A method for extracting electrical parameters of a double-cable random bending three-dimensional path

Abstract

The application provides a double-cable random bending three-dimensional path electric parameter extraction method, relates to the technical field of random bending cables, and provides a double-cable random bending three-dimensional path electric parameter extraction method, which can generate a three-dimensional cable random path meeting the engineering realizability under the condition that cable installation endpoints and geometric constraints are given, and establish a corresponding electric parameter matrix extraction model for the random bending path, so as to obtain an inductance matrix and a capacitance matrix of a double-cable system, and provide a reliable basis for cable electromagnetic parameter analysis.

Description

Technical Field

[0001] This invention relates to the technical field of randomly bent cables, and more particularly to a method for extracting electrical parameters of a three-dimensional path of randomly bent dual cables. Background Technology

[0002] The bending patterns of cables in actual engineering applications are inherently random and non-repeatable; the path shape of cables at the same laying location may differ after each assembly. Therefore, relying solely on measurements of one or a few physical cables to obtain bending paths cannot cover all possible bending situations, nor can it meet the need for prior assessment of unknown cable layouts during the design phase. To perform system-level simulation analysis and reliability assessment of cable crosstalk, engineering projects often require hundreds or thousands of possible bending samples, and statistical methods to analyze the distribution patterns of electrical parameters and their impact on system performance. This necessitates that the path generation method must be able to generate a large number of different random bending pattern samples in batches and automatically under given endpoint constraints, with each sample satisfying physical realizability constraints. Traditional measured path reconstruction methods rely on physical samples, and the cost of sample acquisition is high, failing to meet the practical needs of this large-scale statistical analysis.

[0003] Existing technologies face two main challenges in modeling and extracting parameters for randomly curved cables. First, at the level of generating random geometric paths, while the commonly used random walk algorithm is easy to implement, it cannot naturally satisfy the strong boundary constraints of fixed connection positions at both ends of the cable, easily leading to path divergence. Methods that generate curved cable paths through random point perturbation, spline interpolation, or simple noise superposition often only focus on the "curved appearance," lacking a systematic consideration of the minimum spacing between conductor envelopes, local sharp bend limitations, and the stability of subsequent electrical parameter solutions. While finite element mechanical dynamics simulations generate realistic paths, their computational cost is extremely high, making it difficult to support hundreds or thousands of Monte Carlo (MCM) statistical analyses. Furthermore, when generating parallel bi- or multi-cable systems, these methods struggle to completely eliminate physical penetration and overlap (i.e., cable clipping collisions) between multiple cables at a low cost, often resulting in geometric models that lack true physical realizability.

[0004] In extracting electromagnetic parameters from cables, the commonly used Multi-Conductor Transmission Line (MTL) theory typically employs an approximate method of solving local cross-sections in two dimensions. This method divides the curved cable longitudinally into several tiny cross-sections, assuming that the electromagnetic field distribution within each cross-section conforms to two-dimensional quasi-static laws, extracting the local unit-length parameters separately, and then cascading them. However, this assumption of longitudinal segmentation essentially ignores the parasitic coupling between non-adjacent segments caused by sharp bends in three-dimensional space. At sharp bends in three dimensions, the longitudinal magnetic field cross-inductance and spatial stray capacitance between non-orthogonal segments increase significantly. Traditional two-dimensional cross-section solutions cannot account for this part of the full three-dimensional global coupling field, resulting in distortion of the extracted inductance (L) and capacitance (C) matrices when facing real complex bending conditions. Furthermore, existing solutions typically treat "random path generation" and "electrical parameter extraction" as two independent steps, lacking a technical flow from constrained random path construction to obtaining the global LC matrix.

[0005] Existing methods for modeling electrical parameters of cables are mostly based on ideal straight cables or regular geometric structures, which makes it difficult to reflect the random bending patterns of cables caused by installation deviations, vibrations, or environmental factors in actual applications. Directly performing detailed 3D electromagnetic modeling on randomly bent cables also presents problems such as complex modeling and high computational costs. Furthermore, methods for extracting electrical parameters from bent cables often rely on simplified cross-section approximations or high-cost 3D full-wave modeling, making it difficult to stably obtain engineering-applicable inductance and capacitance matrices under random spatial path conditions. Summary of the Invention

[0006] To address the technical problem mentioned in the background section regarding the difficulty in stably obtaining engineering-applicable inductance and capacitance matrices under random spatial path conditions, this invention provides a method for extracting electrical parameters of a two-cable system with random bending in a three-dimensional path. This method generates a three-dimensional random cable path that meets engineering feasibility requirements given cable installation endpoints and geometric constraints. A corresponding electrical parameter matrix extraction model is then established for this random bending path to obtain the inductance and capacitance matrices of the two-cable system, providing a reliable foundation for cable electromagnetic parameter analysis.

[0007] The technical means employed in this invention are as follows: A method for extracting electrical parameters of a three-dimensional path of random bending of two cables includes the following steps: Step 1: Set the starting coordinates of the two cables, A and B, in three-dimensional space. coordinates of the endpoint , Simultaneously, geometric parameters for physical boundary determination are set; the geometric parameters include: conductor core radius. Insulation layer thickness and the minimum additional safety clearance between the outer surfaces of the two lines. Based on the actual physical outer radius of the cable The minimum distance threshold that the center axes of the two cables can approach each other is calculated. This serves as a hard constraint on the spatial distance between the discrete points of the two cables; Step 2: Connect the start and end points of each cable to construct a linear base path, and calculate the unit tangent vector of the line connecting the two endpoints of the base path. : ;in, These represent the start and end coordinates of any single cable in three-dimensional space; based on the unit tangent vector... Construct three unit vectors that are perpendicular to the main extension direction of the cable, and are orthogonal to each other, satisfying the following conditions: Establish a local orthogonal reference coordinate system; among which, and Let each of these represent a unit basis vector that is orthogonal to the other in the transverse normal plane perpendicular to the main extension direction. Step 3: Use sinusoidal basis functions that satisfy homogeneous boundary conditions. , , Construct the main disturbance term With fine perturbation terms Superimposed two-layer perturbation model The expansion coefficients of the two-layer perturbation are generated by using different modal truncation orders, Gaussian random variables, and spectral attenuation factors. These coefficients are then combined with the linear basis path to generate the initial three-dimensional centerline path of the cable. ; Step 4: Sample the continuous three-dimensional centerline path at equal intervals. A discrete path point sequence is used, and the discrete nodes are smoothed iteratively using the neighbor difference correction formula; the local bending angle and discrete radius of curvature of each node are calculated, combined with the maximum allowable bending angle. radius of curvature The bundle performs mean pullback correction on distorted nodes to complete the path geometric regularization process. Step 5: Perform global minimum distance detection on the discrete path nodes of the two cables. For violation positions where the spatial distance between nodes is less than the minimum distance threshold, adjust the node coordinates through an iterative correction formula based on the connection reverse rejection direction vector and the endpoint zero constraint weight function to eliminate cable path overlap and close contact problems. Step 6: Resample and discretize the corrected 3D cable path into several 3D straight line elements according to the arc length. Based on the Maxwell space Neumann double line integral equation combined with the high-order Gauss-Legendre orthogonal numerical integral, calculate the partial inductance between any two line elements, assemble the global partial inductance matrix, and aggregate it according to the principle of continuous and consistent current in the same cable to obtain the overall equivalent inductance matrix of the two-cable system. ; Step 7: Solve and normalize the capacitance matrix using the electrostatic moment method: Based on the point matching idea of ​​the electrostatic moment method, assuming that the charge of each line element is uniformly distributed, and combining the equivalent dielectric constant and the influence of the ground plane in the image method, construct the overall situation coefficient matrix and solve the linear equation to obtain the charge density distribution of the line elements; integrate and sum to obtain the total induced charge of the cable, and after symmetry processing, obtain the overall equivalent capacitance matrix. Introducing a reference straight-through length Normalization yields the equivalent inductance matrix per unit length. With capacitor matrix Complete the extraction of electrical parameters for the dual-cable system.

[0008] Further, in step 1, the minimum distance threshold The calculation formula is: ; in, Indicates the actual physical outer radius of the cable; This indicates the minimum additional safety clearance between the outer surfaces of the two lines.

[0009] Furthermore, in step 3, the main disturbance term With fine perturbation terms The modal expansion formula is: ; in, and Let these represent the modal truncation orders of the main perturbation and the minor perturbation, respectively; the stochastic expansion coefficients satisfy: ; in, Indicates the amplitude of the controlled disturbance. Indicates the spectral attenuation factor; Both represent independent Gaussian random variables that follow a standard normal distribution; This represents a standard normal distribution with a mean of 0 and a variance of 1.

[0010] Furthermore, in step 4, the formula for the smooth update of discrete nodes is: ; in, Indicates the coordinates of the smoothed nodes; These are the original coordinates of the current node and its preceding and following adjacent nodes, respectively. The formula for calculating the discrete radius of curvature is: ; in, Represents the discrete radius of curvature. Represents the cross product operation of vectors; when included angle According to The weighting ratio will pull the abnormal node back to the average position of the three adjacent points for correction.

[0011] Furthermore, in step 5, the node correction formula is: ; ;in, , This represents the corrected discrete node coordinates; Indicates the iteration correction step size; Represents the unit repulsion direction vector; This represents the position weight function, and This ensures that the coordinates of the cable endpoints remain fixed. and These represent the parameter positions of the two discrete points on the normalized path, respectively.

[0012] Furthermore, in step 6, any two line elements The partial inductance extraction formula is as follows: ; in, Represents the permeability of free space. Let represent the unit tangent vectors of the two line elements, respectively. This represents the spatial distance between integration points. This represents the inductance regularization radius, which is the radius of the conductor core. .

[0013] Furthermore, in step 7, the equivalent capacitance matrix is ​​processed using the following symmetry formula: .

[0014] Furthermore, in step 3, the generated initial three-dimensional centerline path is: ; And satisfy the endpoint constraints , .

[0015] Furthermore, in step 7, the expression for the elements of the potential coefficient matrix is: ; in, Represents the vacuum permittivity. Indicates the effective dielectric constant. Indicates the capacitance regularization radius; Indicates the first i The position vector of the center matching point of each target line element. Indicates the first j Integral position on the source line element The corresponding position vector.

[0016] Compared with the prior art, the present invention has the following advantages: 1. Improved Realism, Constraint Satisfaction, and Sample Acquisition Efficiency in Generating Random Bending Paths for Dual Cables. This invention utilizes a dual-layer spectral attenuation expansion mechanism based on homogeneous boundary sinusoidal modes to generate smooth random paths in batches, exhibiting both macroscopic bending trends and local textures. Compared to traditional methods such as random perturbation and spline interpolation, this invention simultaneously introduces minimum spacing constraints, local curvature constraints, and path smoothing constraints during path generation. This ensures that the generated paths maintain random bending characteristics while meeting the physical feasibility under actual installation conditions, avoiding unrealistic geometric situations such as path penetration and overlap, and sharp local bends. Furthermore, the method proposed in this invention can generate random bending dual cable samples that meet engineering constraints in batches without relying on actual cable samples for path measurement. Single path generation takes only about 0.3 seconds, improving the efficiency of cable path data acquisition and providing a sufficient source of random cable path samples for large-scale statistical analysis during the design phase.

[0017] 2. Significantly improved accuracy and computational efficiency in electrical parameter extraction. This invention abandons the traditional longitudinal segmentation combined with two-dimensional cross-section solution method, directly extracting the overall equivalent inductance and capacitance matrices of the entire curved dual cable based on the global three-dimensional PEEC method and MoM method, fully accounting for the spatial mutual inductance coupling between non-parallel segments caused by bending and the electrostatic coupling between different longitudinal positions. Through typical case testing, the calculation deviation of mutual inductance is reduced from 18.7% in the traditional segmented two-dimensional method to 3.2%, and the calculation deviation of mutual capacitance is reduced from 15.3% to 4.1%, with accuracy improvements of approximately 83% and 73%, respectively. A single parameter calculation takes approximately 2 seconds, and a batch run of 1000 random samples takes no more than 35 minutes. The output unit-length inductance and capacitance matrices are both symmetric positive definite matrices with good physical consistency, allowing direct interface with multi-conductor transmission line solvers without intermediate format conversion. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some 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 of the method proposed in this invention; Figure 2 This is a schematic diagram illustrating a random path generation algorithm for cables according to the present invention. Figure 3 This refers to the cable path generated in a single operation according to the present invention. Figure 4 This is a top view of the cable path generated in a single operation according to the present invention; Figure 5 This is the result curve of the mutual inductance between cables along the longitudinal length according to the present invention; Figure 6 This is the result curve of the self-inductance of the two cables along the longitudinal length of the present invention; Figure 7 This is the result curve of the mutual capacitance between cables along the longitudinal length in this invention; Figure 8 The curves showing the self-capacitance of the two cables along the longitudinal length are the results of this invention. Detailed Implementation

[0020] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0021] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0022] like Figures 1-8 As shown, this invention addresses the shortcomings of the prior art by providing a method for generating a three-dimensional path of random bending of a dual-cable system and extracting its electrical parameters. It can efficiently generate randomly bending paths of cables that satisfy physical constraints, directly calculate and extract the global LC matrix of the dual-cable system in three-dimensional space, and further output the normalized results of the equivalent electrical parameters per unit length. The flowchart of the proposed method is shown below. Figure 1 As shown, the specific steps include the following: Step 1: Set the start and end coordinates of the two cables (line A and line B) in three-dimensional space, which are rigidly fixed. The start coordinate is set to... The endpoint coordinates are set to All three-dimensional coordinates are This design ensures that the cable's two ends are strictly fixed in three-dimensional space. Simultaneously, geometric parameters for physical boundary determination must be set, including the conductor core radius. Insulation layer thickness Minimum additional safety clearance between the outer surfaces of the two lines At this point, the actual physical outer radius of the cable is defined as... Based on this, the minimum distance threshold that the central axes of the two cables can be allowed to approach each other in space is calculated:

[0023] in, This is the minimum allowable axial distance boundary between the centerlines of the two cable paths. This threshold is a hard constraint to prevent geometric clipping collisions; the spatial distance between any discrete points at corresponding positions of the two lines must not be less than this value.

[0024] Step 2: After defining the starting point constraint of the cable, a deterministic linear base path is constructed by connecting the starting and ending points. This base path not only determines the large-scale spatial span of the cable in three-dimensional space but also defines the main extension direction of the cable. To accurately describe this direction, the unit tangent vector of the line connecting the two endpoints is first calculated. This vector serves as the reference axis in the subsequent establishment of the orthogonal coordinate system. The formula for calculating the tangent vector is:

[0025] in, Describes the Euclidean norm of a vector. Let be the unit tangent vector of the base path. These represent the starting and ending coordinates of any single cable in three-dimensional space.

[0026] This tangent vector determines the main extension direction of the cable. To construct a two-dimensional random perturbation within a cross-section perpendicular to the main extension direction, two mutually orthogonal unit basis vectors are further constructed. and The local orthogonal basis satisfies the geometric constraints:

[0027] in, and These are two mutually orthogonal unit basis vectors in the transverse normal plane perpendicular to the main extension direction. These two basis vectors provide a local orthogonal coordinate system for the two-dimensional random perturbation expansion, thereby ensuring that the overall path direction is controlled by the endpoint connection.

[0028] Step 3: Based on the base path, add a two-layer expansion of the main bending mode and the minor perturbation mode to the cable path. Introduce homogeneous boundary conditions. sinusoidal basis functions ,in Furthermore, a spatial transverse perturbation is generated using a finite-dimensional modal expansion mechanism, and sinusoidal basis functions are selected to ensure that the perturbation is always zero at both ends.

[0029] To achieve layered control of large-scale curvature trends and small-scale local textures, perturbation Decomposed into principal disturbance terms With fine perturbation terms Two-layer structure:

[0030] Among them, the main disturbance Control the macroscopic curvature, fine perturbation Add micro-bending. The expansions of the two perturbations under the orthogonal basis are as follows:

[0031] in, and These are the modal truncation orders for the main perturbation and the minor perturbation, respectively. (Expansion coefficients) and The variables are taken as independent Gaussian random variables and multiplied by the modal amplitude and spectral attenuation factor. The expansion coefficients of the main perturbation include weights for slower decay, while small perturbations are weighted for faster decay. The generation mechanism of the random expansion coefficients is as follows:

[0032] in, To control the amplitude of the disturbance intensity, This is the spectral attenuation factor. Power. The attenuation coefficient directly determines the attenuation rate of high-frequency components. Each variable represents an independent Gaussian random variable that follows a standard normal distribution. Combining the basis paths, the initial three-dimensional centerline path is... It naturally satisfies the constraints at its endpoints. .

[0033] Step 4: Divide the continuous path parameter range Equidistant sampling is performed on N discrete points to obtain a discrete path point list. The initial random path samples may contain sharp local bends or excessively small bending radii. To suppress local high-frequency oscillations, regularized smoothing updates are performed on the internal points:

[0034] in, To smoothly update the node's 3D coordinates, These are the original coordinates of the node in the current iteration step. It is the discrete node that is adjacent to it.

[0035] Define the unit tangent vector of adjacent line segments. and If the local angle Exceeding the maximum allowed value Then, local averaging and pullback are applied to that node. Simultaneously, the discrete radius of curvature is defined using the circumradius of the three adjacent points.

[0036] in, For discrete radius of curvature, This represents the cross product operation of vectors. This method requires... If the conditions are not met, the node is pulled back towards the mean position with a weight ratio of 0.3:0.4:0.3 to ensure that any local bending is within the physically tolerable range. By combining the equivalent radius of curvature constraint with regularization of geometric features, the numerical stability of the path in subsequent electrical parameter extraction is guaranteed.

[0037] Step 5: Perform minimum distance detection on the discrete paths of the two cables. If any discrete node is... Spatial Euclidean distance between Less than When this occurs, a repulsive force in the opposite direction is applied along the line connecting them. Let the unit repulsive direction vector be... , and These are discrete points where the two cable paths were not adjusted. The correction and adjustment formula is as follows:

[0038] in, and These are the corrected discrete node coordinates. To control the correction step size for iterative convergence, Let be the position weight function. This weight function satisfies [condition missing]. During the correction process, the endpoints remain stationary. This step effectively eliminates overlap and close contact between dual cable paths while preserving the random bending characteristics.

[0039] Step 6: Resample the final 3D path obtained in Step 5 according to the arc length, and further discretize each cable path into several 3D straight line elements. For any two line elements... and By utilizing the Neumann double-line integral equation in Maxwell space and combining it with the higher-order Gauss-Legendre orthogonal numerical integration rule, the three-dimensional inductance is accurately calculated. (Arbitrary two line elements) and The formula for extracting the inductance between the two parts is:

[0040] in, For line element With line element Inductance in the space between The permeability of free space, and These are the unit direction tangent vectors of the two line elements, respectively. The spatial distance between integration points. To avoid self-inductance singularities, an inductance regularization radius (served by the conductor radius) is introduced. After assembling the partial inductances between all line elements into a global partial inductance matrix, and then following the conductor aggregation principle of continuous and consistent current within the same cable, the overall equivalent inductance matrix of the two-cable system is obtained. :

[0041] Step 7: To solve for the inter-cable capacitance, the global physical equations are established using the point-matching concept of the method of moments (MoM). The system assumes that the charge distribution on each discrete straight line element is uniform. The electrostatic potential generated at the center of the target matching line element is calculated by the one-dimensional line integral of the source charge, thus constructing the global potential coefficient matrix. To account for the influence of complex media, the system uses a compromise equivalent dielectric constant between the insulation layer and air to approximate the non-uniform dielectric environment. The expression for the elements of the potential coefficient matrix is:

[0042] in, The vacuum permittivity, For the effective dielectric constant, Let be the capacitance regularization radius.

[0043] By incorporating the effects of the ground plane using the image method, a global linear equation is established. ,in, It is the vector of line charge density of each line element. Given a voltage vector, after establishing the potential coefficient matrix equation, unit boundary voltage excitation vectors of and are applied sequentially to the entire A and B lines. The discrete line charge density distribution of each line element on the two cables is obtained by solving the matrix inverse equation. and The charge density under different excitation states is integrated and summed along the length of the line segment. The total induced charge is obtained by summing the charges of all line elements in each conductor, and then combined and symmetricized to obtain the overall equivalent capacitance matrix. : (13) Finally, a reference straight-through length is introduced. Normalize the global matrix to a unit length parameter:

[0044] in, and These represent the normalized equivalent inductance matrix and capacitance matrix per unit length, respectively.

[0045] The sequence numbers of the above embodiments of the present invention are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments. In the above embodiments of the present invention, the descriptions of each embodiment have their own emphasis; parts not described in detail in a certain embodiment can be referred to in the relevant descriptions of other embodiments. It should be understood that the disclosed technical content in the several embodiments provided in this application can be implemented in other ways.

[0046] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for extracting electrical parameters of a three-dimensional path of random bending of two cables, characterized in that, Includes the following steps: Step 1: Set the starting coordinates of the two cables, A and B, in three-dimensional space. coordinates of the endpoint , Simultaneously, geometric parameters for physical boundary determination are set; the geometric parameters include: conductor core radius. Insulation layer thickness and the minimum additional safety clearance between the outer surfaces of the two lines. Based on the actual physical outer radius of the cable The minimum distance threshold that the center axes of the two cables can approach each other is calculated. This serves as a hard constraint on the spatial distance between the discrete points of the two cables; Step 2: Connect the start and end points of each cable to construct a linear base path, and calculate the unit tangent vector of the line connecting the two endpoints of the base path. : ;in, These represent the start and end coordinates of any single cable in three-dimensional space; based on the unit tangent vector... Construct three unit vectors that are perpendicular to the main extension direction of the cable, and are orthogonal to each other, satisfying the following conditions: Establish a local orthogonal reference coordinate system; among which, and Let each of these represent a unit basis vector that is orthogonal to the other in the transverse normal plane perpendicular to the main extension direction. Step 3: Use sinusoidal basis functions that satisfy homogeneous boundary conditions. , , Construct the main disturbance term With fine perturbation terms Superimposed two-layer perturbation model The expansion coefficients of the two-layer perturbation are generated by using different modal truncation orders, Gaussian random variables, and spectral attenuation factors. These coefficients are then combined with the linear basis path to generate the initial three-dimensional centerline path of the cable. ; Step 4: Sample the continuous three-dimensional centerline path at equal intervals. A discrete path point sequence is used, and the discrete nodes are smoothed iteratively using the neighbor difference correction formula; the local bending angle and discrete radius of curvature of each node are calculated, combined with the maximum allowable bending angle. radius of curvature The bundle performs mean pullback correction on distorted nodes to complete the path geometric regularization process. Step 5: Perform global minimum distance detection on the discrete path nodes of the two cables. For violation positions where the spatial distance between nodes is less than the minimum distance threshold, adjust the node coordinates through an iterative correction formula based on the connection reverse rejection direction vector and the endpoint zero constraint weight function to eliminate cable path overlap and close contact problems. Step 6: Resample and discretize the corrected 3D cable path into several 3D straight line elements according to the arc length. Based on the Maxwell space Neumann double line integral equation combined with the high-order Gauss-Legendre orthogonal numerical integral, calculate the partial inductance between any two line elements, assemble the global partial inductance matrix, and aggregate it according to the principle of continuous and consistent current in the same cable to obtain the overall equivalent inductance matrix of the two-cable system. ; Step 7: Solve and normalize the capacitance matrix using the electrostatic moment method: Based on the point matching idea of ​​the electrostatic moment method, assuming that the charge of each line element is uniformly distributed, and combining the equivalent dielectric constant and the influence of the ground plane in the image method, construct the overall situation coefficient matrix and solve the linear equation to obtain the charge density distribution of the line elements; integrate and sum to obtain the total induced charge of the cable, and after symmetry processing, obtain the overall equivalent capacitance matrix. Introducing a reference straight-through length Normalization yields the equivalent inductance matrix per unit length. With capacitor matrix Complete the extraction of electrical parameters for the dual-cable system.

2. The method for extracting electrical parameters of a three-dimensional path of random bending of a dual-cable system according to claim 1, characterized in that, In step 1, the minimum distance threshold The calculation formula is: ； in, Indicates the actual physical outer radius of the cable; This indicates the minimum additional safety clearance between the outer surfaces of the two lines.

3. The method for extracting electrical parameters of a three-dimensional path of random bending of a dual-cable system according to claim 1, characterized in that, In step 3, the main disturbance term With fine perturbation terms The modal expansion formula is: ； in, and Let these represent the modal truncation orders of the main perturbation and the minor perturbation, respectively; the stochastic expansion coefficients satisfy: ； in, Indicates the amplitude of the controlled disturbance. Indicates the spectral attenuation factor; Both represent independent Gaussian random variables that follow a standard normal distribution; This represents a standard normal distribution with a mean of 0 and a variance of 1.

4. The method for extracting electrical parameters of a three-dimensional path of random bending of a dual-cable system according to claim 1, characterized in that, In step 4, the formula for smoothing the update of discrete nodes is: ； in, Indicates the coordinates of the smoothed nodes; These are the original coordinates of the current node and its preceding and following adjacent nodes, respectively. The formula for calculating the discrete radius of curvature is: ； in, Represents the discrete radius of curvature. Represents the cross product operation of vectors; when included angle According to The weighting ratio will pull the abnormal node back to the average position of the three adjacent points for correction.

5. The method for extracting electrical parameters of a three-dimensional path of random bending of a dual-cable system according to claim 1, characterized in that, In step 5, the node correction formula is: ； ;in, , This represents the corrected discrete node coordinates; Indicates the iteration correction step size; Represents the unit repulsion direction vector; This represents the position weight function, and This ensures that the coordinates of the cable endpoints remain fixed. and These represent the parameter positions of the two discrete points on the normalized path, respectively.

6. The method for extracting electrical parameters of a three-dimensional path of random bending of a dual-cable system according to claim 1, characterized in that, In step 6, any two line elements The partial inductance extraction formula is as follows: ； in, Represents the permeability of free space. Let represent the unit tangent vectors of the two line elements, respectively. This represents the spatial distance between integration points. This represents the inductance regularization radius, which is the radius of the conductor core. .

7. The method for extracting electrical parameters of a three-dimensional path of random bending of a dual-cable system according to claim 1, characterized in that, In step 7, the equivalent capacitance matrix is ​​processed using the following formula: 。 8. The method for extracting electrical parameters of a three-dimensional path of random bending of a dual-cable system according to claim 1, characterized in that, In step 3, the generated initial three-dimensional centerline path is: ； And satisfy the endpoint constraints , .

9. The method for extracting electrical parameters of a three-dimensional path of random bending of a dual-cable system according to claim 1, characterized in that, In step 7, the expression for the elements of the potential coefficient matrix is: ； in, Represents the vacuum permittivity. Indicates the effective dielectric constant. Indicates the capacitance regularization radius; Indicates the first i The position vector of the center matching point of each target line element. Indicates the first j Integral position on the source line element The corresponding position vector.

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