Global sensitivity analysis method and device for RCS electromagnetic simulation

Abstract

The invention provides a global sensitivity analysis method and device for RCS electromagnetic simulation. The method comprises the steps that input parameters of an electromagnetic scattering simulation model and the value range of the input parameters are obtained; determining an input parameter sample from the value range of the input parameter through sampling; inputting the input parameter sample into the electromagnetic scattering simulation model to obtain an RCS curve; calculating according to the RCS curve to obtain an RCS mean value curve, and comparing the RCS curve with the RCS mean value curve based on a feature selection evaluation method to obtain a global difference measure of the RCS curve; performing sensitivity analysis according to the global difference measure to obtain a sensitivity analysis result; and according to a sensitivity analysis result, carrying out sensitivity sorting on the input parameters to obtain insensitive parameters. According to the scheme, sensitivity sorting and insensitive parameter screening can be effectively carried out, the sensitivity data analysis difficulty is effectively reduced, and the sensitivity analysis efficiency is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of electromagnetic simulation, and particularly to a global sensitivity analysis method and device for RCS electromagnetic simulation. Background Art

[0002] In modern electromagnetic simulation research, the radar cross section (RCS) is an important indicator for measuring the electromagnetic scattering characteristics of target objects, and is widely used in fields such as radar stealth technology, antenna design, target recognition, and electromagnetic compatibility analysis. However, electromagnetic scattering simulation models usually have complex input parameters, involving various variables such as geometric shapes, electromagnetic material properties, and incident wave parameters. The uncertainty of these parameters will significantly affect the accuracy and reliability of the simulation results. Therefore, conducting global sensitivity analysis for the uncertainty of input parameters, identifying key parameters that have a significant impact on the model output, and screening redundant parameters that have a small impact on the results are key links to improve the simulation efficiency and optimize the model design.

[0003] Global Sensitivity Analysis (GSA) is a systematic modeling tool used to quantify the impact of the uncertainty of input parameters on the model output. However, due to the fact that the response of electromagnetic simulation is a "field" that changes with time or space, traditional GSA methods have problems such as a large amount of data in the analysis results, difficulty in effectively performing sensitivity ranking and insensitive parameter screening, and it is difficult to be widely and effectively applied in the electromagnetic field. Therefore, there is an urgent need to provide a global sensitivity analysis method and device for RCS electromagnetic simulation. Summary of the Invention

[0004] The present invention provides a global sensitivity analysis method and device for RCS electromagnetic simulation. This method can effectively perform sensitivity ranking and insensitive parameter screening, effectively reducing the difficulty of sensitivity data analysis and improving the sensitivity analysis efficiency.

[0005] In a first aspect, the present invention provides a global sensitivity analysis method for RCS electromagnetic simulation, including:

[0006] Obtain the input parameters of the electromagnetic scattering simulation model and the value ranges of the input parameters;

[0007] Determine input parameter samples from the value ranges of the input parameters through sampling;

[0008] Input the input parameter samples into the electromagnetic scattering simulation model to obtain an RCS curve;

[0009] Calculate the RCS mean curve based on the RCS curves, and compare the RCS curves and the RCS mean curve based on the feature selection evaluation method to obtain the global difference measure of the RCS curves;

[0010] Perform sensitivity analysis based on the global difference measure to obtain the sensitivity analysis result;

[0011] Rank the sensitivities of the input parameters according to the sensitivity analysis result to obtain the insensitive parameters.

[0012] Optionally, the determining the input parameter samples by sampling from the value range of the input parameters includes:

[0013] Determine the initial input parameter samples according to the value range of the input parameters;

[0014] According to the number of the input parameters and the initial number of samples of the initial input parameter samples, use the Sobol sequence to generate a sample matrix of n×2k; where n is the initial number of samples and k is the number of the input parameters;

[0015] Divide the sample matrix by columns to obtain a first matrix and a second matrix; where the first matrix is the first k columns of the sample matrix;

[0016] Replace the columns in the first matrix with the columns in the same positions in the second matrix to construct k third matrices;

[0017] Obtain the input parameter samples according to the first matrix, the second matrix and the third matrix; where each row in the first matrix, the second matrix and the third matrix corresponds to an input parameter sample.

[0018] Optionally, the calculating the RCS mean curve based on the RCS curves includes:

[0019] Perform a mean operation on the RCS curves obtained from the input parameter samples included in the first matrix to obtain the RCS mean curve.

[0020] Optionally, the comparing the RCS curves and the RCS mean curve based on the feature selection evaluation method to obtain the global difference measure of the RCS curves includes:

[0021] For each of the RCS curves, perform: based on the feature selection evaluation method, compare the RCS curve and the RCS mean curve to obtain the global difference measure of the RCS curve;

[0022] Generate a first index matrix according to the global difference measure obtained from the first matrix;

[0023] Generate a second index matrix based on the global difference measure obtained from the second matrix;

[0024] Generate a third index matrix based on the global difference measure obtained from the third matrix.

[0025] Optionally, the sensitivity analysis based on the global difference measure to obtain the sensitivity analysis result includes:

[0026] Vertically stack the first index matrix and the second index matrix to obtain a fourth index matrix, and calculate the variance of the fourth index matrix;

[0027] Calculate the first-order sensitivity index and the total-order sensitivity index of the input parameters according to the initial sample number, the global difference measure, and the variance of the fourth index matrix; wherein, the sensitivity analysis result includes the first-order sensitivity index and the total-order sensitivity index.

[0028] Optionally, the sensitivity analysis result includes the first-order sensitivity index and the total-order sensitivity index, and the sensitivity ranking of the input parameters according to the sensitivity analysis result to obtain insensitive parameters includes:

[0029] After sorting the first-order sensitivity indexes of the input parameters from large to small to obtain a first order, and accumulating the first-order sensitivity indexes in accordance with the first order until the accumulated value exceeds a first preset threshold, determine the input parameters corresponding to the first-order sensitivity indexes that have not been accumulated as the insensitive parameters;

[0030] And / or

[0031] Judge whether the total-order sensitivity index is less than a second preset threshold;

[0032] If the judgment result is yes, determine the input parameter corresponding to the total-order sensitivity index as the insensitive parameter.

[0033] In a second aspect, the present invention further provides a global sensitivity analysis device for RCS electromagnetic simulation, including:

[0034] An acquisition module for acquiring the input parameters of the electromagnetic scattering simulation model and the value range of the input parameters;

[0035] A simulation module for determining input parameter samples by sampling from the value range of the input parameters; and inputting the input parameter samples into the electromagnetic scattering simulation model to obtain an RCS curve;

[0036] The first analysis module is configured to calculate an RCS mean curve based on the RCS curve, and compare the RCS curve and the RCS mean curve based on a feature selection evaluation method to obtain a global difference measure of the RCS curve;

[0037] The second analysis module is configured to perform sensitivity analysis based on the global difference measure to obtain a sensitivity analysis result; and perform sensitivity ranking on the input parameters according to the sensitivity analysis result to obtain insensitive parameters.

[0038] In a third aspect, the present invention further provides a computing device, including a memory and a processor. A computer program is stored in the memory. When the processor executes the computer program, the global sensitivity analysis method for RCS electromagnetic simulation described in any one of the above is implemented.

[0039] In a fourth aspect, the present invention further provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed on a computer, the computer is made to execute the global sensitivity analysis method for RCS electromagnetic simulation described in any one of the above.

[0040] In a fifth aspect, an embodiment of the present invention further provides a computer program product, including computer instructions. When the computer instructions are executed by a processor, the steps of the method described in any first aspect of this specification are implemented.

[0041] The present invention provides a global sensitivity analysis method and apparatus for RCS electromagnetic simulation. The method first clarifies the input parameters, their uncertainties and responses of the electromagnetic scattering simulation model, obtains input parameter samples by sampling the input parameters, and then calculates the responses (i.e., RCS curves) of each input parameter sample and its RCS mean curve; performs feature selection evaluation (FSV) on each response sample and the mean curve to obtain the global difference measure of each RCS mean curve; then uses the global sensitivity analysis method to calculate the influence of the uncertain input parameters on the uncertainty of the global difference measure, obtains the sensitivity analysis results of each input parameter, and performs parameter sensitivity ranking and insensitive parameter screening on the input parameters according to this result. In this way, the present solution combines the advantages of feature selection evaluation and sensitivity analysis, and can simplify the sensitivity analysis process of input parameters for numerous response points on the RCS curve into a sensitivity analysis process for a single index that can reflect the change of the RCS curve, which is beneficial to more reasonably and effectively identifying significant key factors and screening redundant parameters in electromagnetic simulation, improving the model performance and calculation efficiency, and providing a new technical means for electromagnetic scattering characteristic research and engineering design. Description of the Drawings

[0042] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0043] Figure 1 It is a flowchart of a global sensitivity analysis method for RCS electromagnetic simulation provided by an embodiment of the present invention;

[0044] Figure 2 It is a global sensitivity analysis result diagram in a dielectric sphere provided by Embodiment 1 of the present invention;

[0045] Figure 3 It is a distribution diagram of the first-order sensitivity index in a dielectric sphere provided by the traditional method;

[0046] Figure 4 It is a distribution diagram of the total-order sensitivity index in a dielectric sphere provided by the traditional method;

[0047] Figure 5 It is a global sensitivity analysis result diagram in an amygdala provided by Embodiment 2 of the present invention;

[0048] Figure 6 It is a distribution diagram of the first-order sensitivity index in an amygdala provided by the traditional method;

[0049] Figure 7 It is a distribution diagram of the total-order sensitivity index in an amygdala provided by the traditional method;

[0050] Figure 8 It is a hardware architecture diagram of a computing device provided by an embodiment of the present invention;

[0051] Figure 9 It is a structural diagram of a global sensitivity analysis device for RCS electromagnetic simulation provided by an embodiment of the present invention. Detailed implementation manners

[0052] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts fall within the protection scope of the present invention.

[0053] Due to the particularity of RCS electromagnetic simulation, the output result of the model is a "field", such as a curve varying with the pitch angle, azimuth angle or frequency. This means that an output result of the electromagnetic scattering simulation model needs to be described by multiple response points. According to the step size of the angle or frequency set in the simulation, the number of response points is often in the hundreds or thousands. The traditional global sensitivity analysis method focuses on the influence of parameters on a single response point. Thus, the global sensitivity analysis result of the RCS electromagnetic simulation obtained will also be a curve varying with the angle or frequency, which brings difficulties in data processing for sorting the parameter sensitivities and screening insensitive parameters. Therefore, the present invention proposes to use the feature selection evaluation method to measure the difference between each simulation data and the standard data, and transform the global sensitivity analysis problem of all response points into a global sensitivity analysis problem of a single index value.

[0054] The following is the specific concept of the present invention. Please refer to Figure 1 , an embodiment of the present invention provides a global sensitivity analysis method for RCS electromagnetic simulation, including:

[0055] Step 100, obtain the input parameters of the electromagnetic scattering simulation model and the value range of the input parameters;

[0056] Step 102, determine the input parameter samples from the value range of the input parameters by sampling;

[0057] Step 104, input the input parameter samples into the electromagnetic scattering simulation model to obtain the RCS curve;

[0058] Step 106, calculate the RCS mean curve according to the RCS curve, and compare the RCS curve and the RCS mean curve based on the feature selection evaluation method to obtain the global difference measure of the RCS curve;

[0059] Step 108, perform sensitivity analysis according to the global difference measure to obtain the sensitivity analysis result;

[0060] Step 110, sort the input parameters according to the sensitivity analysis result to obtain insensitive parameters.

[0061] In the present invention, first, the input parameters of the electromagnetic scattering simulation model, their uncertainties and responses are clarified. Input parameter samples are obtained by sampling the input parameters, and then the responses (i.e., RCS curves) of each input parameter sample and their RCS mean curves are calculated. Each response sample is subjected to feature selection evaluation (FSV) with the mean curve to obtain the global difference measure of each RCS mean curve. Then, a global sensitivity analysis method is used to calculate the influence of the uncertain input parameters on the uncertainty of the global difference measure, and the sensitivity analysis results of each input parameter are obtained. From these results, the input parameters are sorted according to parameter sensitivity and insensitive parameters are screened. Thus, this solution combines the advantages of feature selection evaluation and sensitivity analysis, and can simplify the sensitivity analysis process of input parameters for numerous response points on the RCS curve into a sensitivity analysis process for a single index that can reflect the change of the RCS curve, which is conducive to more reasonably and effectively identifying the key factors with significant influence and screening redundant parameters in electromagnetic simulation, improving the model performance and calculation efficiency, and providing a new technical means for electromagnetic scattering characteristic research and engineering design.

[0062] The execution manners of the following described Figure 1 steps are shown.

[0063] First, in step 100, the input parameters of the electromagnetic scattering simulation model are all uncertain parameters, and the input parameters of different electromagnetic scattering simulation models are different. The electromagnetic scattering simulation model includes but is not limited to a dielectric sphere model, an almond body model, etc. The input parameters include but are not limited to the real part of the relative permittivity, the imaginary part of the relative permittivity, the real part of the relative permeability, the imaginary part of the relative permeability, and the coating material thickness, etc. The response of the electromagnetic scattering simulation model is an RCS curve that varies with angle or frequency.

[0064] In step 102, input parameter samples are determined by sampling from the value range of the input parameters, including:

[0065] According to the value range of the input parameters, initial input parameter samples are determined;

[0066] According to the number of input parameters and the initial number of samples of the initial input parameter samples, a sample matrix of n×2k is generated using the Sobol sequence; where n is the initial number of samples and k is the number of input parameters;

[0067] The sample matrix is divided by columns to obtain a first matrix and a second matrix; where the first matrix is the first k columns of the sample matrix;

[0068] The columns in the first matrix are replaced with the columns in the same positions in the second matrix to construct k third matrices;

[0069] An input parameter sample is obtained based on a first matrix, a second matrix, and a third matrix; each row in the first matrix, the second matrix, and the third matrix corresponds to an input parameter sample.

[0070] Specifically, for example, n initial input parameter samples are determined by sampling according to the value range of the uncertainty input parameters, and a sample matrix M of n×2k is generated using the Sobol sequence; n is generally an exponent of 2, and k is the number of input parameters of the electromagnetic scattering simulation model; then the first k columns of the sample matrix M are set as matrix A (i.e., the first matrix), and the last k columns are set as matrix B (i.e., the second matrix); then the j-th (j = 1, 2,..., k) column in matrix B is used to replace the j-th column of matrix A to obtain k matrices AB j (i.e., the third matrix), in this way, matrix A, matrix B, and matrix AB are obtained j A total of n×(k + 2) groups of input parameter samples. Among them, each row in the matrix represents an input parameter sample, that is, it includes the values of different input parameter samples; each column corresponds to the value of a certain input parameter in different input parameter samples.

[0071] In the present invention, in order to consider the uncertainty of the input parameters of the electromagnetic scattering simulation model, a sampling method is selected to obtain the input parameter samples, which not only reduces the data volume, but also expands the number of initial input parameter samples by constructing matrices, so as to accurately and effectively use the sampled input parameter samples to realize the sensitivity ranking of the input parameters and improve the efficiency of the sensitivity analysis method.

[0072] In a preferred embodiment, step 104 inputs the input parameter samples into the electromagnetic scattering simulation model to obtain the RCS curve, including:

[0073] Input the input parameter samples included in the first matrix, the second matrix, and the third matrix into the electromagnetic scattering simulation model, and output the RCS curve of each input parameter sample;

[0074] Generate a first output matrix according to the RCS curve output by the first matrix;

[0075] Generate a second output matrix according to the RCS curve output by the second matrix;

[0076] Generate a third output matrix according to the RCS curve output by the third matrix; where each row in the first output matrix, the second output matrix, and the third output matrix corresponds to an RSC curve.

[0077] It should be noted that for the input parameter samples in the m-th row of the corresponding matrix, the output response is the m-th row of the corresponding output matrix, and the sizes of the matrix and the output matrix are the same. For example, the output response of the m-th row of the first matrix is the m-th row of the first output matrix, the output response of the m-th row of the second matrix is the m-th row of the second output matrix, and the output response of the m-th row of the third matrix is the m-th row of the third output matrix.

[0078] In step 106, the RCS mean curve is calculated based on the RCS curve, including:

[0079] The mean operation is performed on the RCS curves obtained from the input parameter samples included in the first matrix to obtain the RCS mean curve.

[0080] Specifically, the mean operation can also be performed on the RCS curves obtained from the input parameter samples included in the second matrix to obtain the RCS mean curve, or the mean operation is performed on the RCS curves obtained from the input parameter samples included in the third matrix to obtain the RCS mean curve. Specifically, for example, by performing the mean calculation on the first matrix column by column, a 1×k matrix is obtained, which is the RCS mean curve.

[0081] In step 106, the global difference measure of the RCS curve is obtained by comparing the RCS curve and the RCS mean curve based on the feature selection evaluation method, including:

[0082] For each RCS curve, the following is performed: Based on the feature selection evaluation method, the RCS curve and the RCS mean curve are compared to obtain the global difference measure of the RCS curve;

[0083] According to the global difference measure obtained from the first matrix, the first index matrix is generated;

[0084] According to the global difference measure obtained from the second matrix, the second index matrix is generated;

[0085] According to the global difference measure obtained from the third matrix, the third index matrix is generated.

[0086] It should be noted that the m-th row of the index matrix is the global difference measure between the m-th row of the corresponding output matrix and the RCS mean curve. For example, the m-th row of the first index matrix corresponds to the global difference measure between the m-th row of the first output matrix and the RCS mean curve, and the elements in the second index matrix and the third index matrix are the same.

[0087] In the present invention, by using the feature selection evaluation method, the global difference measure of each RCS curve is obtained. By using this global difference measure as the representative of the RCS curve and then performing global sensitivity analysis, the influence of the uncertainty of the input parameters on the evaluation result of the simulation data difference can be directly obtained, which is more in line with the purpose of uncertainty analysis, and thus the rationality of parameter sensitivity ranking and insensitive parameter screening is improved.

[0088] For step 108, sensitivity analysis is performed according to the global difference measure to obtain the sensitivity analysis result, including:

[0089] Vertically stack the first index matrix and the second index matrix to obtain the fourth index matrix, and calculate the variance of the fourth index matrix;

[0090] According to the initial sample number, the global difference measure, and the variance of the fourth index matrix, the first-order sensitivity index and the total-order sensitivity index of the input parameters are calculated; wherein, the sensitivity analysis result includes the first-order sensitivity index and the total-order sensitivity index.

[0091] Specifically, the first-order sensitivity index S 1 (x j ) is determined by the following formula (1):

[0092]

[0093] The total-order sensitivity index S T (x j ) is determined by the following formula (2):

[0094]

[0095] Wherein, x j is the jth input parameter, j = 1, 2, ……, k; k is the number of input parameters; S 1 (x j ) is the first-order sensitivity index of the jth input parameter; S T (x j ) is the total-order sensitivity index of the jth input parameter; (·) m represents the mth row of the matrix, that is, the global difference measure between the mth row of the corresponding output matrix and the RCS mean curve; n is the initial sample number; represents the fourth index matrix, which is the vertical stacking of the first index matrix GDM A and the second index matrix GDM B of the two matrices, var(·) represents the calculation of the variance of the matrix, and GDM ABj is the third index matrix.

[0096] In the present invention, global sensitivity analysis quantifies the influence of the uncertainty of input parameters on the output of an electromagnetic scattering simulation model, takes into account the variations of input parameters within the entire parameter space, evaluates the response characteristics of the model output from a global perspective, and realizes sensitivity quantification by decomposing the total variance of the output into the contributions of each input parameter and their interaction terms, and is applicable to complex system models.

[0097] In step 110, the sensitivity analysis results include first-order sensitivity indices and total-order sensitivity indices. According to the sensitivity analysis results, sensitivity ranking is performed on the input parameters to obtain insensitive parameters, including:

[0098] After sorting the first-order sensitivity indices of each input parameter from largest to smallest to obtain a first order, and then accumulating the first-order sensitivity indices in accordance with the first order until the accumulated value exceeds a first preset threshold, the input parameters corresponding to the first-order sensitivity indices that have not been accumulated are determined as insensitive parameters;

[0099] and / or,

[0100] Judge whether the total-order sensitivity index is less than a second preset threshold;

[0101] If the judgment result is yes, the input parameter corresponding to the total-order sensitivity index is determined as an insensitive parameter.

[0102] The present invention will be further described below by way of examples, but the protection scope of the present invention is not limited to these embodiments.

[0103] Embodiment 1

[0104] Step 1: Determine the input parameters, their uncertainties, and responses of the dielectric sphere RCS electromagnetic scattering simulation model; the input parameters include the relative permittivity obeying the distribution N(36, 0.36), the sphere density obeying the distribution N(1000, 10), and the operating frequency obeying the distribution N(15000000, 1000); the response of the model is the RCS curve from 0° to 180° with a step size of 2°.

[0105] Step 2: In order to consider the uncertainty of the input parameters of the model, the Saltelli sampling scheme is adopted for sampling the input parameters, and a total of n×(k + 2) = 1024×(3 + 2) = 5120 groups of samples are drawn:

[0106] Determine 1024 initial input parameter samples, use the Sobol sequence to generate a sample matrix M of 1024×6; then set the first 3 columns of the sample matrix M as matrix A (i.e., the first matrix), and the last 3 columns as matrix B (i.e., the second matrix); then replace the jth (j = 1, 2, 3) column in matrix B with the jth column in matrix A to obtain 3 matrices AB j(i.e., the third matrix), thus obtaining matrix A, matrix B, and matrix AB j A total of 5120 groups of input parameter samples;

[0107] Step 3: Call the dielectric sphere RCS electromagnetic scattering simulation model, output the responses of each input parameter sample in Step 2, and obtain 5120 corresponding groups of RCS curve samples, which are recorded using matrix Y A (i.e., the first output matrix), Y B (i.e., the second output matrix), and Y ABj (i.e., the third output matrix);

[0108] Step 4: Calculate the RCS mean curve of the dielectric sphere RCS electromagnetic scattering simulation model under the same input parameter uncertainties. The specific calculation process is as follows: Take the average value of matrix Y A column by column to obtain the mean curve of the 1024 groups of RCS curves in this matrix;

[0109] Step 5: Use the feature selection evaluation method to compare each of the 5120 RCS curve samples obtained in Step 3 with the RCS mean curve in Step 4 to obtain the evaluation index of the difference degree between each RCS curve sample and the RCS mean curve: the global difference measure (GDM);

[0110] Step 6: Adopt the Sobol global sensitivity analysis method, use the input parameters as the input and the global difference measure as the output, and use formulas (1) and (2) to calculate the influence of the uncertainties of each input parameter on the uncertainty of the global difference measure, obtaining the first-order sensitivity index S 11 of each input parameter on the global difference measure and the total-order sensitivity index S T1 , as Figure 2 shown, and regard them as the sensitivity indices of each input parameter to the entire RCS electromagnetic simulation;

[0111] Step 7: According to the first-order sensitivity index S 11 and the total-order sensitivity index S T1 of each input parameter, perform parameter sensitivity ranking. The ranking results are all relative permittivity > operating frequency > sphere density; Set the first preset threshold v 11 to 80% of the sum of the first-order sensitivity indices of all parameters. Accumulate the first-order sensitivity indices in descending order. When the accumulated value exceeds the threshold v 11 , stop accumulating. The input parameters that have not participated in the accumulation are the sphere density and the operating frequency, and regard them as candidate parameters for insensitive parameters; Set the second preset threshold v 21 to 20% of the sum of the total-order sensitivity indices of all input parameters. The total-order sensitivity index values of the sphere density and the operating frequency are both lower than the threshold v 21, so it is considered that the sphere density and operating frequency are insensitive parameters under this uncertainty condition and can be set to fixed values in the subsequent analysis process.

[0112] To compare with the traditional method, the Sobol global sensitivity analysis method is adopted to directly analyze the sensitivity indexes of each input parameter to all response points on the RCS curve under the same uncertainty conditions as those in Example 1. The obtained results are as Figure 3 and Figure 4 shown. It can be directly seen from Figure 3 and Figure 4 that the sorting orders of the first-order sensitivity index and the total-order sensitivity index are both relative permittivity > operating frequency > sphere density. The first-order sensitivity indexes S 11 and the total-order sensitivity indexes of the operating frequency and the sphere density are both close to 0 and are regarded as insensitive parameters, which is consistent with the results of this Example 1.

[0113] Example 2

[0114] Step 1: Determine the input parameters, their uncertainties and responses of the complex amygdala RCS electromagnetic scattering simulation model; the input parameters include the real part of the relative permittivity obeying the distribution U(16.3392, 24.5088), the imaginary part of the relative permittivity obeying the distribution U(2.2797, 3.4196), the real part of the relative permeability obeying the distribution U(0.8629, 1.2944), the imaginary part of the relative permeability obeying the distribution U(1.63391, 2.4586), and the coating material thickness obeying the distribution U(0.1, 0.8); the response of this model is the RCS curve from 0° to 180° with a step size of 0.1°.

[0115] Step 2: To consider the uncertainty of the input parameters of the model, the Saltelli sampling scheme is adopted for sampling the input parameters, and a total of n×(k + 2) = 1024×(5 + 2) = 7168 groups of samples are drawn:

[0116] Determine 1024 initial input parameter samples, and use the Sobol sequence to generate a sample matrix M of 1024×10; then set the first 5 columns of the sample matrix M as matrix A (i.e., the first matrix), and the last 5 columns as matrix B (i.e., the second matrix); then replace the j-th (j = 1, 2, 3, 4, 5) column in matrix B with the j-th column in matrix A to obtain 5 matrices AB j (i.e., the third matrix). In this way, matrix A, matrix B, and matrix AB j are obtained, with a total of 7168 groups of input parameter samples;

[0117] Step 3: Call the amygdala RCS electromagnetic scattering simulation model to output the responses of each input parameter sample in Step 2, and obtain the corresponding 7168 groups of RCS curve samples, which are respectively represented by matrix YA (i.e., the first output matrix), Y B (i.e., the second output matrix), and Y ABj (i.e., the third output matrix) are recorded;

[0118] Step 4: Calculate the mean RCS curve of the dielectric sphere RCS electromagnetic scattering simulation model under the same input parameter uncertainties. The specific calculation process is as follows: For matrix Y A Take the average value column by column to obtain the mean curve of the 1024 groups of RCS curves in this matrix;

[0119] Step 5: Use the feature selection evaluation method to compare the 7168 RCS curve samples obtained in Step 3 with the RCS mean curve in Step 4 respectively, and obtain the evaluation index of the difference degree between each RCS curve sample and the RCS mean curve: Global Difference Measure (GDM);

[0120] Step 6: Adopt the Sobol global sensitivity analysis method, take the input parameters as the input and the global difference measure as the output, and use formulas (1) and (2) to calculate the influence of the uncertainties of each input parameter on the uncertainty of the global difference measure, and obtain the first-order sensitivity index S 12 of each input parameter on the global difference measure and the total-order sensitivity index S T1 , as Figure 5 shown, and regard them as the sensitivity indices of each input parameter to the entire RCS electromagnetic simulation;

[0121] Step 7: According to the first-order sensitivity index S 12 of each input parameter and the total-order sensitivity index S T2 , perform parameter sensitivity ranking. The ranking results are all: coating material thickness (depth) > real part of relative permeability (miuReal) ≈ imaginary part of relative permeability (miuImag) > real part of relative permittivity (epsReal) ≈ imaginary part of relative permittivity (epsImag); Set the first preset threshold v 12 to 80% of the sum of the first-order sensitivity indices of all parameters. Accumulate the first-order sensitivity indices in descending order. When the accumulated value exceeds the threshold v 12 , stop accumulating. The input parameters that have not participated in the accumulation are the real part of relative permittivity and the imaginary part of relative permittivity, and they are regarded as candidate parameters for insensitive parameters; Set the second preset threshold v 22 to 20% of the sum of the total-order sensitivity indices of all input parameters. Both the real part of relative permittivity and the imaginary part of relative permittivity are lower than the threshold v 22 , so it is considered that the real part of relative permittivity and the imaginary part of relative permittivity are insensitive parameters under this uncertainty condition and can be set to fixed values in the subsequent analysis process.

[0122] To compare with traditional methods, the Sobol global sensitivity analysis method is adopted to directly analyze the sensitivity indices of all response points on the RCS curve for each input parameter under the same uncertainty conditions as those in Example 2. The results obtained are as Figure 6 and Figure 7 shown. It can be directly seen from Figure 6 and Figure 7 that the sensitivity analysis results obtained by the traditional method are relatively complex, the sensitivity indices at each angle will fluctuate, and there will be a phenomenon that the sorting of the sensitivity indices of input parameters alternates with each other at different angles, making it difficult to intuitively obtain the sensitivity sorting of input parameters.

[0123] In summary, the present invention is more effective in dealing with the sensitivity analysis problem of the electromagnetic simulation RCS curve; compared with the traditional method, the results obtained by the method of the present invention are more intuitive, and it is more convenient to sort the parameter sensitivity indices and screen insensitive parameters; the results obtained by the present invention reflect the sensitivity of the input parameters of the electromagnetic scattering simulation model to the entire RCS electromagnetic simulation results, and are more reasonable.

[0124] As Figure 8 and Figure 9 shown, an embodiment of the present invention provides a global sensitivity analysis device for RCS electromagnetic simulation. The device embodiment can be implemented by software, or by hardware or a combination of software and hardware. In terms of the hardware level, as Figure 8 shown, it is a hardware architecture diagram of a computing device where a global sensitivity analysis device for RCS electromagnetic simulation provided by an embodiment of the present invention is located. In addition to the Figure 8 shown processor, memory, network interface, and non-volatile memory, the computing device where the device is located in the embodiment usually may also include other hardware, such as a forwarding chip responsible for processing packets, etc. Taking the software implementation as an example, as Figure 9 shown, as a logically meaningful device, it is formed by the CPU of its computing device reading the corresponding computer program in the non-volatile memory into the memory and running. A global sensitivity analysis device for RCS electromagnetic simulation provided by this embodiment includes:

[0125] An acquisition module 900, configured to acquire input parameters of the electromagnetic scattering simulation model and the value range of the input parameters;

[0126] A simulation module 902, configured to determine input parameter samples from the value range of the input parameters by sampling; and input the input parameter samples into the electromagnetic scattering simulation model to obtain an RCS curve;

[0127] The first analysis module 904 is configured to calculate an RCS mean curve based on the RCS curves, and compare the RCS curves and the RCS mean curve based on a feature selection evaluation method to obtain a global difference measure of the RCS curves;

[0128] The second analysis module 906 is configured to perform sensitivity analysis based on the global difference measure to obtain a sensitivity analysis result; and perform sensitivity ranking on the input parameters according to the sensitivity analysis result to obtain insensitive parameters.

[0129] In some specific embodiments, the acquisition module 900 can be used to execute the above step 100, the simulation module 902 can be used to execute the above steps 102 and 104, the first analysis module 904 can be used to execute the above step 106, and the second analysis module 906 can be used to execute the above steps 108 and 110.

[0130] In some specific embodiments, the simulation module 902 is further configured to perform the following operations:

[0131] Determine an initial input parameter sample according to the value range of the input parameters;

[0132] According to the number of input parameters and the initial sample number of the initial input parameter sample, use a Sobol sequence to generate a sample matrix of n×2k; where n is the initial sample number and k is the number of input parameters;

[0133] Divide the sample matrix by columns to obtain a first matrix and a second matrix; where the first matrix is the first k columns of the sample matrix;

[0134] Replace the columns in the first matrix with the columns in the same positions in the second matrix to construct k third matrices;

[0135] Obtain input parameter samples according to the first matrix, the second matrix, and the third matrix; where each row in the first matrix, the second matrix, and the third matrix corresponds to an input parameter sample.

[0136] In some specific embodiments, the simulation module 902 is further configured to perform the following operations:

[0137] Input the input parameter samples included in the first matrix, the second matrix, and the third matrix into an electromagnetic scattering simulation model, and output the RCS curves of each input parameter sample;

[0138] Generate a first output matrix according to the RCS curves output by the first matrix;

[0139] Generate a second output matrix according to the RCS curves output by the second matrix;

[0140] Generate a third output matrix according to the RCS curve output by the third matrix; wherein, each row in the first output matrix, the second output matrix, and the third output matrix corresponds to an RSC curve.

[0141] In some specific embodiments, the first analysis module 904 is further configured to perform the following operations:

[0142] Perform a mean operation on the RCS curves obtained from the input parameter samples included in the first matrix to obtain an RCS mean curve;

[0143] For each RCS curve, perform: based on the feature selection evaluation method, compare the RCS curve with the RCS mean curve to obtain the global difference measure of the RCS curve;

[0144] Generate a first index matrix according to the global difference measure obtained from the first matrix;

[0145] Generate a second index matrix according to the global difference measure obtained from the second matrix;

[0146] Generate a third index matrix according to the global difference measure obtained from the third matrix.

[0147] In some specific embodiments, the second analysis module 906 is further configured to perform the following operations:

[0148] Vertically stack the first index matrix and the second index matrix to obtain a fourth index matrix, and calculate the variance of the fourth index matrix;

[0149] Calculate the first-order sensitivity index and the total-order sensitivity index of the input parameters according to the initial sample number, the global difference measure, and the variance of the fourth index matrix; wherein, the sensitivity analysis result includes the first-order sensitivity index and the total-order sensitivity index.

[0150] In some specific embodiments, the second analysis module 906 is further configured to perform the following operations:

[0151] Sort the first-order sensitivity indexes of the input parameters from largest to smallest to obtain a first order, and then accumulate the first-order sensitivity indexes in the first order until the accumulated value exceeds a first preset threshold, and determine the input parameters corresponding to the first-order sensitivity indexes that have not been accumulated as insensitive parameters;

[0152] and / or,

[0153] Judge whether the total-order sensitivity index is less than a second preset threshold;

[0154] If the judgment result is yes, determine the input parameters corresponding to the total-order sensitivity index as insensitive parameters.

[0155] It can be understood that the structure illustrated in the embodiments of the present invention does not constitute a specific limitation on a global sensitivity analysis device for RCS electromagnetic simulation. In other embodiments of the present invention, a global sensitivity analysis device for RCS electromagnetic simulation may include more or fewer components than those illustrated, or combine certain components, or split certain components, or have different component arrangements. The illustrated components can be implemented in hardware, software, or a combination of software and hardware.

[0156] Regarding the information interaction, execution process, etc. between the various modules within the above-mentioned device, since it is based on the same concept as the method embodiments of the present invention, the specific content can be referred to the description in the method embodiments of the present invention, and will not be elaborated here.

[0157] The embodiments of the present invention also provide a computing device, including a memory and a processor. A computer program is stored in the memory. When the processor executes the computer program, it implements a global sensitivity analysis method for RCS electromagnetic simulation in any one of the embodiments of the present invention.

[0158] The embodiments of the present invention also provide a computer-readable storage medium. A computer program is stored on the computer-readable storage medium. When the computer program is executed by a processor, the processor is enabled to execute a global sensitivity analysis method for RCS electromagnetic simulation in any one of the embodiments of the present invention.

[0159] The embodiments of the present application also provide a computer program product. The computer program product includes a computer program. The processor of a computer device reads the computer program from a computer-readable storage medium, and the processor executes the computer program, so that the computer device executes a global sensitivity analysis method for RCS electromagnetic simulation described in any one of the above embodiments.

[0160] Specifically, a system or device equipped with a storage medium can be provided. A software program code for implementing the functions in any one of the above embodiments is stored on the storage medium, and the computer (or CPU or MPU) of the system or device reads and executes the program code stored on the storage medium.

[0161] In this case, the program code read from the storage medium itself can implement the functions of any one of the above embodiments. Therefore, the program code and the storage medium storing the program code constitute a part of the present invention.

[0162] Embodiments of the storage medium for providing program code include floppy disks, hard disks, magneto-optical disks, optical disks (such as CD-ROM, CD-R, CD-RW, DVD-ROM, DVD-RAM, DVD-RW, DVD+RW), magnetic tapes, non-volatile memory cards, and ROMs. Optionally, the program code can be downloaded from a server computer via a communication network.

[0163] In addition, it should be clear that not only can part or all of the actual operations be completed by executing the program code read by a computer, but also by the operating system operating on the computer based on the instructions of the program code, thereby implementing the functions of any one of the above embodiments.

[0164] In addition, it can be understood that the program code read from the storage medium is written into the memory provided in the expansion board inserted into the computer or into the memory provided in the expansion module connected to the computer, and then based on the instructions of the program code, the CPU etc. installed on the expansion board or the expansion module execute part or all of the actual operations, thereby implementing the functions of any one of the above embodiments.

[0165] It should be noted that in this text, relational terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the term "comprising", "including" or any other variant thereof is intended to cover non-exclusive inclusion, so that a process, method, article or device comprising a series of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article or device. Without further limitation, an element defined by the statement "comprising one..." does not exclude the existence of additional identical elements in the process, method, article or device comprising the element.

[0166] Those of ordinary skill in the art can understand that all or part of the steps of implementing the above method embodiments can be completed by hardware related to program instructions. The foregoing program can be stored in a computer-readable storage medium. When the program is executed, it performs the steps including the above method embodiments; and the foregoing storage medium includes various media such as ROM, RAM, magnetic disk or optical disc that can store program code.

[0167] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A global sensitivity analysis method for RCS electromagnetic simulation, characterized in that: include: Obtaining input parameters of an electromagnetic scattering simulation model and value ranges of the input parameters; Determine an input parameter sample from the value range of the input parameter by sampling; Inputting the input parameter sample into the electromagnetic scattering simulation model to obtain an RCS curve; Calculating an RCS mean curve according to the RCS curve, and comparing the RCS curve with the RCS mean curve based on a feature selection evaluation method to obtain a global difference measure of the RCS curve; Performing sensitivity analysis according to the global difference measure to obtain a sensitivity analysis result; The input parameters are sorted by sensitivity according to the sensitivity analysis result to obtain insensitive parameters.

2. The method according to claim 1, characterized in that The step of determining the input parameter sample from the value range of the input parameter by sampling includes: Determining an initial input parameter sample according to the value range of the input parameter; Generate an n×2k sample matrix using a Sobol sequence according to the number of the input parameters and the initial sample number of the initial input parameter samples; wherein n is the initial sample number and k is the number of the input parameters; Divide the sample matrix by columns to obtain a first matrix and a second matrix; wherein the first matrix is ​​the first k columns of the sample matrix; Replacing the columns in the first matrix with the columns at the same positions in the second matrix, to construct k third matrices; The input parameter samples are obtained according to the first matrix, the second matrix and the third matrix; wherein each row in the first matrix, the second matrix and the third matrix corresponds to an input parameter sample.

3. The method according to claim 2, characterized in that The step of calculating the RCS mean curve according to the RCS curve includes: An RCS curve obtained by the input parameter samples included in the first matrix is ​​averaged to obtain the RCS mean curve.

4. The method according to claim 2, characterized in that: The method of comparing the RCS curve with the RCS mean curve based on the feature selection evaluation method to obtain a global difference measure of the RCS curve includes: For each of the RCS curves, performing: based on a feature selection evaluation method, comparing the RCS curve with the RCS mean curve to obtain a global difference measure of the RCS curve; generating a first indicator matrix according to the global difference measure obtained from the first matrix; generating a second indicator matrix according to the global difference measure obtained from the second matrix; A third indicator matrix is ​​generated according to the global difference measure obtained from the third matrix.

5. The method according to claim 4, characterized in that The sensitivity analysis is performed according to the global difference measure to obtain a sensitivity analysis result, including: Vertically stacking the first indicator matrix and the second indicator matrix to obtain a fourth indicator matrix, and calculating the variance of the fourth indicator matrix; According to the initial sample number, the global difference measure and the variance of the fourth indicator matrix, the first-order sensitivity index and the total-order sensitivity index of the input parameter are calculated; wherein the sensitivity analysis result includes the first-order sensitivity index and the total-order sensitivity index.

6. The method according to any one of claims 1 to 5, characterized in that: The sensitivity analysis result includes a first-order sensitivity index and a total-order sensitivity index. The sensitivity ranking of the input parameters according to the sensitivity analysis result to obtain insensitive parameters includes: After sorting the first-order sensitivity indicators of the input parameters from large to small to obtain a first order, the first-order sensitivity indicators are accumulated according to the first order until the accumulated value exceeds a first preset threshold value, and the input parameter corresponding to the first-order sensitivity indicator that has not been accumulated is determined as the insensitive parameter; and / or, Determining whether the total order sensitivity index is less than a second preset threshold; If the judgment result is yes, the input parameter corresponding to the overall order sensitivity index is determined as the insensitive parameter.

7. A global sensitivity analysis device for RCS electromagnetic simulation, characterized in that: include: An acquisition module, used to acquire input parameters of an electromagnetic scattering simulation model and a value range of the input parameters; A simulation module, used for determining an input parameter sample from a value range of the input parameter by sampling; and inputting the input parameter sample into the electromagnetic scattering simulation model to obtain an RCS curve; A first analysis module, configured to calculate an RCS mean curve according to the RCS curve, and compare the RCS curve with the RCS mean curve based on a feature selection evaluation method to obtain a global difference measure of the RCS curve; A second analysis module, used to perform sensitivity analysis according to the global difference measure to obtain a sensitivity analysis result; And according to the sensitivity analysis result, the input parameters are sorted by sensitivity to obtain insensitive parameters.

8. A computing device, comprising a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, the method according to any one of claims 1 to 6 is implemented.

9. A computer-readable storage medium having a computer program stored thereon, which, when executed in a computer, causes the computer to execute the method according to any one of claims 1 to 6.

10. A computer program product, characterized in that The method comprises computer instructions, which, when executed by a processor, implement the steps of the method according to any one of claims 1 to 6.

Images