Statistical evaluation method of multi-dimensional similarity between lightning attachment point simulation and test results
By constructing n-dimensional simulation and experimental attachment vectors, eliminating outliers, and using multidimensional root mean square error and Hotelling's T² test, the multidimensional problem in the similarity assessment of lightning attachment point simulation and experimental results is solved, achieving efficient and accurate similarity assessment.
Patent Information
- Application Number
- CN202510453832.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2025-04-11
- Publication Date
- 2025-11-11
- Estimated Expiration
- 2045-04-11
AI Technical Summary
Existing technologies for assessing the similarity between simulation and experimental results of lightning attachment points suffer from limitations such as single-dimensional analysis, poor adaptability to small samples, sensitivity to outliers, and low computational efficiency, making it difficult to effectively assess multi-dimensional similarity.
A multidimensional similarity statistical evaluation method is adopted. By constructing an n-dimensional simulation attachment vector and an n-dimensional experimental attachment vector, outliers are eliminated, and the weighted multidimensional root mean square error and Hotelling's T² test are used to evaluate the similarity between simulation and experimental results.
It improves the robustness of evaluation under small sample sizes, enhances the comprehensiveness of the evaluation, reduces computational complexity, saves experimental costs, and ensures the accuracy and efficiency of similarity evaluation.
Smart Images
Figure CN119989541B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of data digital processing technology for lightning test and simulation results, and relates to a method for multidimensional similarity statistical evaluation of lightning attachment point simulation and test results. Background Technology
[0002] With the increasing frequency of lightning strikes, identifying lightning strike points on aircraft surfaces and implementing lightning zoning to ensure necessary protective measures has become a crucial step in ensuring flight safety. Analyzing lightning strike points on aircraft structures is a key foundation for lightning zoning and surface lightning protection design and evaluation. Since lightning strike testing is time-consuming and costly, determining lightning strike points through numerical simulation models offers advantages such as speed, efficiency, and cost savings. However, the similarity assessment between simulation results and experimental data regarding lightning strike points remains a challenging problem.
[0003] The existing similarity assessment techniques for lightning attachment point simulation and test results have the following shortcomings: (1) Limitations of single-dimensional analysis: Traditional methods (such as RMSE and correlation coefficient) can only assess a single dimension and ignore the correlation between variables, leading to misjudgment of overall similarity; (2) Poor adaptability to small samples: Conventional tests require a large sample size, while in engineering scenarios, attachment point tests often face the problem of n<50; (3) Sensitivity to outliers: Standardization methods rely on mean and variance, and high-dimensional outliers are prone to distorting the similarity assessment results; (4) Low computational efficiency: The computational complexity of multidimensional tests is O(n2). Summary of the Invention
[0004] The purpose of this invention is to provide a statistical evaluation method for the multidimensional similarity of lightning attachment point simulation and experimental results, which solves the problems of instability, sensitivity to outliers, and low power of small sample tests in high-dimensional covariance estimation.
[0005] The technical solution adopted in this invention is a multi-dimensional similarity statistical evaluation method for lightning attachment point simulation and experimental results, and the specific steps are as follows:
[0006] S1. Construct evaluation vectors: Divide the attachment regions of the simulation object and the test object, construct an n-dimensional simulation attachment vector and an n-dimensional test attachment vector, and assign values to them respectively;
[0007] S2. Data preprocessing: Perform outlier detection and remove outliers from the data in the n-dimensional simulated attachment vector and the n-dimensional experimental attachment vector.
[0008] S3. Determine data similarity: Calculate the weighted multidimensional root mean square error of the n-dimensional simulated attachment vector and the n-dimensional experimental attachment vector, and then determine whether the corresponding n-dimensional simulated attachment vector and n-dimensional experimental attachment vector are similar. If they are not similar, proceed to S5; if they are similar, proceed to S4.
[0009] S4. Hypothesis testing: If the n-dimensional simulated attachment vector and the n-dimensional experimental attachment vector satisfy the similarity index, adaptively select Hotelling's T² or permutation test;
[0010] S5. Generate a conclusion report.
[0011] The invention is further characterized by:
[0012] The specific method for S1 is as follows:
[0013] S1.1 Constructing n-dimensional simulated adhesion vector and n-dimensional experimental adhesion vector
[0014] Assuming consistency between the simulation model and the experimental model, the surface regions of both models are divided into n regions, and an n-dimensional simulation adhesion vector is constructed. and n-dimensional test attachment vector , where m is the number of attachment postures of the simulation object or the test object;
[0015] S1.2. Assign values to the n-dimensional simulated adhesion vector and the n-dimensional experimental adhesion vector respectively.
[0016] When assigning values to the n-dimensional simulated attachment vector, for a specific attitude numbered... ,in In the simulation results, if the region There are attachments, among which Then the simulation vector Assign a value of 1; if the region i S If there is no attachment, the simulation vector will be... The value is assigned to 0;
[0017] When assigning values to the n-dimensional test attachment vector, for a specific posture numbered as follows: ,in In the test results, if the area There is attachment, among which Then the test vector Assign a value of 1; if the region If there is no attachment, then the test vector will be... The value is assigned to 0.
[0018] The specific method for S2 is as follows:
[0019] S2.1 Data Alignment and Standardization
[0020] attach vector to n-dimensional simulation Data and n-dimensional experimental attachment vector The data are spatially correlated one-to-one;
[0021] S2.2 Outlier Detection
[0022] Calculate the n-dimensional simulated attachment vector respectively and n-dimensional test attachment vector The Mahalanobis distance for each data point is calculated using the following formula:
[0023] (1)
[0024] (2)
[0025] In the above formula, For simulation vectors Mahalanobis distance in the data For the test vector The Mahalanobis distance of the data is given by μ, where μ is the mean vector of all vectors (p×1), and Σ is the covariance matrix of all vectors (p×p). S For simulation vector subscripts, R The subscript for the test vector;
[0026] S2.3 Outlier Handling and Removal
[0027] Select the significance level of outliers α ,make α The value is set to 0.05 or 1. An outlier threshold T is set. When the Mahalanobis distance of a certain data is greater than the outlier threshold T, the data is marked as an outlier and the data is either backtracked or discarded.
[0028] The specific method for S3 is as follows:
[0029] S3.1, Indicator Calculation
[0030] Using multidimensional root mean square error Multi-RMSE As a similarity index, the calculation formula is as follows:
[0031] (3)
[0032] In the formula, For simulation vector data, The data for the test vectors are m, where m is the number of attachment postures of the simulation object or test object, and n is the number of model partitions;
[0033] S3.2 Similarity Judgment
[0034] When multidimensional root mean square error Multi-RMSE When the result is less than the anomaly threshold T, the n-dimensional simulated attachment vector and the n-dimensional experimental attachment vector are similar. This is especially true when the multidimensional root mean square error... Multi-RMSE If the result is greater than the anomaly threshold T, then the n-dimensional simulated attachment vector and the n-dimensional experimental attachment vector are not similar.
[0035] The specific method for S4 is as follows:
[0036] S4.1. Define the null hypothesis and alternative hypothesis.
[0037] Null hypothesis H0: The mean vectors of the n-dimensional simulated attachment vector and the n-dimensional experimental attachment vector are equal, i.e., μ1=μ2;
[0038] Alternative hypothesis H1: The mean vectors of the n-dimensional simulated attachment vector and the n-dimensional experimental attachment vector differ in at least one dimension, i.e., μ1 ≠ μ2;
[0039] S4.2 Constructing Statistics
[0040] Hotelling's T² test was used to examine the similarity of the mean vectors of the n-dimensional simulated attachment vector and the n-dimensional experimental attachment vector multivariate normally distributed data.
[0041] S4.3, Hypothetical Decision Making
[0042] If probability or If so, then reject H0;
[0043] in, The F-distribution with degrees of freedom p and m+np-1 at a multidimensional similarity significance level of α The value at time.
[0044] The specific method of S4.2 is as follows:
[0045] S4.2.1 Calculate the difference in mean vectors between the simulation object and the experimental object, using the following formula:
[0046] (4)
[0047] In the formula, This is the mean vector of the simulation model; This represents the mean vector of the experimental model;
[0048] S4.2.2 Calculate the covariance matrix of the combined simulation object and the experimental object, using the following formula:
[0049] (5)
[0050] In the formula, S S The covariance matrix of the simulation model; S R The covariance matrix of the experimental model;
[0051] S4.2.3 Calculate Hotelling's T² statistic using the difference in the mean vector and the combined covariance matrix, as shown in the following formula:
[0052] (6)
[0053] S4.2.4. Convert Hotelling's T² statistic to F statistic:
[0054] (7)
[0055] It follows an F-distribution with degrees of freedom p and m+np-1.
[0056] The specific method for S5 is as follows:
[0057] A multidimensional similarity assessment of lightning attachment point simulation and experimental results was conducted, defining the L2 norm of the experimental and simulation data for m sets of n-dimensional vector data as follows:
[0058] (8)
[0059] (9)
[0060] in, It is the test vector The value of the i-th element in the array. It is a simulation vector Given the i-th element value, calculate the norm mean of Rn1 for n1 sets of experimental data. for:
[0061] (10)
[0062] Calculate the norm mean of n² sets of simulation data Sn² for:
[0063] (11)
[0064] Define the accuracy of simulation / experiment comparison for:
[0065] (12)
[0066] Generate interpretable evaluation reports.
[0067] The beneficial effects of this invention are:
[0068] (1) The method for multidimensional similarity statistical evaluation of lightning attachment point simulation and test results of this invention conforms to the standard specifications for the construction of attachment vector pairs, and does not affect the partitioning results; small sample robustness: through Ledoit-Wolf covariance estimation and permutation test, it supports n≥20; multidimensional comprehensive evaluation: integrates error, distribution and correlation indicators to improve the comprehensiveness of evaluation; computational efficiency: the energy distance calculation complexity is reduced to O(nlogn), which is convenient for calculation. The similarity statistical evaluation method of this invention can optimize the attachment point simulation algorithm and save test costs.
[0069] (2) The present invention provides a multidimensional similarity statistical evaluation method for lightning attachment point simulation and test results. In view of the problems existing in the comparison between existing lightning attachment point simulation results and test results, this invention utilizes the one-to-one correspondence between the aircraft attitude and electrode position used in lightning attachment point test and simulation to propose a simulation-test similarity evaluation method for multidimensional small sample data. The key point is to construct a set of corresponding attachment vectors from the simulation data and the test data and use statistical methods to evaluate their similarity. Attached Figure Description
[0070] Figure 1 This is a flowchart illustrating the multidimensional similarity statistical evaluation method for lightning attachment point simulation and experimental results according to the present invention. Detailed Implementation
[0071] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.
[0072] This invention provides a multidimensional similarity statistical evaluation method for lightning attachment point simulation and experimental results, such as... Figure 1 As shown, the specific steps are as follows:
[0073] S1. Constructing Evaluation Vectors: The attachment regions of the simulation object and the test object are divided, and an n-dimensional simulation attachment vector and an n-dimensional test attachment vector are constructed and assigned values respectively. The specific method is as follows:
[0074] S1.1 Constructing n-dimensional simulated adhesion vector and n-dimensional experimental adhesion vector
[0075] Assuming consistency between the simulation model and the experimental model, the surface regions of both models are divided into n regions, and an n-dimensional simulation adhesion vector is constructed. and n-dimensional test attachment vector , where m is the number of attachment postures of the simulation object or the test object;
[0076] S1.2. Assign values to the n-dimensional simulated adhesion vector and the n-dimensional experimental adhesion vector respectively.
[0077] When assigning values to the n-dimensional simulated attachment vector, for a specific attitude numbered... ,in In the simulation results, if the region There is attachment, among which Then the simulation vector Assign a value of 1; if the region i S If there is no attachment, the simulation vector will be... The value is assigned to 0;
[0078] When assigning values to the n-dimensional test attachment vector, for a specific posture numbered as follows: ,in In the test results, if the area There is attachment, among which Then the test vector Assign a value of 1; if the region If there is no attachment, then the test vector will be... The value is assigned to 0.
[0079] S2. Data Preprocessing: Outlier detection and removal are performed on the data in the n-dimensional simulated attachment vector and the n-dimensional experimental attachment vector. The specific method is as follows:
[0080] S2.1 Data Alignment and Standardization
[0081] attach vector to n-dimensional simulation Data and n-dimensional experimental attachment vector The data are spatially correlated one-to-one;
[0082] S2.2 Outlier Detection
[0083] Calculate the n-dimensional simulated attachment vector respectively and n-dimensional test attachment vector The Mahalanobis distance for each data point is calculated using the following formula:
[0084] (1)
[0085] (2)
[0086] In the above formula, For simulation vectors Mahalanobis distance in the data For the test vector The Mahalanobis distance of the data is given by μ, where μ is the mean vector of all vectors (p×1), and Σ is the covariance matrix of all vectors (p×p). S For simulation vector subscripts, R The subscript for the test vector;
[0087] S2.3 Outlier Handling and Removal
[0088] Select the significance level of outliers α ,make α The value is set to 0.05 or 1. An outlier threshold T is set. When the Mahalanobis distance of a certain data is greater than the outlier threshold T, the data is marked as an outlier and the data is either backtracked or discarded.
[0089] S3. Determine data similarity: Calculate the weighted multidimensional root mean square error of the n-dimensional simulated attachment vector and the n-dimensional experimental attachment vector, and then determine whether the corresponding n-dimensional simulated attachment vector and n-dimensional experimental attachment vector are similar. If they are not similar, proceed to S5; if they are similar, proceed to S4. The specific method for determining data similarity is as follows:
[0090] S3.1, Indicator Calculation
[0091] Using multidimensional root mean square error Multi-RMSE As a similarity index, the calculation formula is as follows:
[0092] (3)
[0093] In the formula, For simulation vector data, The data for the test vector, m is the number of attachment postures of the simulation object or test object, and n is the number of model partitions;
[0094] S3.2 Similarity Judgment
[0095] When multidimensional root mean square error Multi-RMSE When the result is less than the anomaly threshold T, the n-dimensional simulated attachment vector and the n-dimensional experimental attachment vector are similar. This is especially true when the multidimensional root mean square error... Multi-RMSE If the result is greater than the anomaly threshold T, then the n-dimensional simulated attachment vector and the n-dimensional experimental attachment vector are not similar.
[0096] S4. Hypothesis Testing: If the n-dimensional simulated attachment vector and the n-dimensional experimental attachment vector satisfy the similarity index, adaptively select Hotelling's T² or permutation test. The specific method is as follows:
[0097] S4.1. Define the null hypothesis and alternative hypothesis.
[0098] Null hypothesis H0: The mean vectors of the n-dimensional simulated attachment vector and the n-dimensional experimental attachment vector are equal, i.e., μ1=μ2;
[0099] Alternative hypothesis H1: The mean vectors of the n-dimensional simulated attachment vector and the n-dimensional experimental attachment vector differ in at least one dimension, i.e., μ1 ≠ μ2;
[0100] S4.2 Constructing Statistics
[0101] The Hotelling's T² test is used to examine the similarity of the mean vectors of n-dimensional simulation attachment vectors and n-dimensional experimental attachment vectors from multivariate normally distributed data. The Hotelling's T² test is an extension of the univariate t-test in multivariate scenarios, used to test whether the mean vectors of two sets of multivariate normally distributed data are equal. The specific method is as follows:
[0102] S4.2.1 Calculate the difference in mean vectors between the simulation object and the experimental object, using the following formula:
[0103] (4)
[0104] In the formula, This is the mean vector of the simulation model; This represents the mean vector of the experimental model;
[0105] S4.2.2 Calculate the covariance matrix of the combined simulation object and the experimental object, using the following formula:
[0106] (5)
[0107] In the formula, S S The covariance matrix of the simulation model; S R The covariance matrix of the experimental model;
[0108] S4.2.3 Calculate Hotelling's T² statistic using the difference in the mean vector and the combined covariance matrix, as shown in the following formula:
[0109] (6)
[0110] S4.2.4. Convert Hotelling's T² statistic to F statistic:
[0111] (7)
[0112] It follows an F-distribution with degrees of freedom p and m+np-1.
[0113] S4.3, Hypothetical Decision Making
[0114] If probability or If so, then reject H0;
[0115] in, The F-distribution with degrees of freedom p and m+np-1 at a multidimensional similarity significance level of α The value at time.
[0116] S5. Generate a conclusion report, the specific method is as follows:
[0117] A multidimensional similarity assessment of lightning attachment point simulation and experimental results was conducted, defining the L2 norm of the experimental and simulation data for m sets of n-dimensional vector data as follows:
[0118] (8)
[0119] (9)
[0120] in, It is the test vector The value of the i-th element in the array. It is a simulation vector Given the i-th element value, calculate the norm mean of Rn1 for n1 sets of experimental data. for:
[0121] (10)
[0122] Calculate the norm mean of n² sets of simulation data Sn² for:
[0123] (11)
[0124] Define the accuracy of simulation / experiment comparison for:
[0125] (12)
[0126] Generate interpretable evaluation reports.
[0127] Example 1
[0128] The specific steps of the multidimensional similarity statistical evaluation method for lightning attachment point simulation and experimental results in this embodiment are as follows:
[0129] S1. Construct evaluation vectors: Divide the attachment regions of the simulation object and the test object, construct an n-dimensional simulation attachment vector and an n-dimensional test attachment vector, and assign values to them respectively;
[0130] S2. Data preprocessing: Perform outlier detection and remove outliers from the data in the n-dimensional simulated attachment vector and the n-dimensional experimental attachment vector.
[0131] S3. Determine data similarity: Calculate the weighted multidimensional root mean square error of the n-dimensional simulated attachment vector and the n-dimensional experimental attachment vector, and then determine whether the corresponding n-dimensional simulated attachment vector and n-dimensional experimental attachment vector are similar. If they are not similar, proceed to S5; if they are similar, proceed to S4.
[0132] S4. Hypothesis testing: If the n-dimensional simulated attachment vector and the n-dimensional experimental attachment vector satisfy the similarity index, adaptively select Hotelling's T² or permutation test;
[0133] S5. Generate a conclusion report.
[0134] Example 2
[0135] The method in this embodiment is the same as that in embodiment 1. The specific method of S1, based on the method in embodiment 1, is as follows:
[0136] S1.1 Constructing n-dimensional simulated adhesion vector and n-dimensional experimental adhesion vector
[0137] Assuming consistency between the simulation model and the experimental model, the surface regions of both models are divided into n regions, and an n-dimensional simulation adhesion vector is constructed. and n-dimensional test attachment vector , where m is the number of attachment postures of the simulation object or the test object;
[0138] S1.2. Assign values to the n-dimensional simulated adhesion vector and the n-dimensional experimental adhesion vector respectively.
[0139] When assigning values to the n-dimensional simulated attachment vector, for a specific attitude numbered... ,in In the simulation results, if the region There is attachment, among which Then the simulation vector Assign a value of 1; if the region i S If there is no attachment, the simulation vector will be... The value is assigned to 0;
[0140] When assigning values to the n-dimensional test attachment vector, for a specific posture numbered as follows: ,in In the test results, if the area There is attachment, among which Then the test vector Assign a value of 1; if the region If there is no attachment, then the test vector will be... The value is assigned to 0.
[0141] Example 3
[0142] The method in this embodiment is the same as that in embodiment 2. The specific method of S2, based on the method in embodiment 2, is as follows:
[0143] S2.1 Data Alignment and Standardization
[0144] attach vector to n-dimensional simulation Data and n-dimensional experimental attachment vector The data are spatially correlated one-to-one;
[0145] S2.2 Outlier Detection
[0146] Calculate the n-dimensional simulated attachment vector respectively and n-dimensional test attachment vector The Mahalanobis distance for each data point is calculated using the following formula:
[0147] (1)
[0148] (2)
[0149] In the above formula, For simulation vectors Mahalanobis distance in the data For the test vector The Mahalanobis distance of the data is given by μ, where μ is the mean vector of all vectors (p×1), and Σ is the covariance matrix of all vectors (p×p). S For simulation vector subscripts, R The subscript for the test vector;
[0150] S2.3 Outlier Handling and Removal
[0151] Select the significance level of outliers α ,make α The value is set to 0.05 or 1. An outlier threshold T is set. When the Mahalanobis distance of a certain data is greater than the outlier threshold T, the data is marked as an outlier and the data is either backtracked or discarded.
[0152] Example 4
[0153] The method in this embodiment is the same as that in embodiment 3. The specific method of S3, based on the method in embodiment 3, is as follows:
[0154] S3.1, Indicator Calculation
[0155] Using multidimensional root mean square error Multi-RMSE As a similarity index, the calculation formula is as follows:
[0156] (3)
[0157] In the formula, For simulation vector data, The data for the test vectors are m, where m is the number of attachment postures of the simulation object or test object, and n is the number of model partitions;
[0158] S3.2 Similarity Judgment
[0159] When multidimensional root mean square errorMulti-RMSE When the result is less than the anomaly threshold T, the n-dimensional simulated attachment vector and the n-dimensional experimental attachment vector are similar. This is especially true when the multidimensional root mean square error... Multi-RMSE If the result is greater than the anomaly threshold T, then the n-dimensional simulated attachment vector and the n-dimensional experimental attachment vector are not similar.
[0160] Example 5
[0161] The method in this embodiment is the same as that in embodiment 4. The specific method of S4, based on the method in embodiment 4, is as follows:
[0162] S4.1. Define the null hypothesis and alternative hypothesis.
[0163] Null hypothesis H0: The mean vectors of the n-dimensional simulated attachment vector and the n-dimensional experimental attachment vector are equal, i.e., μ1=μ2;
[0164] Alternative hypothesis H1: The mean vectors of the n-dimensional simulated attachment vector and the n-dimensional experimental attachment vector differ in at least one dimension, i.e., μ1 ≠ μ2;
[0165] S4.2 Constructing Statistics
[0166] The similarity of the mean vectors of the n-dimensional simulated attachment vector and the n-dimensional experimental attachment vector multivariate normally distributed data is tested using Hotelling's T². The specific method in S4.2 is as follows:
[0167] S4.2.1 Calculate the difference in mean vectors between the simulation object and the experimental object, using the following formula:
[0168] (4)
[0169] In the formula, This is the mean vector of the simulation model; This represents the mean vector of the experimental model;
[0170] S4.2.2 Calculate the covariance matrix of the combined simulation object and the experimental object, using the following formula:
[0171] (5)
[0172] In the formula, S S The covariance matrix of the simulation model; S R The covariance matrix of the experimental model;
[0173] S4.2.3 Calculate Hotelling's T² statistic using the difference in the mean vector and the combined covariance matrix, as shown in the following formula:
[0174] (6)
[0175] S4.2.4. Convert Hotelling's T² statistic to F statistic:
[0176] (7)
[0177] It follows an F-distribution with degrees of freedom p and m+np-1.
[0178] S4.3, Hypothetical Decision Making
[0179] If probability or If so, then reject H0;
[0180] in, The F-distribution with degrees of freedom p and m+np-1 at a multidimensional similarity significance level of α The value at time.
[0181] Example 6
[0182] The method in this embodiment is the same as that in embodiment 5. The specific method of S5, based on the method in embodiment 5, is as follows:
[0183] A multidimensional similarity assessment of lightning attachment point simulation and experimental results was conducted, defining the L2 norm of the experimental and simulation data for m sets of n-dimensional vector data as follows:
[0184] (8)
[0185] (9)
[0186] in, It is the test vector The value of the i-th element in the array. It is a simulation vector Given the i-th element value, calculate the norm mean of Rn1 for n1 sets of experimental data. for:
[0187] (10)
[0188] Calculate the norm mean of n² sets of simulation data Sn² for:
[0189] (11)
[0190] Define the accuracy of simulation / experiment comparison for:
[0191] (12)
[0192] Generate interpretable evaluation reports.
Claims
1. A method for statistically evaluating the multidimensional similarity between simulation and experimental results of lightning attachment points, characterized in that... The specific steps are as follows: S1. Construct evaluation vectors: Divide the attachment regions of the simulation object and the test object, construct an n-dimensional simulation attachment vector and an n-dimensional test attachment vector, and assign values to them respectively; S2. Data preprocessing: Perform outlier detection and remove outliers from the data in the n-dimensional simulated attachment vector and the n-dimensional experimental attachment vector. S3. Determine data similarity: Calculate the weighted multidimensional root mean square error of the n-dimensional simulated attachment vector and the n-dimensional experimental attachment vector, and then determine whether the corresponding n-dimensional simulated attachment vector and n-dimensional experimental attachment vector are similar. If they are not similar, proceed to S5; if they are similar, proceed to S4. S4. Hypothesis Testing: If the n-dimensional simulated attachment vector and the n-dimensional experimental attachment vector satisfy the similarity index, adaptively select Hotelling's T. 2 Or displacement test; S5. Generate a conclusion report; The specific method of S4 is as follows: S4.
1. Define the null hypothesis and alternative hypothesis. Null hypothesis H0: The mean vectors of the n-dimensional simulated attachment vector and the n-dimensional experimental attachment vector are equal, i.e., μ1=μ2; Alternative hypothesis H1: The mean vectors of the n-dimensional simulated attachment vector and the n-dimensional experimental attachment vector differ in at least one dimension, i.e., μ1 ≠ μ2; S4.2 Constructing Statistics Using Hotelling's T 2 Test the similarity of the mean vectors of the n-dimensional simulated attachment vector and the n-dimensional experimental attachment vector multivariate normal distribution data; S4.3, Hypothetical Decision Making If probability or If so, then reject H0; in, The F-distribution with degrees of freedom p and m+np-1 at a multidimensional similarity significance level of α The value at time; The specific method of S4.2 is as follows: S4.2.1 Calculate the difference in mean vectors between the simulation object and the experimental object, using the following formula: （4） In the formula, This is the mean vector of the simulation model; This represents the mean vector of the experimental model; S4.2.2 Calculate the covariance matrix of the combined simulation object and the experimental object, using the following formula: （5） In the formula, S S The covariance matrix of the simulation model; S R The covariance matrix of the experimental model; S4.2.3 Calculate Hotelling's T using the difference in mean vectors and the combined covariance matrix. 2 The statistic is calculated using the following formula: （6） S4.2.4, Hotelling's T 2 Convert the statistic to the F-statistic: （7） It follows an F-distribution with degrees of freedom p and m+np-1.
2. The method for multidimensional similarity statistical evaluation of lightning attachment point simulation and experimental results according to claim 1, characterized in that, The specific method of S1 is as follows: S1.1 Constructing n-dimensional simulated adhesion vector and n-dimensional experimental adhesion vector Assuming consistency between the simulation model and the experimental model, the surface regions of both models are divided into n regions, and an n-dimensional simulation adhesion vector is constructed. and n-dimensional test attachment vector , where m is the number of attachment postures of the simulation object or the test object; S1.
2. Assign values to the n-dimensional simulated adhesion vector and the n-dimensional experimental adhesion vector respectively. When assigning values to the n-dimensional simulated attachment vector, for a specific attitude numbered... ,in In the simulation results, if the region There is attachment, among which Then the simulation vector Assign a value of 1; if the region i S If there is no attachment, the simulation vector will be... The value is assigned to 0; When assigning values to the n-dimensional test attachment vector, for a specific posture numbered as follows: ,in In the test results, if the area There is attachment, among which Then the test vector Assign a value of 1; if the region If there is no attachment, then the test vector will be... The value is assigned to 0.
3. The method for multidimensional similarity statistical evaluation of lightning attachment point simulation and experimental results according to claim 2, characterized in that, The specific method of S2 is as follows: S2.1 Data Alignment and Standardization attach vector to n-dimensional simulation Data and n-dimensional experimental attachment vector The data are spatially correlated one-to-one; S2.2 Outlier Detection Calculate the n-dimensional simulated attachment vector respectively and n-dimensional test attachment vector The Mahalanobis distance for each data point is calculated using the following formula: （1） （2） In the above formula, For simulation vectors Mahalanobis distance in the data For the test vector The Mahalanobis distance of the data is given by μ, where μ is the mean vector of all vectors and Σ is the covariance matrix of all vectors. S For simulation vector subscripts, R The subscript for the test vector; S2.3 Outlier Handling and Removal Select the significance level of outliers α ,make α The value is set to 0.05 or 1. An outlier threshold T is set. When the Mahalanobis distance of a certain data is greater than the outlier threshold T, the data is marked as an outlier and the data is either backtracked or discarded.
4. The method for multidimensional similarity statistical evaluation of lightning attachment point simulation and experimental results according to claim 3, characterized in that, The specific method of S3 is as follows: S3.1, Indicator Calculation Using multidimensional root mean square error Multi-RMSE As a similarity index, the calculation formula is as follows: （3） In the formula, For simulation vector data, The data for the test vector, m is the number of attachment postures of the simulation object or test object, and n is the number of model partitions; S3.2 Similarity Judgment When multidimensional root mean square error Multi-RMSE When the result is less than the anomaly threshold T, the n-dimensional simulated attachment vector and the n-dimensional experimental attachment vector are similar. This is especially true when the multidimensional root mean square error... Multi-RMSE If the result is greater than the anomaly threshold T, then the n-dimensional simulated attachment vector and the n-dimensional experimental attachment vector are not similar.
5. The method for multidimensional similarity statistical evaluation of lightning attachment point simulation and experimental results according to claim 4, characterized in that, The specific method of S5 is as follows: A multi-dimensional similarity assessment of lightning attachment point simulation and experimental results is performed, defining the L2 norm for both the m sets of n-dimensional vector data sets used in the experiment and simulation: （8） （9） in, It is the test vector The value of the i-th element in the array. It is a simulation vector Given the i-th element value, calculate the norm mean of Rn1 for n1 sets of experimental data. for: （10） Calculate the norm mean of n² sets of simulation data Sn² for: （11） Define the accuracy of simulation / experiment comparison for: （12） Generate interpretable evaluation reports.
Citation Information
Patent Citations
Network traffic prediction method based on generative adversarial network
CN112801411A
Aircraft lightning attachment point simulation evaluation method
CN114757018A