EMC uncertainty analysis method applying LSSVR to improve Kriging proxy model

Abstract

The invention provides an EMC uncertainty analysis method applying an LSSVR to improve a Kriging proxy model, and belongs to the technical field of uncertainty analysis methods. According to the method, the least square support vector machine regression (LSSVR) is applied to improve the Kriging agent model, the LSSVR is applied to assist the Kriging model in selecting sampling points, a sequential sampling strategy with high initiative is obtained, and the sample points which enable the agent model to be higher in precision can be actively selected. The efficiency and accuracy of the Kriging agent model during EMC uncertainty analysis are improved to a great extent, and the practicability of EMC uncertainty analysis in practical engineering is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of uncertainty analysis methods, and in particular to an EMC uncertainty analysis method using LSSVR to improve a Kriging proxy model. Background Art

[0002] Uncertainty analysis refers to the process of measuring, describing and evaluating the uncertainty in a system, model or process using probabilistic statistical methods. In the field of electromagnetic compatibility (EMC), uncertainty analysis can significantly improve the reliability and practicality of electromagnetic compatibility simulation models by treating the input parameters in numerical simulation as uncertain parameters (such as random variable models).

[0003] The Monte Carlo method (MCM) is widely considered to be the most accurate uncertainty analysis method. This method describes the randomness of simulation inputs by exhaustively enumerating sampling points. MCM is suitable as a standard in theoretical research to verify the accuracy of other uncertainty analysis methods. Although MCM has the advantages of high computational accuracy and easy implementation, its poor convergence leads to low computational efficiency and is difficult to apply in practical engineering.

[0004] The stochastic Galerkin method (SGM) and the stochastic collocation method (SCM) based on the generalized polynomial chaos (GPC) theory both have good performance. Since SGM is an embedded uncertainty analysis method, the applicability of SCM is higher than that of SGM. However, SCM has a serious "curse of dimensionality" problem and is not suitable for situations with a large number of random variables. The method of moments (MoM) and the stochastic model reduction method (SROM) are better uncertainty analysis methods for dealing with the "curse of dimensionality" problem, but MoM and SROM are only applicable to EMC simulation solvers with good linearity. When the nonlinearity of the solver is high, the complexity of the uncertainty analysis results is also relatively high, and both MoM and SROM have the risk of failure.

[0005] In recent years, uncertainty analysis methods based on surrogate models have been gradually proposed. Among them, the Kriging model is a typical surrogate model used in uncertainty analysis. It is suitable for solvers with high nonlinearity and does not have the "curse of dimensionality" problem. The traditional Kriging model uses the Latin hypercube sampling (LHS) strategy to select sampling points at one time, and cannot actively adjust the sampling points according to the specific characteristics of different situations. This greatly affects the accuracy and computational efficiency of the Kriging model in EMC simulation uncertainty analysis. When a single EMC simulation takes a long time, a lot of computing resources will be wasted. Summary of the invention

[0006] According to the technical problems mentioned in the above background technology, an EMC uncertainty analysis method using LSSVR to improve the Kriging proxy model is provided.

[0007] The technical means adopted by the present invention are as follows:

[0008] An EMC uncertainty analysis method using LSSVR to improve the Kriging surrogate model includes:

[0009] Step 1: Based on the exhaustive sampling method used in MCM uncertainty analysis, describe the random variable ζ;

[0010] Step 2: Select sampling points through Latin hypercube sampling LHS to obtain the initial sample space S0 = [x1, x2, ..., x q ]; Deterministic EMC simulation is performed based on the sampling points to obtain the initial training set

[0011] Step 3: Based on the initial training set Train and build the Kriging model M Kriging and LSSVR model M LSSVR ;

[0012] Step 4: Bring the exhaustive sampling point S1 into the Kriging model M Kriging and LSSVR model M LSSVR , and the obtained Y Kriging and Y LSSVR , which correspond to the response values ​​estimated by the two models at the exhaustive sampling point S1; for Y Kriging and Y LSSVR Perform statistics to obtain a probability density PDF curve; convert the PDF curve into a cumulative distribution function CDF curve, and calculate the KS distance D between the CDF curves of Kriging and LSSVR;

[0013] Step 5: Determine the distance D by the maximum vertical deviation between the two CDF curves; if the distance D is greater than 0.05, find Y Kriging and Y LSSVR The sample point x corresponding to the value with the largest difference i , the sample point x i Add to the initial sample space S0, and re-execute steps 2 to 4. The initial sample space S0 is expanded until the distance D is less than or equal to 0.05, and the final sample space S is output;

[0014] Step 6: Take the EMC simulation results of the sample space S as the training set and construct the final Kriging model M based on the training set Kriging ; Bring the exhaustive sampling point S1 into M Kriging, the response value Y of the exhaustive sampling point S1 Kriging Perform statistics and obtain the uncertainty analysis results based on Kriging-LSSVR;

[0015] Step 7: According to the above steps, the Kriging-LSSVR model proposed in the present invention is applied in actual engineering.

[0016] Furthermore, in step 1, assuming that the number of exhaustive sampling points is n, the exhaustive sampling points S1 = [x1, x2, ..., x n ].

[0017] Furthermore, in step 2, the number of sampling points is set to q, x i is N-dimensional constant value vector data;

[0018] At each sampling point, a deterministic EMC simulation is performed:

[0019] y i =EMC[x i ];

[0020] Where, EMC[] represents a single deterministic EMC simulation process, y i Represents the EMC deterministic simulation results.

[0021] Furthermore, the number of sampling points q is much smaller than the number of exhaustive sampling points in exhaustive sampling.

[0022] Furthermore, the Kriging model is:

[0023]

[0024] Where w=[w1,w2…w L ] T represents the weighting coefficient, q represents the number of sampling points used to train the model;

[0025] Furthermore, the LSSVR model is:

[0026]

[0027] in, α i represents the scalar coefficient, b represents the bias term, K(x i ,x) represents the kernel function, and q represents the number of sampling points used to train the model.

[0028] Furthermore, the KS distance is the test statistic of the Kolmogorov-Smirnov test, and the distance D is determined by the maximum vertical deviation between two curves of the CDF of the data set:

[0029] D = max(|CDF1(x)-CDF2(x)|);

[0030] Among them, CDF1(x) represents the proportion of values ​​less than or equal to x in the Kriging data set, CDF2(x) represents the proportion of values ​​less than or equal to x in the LSSVR data set, and max() represents selecting the maximum value.

[0031] Compared with the prior art, the present invention has the following advantages:

[0032] The present invention uses Least Squares Support Vector Machine Regression (LSSVR) to improve the Kriging proxy model, and uses LSSVR to assist the Kriging model in selecting sampling points, thereby obtaining a highly proactive sequential sampling strategy that can proactively select sample points that make the proxy model more accurate. This greatly improves the efficiency and accuracy of the Kriging proxy model when performing EMC uncertainty analysis, and improves the practicability of EMC uncertainty analysis in actual engineering. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0034] Figure 1 Flow chart of Kriging-LSSVR proposed by the present invention;

[0035] Figure 2 This is a schematic diagram of a parallel cable crosstalk calculation example;

[0036] Figure 3 is the probability density of the crosstalk voltage value at 2MHz;

[0037] Figure 4 is the probability density of the crosstalk voltage value at 50MHz;

[0038] Figure 5 is the expected far-end crosstalk voltage in the frequency range of 1MHz to 100MHz;

[0039] Figure 6 is the standard deviation of the far-end crosstalk voltage in the frequency range of 1MHz to 100MHz. DETAILED DESCRIPTION

[0040] In order to enable those skilled in the art to better understand the scheme of the present invention, the technical scheme in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0041] It should be noted that the terms "first", "second", etc. in the specification and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that the data used in this way can be interchanged where appropriate, so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions, for example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units that are clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0042] like Figure 1 As shown, the present invention provides an EMC uncertainty analysis method using LSSVR to improve the Kriging proxy model, comprising:

[0043] Step 1: Based on the exhaustive sampling method used in MCM uncertainty analysis, the random variable ζ is described; in step 1, it is assumed that the number of exhaustive sampling points is n, and the exhaustive sampling points S1 = [x1, x2, …, x n ].

[0044] Step 2: Select sampling points through Latin hypercube sampling (LHS) to obtain the initial sample space S0 = [x1, x2, ..., x q ]; Deterministic EMC simulation is performed based on the sampling points to obtain the initial training set In step 2, the number of sampling points is set to q, and the number of sampling points q is much smaller than the number of exhaustive sampling points in the exhaustive sampling. i is N-dimensional constant value vector data;

[0045] At each sampling point, a deterministic EMC simulation is performed:

[0046] y i =EMC[x i ];

[0047] Where, EMC[] represents a single deterministic EMC simulation process, y iRepresents the EMC deterministic simulation results.

[0048] Step 3: Based on the initial training set Train and build the Kriging model M Kriging and LSSVR model M LSSVR ; The Kriging model is:

[0049]

[0050] Where w=[w1,w2…w L ] T represents the weighting coefficient, q represents the number of sampling points used to train the model;

[0051] The LSSVR model is:

[0052]

[0053] in, α i represents the scalar coefficient, b represents the bias term, K(x i ,x) represents the kernel function, and q represents the number of sampling points used to train the model.

[0054] Step 4: Bring the exhaustive sampling point S1 into the Kriging model M Kriging and LSSVR model M LSSVR , and the obtained Y Kriging and Y LSSVR , which correspond to the response values ​​estimated by the two models at the exhaustive sampling point S1; for Y Kriging and Y LSSVR Perform statistics to obtain a probability density PDF curve; convert the PDF curve into a cumulative distribution function CDF curve, and calculate the KS distance D between the CDF curves of Kriging and LSSVR; the KS distance is the test statistic of the Kolmogorov-Smirnov test, and the distance D is determined by the maximum vertical deviation between the two curves of the CDF of the data set:

[0055] D = max(|CDF1(x)-CDF2(x)|);

[0056] Among them, CDF1(x) represents the proportion of values ​​less than or equal to x in the Kriging data set, CDF2(x) represents the proportion of values ​​less than or equal to x in the LSSVR data set, and max() represents selecting the maximum value.

[0057] Step 5: Determine the distance D by the maximum vertical deviation between the two CDF curves; if the distance D is greater than 0.05, find Y Kriging and Y LSSVRThe sample point x corresponding to the value with the largest difference i , the sample point x i Add to the initial sample space S0, and re-execute steps 2 to 4. The initial sample space S0 is expanded until the distance D is less than or equal to 0.05, and the final sample space S is output;

[0058] Step 6: Take the EMC simulation results of the sample space S as the training set and construct the final Kriging model M based on the training set Kriging ; Bring the exhaustive sampling point S1 into M Kriging , the response value Y of the exhaustive sampling point S1 Kriging Perform statistics and obtain the uncertainty analysis results based on Kriging-LSSVR;

[0059] Step 7: According to the above steps, the Kriging-LSSVR model proposed in the present invention is applied in actual engineering.

[0060] Example 1

[0061] The prediction of cable crosstalk considering cable uncertainty is a typical EMC problem. The Kriging-LSSVR model proposed in this paper is applied to Figure 2 The parallel line crosstalk example shown in the figure verifies its advantages over the traditional Kriging proxy model. In this example, two cables are parallel to each other and are 1m long. The horizontal distance between them is s. One cable is used as a receiving line and its two ends are grounded to a 50Ω load at a height of h2. The other cable is used as a transmitting line and not only needs to be connected to a 50Ω load, but also needs to be connected to an excitation source E with an amplitude of 1V. m The diameters of the transmitting and receiving lines are d a and d b In the uncertainty analysis of this example, the five variables in the table below are considered as uncertainty factors.

[0062] Table 1 Uncertainty parameters of parallel cables

[0063]

[0064] Firstly, MCM is applied to perform 10000 deterministic simulations in the exhaustive sampling space S1, and its uncertainty analysis results are used as standard data for the subsequent evaluation of the performance of the Kriging-LSSVR model.

[0065] Figure 1 This is a flowchart of how the Kriging-LSSVR model is implemented. Assume that the initial sample space S0 of Kriging-LSSVR has 20 sampling points, that is, q = 20. Perform deterministic simulation on the sampling points to obtain the initial training set Then train and construct the Kriging model M Kriging and LSSVR model N LSSVR .

[0066] Substitute the exhaustive sampling point S1 into the two models respectively, and calculate the response value Y Kriging and Y LSSVR , and generate a PDF curve. Convert the PDF curve into a CDF curve, and calculate the KS distance D according to D = max(|CDF1(x)-CDF2(x)|).

[0067] When D is greater than 0.05, find Y Kriging and Y LSSVR The sample point x corresponding to the value with the largest difference i , add it to the initial sample space S0, and re-perform the above operation. S0 is expanded so that the value of D gradually decreases, and the final sample space S is output when D is less than or equal to 0.05.

[0068] The number of sampling points in the final sample space S obtained by the above sequential sampling strategy is 97. The EMC simulation results obtained from the final sample space are used as the training set, and the final Kriging model M is constructed based on this training set. Kriging . Bring the exhaustive sampling space S1 into the final M Kiging , and obtain the uncertainty analysis result based on the Kriging-LSSVR model proposed in the present invention.

[0069] In order to compare the performance with the traditional Kriging proxy model, the number of sampling points selected at one time by the traditional Kriging using Latin hypercube sampling is also 97, and the performance of the two is compared under the same number of sampling points.

[0070] Figure 3 and Figure 4 The probability density curves of the crosstalk voltage values ​​at frequencies of 2MHz and 50MHz are shown in the figure. The probability density of the crosstalk voltage values ​​using the MCM, Kriging and Kriging-LSSVR models for uncertainty analysis is shown in the figure. It can be seen from the figure that Kriging-LSSVR has higher accuracy than Kriging.

[0071] The average equivalent area method (MEAM) was used for further verification. The evaluation results of MEAM are shown in the following table. The closer the MEAM value is to 1, the higher the accuracy of the tested method.

[0072] Table 2 Evaluation results of MEAM

[0073]

[0074] It can be seen that the accuracy of the Kriging-LSSVR model is higher than that of the Kriging model when the frequencies are 2MHz and 50MHz.

[0075] In order to further study the performance of Kriging-LSSVR, the frequency range is extended to 1-100 MHz. Figure 5 and Figure 6 As shown in the table below, the expected information and standard deviation information are presented respectively. The global difference metric (GDM) value between the test result and the MCM is calculated by using FSV, as shown in the table below.

[0076] Table 3 FSV value results

[0077]

[0078] Table 4 FSV evaluation criteria

[0079]

[0080] According to the results in Table 3, combined with the FSV evaluation criteria in Table 4, the expected value evaluation results of the simulation results of the two proxy models under test are both "Excellent". The standard deviation of Kriging is "Very Good". The standard deviation evaluation result of Kriging-LSSVR is "Excellent". The standard deviation evaluation result of Kriging-LSSVR is one level higher than that of Kriging, which further proves that the accuracy of the Kriging-LSSVR model is higher than that of the Kriging model.

[0081] In terms of computational efficiency, it takes 28.9 seconds to perform a crosstalk calculation. MCM performed 10,000 simulations in total, which took 80 hours. Kriging and Kriging-LSSVR only needed 97 calculations, which took 46.7 minutes. The simulation time of each method is shown in the following table. Kriging-LSSVR model prediction time t modle Slightly longer than the classic Kriging model, but similar to the total time t cost It can be ignored in comparison.

[0082] Table 5 Simulation time

[0083]

[0084] In general, the time consumption of Kriging and Kriging-LSSVR is much less than that of MCM. However, at a similar time consumption, the accuracy of the Kriging-LSSVR model is much better than that of Kriging, and it has stronger practicality.

[0085] The serial numbers of the above embodiments of the present invention are only for description and do not represent the advantages or disadvantages of the embodiments.

[0086] In the above embodiments of the present invention, the description of each embodiment has its own emphasis. For parts that are not described in detail in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.

[0087] In the several embodiments provided in this application, it should be understood that the disclosed technical content can be implemented in other ways. Among them, the device embodiments described above are only schematic. For example, the division of the units can be a logical function division. There may be other division methods in actual implementation. For example, multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some interfaces, indirect coupling or communication connection of units or modules, which can be electrical or other forms.

[0088] The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed on multiple units. Some or all of the units may be selected according to actual needs to achieve the purpose of the present embodiment.

[0089] In addition, each functional unit in each embodiment of the present invention may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit. The above-mentioned integrated unit may be implemented in the form of hardware or in the form of software functional units.

[0090] If the integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution can be embodied in the form of a software product, and the computer software product is stored in a storage medium, including a number of instructions for a computer device (which can be a personal computer, a server or a network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: U disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), mobile hard disk, magnetic disk or optical disk and other media that can store program codes.

[0091] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements 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. An EMC uncertainty analysis method using LSSVR to improve the Kriging surrogate model, characterized in that: include: Step 1: Based on the exhaustive sampling method used in MCM uncertainty analysis, describe the random variable ζ; Step 2: Select sampling points through Latin hypercube sampling LHS to obtain the initial sample space S0 = [x1, x2, ..., x q ]; Deterministic EMC simulation is performed based on the sampling points to obtain the initial training set Step 3: Based on the initial training set Train and build the Kriging model M Kriging and LSSVR model M LSSVR ; Step 4: Bring the exhaustive sampling point S1 into the Kriging model M Kriging and LSSVR model M LSSVR , and the obtained Y Kriging and Y LSSVR , corresponding to the response values ​​estimated by the two models at the exhaustive sampling point S1; for Y Kriging and Y LSSVR Perform statistics to obtain a probability density PDF curve; convert the PDF curve into a cumulative distribution function CDF curve, and calculate the KS distance D between the CDF curves of Kriging and LSSVR; Step 5: Determine the distance D by the maximum vertical deviation between the two CDF curves; if the distance D is greater than 0.05, find Y Kriging and Y LSSVR The sample point x corresponding to the value with the largest difference i , the sample point x i Add to the initial sample space S0, and re-execute steps 2 to 4. The initial sample space S0 is expanded until the distance D is less than or equal to 0.05, and the final sample space S is output; Step 6: Take the EMC simulation results of the sample space S as the training set and build the final Kriging model M based on the training set Kriging ; Bring the exhaustive sampling point S1 into M Kriging , the response value Y of the exhaustive sampling point S1 Kriging Perform statistics and obtain the uncertainty analysis results based on Kriging-LSSVR; Step 7: According to the above steps, the Kriging-LSSVR model proposed in the present invention is applied in actual engineering.

2. The EMC uncertainty analysis method using LSSVR to improve the Kriging proxy model according to claim 1 is characterized in that: In step 1, assuming that the number of exhaustive sampling points is n, the exhaustive sampling points S1 = [x1, x2, ..., x n ].

3. The EMC uncertainty analysis method using LSSVR to improve the Kriging proxy model according to claim 1 is characterized in that: In step 2, the number of sampling points is set to q, x i is N-dimensional constant value vector data; At each sampling point, deterministic EMC simulation: y i =EMC[x i ]; Where, EMC[] represents a single deterministic EMC simulation process, y i Represents the EMC deterministic simulation results.

4. The EMC uncertainty analysis method using LSSVR to improve the Kriging proxy model according to claim 1 is characterized in that: The number of sampling points q is much smaller than the number of exhaustive sampling points in exhaustive sampling.

5. The EMC uncertainty analysis method using LSSVR to improve the Kriging proxy model according to claim 1 is characterized in that: The Kriging model is: Where w=[w1,w2…w L ] T represents the weighting coefficient, and q represents the number of sampling points used to train the model.

6. The EMC uncertainty analysis method using LSSVR to improve the Kriging proxy model according to claim 1 is characterized in that: The LSSVR model is: in, α i represents the scalar coefficient, b represents the bias term, K(x i , x) represents the kernel function, and q represents the number of sampling points used to train the model.

7. The EMC uncertainty analysis method using LSSVR to improve the Kriging proxy model according to claim 1 is characterized in that: The KS distance is Kolmogorov- The test statistic for the Smimov test, the distance D, is determined by the maximum vertical deviation between the two curves of the CDF of the data set: D = max(|CDF1(x)-CDF2(x)|); Among them, CDF1(x) represents the proportion of values ​​less than or equal to x in the Kriging data set, CDF2(x) represents the proportion of values ​​less than or equal to x in the LSSVR data set, and max() represents selecting the maximum value.

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