An EMC uncertainty analysis failure rate prediction method based on a proxy model

Abstract

The application provides an EMC uncertainty analysis failure rate prediction method based on a proxy model. From the practical application angle of the uncertainty analysis method, the concept of failure rate is introduced, the reliability and practicability of electromagnetic compatibility design are enhanced, and the purpose is to more accurately determine which uncertainty analysis method is more suitable for failure rate prediction. The uncertainty analysis methods based on Kriging and least square support vector regression (LSSVR) are applied to EMC failure rate prediction, thereby providing a theoretical basis for guiding actual electromagnetic compatibility design by the uncertainty analysis method.

Description

Technical Field

[0001] This invention relates to the technical field of failure rate prediction, and more particularly to a failure rate prediction method based on surrogate model for EMC uncertainty analysis. Background Technology

[0002] In recent years, uncertainty analysis has formed a complete research system in the field of EMC. Uncertainties in real electromagnetic environments lead to the randomness of inputs. To ensure the reliability and practicality of electromagnetic protection design, uncertainty analysis methods are introduced to study the impact of uncertainties on electromagnetic design. Currently, various uncertainty analysis methods exist, such as the Monte Carlo method (MCM), which has the highest accuracy but poor convergence and lowest efficiency; the Stochastic Galerkin method (SGM), which has limited applicability; and the Stochastic Collocation method (SCM), which has high applicability but suffers from the "curse of dimensionality." With the widespread reputation of machine learning in various research fields, uncertainty analysis methods based on surrogate models are considered promising. The Kriging model and the LSSVR model are two commonly used surrogate models in EMC uncertainty analysis.

[0003] In existing EMC uncertainty analysis studies, the mean, standard deviation, and root mean square error are often used as evaluation criteria. While this can indeed assess the overall quality of uncertainty analysis methods, it fails to consider system failures caused by uncertainties in real-world engineering. Uncertainties exist in practical engineering, causing system inputs to fluctuate within an uncertainty range, resulting in significant output fluctuations, potentially even exceeding near-failure values ​​and causing failure. For example, the uncertainty in the aperture dimensions of an electromagnetic shielding box affects shielding effectiveness. Some specific equipment requires a certain shielding effectiveness to ensure normal operation within the shielded box. If the shielding effectiveness fails to meet the specified value, it is considered a failure. Therefore, failure rate can also serve as an evaluation criterion for EMC uncertainty analysis to improve the reliability and practicality of electromagnetic design. Summary of the Invention

[0004] To address the technical problems mentioned in the background section, this invention provides a failure rate prediction method for EMC uncertainty analysis based on surrogate models. From the perspective of practical application of uncertainty analysis methods, this invention introduces the concept of failure rate to enhance the reliability and practicality of electromagnetic compatibility design, aiming to more accurately determine which uncertainty analysis method is more suitable for failure rate prediction. Uncertainty analysis methods based on two surrogate models—Kriging and Least Squares Support Vector Regression (LSSVR)—are applied to EMC failure rate prediction, thus providing a theoretical basis for uncertainty analysis methods to guide practical electromagnetic compatibility design.

[0005] The technical means employed in this invention are as follows:

[0006] A failure rate prediction method for EMC uncertainty analysis based on a surrogate model includes the following steps:

[0007] Step 1: Use Latin hypercube sampling to sample in the sampling space to obtain m sampling points, each of which is an N-dimensional constant value vector; and perform deterministic EMC simulation on each sampling point:

[0008] y i =EMC[x i ];

[0009] The set of EMC simulation results y is obtained:

[0010] y = [y1, y2, ..., y m ] T ;

[0011] Among them, y i This represents the results of a single EMC simulation; the training set is obtained through the above analysis. Used to train two proxy models, Kriging and LSSVR.

[0012] Step 2: Train the Kriging model and LSSVR model using the set of EMC simulation results; apply the Kriging model to linearly weight the EMC simulation results of the known samples to generate interpolation results, and simultaneously find the optimal weighting coefficient w in the Kriging model, such that... It has the smallest mean square error and satisfies the unbiased condition;

[0013] Step 3: Apply the LSSVR model to map the input space to a high-dimensional feature space through nonlinear mapping, find the optimal linear function in the feature space, and use kernel function technology to simplify the calculation;

[0014] Step 4: Calculate the response values ​​of all sampling points in the exhaustive sampling points using the Kriging and LSSVR models trained in Step 2 and Step 3 to obtain the simulation result set based on these two models;

[0015] Step 5: Introduce the concept of failure rate; the failure rate refers to the proportion of the entire sample space occupied by points within the failure domain;

[0016] Step 6: Statistically analyze the simulation results based on the Kriging model and LSSVR model in Step 4 to obtain uncertainty analysis results such as probability density curves and failure rates.

[0017] Furthermore, the EMC simulation results of the known samples are linearly weighted to generate the interpolation result as follows:

[0018]

[0019] in, Indicates the interpolation result; m represents the number of EMC simulations; w i Indicates the weighting coefficient; y i This represents the EMC simulation result; i indicates the number of times the simulation was performed.

[0020] Furthermore, the formula for calculating the mean square error is:

[0021]

[0022] in, E[] represents the mean square error of the interpolation result; E[] represents the expected value; w T Y represents the transpose of the weighting coefficients; S Y represents a static random process; S =[Y (1) ,Y (2) ,…,Y (m) ] T Used to replace y = [y1, y2, ..., y m ] T .

[0023] Furthermore, the unbiased condition is:

[0024]

[0025] Where, x i This represents each sampling point.

[0026] Furthermore, step 3 includes the following steps:

[0027] Step 31: Map the input space to a high-dimensional feature space through a nonlinear mapping φ(), and find the optimal linear function in the feature space;

[0028] Step 32: Employ kernel function techniques to replace the direct calculation of nonlinear mappings with the inner product of the nonlinear mappings;

[0029] Step 33: The training set is the one obtained in step 1. The LSSVR optimization problem is as follows;

[0030] Step 34: Introduce the Lagrange function and dual optimization to transform the problem into an unconstrained optimization problem;

[0031]

[0032] Where L is the Lagrange function, b is a constant, φ() is the nonlinear mapping, and e is the regularization parameter.

[0033] Step 35: The following conditions are obtained from the optimization of the Karush-Kuhn-Tucker (KKT) conditions:

[0034]

[0035] Where α=[α1,…,α m ] T α i Represents the Lagrange multiplier;

[0036] Transform into a system of linear equations:

[0037]

[0038] Where y = [y1, ..., y m ] T α=[α1,…,α m ] T 1 m =[1,…,1] T It is an m×1 matrix, I m It is an m×m identity matrix

[0039] Step 36: Solve formula (9) to obtain the LSSVR model:

[0040]

[0041] Furthermore, the failure rate is:

[0042]

[0043] Where pdf(ε) represents the probability density function.

[0044] Furthermore, the kernel function is:

[0045] K(x i ,x j )=φ(x i )*φ(x j );

[0046] Where K(x) i ,x j ) represents the kernel function, and the Gaussian kernel function K(x) is selected. i ,x j )=exp(-||x i -x j || 2 / ρ 2 );

[0047]

[0048] sty i =ω T φ(x i )+b+e i ,i=1,…,m;

[0049] Where ω is the weight vector, representing the complexity of the model; e = [e1,…,e m ] T Represents the error vector; γ∈R + Represents the regularization parameter;

[0050]

[0051] Compared with the prior art, the present invention has the following advantages:

[0052] This invention introduces failure rate as a new evaluation criterion, which can more accurately reflect the impact of uncertainties in actual engineering. While traditional mean, standard deviation, and root mean square error can comprehensively evaluate the quality of uncertainty analysis methods, they fail to fully consider the risk of system failure. The failure rate results of the porous metal box shielding effectiveness are shown in Table 1. The failure rate P of the MCM... r(MCM) The failure rate was 24.50%, which was used as the standard. Kriging's failure rate P... r(Kriging) The failure rate was 22.54%, with a relative error of 8.00% compared to MCM. This demonstrates that Kriging is highly accurate in predicting failure rates. The failure rate P of LSSVR... r(LSSVR) The accuracy was 12.59%, with a relative error of 48.61% compared to MCM. LSSVR is not very accurate in predicting the failure rate of shielding in complex porous metal boxes.

[0053] Table 1. Failure rate results of the shielding effectiveness of the porous metal box.

[0054]

[0055] Meanwhile, this invention effectively improves computational efficiency: the simulation times of the three methods are shown in Table 1. MCM performs a total of 10,000 simulation calculations, consuming t... cost =73.3h. Kriging and LSSVR only require 36 deterministic EMC simulations, taking t... SE =15.8min. Kriging's model prediction time t modle =1.4s, LSSVR model prediction time t modle =2.2s. This demonstrates that the uncertainty analysis method based on the surrogate model is computationally more efficient than the MCM.

[0056] Table 2 Simulation times for three methods

[0057] Attached Figure Description

[0058] 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.

[0059] Figure 1 This is a structural block diagram of the LSSVR of the present invention.

[0060] Figure 2 This is a schematic diagram illustrating the shielding effectiveness calculation of a single-hole metal box according to the present invention.

[0061] Figure 3 This is a probability density diagram of the shielding effectiveness of the single-hole metal box of the present invention.

[0062] Figure 4 The diagram shows the shielding effectiveness failure domain diagram based on three uncertainty analysis methods of this invention; where (a) is the MCM method; (b) is the Kriging method; and (c) is the LSSVR method.

[0063] Figure 5 This is a schematic diagram illustrating the shielding effectiveness calculation of the porous metal box of the present invention.

[0064] Figure 6 This is a schematic diagram of the three-hole metal box slits of the present invention.

[0065] Figure 7 This is a schematic diagram illustrating the construction of the MATLAB and COMSOL software co-simulation platform of this invention.

[0066] Figure 8 This is a probability density diagram of the shielding effectiveness of the porous metal box of the present invention. Detailed Implementation

[0067] 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.

[0068] 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.

[0069] like Figure 1 As shown, this invention provides a method for predicting EMC failure rates based on surrogate models. Addressing the shortcomings of existing technologies, this invention offers an uncertainty analysis method based on surrogate models, specifically utilizing Kriging and Least Squares Support Vector Regression (LSSVR) surrogate models to predict EMC failure rates. These surrogate models can significantly reduce the number of simulations required while maintaining high prediction accuracy, thereby greatly improving computational efficiency. Furthermore, by introducing failure rate as a new evaluation criterion, it can more accurately reflect the impact of uncertainties on system performance in practical engineering, thus improving the reliability and practicality of electromagnetic design. The method includes the following steps:

[0070] Step 1: Use Latin hypercube sampling to sample in the sampling space to obtain m sampling points, each of which is an N-dimensional constant value vector; and perform deterministic EMC simulation on each sampling point:

[0071] y i =EMC[x i ];

[0072] The set of EMC simulation results y is obtained:

[0073] y = [y1, y2, ..., y m ] T (1)

[0074] Among them, y i This represents the results of a single EMC simulation; the training set is obtained through the above analysis. Used to train two proxy models, Kriging and LSSVR.

[0075] Step 2: Obtain the training set through the above steps to train the Kriging and LSSVR surrogate models. Apply the Kriging model to generate interpolation results by linearly weighting the EMC simulation results of known samples, as shown in formula (2). The Kriging model seeks the optimal weighting coefficient w to minimize the mean square error in formula (3) and satisfy the unbiased condition in formula (4).

[0076]

[0077] Among them, Y S =[Y (1) ,Y (2) ,…,Y (m) ] T Used to replace y = [y1, y2, ..., y m ] T .

[0078]

[0079] Step 3: Apply the LSSVR model again; its structure is shown below. Figure 1 The input space is mapped to a high-dimensional feature space through nonlinear mapping, and the optimal linear function is found in the feature space. Kernel function techniques are used to simplify the calculation. Figure 1 This is the block diagram of LSSVR. The input space is mapped to a high-dimensional feature space via a nonlinear mapping φ(), and the optimal linear function is obtained in the feature space. The dimension of the high-dimensional feature space may be infinite, and the specific expression of the nonlinear mapping φ() is usually unknown. Therefore, the kernel function technique of formula (5) is used, replacing the direct calculation of the nonlinear mapping with the inner product of the nonlinear mapping, which significantly simplifies the calculation. The training set is the one obtained earlier. LSSVR can then be expressed as an optimization problem as shown in equation (6).

[0080] To solve this constrained optimization problem, a Lagrange function and dual optimization are introduced, transforming it into an unconstrained optimization problem as shown in equation (7). Equation (8) is obtained from the Karush-Kuhn-Tucker (KKT) optimization conditions. Equation (8) is then transformed into a system of linear equations as shown in equation (9). By solving equation (9), the LSSVR model is obtained, as shown in equation (10).

[0081] K(x i ,x j )=φ(x i )*φ(x j (5)

[0082] Where K(x) i ,x jThe kernel function is represented by ), and this paper selects the Gaussian kernel function K(x). i ,x j )=exp(-||x i -x j || 2 / ρ 2 ).

[0083]

[0084] sty i =ω T φ(x i )+b+e i ,i=1,…,m;(6)

[0085] Where ω represents the weight vector, and e represents the complexity of the model. e = [e1,…,e m ] T It is the error vector. γ∈R + It is the regularization parameter.

[0086]

[0087] Where α=[α1,…,α m ] T , where α i It is a Lagrange multiplier.

[0088]

[0089] Where y = [y1, ..., y m ] T α=[α1,…,α m ] T 1 m =[1,…,1] T It is an m×1 matrix, I m It is an m×m identity matrix.

[0090]

[0091] Step 4: Calculate the response values ​​of all sampling points in the exhaustive sampling points using the trained Kriging and LSSVR models to obtain a set of simulation results based on these two models.

[0092] Step 5: The concept of failure rate is introduced. The example used in this invention is a single-hole metal box, such as... Figure 2 As shown. The shielding box is a "general" electromagnetic shielding box, and its shielding performance requirement S... E >60 [dB]. In other words, the failure domain of the metal enclosure's shielding effectiveness is:

[0093] F = {X:S}E (X)<60[dB]};(11)

[0094] Failure rate refers to the proportion of points within the failure domain that occupy the entire sample space. This invention uses probability density curves to more clearly illustrate the concept of failure rate, as shown in the following formula.

[0095]

[0096] Where pdf(ε) is the probability density function.

[0097] Step 6: Statistically analyze the simulation results based on the Kriging and LSSVR models to obtain uncertainty analysis results such as probability density curves and failure rates. Compare the results based on the three uncertainty analysis methods: MCM, Kriging, and LSSVR. Using the MCM results as a reference standard, evaluate the performance and computational efficiency of the Kriging and LSSVR models in predicting EMC failure rates.

[0098] Figure 2 This is a schematic diagram illustrating a calculation example of the shielding effectiveness of a single-hole metal box. The internal dimensions of the rectangular metal box are a×b×d, and its thickness is t. The rectangular hole at the center of the panel has dimensions l×w. An excitation plane wave radiates from outside the metal box, incident perpendicularly to the panel on the surface of the rectangular cavity with the opening, and polarized along the height of the cavity. The shielding effectiveness test point P is located along the center line of the panel, at a distance p from the opening. Specific values ​​for some parameters are: a = 300mm, b = 120mm, d = 300mm, t = 1mm, p = 150mm. The selected metal is aluminum, with a conductivity of σ = 3.8 × 10⁻⁶. 7 S / m, relative permittivity is ε r =1, and the rest of the solution space is also treated as a vacuum.

[0099] Assume that the length l and width w of the rectangular hole at the center of the panel are the uncertainty factors in this example, and are described by the following random variables (13):

[0100]

[0101] Here, ξ1 and ξ2 are uniformly distributed random variables in the interval [-1, 1].

[0102] According to Robinson's method, assuming the frequency of the excitation plane wave is f = 40MHz, the electric field strength at point P without a metal enclosure is calculated as E0, and the electric field strength at point P with a metal enclosure is calculated as E1. The shielding effectiveness at this frequency is shown in the following equation (14):

[0103]

[0104] Next, we will analyze the simulation results. Figure 3 This is the probability density plot of the shielding effectiveness of a single-hole metal box. Using the uncertainty analysis results of the MCM as standard data, 10,000 deterministic simulations were performed on exhaustive sampling points S1 to ensure convergence. The sample space S2 of Kriging and LSSVR has 36 sampling points, i.e., m = 36. Deterministic simulations were performed on these sampling points to obtain the training set, which was then used to construct a surrogate model, ultimately yielding the uncertainty analysis results. In the figure, the horizontal axis represents shielding effectiveness, and the vertical axis represents probability density.

[0105] Figure 4 The failure domain of shielding effectiveness based on three uncertainty analysis methods is presented. As is well known, the MCM (Mean Conformity Matrix) has extremely high computational accuracy and is a widely accepted reference standard in the field of EMC simulation. Therefore, the closer the results obtained by other uncertainty analysis methods are to the MCM, the higher the accuracy of that method. Figure 4 The size of the failure domain can be used to preliminarily determine the accuracy of Kriging.

[0106] The results show that in the failure rate calculation of the shielding effectiveness of a single-hole metal box based on the Robinson method, both Kriging and LSSVR have high accuracy, with Kriging having slightly higher accuracy than LSSVR.

[0107] To further verify the applicability of the uncertainty analysis method based on the surrogate model in EMC failure rate prediction, this study constructs a porous metal box model based on COMSOL simulation software to investigate the failure rate of the shielding effectiveness of the porous metal box based on the finite element method. Figure 5 This is a schematic diagram illustrating the shielding effectiveness calculation of a perforated metal box. First, an anechoic chamber is constructed to absorb electromagnetic waves within the chamber and block incoming signals from the outside. Then, a biconical antenna is placed at the center of the chamber to transmit electromagnetic waves. Finally, a three-hole metal box is constructed at a certain distance from the antenna. Except for the parameters of the perforations, the parameters of the metal box in this example are the same as those in the previous section. The internal dimensions of the cuboid metal box are a×b×d, where a=300mm, b=120mm, d=300mm. The thickness t=1mm. The shielding effectiveness test point P is located along the center line of the panel, at a distance of p=150mm from the opening. The selected metal is aluminum, with a conductivity of σ=3.8×10⁻⁶. 7 S / m, relative permittivity is ε r =1, and the rest of the solution space is also treated as a vacuum.

[0108] Figure 6 This is a schematic diagram of the slots in a three-hole metal box. The lengths of the three slots are L1, L2, and L3, respectively. The width of each slot is w = 5 mm. Assume that L1, L2, and L3 are the uncertainties in this example, described by the following random variables:

[0109]

[0110] Among them, ξ3, ξ4 and ξ5 are uniformly distributed random variables in the interval [-1,1].

[0111] To ensure the implementation of uncertainty analysis, this example requires joint simulation using COMSOL and MATLAB software. Figure 7 This is a schematic diagram illustrating the construction of a joint simulation platform using MATLAB and COMSOL software. First, based on the uncertainty parameter in formula (16), Latin hypercube sampling is applied to obtain sampling point S2. The number of sampling points in this example is... Figure 2 The same example is used, with m = 36. The metal box model built based on COMSOL is converted into a MATLAB subfunction so that MATLAB can call COMSOL for finite element simulation. The program is modified based on the random variable inputs at the sampling points. After the preparation is complete, MATLAB and COMSOL are linked. MATLAB is used to call COMSOL to perform deterministic EMC simulations at the sampling points, and the generated simulation results are saved in a txt file. MATLAB uses the data in the txt file to build a Kriging model or an LSSVR model. Finally, the exhaustive sampling point S1 is substituted into the surrogate model to obtain the uncertainty analysis results. It is worth noting that this example also performs simulations at a frequency of f = 40MHz to calculate the shielding effectiveness S at point P. E Furthermore, MCM performs 10,000 deterministic simulations at exhaustive sampling point S1 as reference data.

[0112] Figure 8 The graph shows the probability density curve of the shielding effectiveness of the porous metal box. As can be seen from the graph, Kriging outperforms LSSVR in terms of overall performance. As for which uncertainty analysis method performs better in terms of failure rate, it needs to be calculated using formula (15). The critical failure value in this example is also taken as 60 [dB], which is consistent with... Figure 2 The calculation examples are consistent. The results show that the failure rate P of MCM is... r(MCM) The failure rate was 24.50%, which was used as the standard. Kriging's failure rate P... r(Kriging) The failure rate was 22.54%, with a relative error of 8.00% compared to MCM. The failure rate P of LSSVR was... r(LSSVR) The failure rate was 12.59%, with a relative error of 48.61% compared to MCM. This demonstrates that Kriging is highly accurate in predicting failure rates, while LSSVR is less accurate in predicting the failure rates of complex porous metal box shielding.

[0113] 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.

[0114] 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 therein. Such 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 failure rate prediction method for EMC uncertainty analysis based on a surrogate model, characterized in that, Includes the following steps: Step 1: Use Latin hypercube sampling to sample in the sampling space to obtain m sampling points, each of which is an N-dimensional constant value vector data; Deterministic EMC simulations were performed at each sampling point: y i =EMC[x i ]; The set of EMC simulation results y is obtained: y=[y1,y2,…,y m ] T ; Among them, y i This represents the results of a single EMC simulation; the training set is obtained through the above analysis. Used to train two proxy models, Kriging and LSSVR. Step 2: Train the Kriging model and LSSVR model using the set of EMC simulation results; apply the Kriging model to linearly weight the EMC simulation results of the known samples to generate interpolation results, and simultaneously find the optimal weighting coefficient w in the Kriging model, such that... It has the smallest mean square error and satisfies the unbiased condition; Step 3: Apply the LSSVR model to map the input space to a high-dimensional feature space through nonlinear mapping, find the optimal linear function in the feature space, and use kernel function technology to simplify the calculation; Step 4: Calculate the response values ​​of all sampling points in the exhaustive sampling points using the Kriging and LSSVR models trained in Step 2 and Step 3 to obtain the simulation result set based on these two models; Step 5: Introduce the concept of failure rate; the failure rate refers to the proportion of the entire sample space occupied by points within the failure domain; Step 6: Statistically analyze the simulation results based on the Kriging model and LSSVR model in Step 4 to obtain uncertainty analysis results such as probability density curves and failure rates.

2. The method for predicting failure rate in EMC uncertainty analysis based on a surrogate model according to claim 1, characterized in that, The interpolation result is generated by linearly weighting the EMC simulation results of the known samples: in, Indicates the interpolation result; m represents the number of EMC simulations; w i Indicates the weighting coefficient; y i This represents the EMC simulation result; i indicates the number of times the simulation was performed.

3. The method for predicting failure rate in EMC uncertainty analysis based on a surrogate model according to claim 1, characterized in that, The formula for calculating the mean square error is: in, E[ ] represents the mean square error of the interpolation result; E[ ] represents the expected value; w T Y represents the transpose of the weighting coefficients; S Y represents a static random process; S =[Y (1) Y (2) , ..., Y (m) ] T Used to replace y = [y1, y2, ..., y m ] T .

4. The method for predicting failure rate in EMC uncertainty analysis based on a surrogate model according to claim 1, characterized in that, The no-bias condition is: Where, x i This represents each sampling point.

5. The method for predicting failure rate based on surrogate model in EMC uncertainty analysis according to claim 1, characterized in that, Step 3 includes the following steps: Step 31: Map the input space to a high-dimensional feature space through a nonlinear mapping φ(), and find the optimal linear function in the feature space; Step 32: Employ kernel function techniques to replace the direct calculation of nonlinear mappings with the inner product of the nonlinear mappings; Step 33: The training set is the one obtained in step 1. The LSSVR optimization problem is as follows; Step 34: Introduce the Lagrange function and dual optimization to transform the problem into an unconstrained optimization problem; Where L is the Lagrange function, b is a constant, φ() is the nonlinear mapping, and e is the regularization parameter. Step 35: The following conditions are obtained from the optimization of the Karush-Kuhn-Tucker (KKT) conditions: Where α = [α1, ..., α2] m ] T α i Represents the Lagrange multiplier; Transform into a system of linear equations: Where y = [y1, ..., y2] m ] T , α=[α1,…,α m ] T 1 m = [1, ..., 1] T It is an m×1 matrix, I m It is an m×m identity matrix Step 36: Solve formula (9) to obtain the LSSVR model:

6. The failure rate prediction method for EMC uncertainty analysis based on a surrogate model according to claim 1, characterized in that, The failure rate is: Where pdf(ε) represents the probability density function.

7. The method for predicting failure rate in EMC uncertainty analysis based on a surrogate model according to claim 1, characterized in that, The kernel function is: K(x i ,x j )=φ(x i )*φ(x j ); Where K(x) i x j ) represents the kernel function, and the Gaussian kernel function K(x) is selected. i x j )=exp(-||x i -x j || 2 / ρ 2 ); s.t.y i =ω T φ(x i )+b+e i ,i=1,…,m; Where ω is the weight vector, representing the complexity of the model; e = [e1, ..., e2] m ] T Represents the error vector; γ∈R + Represents the regularization parameter;

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