A random morphological cable radiation emission statistical method, device, equipment and medium

Abstract

This invention relates to the field of electromagnetic compatibility and electromagnetic emission prediction technology, and discloses a statistical method, apparatus, device, and medium for random morphology cable radiated emission. The method includes: acquiring a sample set of random morphology cables; establishing a discrete model of the cable wires; establishing an excitation source; assembling an impedance matrix and excitation vector; constructing a DD-PCE-MoM model; solving for the model coefficients based on regularized least squares and empirical Galerkin projection; calculating statistical characteristics of the radiation field; and outputting the statistical results of the radiation field. This invention establishes a discrete model of the cable wires, converting the cable into a structured network suitable for numerical calculation; establishes an excitation source; assembles an impedance matrix and excitation vector; transforms the physical excitation source into a numerical equation using the method of moments; constructs a DD-PCE-MoM model; solves for the model coefficients; and outputs the statistical results of the radiation field. This realizes the transformation of random morphology radiated emission from high-cost sample-by-sample solution to rapid statistical prediction.

Description

Technical Field

[0001] This invention relates to the field of electromagnetic compatibility and electromagnetic emission prediction technology, specifically to a statistical method, apparatus, equipment, and medium for random-form cable radiated emission. Background Technology

[0002] Cables are widely used in rail transportation, automotive, power, aerospace, and industrial equipment, found in wire harness systems, power transmission systems, control systems, and high-voltage connection systems. During operation, cables are frequently affected by factors such as vibration, swaying, tension, bending, installation slack, airflow disturbances, and relative structural displacement, leading to random changes in their spatial shape. Due to their long length, high current carrying capacity, complex installation environments, and the fact that some cables lack complete metallic shielding, they are prone to significant external radiated emissions under interference current excitation.

[0003] Existing radiated emission analyses are typically based on fixed geometric configurations, simplifying cables to straight lines, fixed bends, or a few typical orientations before performing deterministic electromagnetic calculations. While these methods can describe radiation levels under a single configuration, they struggle to reflect the random variations in cable morphology during actual operation. Therefore, how to statistically analyze the radiated emissions of cables with random morphologies has become a pressing issue. Summary of the Invention

[0004] This invention provides a method, apparatus, device, and medium for statistical analysis of the radiated emissions of randomly shaped cables, in order to solve the problem of how to statistically analyze the radiated emissions of randomly shaped cables.

[0005] In a first aspect, the present invention provides a statistical method for the radiation emission of randomly shaped cables, the method comprising: Obtain a sample set of random cable patterns; Establish a discrete model of the cable's thin wires; Establish incentive sources; The impedance matrix and excitation vector corresponding to the random morphology samples of the assembled cable are used to form an impedance matrix sample set and an excitation vector sample set. Construct the DD-PCE-MoM model; Solving the coefficients of the DD-PCE-MoM model based on regularized least squares and empirical Galerkin projection; Calculate the statistical characteristics of the radiation field and output the statistical results of the radiation field.

[0006] This invention obtains a sample set of random morphological patterns of cables, establishes a discrete model of thin cables, and transforms the cables into a structured network suitable for numerical calculation. By establishing an excitation source, assembling the impedance matrix and excitation vector, the physical excitation source is transformed into a numerical equation of the method of moments. By constructing a DD-PCE-MoM model, solving the DD-PCE-MoM model coefficients, and calculating and outputting the statistical results of the radiation field, this invention realizes the transformation of random morphological radiative emission from high-cost sample-by-sample solution to rapid statistical prediction.

[0007] In one alternative implementation, a discrete model of the cable fine wires is established, including: Extract the center axis path of the cable from random morphological samples; The cable's central axis path is discretized into several interconnected thin line units, which together form a discrete cable model.

[0008] This invention discretizes the extracted cable central axis path into fine line units to form a discrete cable model, thereby preserving the spatial configuration differences of the samples and ensuring that the subsequent assembly results of the impedance matrix and excitation vector truly reflect the changes in electromagnetic properties under different random conditions.

[0009] In one alternative implementation, establishing an excitation source includes: When the external radiation of the cable is mainly generated by the same-direction current of each conductor, the common-mode interference current is used as the excitation source. When differential-mode to common-mode conversion occurs, the equivalent common-mode interference current after conversion is used as the excitation source; When the converter devices are switched quickly, the pulsed common-mode current caused by the switching process of the devices and the rate of change of voltage and current is used as the excitation source. When the excitation comes from the conductive coupling of adjacent devices or cables, the conductive coupling current is used as the excitation source.

[0010] This invention determines the excitation source based on the actual operating conditions of the cable to match different actual engineering scenarios, thereby enhancing the versatility for different cable systems and operating scenarios.

[0011] In one alternative implementation, the impedance matrix and excitation vector are calculated as follows: For random morphological parameter samples, calculate the impedance matrix using the method of moments based on the cable axis path, thin wire unit length, and thin wire unit direction corresponding to the random morphological sample. The excitation vector on the right side of the method of moments is calculated based on the location, amplitude, and direction of the disturbance current source.

[0012] This invention reflects the electromagnetic coupling characteristics and excitation distribution of a sample by calculating the impedance matrix and excitation vector using the method of moments, respectively.

[0013] In one alternative implementation, the DD-PCE-MoM model is constructed, including: Construct data-driven orthogonal polynomial basis functions; The impedance matrix, excitation vector, and cable current coefficient are expanded on data-driven orthogonal polynomial basis functions to establish a DD-PCE-MoM stochastic method of moments model under stochastic morphological parameter conditions.

[0014] This invention constructs a data-driven orthogonal polynomial basis function to adapt to the empirical distribution of random morphological samples. The impedance matrix, excitation vector, and cable current coefficient are expanded on the data-driven orthogonal polynomial basis function, providing a mathematical foundation for subsequent coefficient calculation and realizing the transformation from sample-by-sample deterministic solution to one-time rapid statistics.

[0015] In one alternative implementation, the coefficients of the DD-PCE-MoM model are solved based on regularized least squares and empirical Galerkin projection, including: Based on the deterministic method of moments impedance matrix and excitation vector corresponding to the random morphological sample, the DD-PCE expansion coefficients of the impedance matrix and excitation vector are solved by the least squares method with Tikhonov regularization. Using the empirical distribution of random morphological samples as a probability measure, the empirical triple product tensor of the data-driven orthogonal polynomial basis functions is calculated, and the DD-PCE-MoM extended matrix equation is established through Galerkin projection to solve for the DD-PCE expansion coefficients of the cable current. Reconstruct the cable current under given random morphological parameters, and calculate the radiated electric field and / or radiated magnetic field at the preset observation point in combination with the corresponding cable geometric path.

[0016] This invention ensures numerical stability by solving the DD-PCE expansion coefficients of the impedance matrix and excitation vector. By solving the DD-PCE expansion coefficients of the cable current, the expansion coefficients are based on the empirical distribution of samples rather than a predetermined theoretical distribution. By calculating the radiated electric field and / or radiated magnetic field, the radiated field response can be obtained without calling the method of moments solver, thus overcoming the computational efficiency bottleneck of solving samples one by one in traditional techniques.

[0017] In one optional implementation, the statistical characteristics of the radiation field are calculated, and the statistical results of the radiation field are output, including: Fast sampling of the DD-PCE-MoM model, calculation of probability density function, cumulative distribution function, quantiles, and overshoot probability; Frequency points with an excess probability greater than or equal to the excess probability threshold, or with a quantile limit margin less than or equal to zero, are identified as high-risk frequency points.

[0018] This invention rapidly samples the DD-PCE-MoM model and calculates the statistical characteristics of the radiation field, eliminating the need to repeatedly solve the method of moments equations for each random morphology sample in the statistical analysis, thereby reducing the computational load of statistical analysis of the radiation emission of random morphology cables.

[0019] In a second aspect, the present invention provides a random-form cable radiation emission statistics device, the device comprising: The acquisition module is used to acquire a sample set of random cable patterns; The first module is used to create a discrete model of the cable's fine wires. The second module is used to establish the incentive source; The assembly module is used to assemble the impedance matrix and excitation vector corresponding to random morphology samples of cables, forming an impedance matrix sample set and an excitation vector sample set. The third module is used to build the DD-PCE-MoM model; The solver module is used to solve the coefficients of the DD-PCE-MoM model based on regularized least squares and empirical Galerkin projection; The output module is used to calculate the statistical characteristics of the radiation field and output the statistical results of the radiation field.

[0020] Thirdly, the present invention provides an electronic device, comprising: a memory and a processor, wherein the memory and the processor are communicatively connected to each other, the memory stores computer instructions, and the processor executes the computer instructions to perform the random-form cable radiation emission statistics method described in the first aspect or any corresponding embodiment thereof.

[0021] Fourthly, the present invention provides a computer-readable storage medium storing computer instructions for causing a computer to execute the random-form cable radiation emission statistics method described in the first aspect or any corresponding embodiment thereof. Attached Figure Description

[0022] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific 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 from these drawings without creative effort.

[0023] Figure 1 This is a flowchart illustrating the statistical method for the radiation emission of random-shaped cables according to an embodiment of the present invention. Figure 2 This is a flowchart illustrating the overall process of calculating the radiated emission of a randomly shaped cable according to an embodiment of the present invention. Figure 3 A flowchart illustrating the construction of data-driven orthogonal polynomial basis functions according to an embodiment of the present invention; Figure 4 This is a flowchart of solving the expansion coefficients of the DD-PCE-MoM model under unknown probability distribution conditions according to an embodiment of the present invention; Figure 5 This is a flowchart illustrating the output and limit assessment of radiation field statistics according to an embodiment of the present invention. Figure 6 This is a structural block diagram of a random-morphology cable radiation emission statistical device according to an embodiment of the present invention; Figure 7 This is a schematic diagram of the hardware structure of an electronic device according to an embodiment of the present invention. Detailed Implementation

[0024] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0025] It is understood that before using the technical solutions disclosed in the various embodiments of the present invention, users should be informed of the types, scope of use, and usage scenarios of the personal information involved in the present invention in an appropriate manner in accordance with relevant laws and regulations, and their permission should be obtained.

[0026] Regarding the issue of random cable configurations, the relevant technologies have the following two shortcomings: (1) Traditional full-wave or field-path coupled solvers can only solve for a single sample one by one. If the Monte Carlo method is used to statistically analyze the radiation response, the computational load is extremely large and it is difficult to meet the needs of engineering iteration. (2) Existing uncertainty analysis methods often assume that random parameters follow a Gaussian or uniform distribution. However, random morphological samples are often from complex sources in engineering, and statistical laws are difficult to give accurately in advance. If a mismatched prior distribution is used, it is easy to cause statistical distortion.

[0027] This invention provides a statistical method for the radiated emission of cables with random morphology. It is designed for engineering scenarios where the shape of cables changes randomly during operation, vibration, swaying, stretching, bending, or installation disturbances, and the probability distribution of morphological parameters is unknown. Compared with existing radiation calculation methods based on fixed geometry and preset probability distribution, this method does not require prior assumptions about the distribution of random morphological parameters. It can significantly improve the efficiency of statistical prediction of radiated emission under random morphological conditions while ensuring accuracy. It is applicable to the radiated emission analysis, limit verification, and electromagnetic compatibility optimization design of rail transit cables, automotive cables, power cables, aerospace cables, and industrial equipment connection cables.

[0028] According to an embodiment of the present invention, a method for statistical analysis of the radiation emissions of random-morphology cables is provided. It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions. Furthermore, although a logical order is shown in the flowchart, in some cases, the steps shown or described may be executed in a different order than that shown here.

[0029] This embodiment provides a statistical method for the radiation emission of randomly shaped cables. Figure 1 This is a flowchart of a statistical method for the radiated emission of random-morphology cables according to an embodiment of the present invention, as shown below. Figure 1 As shown, the process includes the following steps: Step S101: Obtain a sample set of random cable patterns.

[0030] In this embodiment of the invention, the random shape of the cable is represented as one or more sets of spatial axis coordinate sequences. Each set of coordinate sequences corresponds to a random shape sample, and each sample contains three-dimensional coordinate information of several discrete nodes on the cable axis. The random shape samples form a random shape sample set. The random shape sample set of the cable is used to describe the changes in the axis coordinates of the cable under different spatial configurations. This sample set can be provided by one or more of the following: an external shape modeling module, a dynamic simulation module, a measured sampling system, or a historical sample database. This embodiment of the invention does not limit the generation mechanism of the random shape samples, nor does it make any preset assumptions about the probability distribution of the shape parameters.

[0031] Step S102: Establish a discrete model of the cable thin wire.

[0032] In this embodiment of the invention, a discrete model of a cable with random morphological samples is established as a geometric discrete sub-step in the deterministic radiation solution model. The deterministic radiation solution model consists of the discrete cable model, excitation vectors, solution of the method of moments equations, and post-processing of the radiation field.

[0033] Step S103: Establish the incentive source.

[0034] In this embodiment of the invention, depending on the specific application, the interference current caused by the operation of the switching device, the interference current formed by conductive coupling, or the equivalent common-mode interference current formed by differential-mode imbalance conversion is used as the excitation. The excitation current is equivalent to an axial incident electric field applied to the cable port unit, forming a moment method excitation vector based on the thin-wire electric field integral equation.

[0035] Step S104: Assemble the impedance matrix and excitation vector corresponding to the random morphology samples of the cable to form an impedance matrix sample set and an excitation vector sample set.

[0036] In this embodiment of the invention, for each random cable morphology sample, a deterministic method of moments impedance matrix and excitation vector are assembled and saved according to the corresponding cable axis path, thin wire unit length and thin wire unit direction, forming an impedance matrix sample set and an excitation vector sample set.

[0037] Step S105: Construct the DD-PCE-MoM model.

[0038] In this embodiment of the invention, a DD-PCE-MoM stochastic method of moments model under stochastic morphological parameter conditions is established.

[0039] Step S106: Solve for the coefficients of the DD-PCE-MoM model based on regularized least squares and empirical Galerkin projection.

[0040] In this embodiment of the invention, the DD-PCE expansion coefficients of the impedance matrix and the excitation vector are solved, the DD-PCE expansion coefficients of the cable current are solved, the cable current coefficient is reconstructed, and the radiated electric field and / or radiated magnetic field at the preset observation point are calculated.

[0041] Step S107: Calculate the statistical characteristic quantities of the radiation field and output the statistical results of the radiation field.

[0042] In this embodiment of the invention, the statistical characteristics of the radiation field include the mean, variance, standard deviation, probability density function, cumulative distribution function, quantile, exceedance probability, and limit margin at each frequency point, and output the statistical results of the radiation field.

[0043] The random morphology cable radiation emission statistical method provided in this embodiment obtains a random morphology sample set of cables, establishes a discrete model of the cable thin wires, and converts the cables into a structured network suitable for numerical calculation. By establishing an excitation source, assembling the impedance matrix and excitation vector, the physical excitation source is transformed into a numerical equation of the method of moments. By constructing a DD-PCE-MoM model, solving the DD-PCE-MoM model coefficients, and calculating and outputting the statistical results of the radiation field, the method realizes the transformation of random morphology radiation emission from high-cost sample-by-sample solution to rapid statistical prediction.

[0044] This embodiment provides a statistical method for the radiated emission of randomly shaped cables, the process of which includes the following steps: Step S201: Obtain a sample set of random cable patterns.

[0045] Please see details Figure 1 Step S101 of the illustrated embodiment will not be described again here.

[0046] Step S202: Establish a discrete model of the cable thin wire.

[0047] Specifically, step S202 includes: Step S2021: Extract the cable center axis path of the random morphology sample of the cable; Step S2022: Discretize the cable's central axis path into several thin line units connected end to end, and construct a discrete cable model from these thin line units.

[0048] In embodiments of the present invention, such as Figure 2 As shown, for each random cable morphology sample, the central axis path of the cable is extracted, and the axis path is discretized into N continuous thin line units connected end to end. The thin line units constitute the discrete model of the cable.

[0049] When the cross-sectional area of ​​the cable is much smaller than the wavelength, the relationship between the axial current of the cable and the electromagnetic field in space is described by the thin-wire electric field integral equation.

[0050] For an ideal conductor cable, the total tangential electric field on the conductor surface is zero, that is:

[0051] in, The unit vector normal to the conductor surface. For the incident electric field, The scattered field generated by the cable current. Let be the position vector of the field point on the conductor surface. The surface of the cable conductor.

[0052] After representing the scattered field using vector and scalar potentials, the integral equation of the electric field is obtained:

[0053] in, , , The source or integration point position vector. For wave number, Angular frequency, The permeability of the medium, The dielectric constant of the medium, The surface current density at the source point. For free space scalar Green's function, The integral surface where the source point is located. For the gradient operator with respect to the field point coordinates, It is a differential operator with respect to the coordinates of the source point.

[0054] When the cable radius is much smaller than the wavelength and cable length, the surface current can be approximated as an axial current flowing tangentially along the cable axis. And the integration region extends from the conductor surface. Simplified to cable axis path .

[0055] The unknown axial current is expanded using one-dimensional piecewise linear basis functions, and the impedance matrix equation based on the method of moments is established.

[0056] Expanding the axial current using one-dimensional piecewise linear basis functions:

[0057] Using the Galerkin test, let the test function... The equation of the method of moments is obtained as follows:

[0058] Or written in matrix form:

[0059] The elements of the impedance matrix are:

[0060] when m = n At that time, cable radius regularization is applied to the self-actualizing singularity term, which can reduce the distance in the distance kernel. R eff Approximately:

[0061] in, For cable radius, The distance between integration points is denoted as .

[0062] By discretizing the extracted cable central axis path into thin line units, a discrete cable model is constructed to preserve the spatial configuration differences of the samples and ensure that the subsequent assembly results of the impedance matrix and excitation vector truly reflect the changes in electromagnetic properties under different random morphologies.

[0063] Step S203: Establish the incentive source.

[0064] Specifically, step S203 includes: Step S2031: When the external radiation of the cable is mainly generated by the same-direction current of each conductor, the common-mode interference current is used as the excitation source. Step S2032: When differential-mode to common-mode conversion occurs, the equivalent common-mode disturbance current after conversion is used as the excitation source; Step S2033: When the converter devices are switched quickly, the pulsed common-mode current caused by the device switching process and the rate of change of voltage and current is used as the excitation source. Step S2034: When the excitation comes from the conductive coupling of adjacent devices or cables, the conductive coupling current is used as the excitation source.

[0065] In this embodiment of the invention, common-mode interference current, equivalent common-mode interference current, pulsed common-mode current, or conducted coupling current are used as excitation sources according to the actual operating conditions of the cable system.

[0066] Specifically, for the case where the external radiation of the cable is mainly generated by the same-direction current of each conductor, the common-mode interference current obtained by actual measurement or circuit simulation is used as the excitation source.

[0067] For high-voltage through-line or multi-conductor cable, differential-mode to common-mode conversion occurs due to imbalances in terminal impedance, grounding impedance, or parasitic parameters. The converted equivalent common-mode disturbance current is used as the excitation source.

[0068] For fast switching conditions of converters such as IGBTs and SiC devices, the switching process and voltage change rate are used as the basis for analysis. Current change rate The resulting pulsed common-mode current serves as the excitation source.

[0069] When the excitation comes from the conductive coupling of adjacent devices or cables, the conductive coupling current measured at the cable port or calculated through the field-circuit coupling model is used as the excitation source.

[0070] The disturbance current source at the port is equivalent to a uniform axial incident electric field acting along the direction of the excitation line segment, forming the right-hand excitation vector based on the integral equation of the thin-line electric field.

[0071] Let the port interference current be I 0, the parallel internal resistance of the current source is r inp Then the equivalent port voltage V 0 is:

[0072] Let the coordinates of the two ends of the excitation line segment be... and line segment length for:

[0073] Axial unit vector for:

[0074] Then the uniform axial incident electric field E inc It can be represented as:

[0075] Its positive and negative directions are determined according to the reference direction of the port current.

[0076] The elements of the right-hand vector of the method of moments are:

[0077] By determining the excitation source based on the actual operating conditions of the cable, different practical engineering scenarios can be matched, thereby enhancing the versatility for different cable systems and operating scenarios.

[0078] Step S204: Assemble the impedance matrix and excitation vector corresponding to the random morphology samples of the cable to form an impedance matrix sample set and an excitation vector sample set.

[0079] Specifically, for each set of random morphological parameter samples, a deterministic method of moments impedance matrix and excitation vector are assembled according to the corresponding cable axis path, thin wire unit length, and thin wire unit direction, forming an impedance matrix sample set and an excitation vector sample set. The impedance matrix sample set and excitation vector sample set are used in step S206 to identify the DD-PCE expansion coefficients of the impedance matrix and excitation vector. For selected random morphological samples, the deterministic method of moments equations can be further solved, and the radiated electric field and / or radiated magnetic field at preset observation points can be calculated to verify the calculation accuracy of the DD-PCE-MoM model.

[0080] Specifically, the impedance matrix and excitation vector are calculated as follows: Step S2041: For the random morphological parameter sample, calculate the impedance matrix using the method of moments based on the cable axis path, thin wire unit length, and thin wire unit direction corresponding to the random morphological sample.

[0081] Step S2042: Calculate the excitation vector on the right end of the method of moments based on the location, amplitude, and direction of the disturbance current source.

[0082] In this embodiment of the invention, the random morphological parameter vector is denoted as... Because the cable axis path, thin wire unit length, and thin wire unit direction vary with random morphological parameters... Therefore, the impedance matrix obtained by the method of moments, assembled according to the aforementioned formula for calculating the elements of the impedance matrix, also changes with the random shape parameters. Change, denoted as .

[0083] Regarding the first i Group of random morphological parameter samples Substituting the cable axis path, thin wire unit length, and thin wire unit direction corresponding to the random morphology sample into the aforementioned impedance matrix element calculation formula, we obtain each impedance matrix element. Assemble all impedance matrix elements according to their row and column positions to obtain the deterministic method of moments impedance matrix corresponding to the i-th group of random morphological parameter samples:

[0084] in, For the stochastic parameterized impedance matrix The deterministic sample value at that location, i.e.:

[0085] Calculate the first [unclear] based on the location, amplitude, and direction of the disturbance current source. i The right-hand excitation vector of the method of moments corresponding to a group of random morphological parameter samples Then, the deterministic method of moments equations are established:

[0086] in, For the first i The axial current coefficient of the cable corresponding to a set of random morphological samples. .

[0087] Obtaining the axial current coefficient of the cable Then, the electric field contributions generated by each current basis function at the preset observation point are superimposed, and the preset observation point is calculated according to the following formula. Radiated electric field at the location :

[0088] in, For the first i In the group of random morphological samples, the first n Complex current coefficients of each current basis function For the first n The cable axis path corresponding to each fine wire unit. For the first n One-dimensional piecewise linear basis functions For the first n The axial unit vector of a thin line unit. is a free-space scalar Green's function.

[0089] No. i Radiative electric field response of a group of random morphological samples for:

[0090] When the object of calculation is a radiated magnetic field, based on the obtained axial current distribution of the cable, the magnetic field generated by the current of each thin wire unit at the preset observation point is calculated and superimposed. i Radiation magnetic field vector corresponding to a group of random morphological samples for:

[0091] in, This indicates that the gradient is calculated with respect to the coordinates of the observation point.

[0092] Equivalent land, utilizing The above formula can be written as:

[0093] No. i The amplitude of the radiation magnetic field intensity corresponding to the group of random morphological samples Recorded as:

[0094] Therefore, deterministic calculation results of cable current, radiated electric field, and / or radiated magnetic field can be obtained for selected random morphology samples, which can be compared with the results of the DD-PCE-MoM model established in step S206. The basic sample data required for constructing the DD-PCE-MoM model are the method of moments impedance matrix and excitation vector corresponding to each random morphology sample. The radiated electric field and radiated magnetic field samples are not necessary inputs for solving the DD-PCE expansion coefficients of the cable current.

[0095] The electromagnetic coupling characteristics and excitation distribution of the sample are reflected by calculating the impedance matrix and excitation vector using the method of moments (MoM) respectively.

[0096] Step S205: Construct the DD-PCE-MoM model.

[0097] Specifically, step S205 includes: Step S2051: Construct data-driven orthogonal polynomial basis functions; Step S2052: Expand the impedance matrix, excitation vector, and cable current coefficient on the data-driven orthogonal polynomial basis functions to establish the DD-PCE-MoM stochastic moment method model under the stochastic morphological parameter conditions.

[0098] In embodiments of the present invention, such as Figure 3As shown, the random morphological parameters are defined as random input variables. Based on the empirical distribution of the random morphological samples, the first 2p sample moments, and the empirical inner product relationship, a data-driven orthogonal polynomial basis function satisfying the orthogonality of the empirical distribution is constructed. The moment method impedance matrix, excitation vector, and cable current coefficient obtained in step S204 are expanded using DD-PCE on the data-driven orthogonal polynomial basis function to establish a DD-PCE-MoM random moment method model under the random morphological parameter conditions.

[0099] We construct the DD-PCE-MoM model under unknown probability conditional distribution. Instead of directly calling the classic Hermite or Legendre orthogonal polynomials to address the problem of unknown probability distribution of random morphological parameters, we construct data-driven orthogonal polynomial basis functions that match the sample distribution by recursion and orthogonalization based on the empirical distribution of random morphological samples, the first 2p order statistical moments, and empirical inner product relationships.

[0100] Let the random morphological parameter sample set be: .

[0101] in, Indicates the first i A set of random morphological parameter samples, M For the sample size, d Let be the dimension of the random morphological parameters.

[0102] Specifically, the steps include the following: (1) Selecting data-driven orthogonal polynomials based on unknown probability distributions Classical chaotic polynomial expansion methods require selecting the appropriate orthogonal polynomial based on the known probability distribution of the random variable. For example, when the random variable follows a Gaussian distribution, the Hermite orthogonal polynomial is usually used; when the random variable follows a uniform distribution over a finite interval, the Legendre orthogonal polynomial is usually used.

[0103] Hermite and Legendre orthogonal polynomials use Gaussian and uniform probability density functions, respectively, as orthogonal weight functions. If the true probability distribution of the random morphological parameters of a cable is unknown, or exhibits a non-Gaussian, non-uniform, skewed, or multimodal distribution, directly using Hermite or Legendre orthogonal polynomials may result in the selected polynomial basis functions failing to maintain orthogonality under the true probability measure of the random morphological parameters. This leads to a slower convergence speed of the surrogate model and causes deviations in the calculated mean, variance, quantiles, and out-of-range probabilities.

[0104] Therefore, instead of directly calling the pre-specified Hermite or Legendre orthogonal polynomials, we adaptively construct data-driven orthogonal polynomial basis functions that match the distribution of random morphological parameters based on the empirical distribution and empirical statistical moments of the random morphological parameter samples.

[0105] Compared with directly using classical orthogonal polynomials, data-driven orthogonal polynomials do not require the probability distribution type of random morphological parameters to be determined in advance. They can adapt to non-Gaussian, non-uniform, and irregular sample distributions, and can improve the adaptability of the surrogate model to the actual sample distribution and the accuracy of the calculation of radiation response statistics under the same polynomial expansion order.

[0106] (2) Establishing an empirical probability measure for random morphological parameters When the probability density function of the random morphological parameters is unknown, the empirical distribution formed by finite random morphological samples is used as the probability measure of the random input. The calculation formula is as follows:

[0107] in, For the Dirac function, The total number of samples with random morphological parameters. A vector of random morphological parameters. For the i-th group of random morphological parameter samples.

[0108] Define any two functions based on the empirical distribution. f and g Empirical inner product :

[0109] The empirical inner product is used to determine and construct the orthogonality of polynomial basis functions in the sense of empirical distribution of random morphological samples.

[0110] (3) Calculate the empirical statistical moments of random morphological parameters Let the highest order of the data-driven orthogonal polynomial be p, and for the k-th random morphological parameter... The first 2p order empirical statistical moments are calculated based on the random morphological parameter samples. :

[0111] in, Indicates the first k The th random morphological parameter of the th r Empirical statistical moments of order.

[0112] The empirical statistical moments of the first 2p orders are used because when constructing an orthogonal polynomial with the highest order of p, the highest order of the polynomial product can reach 2p, and its empirical inner product needs to be calculated using statistical moments of no higher than 2p.

[0113] (4) Construct a single-variable orthogonal polynomial through a three-term recursion For the k Random morphological parameters Define the zeroth-order data-driven orthogonal polynomial as:

[0114] Higher-order orthogonal polynomials are constructed using the following three recurrence relations:

[0115] in, r =0,1,... p -1, the recursive coefficient is:

[0116]

[0117] The initial calculation instructions are as follows:

[0118] After construction, the polynomials of each order are normalized:

[0119] Make the normalized univariate basis functions satisfy:

[0120] in, For the Kronecker function, when r = s When its value is 1, r ≠ s When its value is 0.

[0121] Alternatively, it can be based on a set of monomials:

[0122] The Gram-Schmidt orthogonalization method is employed to construct data-driven orthogonal polynomials by successive orders based on empirical inner products. Either the three-term recursive method or the Gram-Schmidt orthogonalization method can be chosen.

[0123] (5) Constructing multivariate data-driven orthogonal polynomial basis functions When the random morphological parameters are independent of each other, a multivariable basis function is constructed by multiplying the orthogonal polynomials driven by the univariate data:

[0124] in, For multiple indexes, retain multiple indexes that satisfy the following formula according to the total order truncation rule:

[0125] When there is a non-negligible statistical correlation among the random morphological parameters, it is preferable to directly perform Gram-Schmidt orthogonalization on the set of multivariate unimials according to the joint empirical inner product of the random morphological parameters, thus constructing multivariate data-driven orthogonal polynomial basis functions that are orthogonal in the sense of joint empirical distribution. For random morphological parameters that can be made independent through variable transformation, the corresponding independence transformation can also be performed first, and then the multivariate basis functions can be constructed using the product of univariate orthogonal polynomials.

[0126] When a cutoff rule with a total order not exceeding p is adopted, the total number of multivariable basis functions is:

[0127] The constructed multivariate data-driven orthogonal polynomial basis functions satisfy:

[0128] (6) Establish the DD-PCE expansion model of random quantities using the method of moments. When the cable morphology changes randomly, the impedance matrix, excitation vector, and cable current coefficient established in steps S202 to S204 all change with the random morphological parameters. change.

[0129] Expanding the impedance matrix using the method of moments, we get:

[0130] in, For frequency f The impedance matrix at the first position j The coefficient matrix of the DD-PCE expansion.

[0131] The method of moments excitation vector is expanded as follows:

[0132] in, For frequency f The first activation vector j The coefficient vector of the DD-PCE expansion.

[0133] Expanding the cable current coefficient as follows:

[0134] in, For frequency f The first cable current k The coefficient vector of the DD-PCE expansion.

[0135] The impedance matrix expansion coefficient, excitation vector expansion coefficient, and cable current expansion coefficient are all solved in step S206.

[0136] (7) Establish the calculation relationship between cable current and radiation field. Step S205 establishes the DD-PCE expansion of the impedance matrix, excitation vector, and cable current coefficient using the method of moments. Each DD-PCE expansion coefficient is solved in step S206.

[0137] Given random morphological parameters At that time, the cable current coefficient is reconstructed based on the DD-PCE expansion formula of the cable current:

[0138] Based on the cable axis path, thin wire unit direction, and reconstructed cable current coefficient corresponding to the random morphological parameters, the radiation electric field at the preset observation point is calculated using the radiation field integral formula in step S204. and / or radiated magnetic field The radiated electric and magnetic fields are calculated from the cable current DD-PCE expansion results, without separately introducing the unsolved DD-PCE expansion coefficients of the radiated field.

[0139] By constructing data-driven orthogonal polynomial basis functions to adapt to the empirical distribution of random morphological samples, the impedance matrix, excitation vector, and cable current coefficient are expanded on the data-driven orthogonal polynomial basis functions, providing a mathematical foundation for subsequent coefficient solving, and realizing the transformation from sample-by-sample deterministic solution to one-time rapid statistics.

[0140] Step S206: Solve for the coefficients of the DD-PCE-MoM model based on regularized least squares and empirical Galerkin projection.

[0141] Specifically, step S206 includes: Step S2061: Based on the deterministic method of moments impedance matrix and excitation vector corresponding to the random morphological sample, the DD-PCE expansion coefficients of the impedance matrix and excitation vector are solved by the least squares method with Tikhonov regularization. Step S2062: Using the empirical distribution of random morphological samples as a probability measure, calculate the empirical triple product tensor of the data-driven orthogonal polynomial basis functions, and establish the DD-PCE-MoM extended matrix equation through Galerkin projection to solve for the DD-PCE expansion coefficients of the cable current. Step S2063: Reconstruct the cable current under given random morphological parameters, and calculate the radiated electric field and / or radiated magnetic field at the preset observation point in combination with the corresponding cable geometric path.

[0142] In embodiments of the present invention, such as Figure 4 As shown, firstly, based on the deterministic method of moments impedance matrix, excitation vector, and data-driven orthogonal polynomial basis function values ​​at the sample points corresponding to each random morphological sample, the DD-PCE expansion coefficients of the impedance matrix and excitation vector are solved using the least squares method with Tikhonov regularization. Secondly, the DD-PCE expansions of the impedance matrix, excitation vector, and cable current coefficients are substituted into the random method of moments equations. Using the empirical distribution of the random morphological samples as a probability measure, the triple tensor product of the data-driven orthogonal polynomial basis functions is calculated through sample averaging, and the extended matrix equation is established using Galerkin projection. Then, the LU decomposition method is used to solve for the DD-PCE expansion coefficients of the cable current. Finally, under given random morphological parameters, the corresponding cable current coefficients are reconstructed through the DD-PCE expansion of the cable current, and combined with the cable axis path corresponding to the random morphological parameters and the radiation field integral formula in step S204, the radiation electric field and / or radiation magnetic field at the preset observation point are calculated.

[0143] It should be noted that the randomized parameterized impedance matrix in this step... With the deterministic impedance matrix in step S204 Corresponding to the same impedance matrix in the method of moments.

[0144] in, Used to represent the impedance matrix of the method of moments as a function of random shape parameters The changing functional relationship; This indicates that the stochastically parameterized impedance matrix is ​​in the th... i The deterministic values ​​of the random morphological parameter samples are given. Therefore, they are not two different impedance matrices, but rather the random parameterized expression and the deterministic sample expression of the same method of moments impedance matrix.

[0145] Based on the data-driven orthogonal polynomial basis functions constructed in step S205, the moment method impedance matrix corresponding to the random morphology cable is... Represented as:

[0146] in, P is the number of terms in the DD-PCE expansion. For the first j Data-driven orthogonal polynomial basis functions For frequency f The impedance matrix at the first position jThe DD-PCE expansion coefficient matrix of order 1, whose matrix dimension is the same as the deterministic method of moments impedance matrix. same.

[0147] For each of the M sets of random morphological parameter samples, assemble the corresponding deterministic method of moments impedance matrix. The frequency is obtained by solving the least squares problem with Tikhonov regularization. f DD-PCE expansion coefficients of the impedance matrix at:

[0148] in, It is the Frobenius norm. For regularization parameters, For the least squares optimization process j Candidate coefficient matrix of order, The value is the estimated value of the j-th order DD-PCE coefficient matrix obtained from M sets of deterministic impedance matrix samples.

[0149] The impedance matrix can also be decomposed into vector bit terms and scalar bit terms:

[0150] and respectively M mn and W mn Data-driven chaotic polynomial expansion is performed to improve the numerical stability of the impedance matrix coefficient solution.

[0151] The method of moments excitation vector and cable current coefficient Expanded separately as follows:

[0152]

[0153] The DD-PCE expansion coefficients of the activation vectors are obtained by solving the following least squares problem with Tikhonov regularization:

[0154] in, The Tikhonov regularization parameters used to solve for the expansion coefficients of the activation vector. For the least squares optimization process j Candidate coefficient matrix of order, According to M The first set of deterministic impedance matrix samples obtained j Estimates of the DD-PCE coefficient matrix.

[0155] The number of random morphological samples M should, in principle, be no less than the number of terms P in the DD-PCE expansion, and the sample design matrix should have a sufficient numerical rank. When the rank of the sample design matrix is ​​insufficient or the condition number is too large, the solution stability can be improved by increasing the number of random morphological samples, reducing the highest order of the polynomial, or adjusting the regularization parameter.

[0156] Substituting the DD-PCE expansions of the impedance matrix, excitation vector, and cable current coefficient into the stochastic method of moments equations:

[0157] get:

[0158] Define the inner product based on the empirical distribution of random morphological parameter samples:

[0159] The equations of the method of moments of random moments are respectively compared with the first... l Data-driven orthogonal polynomial basis functions Taking the empirical inner product, we get:

[0160] The coefficients of the triple tensor product are: .

[0161] And calculated using empirical averages from a finite sample:

[0162] For all l =0,1,… P -1 Assemble the extended matrix equations and use the LU decomposition method or other linear equation solving methods to solve for the DD-PCE expansion coefficients of the cable current at each order: .

[0163] Substitute the obtained cable current DD-PCE expansion coefficients into the cable current expansion formula. Given random morphological parameters... At that time, by calculating the values ​​of the orthogonal polynomial basis functions driven by each data at the random morphological parameter, the corresponding cable current coefficient is reconstructed:

[0164] Then, based on the cable axis path, thin wire unit direction, and reconstructed cable current coefficient corresponding to the random morphological parameters, the radiation electric field and / or radiation magnetic field at the preset observation point are calculated using the radiation field integral formula in step S204. This completes the construction of the DD-PCE-MoM model, and the calculated radiation field results are input into step S207 for statistical analysis.

[0165] By solving the DD-PCE expansion coefficients of the impedance matrix and excitation vector, the numerical stability of the solution is guaranteed. By solving the DD-PCE expansion coefficients of the cable current, the expansion coefficients are based on the empirical distribution of samples rather than a pre-set theoretical distribution. By calculating the radiated electric field and / or radiated magnetic field, the radiated field response can be obtained without calling the method of moments solver, thus overcoming the computational efficiency bottleneck of solving samples one by one in traditional techniques.

[0166] Step S207: Calculate the statistical characteristic quantities of the radiation field and output the statistical results of the radiation field.

[0167] Specifically, step S207 includes: Step S2071: Quickly sample the DD-PCE-MoM model and calculate the probability density function, cumulative distribution function, quantiles, and out-of-target probability; Step S2072: Identify frequency points with an excess probability greater than or equal to the excess probability threshold, or with a quantile limit margin less than or equal to zero, as high-risk frequency points.

[0168] In embodiments of the present invention, such as Figure 5 As shown, based on the completed DD-PCE-MoM model, the mean, standard deviation, variance, probability density function, cumulative distribution function, quantile, exceedance probability, and limit margin of the radiative response within the target frequency band are quickly calculated, thereby determining high-risk frequency points and corresponding operating conditions.

[0169] make: This represents the radiation field statistics selected at the preset observation points, where E represents the amplitude of the radiated electric field and H represents the amplitude of the radiated magnetic field. For K samples drawn from the empirical distribution of random morphological parameters... The cable current was reconstructed and the radiation field was calculated to obtain the results. .

[0170] The mean value of the radiation field is

[0171] variance is

[0172] Standard deviation is

[0173] The empirical cumulative distribution function is

[0174] in, This is an indicator function; it takes the value 1 if the condition within the parentheses is true, and 0 otherwise.

[0175] The probability density function of radiation field statistics can be calculated using the kernel density estimation method:

[0176] in, For kernel function, h This is the bandwidth parameter.

[0177] The quantile value corresponding to the confidence level q is defined as:

[0178] The limit margin at confidence level q is:

[0179] Given electromagnetic emission limits The probability of exceeding the standard is .

[0180] in, A preset threshold for the probability of exceeding the limit is set. A frequency point is designated as a high-risk frequency point when any of the following conditions are met:

[0181] or

[0182] Based on this, the following specific implementation methods are used to generate radiation field statistics samples, determine whether the statistical results converge, and identify the random morphological conditions corresponding to high-risk frequency points.

[0183] Specifically, multiple sets of statistical analysis samples are extracted from the empirical distribution of random morphological parameters. For each set of random morphological parameter samples, the values ​​of the data-driven orthogonal polynomial basis functions are calculated, and the corresponding cable current is reconstructed based on the cable current DD-PCE expansion coefficients obtained in step S206. The radiated electric field and / or radiated magnetic field at the preset observation point are calculated in conjunction with the cable axis path corresponding to the random morphological parameter. Based on the obtained radiation field samples, the mean, variance, standard deviation, probability density function, cumulative distribution function, quantile, probability of exceeding the standard, and limit margin of each frequency point are calculated and compared with the electromagnetic emission standard limit to identify high-risk frequency points and corresponding random morphological conditions.

[0184] Specifically, for each frequency point, K sets of statistical analysis samples are drawn from the empirical distribution of random morphological parameters. For the k-th set of random morphological parameter samples, the values ​​of the data-driven orthogonal polynomial basis functions at that sample are calculated. The cable current is reconstructed based on the DD-PCE expansion coefficients of the cable current, and the radiated electric field and / or radiated magnetic field at the preset observation point are calculated in conjunction with the corresponding cable axis path to obtain a sample of radiation field statistics. R k ( f Based on all K groups of radiation field statistics samples, calculate the mean, variance, standard deviation, probability density function, cumulative distribution function, quantile, probability of exceeding the standard, and limit margin according to the aforementioned formula.

[0185] The probability density function, cumulative distribution function, quantiles, and over-standard probability are obtained by quickly sampling the surrogate model.

[0186] In one alternative implementation, the empirical distribution resampling method is used to generate the statistical analysis input samples for the DD-PCE-MoM model. Assume there are already M sets of random morphological parameter samples. The surrogate model input samples are obtained by drawing K samples with replacement from a pool of samples with equal probability 1 / M. For the kth group of statistical analysis samples By reconstructing the cable current and calculating the radiation field, we obtain:

[0187] The statistical results of the radiation field are calculated for all K groups of radiation field statistics samples according to the aforementioned formula. The statistical sampling size K is determined based on the convergence accuracy requirements of the radiation field mean, variance, quantiles, and exceedance probability. As K increases, the statistical sampling size is stopped when the relative change of the statistical indicators is less than the preset convergence tolerance. Alternatively, kernel density estimation can be performed on the original morphological parameter samples first, and then random sampling can be performed from the estimated probability density.

[0188] For each discrete frequency point within the target frequency band Calculate the probability of exceeding the standard according to the aforementioned formula. quantile margin at confidence level q .

[0189] For example, if the confidence level q is 0.95, then:

[0190] A frequency point is identified as a high-risk frequency point when either of the following conditions is met: the probability of exceeding the limit is greater than or equal to the probability threshold of exceeding the limit, or the quantile limit margin is less than or equal to zero.

[0191] or

[0192] when ,or At that time, the frequency point These frequencies were identified as high-risk. The threshold for the probability of exceeding the limit is set according to applicable electromagnetic emission standards, engineering design requirements, or risk assessment requirements.

[0193] When multiple high-risk frequency points exist, sorting them from highest to lowest probability of exceeding the standard will increase the radiation field statistics. The random morphological parameter sample that achieves the maximum value is identified as the corresponding high-risk random morphological condition.

[0194] By rapidly sampling the DD-PCE-MoM model and calculating the statistical characteristics of the radiation field, it is not necessary to repeatedly solve the method of moments equations for each random morphology sample in the statistical analysis, thereby reducing the computational workload of statistical analysis of random morphology cable radiation emission.

[0195] The statistical method for statistical analysis of random-morphology cable radiation emissions provided in this embodiment has the following advantages: (1) The prior probability distribution assumptions that do not rely on random morphological parameters are applicable to engineering sample scenarios where the probability distribution is unknown or difficult to describe accurately. (2) By combining the deterministic solution of the method of moments with data-driven chaotic polynomial expansion, the transformation of random morphological radiation emission from high-cost solution per sample to rapid prediction of statistics is realized; (3) The DD-PCE expansion coefficients of the impedance matrix and excitation vector of the method of moments are stably solved by the least squares method with Tikhonov regularization, and the DD-PCE expansion coefficients of the cable current are solved by Galerkin projection based on the empirical distribution of random morphology samples. After the DD-PCE-MoM model is completed, it is not necessary to repeatedly solve the method of moments equations for each set of random morphology samples in the statistical analysis, thereby reducing the computational workload of statistical analysis of radiated emission from random morphology cables; (4) It can simultaneously output statistical indicators such as mean, variance, probability density function and probability of exceeding the standard, making it more suitable for radiation emission limit verification and electromagnetic compatibility risk assessment of various cable systems; (5) It is applicable to rail transit cables, automotive cables, power cables and other cables with random morphological changes, and has good engineering versatility.

[0196] It should be noted that automotive high-voltage cables, vehicle wiring harnesses, and power connection cables are prone to swaying, sagging, and S-shaped bending under vehicle vibration, road impact, wind load, equipment start-up and shutdown, or support point displacement. For these types of cables, the interference current generated by the inverter, converter, switching power supply, or conducted network can be used as the excitation input.

[0197] By setting the straight-line span at both ends of the cable, the installation redundancy length, and the observation distance, and using multiple sets of random morphology samples as input, the radiated magnetic field strength or radiated electric field strength within a preset frequency band is calculated. The cable current under different random morphology parameters is reconstructed using the DD-PCE-MoM model, and the radiated electric field and / or radiated magnetic field at key frequency points are calculated. Based on this, the corresponding probability distribution, quantile values, and exceedance probabilities are obtained, and high-risk random morphology operating conditions are evaluated.

[0198] This embodiment also provides a random-pattern cable radiation emission statistics device, which is used to implement the above embodiments and preferred embodiments; details already described will not be repeated. As used below, the term "module" can refer to a combination of software and / or hardware that performs a predetermined function. Although the device described in the following embodiments is preferably implemented in software, hardware implementation, or a combination of software and hardware, is also possible and contemplated.

[0199] This embodiment provides a random-form cable radiation emission statistics device, such as... Figure 6 As shown, it includes: The acquisition module 601 is used to acquire a sample set of random cable patterns; The first module 602 is used to establish a discrete model of the cable fine wire; The second module 603 is used to establish the excitation source; Assembly module 604 is used to assemble the impedance matrix and excitation vector corresponding to the random morphology samples of the cable, forming an impedance matrix sample set and an excitation vector sample set; The third module, 605, is used to construct the DD-PCE-MoM model. Solver module 606 is used to solve the coefficients of the DD-PCE-MoM model based on regularized least squares and empirical Galerkin projection; Output module 607 is used to calculate the statistical characteristics of the radiation field and output the statistical results of the radiation field.

[0200] In some alternative implementations, the first establishment module 602 includes: The extraction unit is used to extract the central axis path of the cable in random morphological samples of the cable. The building blocks are used to discretize the central axis path of the cable into several thin line units connected end to end, and the thin line units constitute the discrete model of the cable.

[0201] In some alternative implementations, the second establishment module 603 includes: The first determining unit is used to use common-mode interference current as the excitation source when the external radiation of the cable is mainly generated by the unidirectional current of each conductor. The second determining unit is used to use the converted equivalent common-mode disturbance current as the excitation source when a differential-mode to common-mode conversion occurs; The third determining unit is used to use the pulsed common-mode current caused by the device switching process and the rate of voltage and current change as the excitation source when the converter device is rapidly switched. The fourth determining unit is used to use the conductive coupling current as the excitation source when the excitation comes from the conductive coupling of adjacent devices or cables.

[0202] In some alternative implementations, the impedance matrix and excitation vector are calculated as follows: For random morphological parameter samples, calculate the impedance matrix using the method of moments based on the cable axis path, thin wire unit length, and thin wire unit direction corresponding to the random morphological sample. The excitation vector on the right side of the method of moments is calculated based on the location, amplitude, and direction of the disturbance current source.

[0203] In some alternative implementations, the third establishment module 605 includes: Function building unit, used to construct data-driven orthogonal polynomial basis functions; The model building unit is used to expand the impedance matrix, excitation vector, and cable current coefficient on the data-driven orthogonal polynomial basis functions to establish the DD-PCE-MoM stochastic method of moments model under stochastic morphological parameter conditions.

[0204] In some alternative implementations, the solver module 606 includes: The first solution unit is used to solve the DD-PCE expansion coefficients of the impedance matrix and the excitation vector corresponding to the deterministic method of moments for random morphological samples, respectively, using the least squares method with Tikhonov regularization. The second solution unit is used to calculate the empirical triple product tensor of the data-driven orthogonal polynomial basis function using the empirical distribution of random morphological samples as the probability measure, and to establish the DD-PCE-MoM extended matrix equation through Galerkin projection to solve the DD-PCE expansion coefficient of the cable current. The first calculation unit is used to reconstruct the cable current under given random morphological parameters, and calculate the radiated electric field and / or radiated magnetic field at the preset observation point in combination with the corresponding cable geometric path.

[0205] In some alternative implementations, the output module 607 includes: The second computing unit is used to quickly sample the DD-PCE-MoM model and calculate the probability density function, cumulative distribution function, quantiles, and overshoot probability. The identification unit is used to identify frequency points with an excess probability greater than or equal to the excess probability threshold, or with a quantile limit margin less than or equal to zero, as high-risk frequency points.

[0206] The random-morph cable radiation emission statistics device provided in this embodiment of the invention can execute the random-morph cable radiation emission statistics method provided in any embodiment of the invention, and has the corresponding functional modules and beneficial effects for executing the method. Further functional descriptions of the above modules and units are the same as in the corresponding embodiments described above, and will not be repeated here.

[0207] Figure 7This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present invention.

[0208] The following is a detailed reference. Figure 7 This diagram illustrates a suitable structural schematic for implementing an electronic device according to embodiments of the present invention. The electronic device may include a processor (e.g., a central processing unit, graphics processor, etc.) 701, which can perform various appropriate actions and processes based on a program stored in read-only memory (ROM) 702 or a program loaded from memory 708 into random access memory (RAM) 703. The RAM 703 also stores various programs and data required for the operation of the electronic device. The processor 701, ROM 702, and RAM 703 are interconnected via a bus 704. An input / output (I / O) interface 705 is also connected to the bus 704.

[0209] Typically, the following devices can be connected to I / O interface 705: input devices 706 including, for example, touchscreens, touchpads, keyboards, mice, cameras, microphones, accelerometers, gyroscopes, etc.; output devices 707 including, for example, liquid crystal displays (LCDs), speakers, vibrators, etc.; memory devices 708 including, for example, magnetic tapes, hard disks, etc.; and communication devices 709. Communication device 709 allows electronic devices to exchange data via wireless or wired communication with other devices. Although Figure 7 Electronic devices with various devices are shown, but it should be understood that it is not required to implement or have all of the devices shown, and more or fewer devices may be implemented or have instead.

[0210] In particular, according to embodiments of the present invention, the processes described above with reference to the flowcharts can be implemented as computer software programs. For example, embodiments of the present invention include a computer program product comprising a computer program carried on a non-transitory computer-readable medium, the computer program containing program code for performing the methods shown in the flowcharts. In such embodiments, the computer program can be downloaded and installed from a network via a communication device 709, or installed from a memory 708, or installed from a ROM 702. When the computer program is executed by the processor 701, it performs the functions defined in the random-morphology cable radiated emission statistics method of the embodiments of the present invention.

[0211] Figure 7 The electronic device shown is merely an example and should not be construed as limiting the functionality and scope of use of the embodiments of the present invention.

[0212] This invention also provides a computer-readable storage medium. The methods described above according to embodiments of the invention can be implemented in hardware or firmware, or implemented as computer code that can be recorded on a storage medium, or implemented as computer code downloaded via a network and originally stored on a remote storage medium or a non-transitory machine-readable storage medium and then stored on a local storage medium. Thus, the methods described herein can be processed by software stored on a storage medium using a general-purpose computer, a dedicated processor, or programmable or dedicated hardware. The storage medium can be a magnetic disk, optical disk, read-only memory, random access memory, flash memory, hard disk, or solid-state drive, etc.; further, the storage medium can also include combinations of the above types of memory. It is understood that computers, processors, microprocessor controllers, or programmable hardware include storage components capable of storing or receiving software or computer code. When the software or computer code is accessed and executed by the computer, processor, or hardware, the random-form cable radiation emission statistics method shown in the above embodiments is implemented.

[0213] A portion of this invention can be applied as a computer program product, such as computer program instructions, which, when executed by a computer, can invoke or provide the methods and / or technical solutions according to the invention through the operation of the computer. Those skilled in the art will understand that the forms in which computer program instructions exist in a computer-readable medium include, but are not limited to, source files, executable files, installation package files, etc. Correspondingly, the ways in which computer program instructions are executed by a computer include, but are not limited to: the computer directly executing the instructions, or the computer compiling the instructions and then executing the corresponding compiled program, or the computer reading and executing the instructions, or the computer reading and installing the instructions and then executing the corresponding installed program. Here, the computer-readable medium can be any available computer-readable storage medium or communication medium accessible to a computer.

[0214] Although embodiments of the invention have been described in conjunction with the accompanying drawings, those skilled in the art can make various modifications and variations without departing from the spirit and scope of the invention, and all such modifications and variations fall within the scope defined by the appended invention.

Claims

1. A method of statistical analysis of stochastic morphological cable emissions, characterized in that, The method includes: Obtain a sample set of random cable patterns; Establish a discrete model of the cable's thin wires; Establish incentive sources; The impedance matrix and excitation vector corresponding to the random morphology samples of the assembled cable are used to form an impedance matrix sample set and an excitation vector sample set. Construct the DD-PCE-MoM model; Solving the coefficients of the DD-PCE-MoM model based on regularized least squares and empirical Galerkin projection; Calculate the statistical characteristics of the radiation field and output the statistical results of the radiation field.

2. The method of claim 1, wherein, The establishment of the discrete model of the cable fine wires includes: Extract the center axis path of the cable from random morphological samples; The central axis path of the cable is discretized into several thin line units connected end to end, and the thin line units constitute the discrete model of the cable.

3. The method of claim 1, wherein, The establishment of the incentive source includes: When the external radiation of the cable is mainly generated by the same-direction current of each conductor, the common-mode interference current is used as the excitation source. When differential-mode to common-mode conversion occurs, the equivalent common-mode interference current after conversion is used as the excitation source; When the converter devices are switched quickly, the pulsed common-mode current caused by the switching process of the devices and the rate of change of voltage and current is used as the excitation source. When the excitation comes from the conductive coupling of adjacent devices or cables, the conductive coupling current is used as the excitation source.

4. The method of claim 1, wherein, The impedance matrix and excitation vector are calculated as follows: For random morphological parameter samples, calculate the impedance matrix using the method of moments based on the cable axis path, thin wire unit length, and thin wire unit direction corresponding to the random morphological sample. The excitation vector on the right side of the method of moments is calculated based on the location, amplitude, and direction of the disturbance current source.

5. The method according to claim 1, characterized in that, The construction of the DD-PCE-MoM model includes: Construct data-driven orthogonal polynomial basis functions; The impedance matrix, excitation vector, and cable current coefficient are expanded on the data-driven orthogonal polynomial basis functions to establish a DD-PCE-MoM stochastic method of moments model under stochastic morphological parameter conditions.

6. The method according to claim 1, characterized in that, The method for solving the DD-PCE-MoM model coefficients based on regularized least squares and empirical Galerkin projection includes: Based on the deterministic method of moments impedance matrix and excitation vector corresponding to the random morphological sample, the DD-PCE expansion coefficients of the impedance matrix and excitation vector are solved by the least squares method with Tikhonov regularization. Using the empirical distribution of random morphological samples as a probability measure, the empirical triple product tensor of the data-driven orthogonal polynomial basis functions is calculated, and the DD-PCE-MoM extended matrix equation is established through Galerkin projection to solve for the DD-PCE expansion coefficients of the cable current. Reconstruct the cable current under given random morphological parameters, and calculate the radiated electric field and / or radiated magnetic field at the preset observation point in combination with the corresponding cable geometric path.

7. The method according to claim 1, characterized in that, The calculation of statistical characteristic quantities of the radiation field and the output of statistical results of the radiation field include: The DD-PCE-MoM model is sampled rapidly to calculate the probability density function, cumulative distribution function, quantiles, and probability of exceeding the standard. Frequency points with an excess probability greater than or equal to the excess probability threshold, or with a quantile limit margin less than or equal to zero, are identified as high-risk frequency points.

8. A random-form cable radiation emission statistical device, characterized in that, The device includes: The acquisition module is used to acquire a sample set of random cable patterns; The first module is used to create a discrete model of the cable's fine wires. The second module is used to establish the incentive source; The assembly module is used to assemble the impedance matrix and excitation vector corresponding to random morphology samples of cables, forming an impedance matrix sample set and an excitation vector sample set. The third module is used to build the DD-PCE-MoM model; The solver module is used to solve the coefficients of the DD-PCE-MoM model based on regularized least squares and empirical Galerkin projection; The output module is used to calculate the statistical characteristics of the radiation field and output the statistical results of the radiation field.

9. An electronic device, characterized in that, include: A memory and a processor are communicatively connected, the memory storing computer instructions, and the processor executing the computer instructions to perform the statistical method for random-morphology cable radiation emission according to any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer instructions for causing the computer to execute the statistical method for random-morphology cable radiation emission as described in any one of claims 1 to 7.

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