asynchrony and inability to directly align phases in multimodal data, this invention introduces a covariant derivative into the parameterized Schrödinger equation. When constructing the parameterized Schrödinger equation, the covariant derivative replaces the Laplace operator to characterize the relative phase and equivalent gauge transformation between different modes, ensuring that the complex-valued probability amplitude field satisfies gauge invariance, i.e., when... When a gauge transformation is performed with A, the physical observables of the field (amplitude, energy, topological characteristics) remain unchanged. This allows for automatic absorption of time / phase deviations between multimodal modes through adaptive adjustment of the gauge field, achieving gauge-invariant alignment across modes without the need for hardware synchronization equipment or manual absolute calibration. Its covariant derivative is expressed as: ,in To standardize the field.

[0031] S3. Map the observation set Y to the complex-valued probability amplitude field and iteratively fit the implicit neural network to obtain the initial solution of the unified field and the initial value of the gauge field under the constraint of the parameterized Schrödinger type equation. In some implementations of step S3, after completing the implicit neural network parameterization representation of the complex-valued probability amplitude field, the construction of the parameterized Schrödinger-type equation, and the introduction of the covariant derivative, the complex-valued probability amplitude field is defined for each observation mode in the observation set Y. Corresponding observation operator This establishes a differentiable and optimizable mapping relationship between a unified field space and the actual observation space. Specifically, for the triaxial magnetic / electric field sensing mode corresponding to the low-frequency current injection response, the observation operator is designed as a projection operator of the equivalent electromagnetic potential component in the complex probability amplitude field at z=0 on the Earth's surface, which can transform the spatial electromagnetic distribution of the field into a triaxial electromagnetic time series that matches the dimension of the measured data. For ground-penetrating radar echo modes, the observation operator is designed as an integral projection operator of the scattered field components in the medium in the depth domain, which can map the scattering characteristics at different depths underground into radar A-scan echo sequences. For distributed fiber vibration and temperature sensing modes, the observation operator is designed as a line integral operator of the thermal potential / stress potential components in the field along the predicted cable path, which can convert the heat diffusion and stress propagation characteristics along the line into time series corresponding to fiber sampling points. Using the above mode-specific observation operators, the prediction sequence of the m-th mode can be directly generated through an implicit neural network. Its calculation expression is: This enables the previously independent multimodal observation data to be uniformly mapped to the mathematical framework of complex-valued probability amplitude fields, providing a differentiable computational basis for subsequent iterative fitting and parameter optimization.

[0032] Furthermore, focusing on multimodal data consistency and incorporating evolutionary rule constraints from parameterized Schrödinger-type equations, an initial solution fitting loss function is constructed, comprising a robust loss term, equation residuals, and parameter regularization terms. The robust loss term is constructed using the Huber loss function, obtained by applying measured sequences from each modality. With predicted sequence The bias is weighted and calculated to effectively suppress the adverse effects of strong on-site interference, outliers, and signal saturation segments on the fitting process. Simultaneously, appropriate weight coefficients are assigned to modes with different signal-to-noise ratios to avoid a single high-noise mode dominating the fitting process. The residual term of the equation is constructed based on a parameterized Schrödinger-type equation. By calculating the residual norm between the temporal evolution term, spatial diffusion term, potential term, decoherence term, and source term of the field, the iterative optimization process is forced to always follow the spatiotemporal evolution rules set by the equation, avoiding deviations from the objective physical laws of the underground caused by purely data-driven fitting. The parameter regularization term targets the equivalent diffusion coefficient α and the decoherence intensity coefficient. Equivalent electromagnetic potential Thermal coupling potential The equivalent source term S and other physical properties, along with the spatial distribution of the gauge field A, are used to constrain all parameters within a physically reasonable range determined based on prior field data. This ensures the spatiotemporal smoothness of the parameters, preventing parameter mutations and model divergence during optimization. The final expression for the initial solution fitting loss function L is:

[0033]

[0034]

[0035] in, , , These are preset positive weighting coefficients, corresponding to the constraint strength of the data consistency term, equation residual term, and parameter regularization term, respectively. They can be adaptively adjusted according to the on-site working conditions and modal signal-to-noise ratio. For multimodal data robust loss terms, To parameterize the residuals of Schrödinger-type equations, The square of the L2 norm of the residual. For parameter regularization terms, These are the weighting coefficients for the m-th mode. This is the robust loss function for Huber.

[0036] Based on the constructed initial solution fitting loss function, backpropagation and adaptive gradient descent algorithms are used to update the unified field and gauge field through an alternating iterative strategy under the full constraint of the parameterized Schrödinger equation. The entire iterative process is based on the gauge invariance of the parameterized Schrödinger equation, dividing the complete iteration cycle into two alternately executed optimization stages. In the first optimization stage, the current value of the gauge field A is kept unchanged and included as a constant in the calculation of the covariant derivative of the parameterized Schrödinger equation. The goal is to minimize the initial solution fitting loss function. By calculating the gradient of the loss function with respect to the implicit neural network weights and bias parameters, the Adam adaptive optimizer is used to update the network parameters, so that the complex-valued probability amplitude field satisfies the fitting requirements of multimodal observation data and the evolution rule constraints of the parameterized Schrödinger equation within the fixed gauge framework. In the second optimization stage, the parameters of the implicit neural network are fixed and kept unchanged, the overall distribution of the complex probability amplitude field is locked, and the gradient of the loss function with respect to the initial solution fitting is calculated and iterative update is completed with the goal of minimizing the initial solution fitting loss function. Through the normative transformation characteristics of the covariant derivative, the normative field automatically absorbs the relative phase shift, local clock drift and time base deviation between different modes, and completes the initial calibration-free alignment of multimodal data without the need for hardware synchronization equipment and manual absolute calibration.

[0037] Furthermore, during the iterative process, a sliding time window is used to continuously evaluate the robustness of the fitting effect of each sensing channel, thereby quantifying the interpretability of the complex-valued probability amplitude field for multimodal observation data and the model robustness. Within each sliding time window, the coefficient of determination R², root mean square error RMSE, and observation variance Var are calculated for the corresponding modal measured and predicted sequences. The coefficient of determination R² measures the fitting and interpretability of the unified field for the main trend of the modal signal, the root mean square error RMSE characterizes the fitting deviation at the amplitude level, and the observation variance Var reflects the natural fluctuation level of the signal within that time window. Based on these, a comprehensive robustness index is calculated. Their calculation expressions are as follows:

[0038] RMSE

[0039] Var

[0040]

[0041] By simultaneously considering explanatory power and relative error, the fitting results of different modes under different amplitudes and noise levels are unified to the same evaluation scale, avoiding the problem of a single index biasing towards a certain type of mode. This ensures a unified field... To maintain adaptive consistency with on-site operating conditions, this invention sets an adaptive threshold Δr*. Monitor the temporal changes, and when they occur within a continuous time window When the temperature drops significantly and the cumulative decrease exceeds a preset threshold Δr*, it is determined that the current unified field model's explanatory power for that mode or corresponding region has significantly degraded. This may be due to changes in environmental conditions, abnormal sensor status, or shifts in physical property parameters. Subsequently, the gauge field A and the set of relevant physical property parameters are triggered. The adaptive update, through backpropagation and gradient optimization, re-adjusts the unified field and gauge field under a unified loss function, enabling the updated complex-valued probability amplitude field to re-balance between physical and data constraints. If the model remains stable and does not show a significant decrease within the sliding time window, it is determined that the current model still has good interpretability and robustness in this region. The existing parameters are kept unchanged and the model proceeds to the next time window for rolling evaluation.

[0042] When the iterative process meets the preset convergence conditions, the optimization process terminates, and the final unified field initial solution and normalized field initial values ​​are output. The convergence conditions include three criteria: first, the relative change of the initial solution fitting loss function is lower than the preset convergence threshold for multiple consecutive iterations, indicating that the loss function has reached a stable convergence state; second, the average comprehensive robustness index of all modes... The unified field maintains stability, and the average coefficient of determination R² reaches the preset fitting requirement threshold, demonstrating a stable interpretability for multimodal observation data. Thirdly, the residual norm of the parameterized Schrödinger-type equation is lower than the preset threshold, ensuring that the spatiotemporal evolution of the complex-valued probability amplitude field always follows the set physical rules, without any false fitting results that deviate from objective laws.

[0043] The unified field initial solution output after convergence is the convergence result of the complex-valued probability amplitude field after completing the initial multimodal fitting and cross-modal alignment. Its essence is still a continuously differentiable complex-valued function defined in the spatiotemporal domain. At the same time, the output gauge field initial value has completed the absorption of the main phase and time deviations between the multimodal modes. The output also includes the converged set of physical property parameters and the distribution of fitting residuals for each mode. The above outputs not only provide a continuous, differentiable field representation and reliable initial values ​​for the subsequent physical consistency reconstruction by introducing Maxwell's electromagnetic constraints and thermal conduction constraints, but also physically guarantee the consistent description of different modal signals within the same spatiotemporal framework.

[0044] S4. Based on the initial solution of the unified field, a joint loss function containing physical consistency terms and data consistency terms is constructed. The unified field and the gauge field are alternately updated through the joint loss function during the iteration process to complete the reconstruction of the unified field. In some implementations of step S4, after obtaining the initial solution of the unified field, the initial value of the gauge field, and the matching set of physical property parameters output in the aforementioned steps, three types of core physical residual terms are constructed based on the parameterized unified field, serving as the core of the physical consistency constraint for the joint loss function. The constructed Schrödinger-type equation residuals are used to quantify the deviation between the parameterized unified field and the previously established core evolution rules by calculating the deviations between the time evolution term, spatial diffusion term, double-potential-well coupling term, decoherence term, and equivalent source term of the unified field. This ensures that the reconstruction process always follows the core mathematical and physical framework of the quantum-inspired unified field. Furthermore, the residuals of Maxwell's electromagnetic equations are introduced. (Depend on , The residuals (comprising the electromagnetic residuals, thermal conductivity residuals, and thermal conductivity residuals) are constructed based on the objective physical laws of magnetic field curl and divergence. The electromagnetic residuals are used to ensure that the distribution of the equivalent electromagnetic potential in the unified field is consistent with the underground electromagnetic propagation characteristics. The thermal conductivity residuals are constructed based on the thermal diffusion equation and are used to ensure that the evolution of the equivalent thermal coupling potential in the unified field matches the propagation laws of temperature and vibration along the cable. These three types of residuals together constitute the physical consistency constraint. The expression for the thermal conductivity residual is:

[0045] Where T represents the temperature field along the line, κ is the thermal diffusivity, and Q(ψ) represents the equivalent heat source introduced by the unified field. The residuals described above characterize the deviation between the model field and the actual physical laws. The dedicated observation operators defined for each observation mode in the previous steps are reused to generate predicted observation sequences for each mode based on the parameterized unified field. A data consistency term is constructed in the form of a weighted robust loss. For each mode, the deviation between the measured observation sequence and the model prediction sequence is calculated. The Huber robust loss function is used to replace the traditional mean square error loss to effectively suppress the adverse effects of strong on-site interference, isolated outliers, and signal saturation segments on the fitting process. At the same time, appropriate weight coefficients are assigned to different modes. The weight coefficients can be adaptively adjusted according to the fit robustness index of each mode obtained in the previous steps. Higher weights are assigned to modes with high signal-to-noise ratio and stable fitting effect, while the weights are reduced for modes that are severely disturbed and have insufficient robustness. This avoids a single high-noise mode dominating the reconstruction process and ensures that the data consistency term can truly reflect the degree of fitting of the unified field to the effective observation information of multiple modes.

[0046] To further improve the stability of the reconstruction process under strong scattering environments, a decoherence suppression regularization term and a parameter prior regularization term are added to the joint loss function. The decoherence suppression regularization term is achieved by imposing constraints on the temporal and spatial smoothness of the unified field phase field. By minimizing the L2 norm of the temporal partial derivative and spatial gradient of the phase field, it reduces the phase random walk problem caused by steel bars, concrete, and local strong scatterers in urban environments, and improves the continuity and interpretability of the phase field in the spatiotemporal domain. The parameter prior regularization term is based on prior information from the field engineering and applies soft constraints to physical property parameters such as the equivalent diffusion coefficient, decoherence intensity coefficient, equivalent electromagnetic potential, thermal coupling potential, and equivalent source term. This ensures that the parameters remain within the physically reasonable range corresponding to field conditions such as soil conductivity and cable laying parameters during the optimization process. At the same time, it constrains the spatial smoothness of the parameters to avoid parameter abrupt changes and model divergence during the optimization process.

[0047] The physical consistency term, data consistency term, and regularization term are weighted and combined according to preset weights to form a complete joint loss function. The weights of each term can be adaptively adjusted according to the on-site working conditions, signal-to-noise ratio level, and reconstruction requirements. The expression of the joint loss function is as follows:

[0048] in, , , , , , For each weight, For decoherence suppression regularization, For parameter smoothing and prior constraints, decoherence suppression regularization is achieved through temporal and spatial smoothing constraints on the phase field φ(x,z,t)=argψ(x,z,t):

[0049] This reduces phase random walks caused by steel bars, concrete, and local strong scatterers, and improves the continuity and interpretability of the phase field in space and time.

[0050] In terms of optimization strategy, a sliding time window and multi-resolution joint reconstruction strategy is adopted. First, preliminary reconstruction is carried out on a coarser spatial grid and a longer time window. By reducing the optimization degrees of freedom in the spatiotemporal dimension, the parameterized unified field can quickly approximate the overall shape of the underground cable field distribution, lock the neighborhood range of the global optimum, and avoid the local optimum problem that is prone to occur when optimizing directly on a high-resolution grid. Subsequently, the spatial grid and time step are gradually refined. In local key areas such as cable bends, branch areas, and burial depth variation areas, the constraint strength of physical residuals and data residuals is gradually increased to restore the local detailed structure of the field distribution in a targeted manner, taking into account both reconstruction efficiency and detail accuracy.

[0051] To achieve accurate cross-modal alignment without the need for hardware synchronization and absolute calibration, an alternating update strategy is adopted in each round of iterative optimization. The unified field and the gauge field are jointly adjusted separately. In the first optimization stage, the current spatial distribution of the gauge field is kept unchanged and is included as a constant in the calculation of the covariant derivative. With the goal of minimizing the joint loss function, the gradient of the loss function with respect to the neural network parameter θ is calculated through an automatic differentiation framework. An adaptive gradient descent optimizer is used to update the parameters of the unified field, so that the unified field can simultaneously meet the constraints of multiple physical laws and the fitting requirements of multimodal observation data under a fixed gauge framework. In the second optimization stage, the parameters of the unified field neural network are kept unchanged after the fixed update. The overall amplitude and energy distribution of the unified field are locked. With the goal of minimizing the joint loss function, the gradient of the loss function with respect to the gauge field is calculated and iterative updates are completed. Through the gauge invariance property of the covariant derivative, the gauge field automatically absorbs the relative phase shift, local clock drift and time base deviation between different modes during the optimization process. Without the need for any hardware synchronization device, the gauge invariance and accurate alignment of multimodal data are completed.

[0052] During the iteration process, the norms of the three types of physical residuals, the statistical characteristics of the data residuals of each modality, and the convergence status of the joint loss function are continuously monitored. For local areas with severe occlusion, signal loss, or strong interference, when it is detected that the data term loss and physical residual cannot decrease simultaneously for a long time, a local re-initialization and constraint strengthening mechanism is triggered. That is, the initial field value is resampled in the region, the weight of the physical constraint term is increased, or the strength of the phase smoothing constraint is increased to avoid reconstruction failure caused by local optima. At the same time, the prior information of the field is comprehensively utilized. For source terms or boundary conditions that cannot be directly measured, they are regarded as latent variables and synchronously inverted and estimated by minimizing the joint loss function. When the physical residuals and data residuals have both converged stably to below the preset threshold after multiple iterations, and the amplitude and phase of the unified field no longer show large oscillations in the time domain, it is determined that the spatiotemporal neural field and the gauge field have achieved stable convergence in both physical and data senses, and the iterative optimization process is terminated.

[0053] After completing iterative convergence, the system outputs the unified field complex-valued probability amplitude distribution that is stably converged within the entire time window, the matching gauge field spatial distribution, the updated set of physical property parameters, the equivalent source term distribution, and the physical residual distribution map, data residual distribution map, and phase continuity evaluation results in the entire time and space domain. The above outputs not only provide a stable, consistent, and physically meaningful field basis for subsequent cable path extraction, burial depth estimation, and branch node identification based on energy field and phase topology, but also significantly improve the robustness and interpretability of the method under strong interference and complex working conditions through the embedding of multiple physical constraints.

[0054] S5. Based on the reconstructed unified field output cable three-dimensional path, burial depth curve, and branch and joint node positioning results, generate the corresponding confidence assessment information of the positioning results.

[0055] In some implementations of step S5, the amplitude information of the unified field is transformed into an energy distribution representation that can be used for target feature extraction, using the formula... The calculated energy field in the spatiotemporal domain exhibits significant high-energy concentration characteristics at the cable's spatial location, directly reflecting the cable's spatial distribution characteristics. To further suppress transient interference and enhance the stability of the cable trunk, the energy field is weighted and accumulated along the time dimension to form a saliency map reflecting the cable trunk's distribution characteristics. Its calculation expression is as follows:

[0056] in, The weighting coefficients in the time dimension are used to emphasize high-quality observation information within stable signal periods or specific time windows. Time segments affected by strong interference or signal saturation are assigned low weights to weaken the interference of transient noise and outliers on the spatial distribution characteristics of the cable. The resulting saliency map shows a clear and continuous high-energy ridge structure at the corresponding cable location, providing a core basis for the subsequent extraction of cable path, burial depth, and branch nodes.

[0057] Furthermore, based on the generated saliency map, a ridge tracing algorithm is used to extract the cable's center path. During the tracing process, directional consistency constraints and local gradient stability criteria are introduced simultaneously to constrain the forward direction of each tracing node, ensuring that the path extension direction is consistent with the gradient direction of the saliency ridge, avoiding path jumps and branch artifacts. Simultaneously, phase gradient information from the gauge field A is used to assist in determining the path extension direction, ensuring stable continuity of the path even in structurally complex regions with low energy. After completing the initial ridge tracing, the initial path is optimized using curvature and connectivity rules, eliminating jump points with abrupt curvature changes and pseudo-short branches with lengths below a preset threshold. Interpolation and smoothing fitting are then used to obtain a continuous, smooth, and abrupt three-dimensional cable path centerline. This centerline is stored as a point set arranged along a spatial coordinate sequence, completely covering the entire cable path and providing a spatial reference for the subsequent generation of the burial depth curve.

[0058] Furthermore, along the extracted three-dimensional cable path, a saliency curve corresponding to the depth direction is extracted at each lateral position x. Peak search is used to determine the depth position corresponding to the maximum energy value, thereby obtaining the initial value of the cable burial depth at that lateral position. The calculation expression is as follows:

[0059] To further improve the accuracy and stability of burial depth estimation, the initial burial depth value is refined. First, the phase continuity condition of the complex-valued probability amplitude field is combined with the constraint on the partial derivative of the phase field φ(x,z,t)=argψ(x,z,t) in the depth direction. φ / The smoothness of z effectively mitigates the burial depth estimation bias caused by energy peak drift in high-noise environments. Furthermore, by utilizing the group delay correlation characteristics of the complex-valued probability amplitude field, the initial burial depth value is directionally corrected, ensuring that the burial depth curve remains continuous and stable at path inflection points and areas of underground structural change. Finally, a fine burial depth curve distributed along the cable path is output. Simultaneously, the peak steepness and residual stability index corresponding to each burial depth point are calculated, providing basic data for subsequent confidence assessment.

[0060] Furthermore, to address the identification requirements of cable branches and joints, a closed loop C is constructed in candidate regions with local maxima of energy and potential bifurcations in the path direction in the saliency map. The topological verification of branches and joints is achieved by calculating the phase winding number (i.e., topological charge) of the complex-valued probability amplitude field. The expression for calculating the topological charge is as follows:

[0061] in, The phase field of the complex-valued probability amplitude field. When the calculated phase winding number q≠0, it indicates the presence of a topological defect point within the closed loop, which can serve as a preliminary basis for determining cable branches or joint nodes. To distinguish between genuine branch nodes and pseudo-branches caused by strong underground scatterers, the topology test results are jointly evaluated with the energy distribution characteristics and path direction field characteristics of the saliency map. Only when the phase winding number is non-zero and simultaneously satisfies both the local energy maxima and the direction field bifurcation characteristics are the candidate nodes determined as genuine cable branches and joint nodes. After node identification, based on the local energy gradient and direction field trend of the complex-valued probability amplitude field, the branch path is extended into a skeletonized form, and a low-saliency pruning operation is performed to remove pseudo-branches without physical meaning. Finally, structured information of branch and joint nodes with spatial location, direction vector, and connection relationships is obtained, completely restoring the cable's topology.

[0062] In some embodiments of this application, a structured output and uncertainty assessment mechanism for the positioning results is constructed based on the extracted cable centerline, burial depth curve, and branch topology nodes. This enables the final three-dimensional cable positioning results to not only have a visual spatial expression capability but also a quantifiable confidence level, which can be directly used for the above applications and operation and maintenance decisions.

[0063] In terms of structured output, the cable path is represented as a set of centerline points arranged along a spatial coordinate sequence. Furthermore, interpolation and smoothing fitting methods are used to ensure that the centerline is geometrically continuous, smooth, and without abrupt changes; the burial depth result is represented as a continuous curve that varies with path parameters. It retains environmental information along the route, path curvature, and estimated stability indicators to verify the burial depth under different engineering scenarios; for branch and joint structures, it provides a clear topological description in the form of branch point location, branch direction vector, connection relationship matrix, etc., thus forming a structured dataset that can be directly called by GIS system, BIM platform or cable survey platform.

[0064] In terms of uncertainty assessment, this invention fully considers multimodal data noise, physical residual fluctuations, and local instabilities in the unified field reconstruction process, propagating these factors spatially to form confidence interval estimates for the path, burial depth, and branch nodes. Since the path and burial depth are derived from features such as the energy peak, phase gradient, and saliency map of the unified field, their errors can be propagated through the gradient sensitivity of the unified field to obtain a statistically significant uncertainty range. For example, when... When the energy distribution in a certain region is relatively flat or the phase change is not stable enough, the path position or burial depth deviation in that region will exhibit a wider range; conversely, when the significant ridge is narrow and the phase is stable, the output range will be narrower. For branch nodes, since the identification of branches depends on the phase winding number, local energy peaks, and the bifurcation structure of the orientation field, the estimation of their confidence simultaneously integrates topological consistency, energy steepness, and the stability of the reconstruction residual.

[0065] Based on the aforementioned uncertainty quantification, this invention uses a threshold determination strategy to classify the positioning results into engineering-level usability segments. When a path segment has a small interval width and stable residuals, it can be marked as a high-confidence segment; if a path segment has a wide interval or significant fluctuations in the physical residuals of the local unified field, it is marked as a segment requiring verification, and the potential source of error for that segment is clearly indicated in the output. For branch nodes, when topological consistency is insufficient or energy peaks are not obvious, the system will mark low-confidence scores or candidate branches in the output, prompting manual or subsequent algorithm verification. Finally, a comprehensive output dataset is generated, containing three-dimensional path coordinates, burial depth curves, a list of branch nodes, confidence intervals, and threshold determination results. This output can not only be directly rendered by subsequent visualization platforms but also used by cable asset management systems or emergency operation and maintenance systems for construction avoidance, planning and design, fault location, and underground space information integration. This step creates a closed loop at the engineering implementation level, transforming the results of the quantum-inspired unified field model from physical field-level information into structured positioning information directly applicable to power engineering applications, thereby significantly improving the usability, reliability, and practical application value of the method.

[0066] The above are merely specific embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. The scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A calibration-free positioning method for directly buried cables based on quantum heuristic fields and topological sensing, characterized in that, The aforementioned method includes the following steps: Obtain an observation set Y characterizing the multi-physics field properties of underground cables, wherein the observation set Y contains multi-modal observation data; We define the complex-valued probability amplitude field as a unified field, transform the complex-valued probability amplitude field into an implicit neural network, and establish a parameterized Schrödinger-type equation. The observation set Y is mapped to a complex probability amplitude field, and the implicit neural network is iteratively fitted to obtain the initial solution of the unified field and the initial value of the gauge field under the constraint of the parameterized Schrödinger type equation. Based on the initial solution of the unified field, a joint loss function containing physical consistency terms and data consistency terms is constructed. The unified field and the gauge field are alternately updated through the joint loss function during the iteration process to complete the reconstruction of the unified field. Based on the reconstructed three-dimensional path, burial depth curve, and branch and joint node positioning results of the unified field output cable, confidence assessment information of the corresponding positioning results is generated. Define the complex-valued probability amplitude field in the space-time domain. As a unified field, where x represents the spatial coordinates of the lateral survey line on the ground surface, z represents the subsurface depth coordinates, and t represents the time dimension, the complex-valued probability amplitude field... It is a complex-valued function that is square-integrable; The constructed parameterized Schrödinger type equation is expressed as follows: in, This represents the diffusion or equivalent migration coefficient of the field. For equivalent electromagnetic potential, This is the thermo-stress coupling potential. For equivalent source terms, Here, i is the Laplace operator, and i is the imaginary unit. The decoherence intensity coefficient, For complex-valued probability amplitude fields, Represents the time evolution operator of the field; When constructing parameterized Schrödinger-type equations, a covariant derivative is introduced to replace the Laplace operator to characterize the relative phase and equivalent gauge transformation between different modes. The covariant derivative is expressed as follows: in To standardize the field; The expression for its joint loss function is: in, , , , , , For each weight, For decoherence suppression regularization, For parameter smoothing and prior constraint terms, For multimodal data, robust loss term, To parameterize the residuals of Schrödinger-type equations, The square of the L2 norm of the residual. For the residuals of Maxwell's electromagnetic equations, For the thermal conductivity residual, For each modal measured sequence, For the predicted sequence, The weighting coefficients for the m-th mode are... This is the Huber robust loss function.

2. The calibration-free positioning method for direct-buried cables based on quantum heuristic fields and topological sensing according to claim 1, characterized in that, Obtain the observation set Y characterizing the multiphysics properties of underground cables, specifically including: Multimodal sensors are deployed along the surface within the corridor of the underground cable. The multimodal sensors include at least a triaxial magnetic field sensor or a triaxial electric field sensor for acquiring low-frequency current injection response data, a ground-penetrating radar antenna for acquiring underground medium scattering echo data, and distributed optical fibers for vibration and temperature response along the line. Set the deployment parameters and sampling parameters for each sensor, and use a loosely coupled time base to record the timestamps and clock drift parameters of each channel's data; Multimodal data acquisition is performed based on multimodal sensors to obtain low-frequency electromagnetic three-component sequences, ground-penetrating radar echo sequences, and distributed optical fiber vibration and temperature sequences, thereby obtaining raw multimodal observation data. After performing denoising, outlier removal and correction preprocessing on the original multimodal observation data, it is unified to a common spatiotemporal reference to generate an observation set Y with a unified spatiotemporal index.

3. The calibration-free positioning method for direct-buried cables based on quantum heuristic fields and topological sensing according to claim 2, characterized in that, Hidden Neural Networks Using spacetime coordinate triples As input, the real part of the complex-valued probability amplitude field. With the imaginary part As a dual-output, it realizes a continuously differentiable representation of the complex-valued probability amplitude field in the spatiotemporal domain. It is the set of all parameters in a neural network.

4. The calibration-free positioning method for direct-buried cables based on quantum heuristic fields and topological sensing according to claim 3, characterized in that, The observation set Y is mapped to a complex-valued probability amplitude field, and the implicit neural network is iteratively fitted to obtain the initial solution of the unified field and the initial value of the gauge field under the constraint of the parameterized Schrödinger-type equation. Specifically, this includes: Define a complex-valued probability amplitude field for each observation mode. Corresponding observation operator The implicit neural network generates the prediction sequence for the m-th mode. Its calculation expression is: ; With multimodal data consistency as the core, an initial solution fitting loss function containing robust loss terms and parameter regularization terms is constructed. Based on backpropagation and gradient descent algorithms, under the constraint of parameterized Schrödinger-type equations, the unified field and the gauge field are alternately and iteratively updated to obtain the initial solution of the unified field and the initial value of the gauge field.

5. The calibration-free positioning method for direct-buried cables based on quantum heuristic fields and topological sensing according to claim 4, characterized in that, Based on backpropagation and gradient descent algorithms, the unified field and gauge field are iteratively updated alternately under the constraint of the parameterized Schrödinger-type equation. To obtain the initial solution for the unified field and the initial values ​​for the normalized field, the process includes: using the Adam adaptive optimizer to minimize the loss function fitting the initial solution through backpropagation, and iteratively updating... All parameters in the output are used to converge. All parameters in the trained implicit neural network As the initial solution for the unified field, the comprehensive robustness index is calculated within a sliding time window. If the comprehensive robustness index decreases within a continuous time window and the decrease exceeds a preset threshold, the Adam adaptive optimizer is used to adaptively update the gauge field A. Through the above alternating updates, the initial solution for the unified field and the initial value of the gauge field are obtained.

6. The calibration-free positioning method for direct-buried cables based on quantum heuristic fields and topological sensing according to claim 5, characterized in that, The comprehensive robustness index is calculated within a sliding time window, specifically by dividing the data into multiple time windows and traversing the full-time series data. For the m-th observation mode within a single sliding time window, the actual observation sequence within the window is extracted. Predicted observation sequences generated by the unified field observation operator Mean of the observed sequence within the window The coefficient of determination, root mean square error, and observation variance are calculated based on the number of sample points n. A comprehensive robustness index is obtained based on the calculation results. This index is used to uniformly measure the fit and robustness of different modes.

7. The calibration-free positioning method for direct-buried cables based on quantum heuristic fields and topological sensing according to claim 6, characterized in that, Using the initial solution of the unified field as the object to be estimated, electromagnetic and thermal conduction physical constraints are introduced as soft constraints, which, together with the observation consistency terms of each observation mode, drive the optimization. A sliding window and multi-resolution strategy are adopted to refine the field distribution and boundary and source term descriptions at coarse to fine spatial and temporal scales, thereby completing the reconstruction of the unified field.

8. The calibration-free positioning method for direct-buried cables based on quantum heuristic fields and topological sensing according to claim 7, characterized in that, The energy field is calculated based on the reconstructed unified field, and a saliency map is formed by weighted accumulation of the energy field in the time dimension. Ridge tracing is performed on the saliency map and combined with directional consistency constraints to obtain a continuous and smooth three-dimensional cable path centerline. At each lateral position along the three-dimensional path of the cable, the peak value of the significance curve in the depth direction is searched to obtain the initial value of the burial depth. The initial value of the burial depth is fine-tuned and de-biased by combining phase continuity and group delay consistency, and the fine burial depth curve distributed along the path is output. In the candidate region of the saliency map, a closed loop is constructed, and the complex-valued probability amplitude field phase winding number, i.e. the topological charge, is calculated. When the phase winding number is non-zero and simultaneously satisfies the characteristics of local energy maxima and direction field bifurcation, it is determined to be a real cable branch and joint node. The identified branch and joint nodes are skeletonized and connected and then pruned with low saliency to obtain the structured information of branch and joint nodes with spatial location and connection relationship.

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