Multidimensional correlation response system confirmation measurement method based on PCA and FSV double-layer feature extraction

Abstract

The invention discloses a multi-dimensional correlation response system confirmation measurement method based on PCA and FSV double-layer feature extraction, and relates to a confirmation measurement method. Distinguishing the responses according to correlation types; the uncertainty of simulation model input parameters is considered, Monte Carlo sampling is adopted, and simulation samples are obtained; test uncertainty is considered, multiple tests are repeated, and a test sample is obtained; performing data joint preprocessing and joint principal component analysis on each simulation and test sample pair to complete first-layer feature extraction, performing FSV evaluation on each pair of principal component features, and calculating the weighted sum of the principal component features to obtain PCDM (principal component difference measurement); and performing statistical analysis on the PCDM indexes of all the data sample pairs to obtain uncertainty description of the PCDM indexes and a final U-PCDM index. Different correlation types between responses are reasonably decoupled, different methods are used according to response characteristics of different correlation types, and the difference between principal components of simulation and test data is visually and reasonably evaluated.

Description

Technical Field

[0001] The invention relates to a confirmation measurement method, in particular to a multidimensional correlation response system confirmation measurement method based on PCA and FSV double-layer feature extraction, which is applicable to the multidimensional correlation response system. Background Art

[0002] The development of science and technology and the research of engineering structures are inseparable from the application of experimental technology. However, with the deepening of research, the research objects in engineering are becoming more and more complex, and the cost and risk of conducting real physical experiments are getting higher and higher. In contrast, modeling and simulation (M&S) technology has become an important tool in the study of complex systems with its advantages such as low cost and strong controllability. However, the accuracy and confidence of the response prediction of finite element models are becoming increasingly prominent. Model validation is a type of technology developed on this issue.

[0003] Model validation is defined as the process of determining the degree to which a model accurately represents the real world from the perspective of its intended use (Oberkampf WL, Baron MF. Measures of agreement between computation and experiment: validation metrics. J Comput Phys 2006;217:5-36). Developing appropriate validation metrics is the primary task of model validation. Validation metrics are defined as a mathematical operator that measures the difference between the system response obtained from simulation results and the system response obtained from experimental measurements. A large number of research results have been produced in this direction at home and abroad. The hypothesis testing method and the Bayesian factor method only give a Boolean conclusion on whether to accept the model, without a quantitative description of the model deviation; the frequency index method only considers the sample mean in the process of quantifying the deviation, and lacks a description of characteristic quantities such as the degree of sample dispersion; in contrast, the area metric method based on uncertainty quantification obtains a validation metric that can compare and quantify the difference and uncertainty between the experimental and simulation data by quantifying the difference between the CDF curve or P-box of the experimental and simulation data. However, the above validation metrics can only solve the problem of single-response systems.

[0004] Ferson et al. (Ferson, S., Oberkampf, WL,&Ginzburg, L. (2008). Model validation and predictive capability for the thermal challenge problem. Computer Methods in Applied Mechanics and Engineering, 197(29-32), 2408-2430.doi:10.1016 / j.cma.2007.07.030) proposed the u-pooling method based on area metric. The distribution information of multiple confirmation points is pooled through probability integral transformation (PIT), thereby obtaining an objective and quantitative evaluation between the simulation and experiment of the multi-response system. Since the u-pooling method does not consider the correlation between responses, it can only be applied to multi-response systems with uncorrelated responses. Wei Li et al. (Wei Li, Wei Chen, Zhen Jiang, Zhenzhou Lu, Yu Liu, New validation metrics for models with multiple correlated responses, Reliability Engineering & System Safety, Volume 127, 2014, Pages 1-11, ISSN 0951-8320, https: / / doi.org / 10.1016 / j.ress.2014.02.002.) proposed the PIT area index and t-pooling index on this basis, which are used to deal with correlated response systems and multi-dimensional correlated response systems, respectively. However, since these two methods need to solve the joint cumulative distribution function of the responses, it is extremely difficult to solve the joint cumulative distribution function when the dimension of the responses is very high.Hu Jiarui et al. (Hu Jiarui, Lü Zhenzhou. Model validation method with multivariate output based on kernel principal component analysis[J]. Journal of Beijing University ofAeronautics and Astronautics,2017,43(7) : 1470-1480.HU JR,LYU ZZ. Model validation method with multivariate output basedon kernel principal component analysis[J]. Journal of Beijing University ofAeronautics and Astronautics,2017,43(7) : 1470-1480(in Chinese)) proposed a validation metric method for correlated multi-response systems by combining kernel principal component analysis and u-pooling method, avoiding the solution of complex cumulative distribution function. However, this method is only applicable to multi-response systems of a single correlation type, and cannot effectively deal with the validation metric problem of multi-dimensional correlated systems.

[0005] Principal Component Analysis (PCA) is a feature extraction method based on the minimum mean square error in statistical significance. It can project a data set from high dimension to low dimension while retaining the maximum amount of information. After dimensionality reduction, all features of the data are independent of each other. The eigenvalue corresponding to the eigenvector reflects the variance of the data in this direction. Therefore, the larger the eigenvalue, the more information the data retains in this direction.

[0006] Feature Selective Validation (FSV) is a data difference evaluation method developed from the electromagnetic field. By extracting the differences in amplitude, trend, details, etc. between two sets of data sets, it can comprehensively reflect the overall and local differences in the data. Since the FSV method focuses on the differences in amplitude, trend and details of the data set, it is more suitable for the evaluation of "field-related response" systems. At present, the FSV method has been widely used in various fields of electromagnetics, but the expansion of its application in other fields and its combination with other research methods are still hot topics that have received widespread attention. The traditional FSV method conducts deterministic comparisons between data, while uncertainty is common in experiments, simulations and applications in engineering. Therefore, how to reasonably reflect the uncertainty of data in the evaluation results of FSV is also one of the challenges of current research. Jauregui R. et al. (Jauregui R., Aragon M. and Silva F., "The Role of Uncertainty in the Feature Selective Validation (FSV) Method", in IEEE Transactions on Electromagnetic Compatibility, vol. 55, no. 1, pp. 217-220, Feb. 2013, doi: 10.1109 / TEMC.2012.2227262) introduced uncertainty into the metric of the FSV method by constructing the best and worst curves within the uncertainty interval of one of the data sets and performing FSV with the other data set respectively, thereby obtaining the uncertainty interval of the FSV metric. However, at this time, only the uncertainty of one of the data sets was considered.Azpúrua MA et al. (Azpúrua MA, Páez E. and Jauregui R., "Measurementuncertainty propagation through the Feature Selective Validation method," 2014 IEEE International Symposium on Electromagnetic Compatibility (EMC), Raleigh, NC, USA, 2014, pp. 328-333, doi: 10.1109 / ISEMC.2014.6898992.) considered the uncertainties of both experiments and simulations at the same time, and used the Monte Carlo method to propagate the uncertainty of the input data set through the simulation model. The simulation samples and the Monte Carlo samples within the experimental error range were combined into multiple groups of sample pairs and FSV was performed separately to estimate the confidence interval of each FSV indicator. Summary of the invention

[0007] The purpose of the present invention is to address the above-mentioned deficiencies in the prior art and take into account the uncertainties of simulation and experiment, and to provide a method for handling the confirmation measurement problem of a multi-dimensional correlated response system. The method can decouple different correlation types between responses, and use different processing methods according to the response characteristics of different correlation types to evaluate the differences in the multi-dimensional correlated response data of simulation and experiment, and obtain quantitative indicators of the differences between simulation and experiment.

[0008] The present invention comprises the following steps:

[0009] Step 1: For a multi-dimensional correlation response system, the responses are classified according to the correlation type;

[0010] In step 1, the specific method of distinguishing the responses by correlation type is: the correlation of the responses is divided into field correlation and physical correlation, the field correlation represents the correlation in time or space, there is a clear relative position between the responses, and the trend of the response change needs to be considered during the analysis, and the physical correlation represents the mutual correlation caused by the same physical mechanism, and there is no clear order requirement between the responses.

[0011] In step 1, the multi-dimensional correlation response system refers to: a system in which responses have both field correlation and physical correlation;

[0012] Step 2: Consider the parameter uncertainty of the simulation model and perform Monte Carlo sampling to obtain A set of simulation data samples, considering the experimental uncertainty, repeated the experiment multiple times, and obtained Each group of simulation data samples is paired with each group of test data samples to obtain For each pair of data samples, steps 3 to 5 are performed to evaluate the data difference. When all pairs of data samples have completed the data difference evaluation, step 6 is performed.

[0013] In step 2, Center the data sample ( ), simulation data sample Recorded in the following format:

[0014] (1)

[0015] in, Data representing different physical quantities in the response, with "physical correlation", Represents the total number of physical quantities, each column is The vector represents the data of the physical quantity in the time or space field and has "field correlation". Indicates the length of the field;

[0016] Test data sample Recorded in the following format:

[0017] (2)

[0018] in, The data representing different physical quantities in different columns as responses have physical relevance, Represents the total number of physical quantities, each column is The vector represents the data of the physical quantity in the time or space field and has field correlation. Indicates the length of the field.

[0019] Step 3: Data preprocessing: The simulation data samples and the test data samples in the data sample pair are stacked in the vertical direction, and are jointly centered and dedimensionalized to obtain preprocessed stacked data;

[0020] The pre-processing steps in step 3 are:

[0021] Step 3.1: Stack the simulation data samples and the test data samples vertically, that is:

[0022] (3)

[0023] Step 3.2: Calculate stacking data The mean of each column of data ;

[0024] Step 3.3: Centering and de-dimensionalization: Stacking data After subtracting the mean of the corresponding column from each column of data, divide it by the mean of the corresponding column to obtain the preprocessed data .

[0025] Step 4: Perform the first-layer feature extraction: Use the joint PCA method on the preprocessed stacked data obtained in step 3 to obtain several pairs of principal component features and corresponding weights of the test and simulation;

[0026] The steps of the joint PCA method used in step 4 are:

[0027] Step 4.1: Calculate the covariance matrix between different columns of the preprocessed stacked data obtained in step 3;

[0028] Step 4.2: Perform eigenvalue decomposition on the covariance matrix in step 4.1 to obtain the eigenvalues and its corresponding eigenvector , each eigenvector is A vector of

[0029] Step 4.3: Sort the eigenvalues ​​from large to small, and add up the percentage of each eigenvalue to all eigenvalues ​​from large to small. When the accumulated value exceeds 90%, stop adding up and only keep the eigenvalues ​​involved in the accumulation and their corresponding eigenvectors. The eigenvectors at this time constitute the eigenvector set , recalculate the percentage of each retained eigenvalue to all retained eigenvalues ;

[0030] Step 4.4: Stack the preprocessed data obtained in step 3 With the feature vector set in step 4.3 Do the dot product to get the data projected into the feature space :

[0031] (4)

[0032] Step 4.5: Project the data obtained in step 4.4 into the feature space Before The rows are the simulated data after being projected into the feature space , each column is called a principal component feature of the simulation data; After The rows are the test data after projection into the feature space , each column is called a principal component feature of the test data.

[0033] Step 5: Perform the second-level feature extraction: Use the FSV method to evaluate the difference between each pair of principal component features obtained in step 4 and the simulation, obtain the global difference measure (GDM) index of each pair of principal component features, and perform weighted average according to the weight obtained in step 4 to obtain the principal component difference measure (PCDM) index. The smaller the PCDM index, the smaller the difference between the two data sets.

[0034] The specific steps of the second layer feature extraction in step 5 are:

[0035] Step 5.1: Perform FSV on each pair of principal component features obtained in step 4.5 between the simulation and the test to obtain the global difference measure for each pair of principal component features. ;

[0036] Step 5.2: Convert the As obtained in step 5.1 The weights of the principal components are averaged to obtain the principal component difference measure ,Right now:

[0037] (5)

[0038] Step 6: After all data sample pairs have completed data difference evaluation, this step is performed: statistical analysis is performed on the PCDM indicators of all data sample pairs to obtain the uncertainty description of the PCDM indicators and the final U-PCDM indicators;

[0039] The specific statistical analysis process for all PCDM indicators in step 6 is as follows: For the PCDM index of data sample pairs, the matrix can be constructed , Each row in represents the PCDM index value of a data sample pair consisting of a set of simulation data samples and different experimental data samples. Find the minimum value of the PCDM index in each row and calculate the mean of all minimum values. and standard deviation , with interval ( is the control factor, the default value is 1) as the uncertainty interval of the PCDM indicator, with the upper limit of the uncertainty interval as the final metric.

[0040] The present invention reasonably decouples different correlation types between responses, and uses different processing methods according to the response characteristics of different correlation types to evaluate the differences in multi-dimensional correlated response data of simulation and experiment, and obtains quantitative indicators of the differences between the principal components of simulation and experimental data. Compared with the confirmation measurement method that performs the same processing on the correlation of responses, the obtained measurement results are more reasonable and intuitive, and can be easily simplified and applied to systems with only a single response correlation type.

[0041] Compared with the prior art, the present invention has the following beneficial effects:

[0042] 1) Decompose the response correlation into field correlation and physical correlation. One of the characteristics of physical correlation is that it is not sequential, which is suitable for processing by PCA method. One of the characteristics of field correlation is that it is sequential, focusing on the trend and details of the data, which is suitable for processing by FSV method. By classifying the responses according to the correlation type and performing different treatments according to the characteristics of the correlation type, compared with the confirmation measurement method that performs the same treatment on the response correlation, the measurement results obtained are more reasonable and intuitive, and can be easily simplified and applied to systems with only a single response correlation type.

[0043] 2) The double-layer feature extraction method based on PCA and FSV can handle the confirmation measurement problem of multi-dimensional correlated response systems. PCA only retains the first few principal components of the data that account for a large proportion of information. While retaining the main information, it saves a lot of calculations on other characteristic components and avoids the calculation of multi-dimensional joint distribution functions, with high computational efficiency.

[0044] 3) When preprocessing data and performing PCA operations, the simulation and experimental data are stacked and jointly analyzed and transformed to avoid additional errors caused by different transformations of the two data sets. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 Comparison of a pair of samples between the test data and the simulation data of model B (3D perspective);

[0046] Figure 2 Comparison of a pair of samples between the test data and the simulation data of model B (2D perspective);

[0047] Figure 3 Comparison of a pair of samples after preprocessing;

[0048] Figure 4 It is the comparison of the principal components of a pair of samples after the first layer of feature extraction;

[0049] Figure 5 A flowchart of a multi-dimensional correlation response system validation measurement method based on PCA and FSV double-layer feature extraction;

[0050] Figure 6 The analysis results of the example. DETAILED DESCRIPTION

[0051] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the following embodiments will further illustrate the present invention in conjunction with the accompanying drawings. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. On the contrary, the present invention covers any substitution, modification, equivalent method and scheme made on the essence and scope of the present invention as defined by the claims.

[0052] The embodiment of the present invention includes the following steps:

[0053] Step 1: For a multi-dimensional correlated response system, the response correlation is divided into "field correlation" and "physical correlation". The following is a description of the multi-dimensional response system example:

[0054] 1) Input parameters include four fixed parameters ( ) and two parameters containing random uncertainties ( ),in It obeys the uniform distribution on the interval [4.75,5], It obeys the uniform distribution in the interval [6.9,7.2];

[0055] 2) The response includes two physical quantities with physical correlation ( ), and It’s also time ( ), that is, There is field correlation between the responses at these 11 time points. There were also field correlations between the responses at these 11 time points;

[0056] 3) In the simulation model, and The analytical expression of (superscript m indicates simulation model) is as follows:

[0057] (6)

[0058] (7)

[0059] in is 1.01 or 1, The model with a value of 1.01 (model A) is closer to the correct model than the model with a value of 1 (model B);

[0060] 4) For the convenience of explanation, the analytical expression of the correct model is used as the source of experimental data. and The analytical formula of (superscript e indicates test) is as follows:

[0061] (8)

[0062] (9)

[0063] in Both are 1.01, is a random disturbance that follows a normal distribution with a mean of 0 and a variance of 0.02;

[0064] The description of the simulation model and the correct model (source of experimental data) is shown in Table 1:

[0065] Table 1

[0066]

[0067] Step 2: Considering the parameter uncertainty of the simulation model, Monte Carlo sampling is performed to obtain 100 sets of simulation data samples. Considering the experimental uncertainty, the experiment is repeated many times to obtain 3 sets of experimental data samples. Each set of simulation data samples is paired with each set of experimental data samples to obtain For data sample pairs; use Python to program the above process and get a comparison between model B and a pair of sample data in the experiment. Figure 1 and Figure 2 As shown; each pair of data samples performs steps 3 to 5 to perform data difference evaluation. When all data sample pairs have completed data difference evaluation, step 6 is performed;

[0068] Step 3: Data preprocessing: The simulation data samples and the experimental data samples in the data sample pair are stacked vertically, and centralized and dedimensionalized together to obtain the preprocessed stacked data. , a pair of sample data after preprocessing is compared as follows Figure 3 As shown;

[0069] Step 4: First-layer feature extraction: Use the joint PCA method on the preprocessed stacked data obtained in step 3 to obtain several pairs of principal component features of the test and simulation and corresponding weights ,like Figure 4 As shown;

[0070] Step 5: Second-layer feature extraction: Use the FSV method to evaluate the difference between each pair of principal component features obtained in step 4 and the simulation, and obtain the global difference measure (GDM) index of each pair of principal component features. Then, perform weighted average according to the weights obtained in step 4 to obtain the principal component difference measure (PCDM) index. The smaller the PCDM index, the smaller the difference between the two data sets.

[0071] Step 6: After all data sample pairs have completed data difference evaluation, perform this step: Statistical analysis of the PCDM indicators of all data sample pairs is performed to obtain the uncertainty description of the PCDM indicators: For the PCDM index of data sample pairs, the matrix can be constructed , Each row in represents the PCDM index value of a data sample pair consisting of a set of simulation data samples and different experimental data samples. Find the minimum value of the PCDM index in each row and calculate the mean of all minimum values. and standard deviation , with interval ( is the control factor, the default value is 1) as the uncertainty interval of the PCDM indicator, with the upper limit of the uncertainty interval as the final metric.

[0072] Figure 5 Flow chart of a multi-dimensional correlation response system validation measurement method based on PCA and FSV double-layer feature extraction.

[0073] Using Python programming, model A and model B were compared with the correct model (experiment) to perform the above steps, and the U-PCDM index results were obtained as follows Figure 6 As shown; in fact, the values ​​of the fixed parameters of model A are consistent with the correct model, and the values ​​of the fixed parameters of model B are inconsistent with the correct model, that is, model A is closer to the correct model than model B; from Figure 6 It can be seen that the U-PCDM index of model A is generally smaller than the PCDM index of model B, that is, the PCDM index of model A should be better than the U-PCDM index of model B, which is consistent with the actual situation.

[0074] The final U-PCDM index of model A is 0.1176, and the average U-PCDM index of model B is 0.1217.

[0075] The present invention subdivides the correlation of a multidimensional correlated response system into "field correlation" and "physical correlation", obtains simulation data samples through Monte Carlo sampling, and obtains test data samples by repeating multiple experiments to achieve quantitative evaluation of the difference between simulation and test data. The data preprocessing steps (centralization and dedimensionalization) and the two-layer feature extraction method (joint PCA and FSV) can efficiently extract the key features of simulation and test data and reduce redundant information in the data, thereby improving the efficiency of data analysis and processing. The present invention obtains the uncertainty description of the PCDM index by statistically analyzing the PCDM index of all data sample pairs, and uses the upper bound of the uncertainty interval as the final measurement index. This method can more accurately reflect the uncertainty of the difference between simulation and test data, and provide a more reliable basis for model verification. By comparing the U-PCDM index of model A and model B, the present invention can intuitively judge which model is closer to the correct model. Thereby improving the accuracy and practicality of the model. The present invention can more accurately and efficiently evaluate the difference between simulation and test data in a multidimensional correlated response system by reasonably distinguishing the correlation types of the response and adopting a two-layer feature extraction method.

[0076] The present invention can be applied to the verification of simulation models of aircraft to ensure the consistency of simulation results with real flight test data. Or it can be applied to the verification of automobile collision simulation to ensure that the simulation model can accurately predict the vehicle behavior in the actual collision. Optimize automobile design and improve vehicle performance by comparing simulation and experimental data. It can also be applied to the field of mechanical engineering to verify simulation models of complex mechanical systems, such as robots, CNC machine tools, etc. Evaluate the durability, reliability and performance of mechanical parts. It can verify the simulation models of structures such as bridges and buildings to ensure the safety of the design and evaluate the impact of natural disasters such as earthquakes and wind loads on the structure. It can also be applied to the fields of electronics and communications engineering, biomedical engineering, etc.

[0077] The above embodiments are only preferred embodiments of the present invention and cannot be considered to limit the scope of the present invention. All equivalent changes and improvements made within the scope of the present invention should still fall within the scope of the present invention.

Claims

1. A multi-dimensional correlation response system confirmation measurement method based on PCA and FSV double-layer feature extraction, characterized in that The following steps are involved: Step 1: Response differentiation: For a multi-dimensional correlated response system, the responses are differentiated according to the correlation type; Step 2: Data acquisition and pairing: Considering the parameter uncertainty of the simulation model, Monte Carlo sampling is performed to obtain A set of simulation data samples, considering the experimental uncertainty, repeated the experiment multiple times, and obtained Each group of simulation data samples is paired with each group of test data samples to obtain For each pair of data samples, perform steps 3 to 5 to evaluate the data difference. When all data sample pairs have completed the data difference evaluation, proceed to step 6. Step 3: Data preprocessing: The simulation data samples and the test data samples in the data sample pair are stacked in the vertical direction, and are jointly centered and dedimensionalized to obtain preprocessed stacked data; Step 4, first layer feature extraction: Use the joint PCA method on the preprocessed stacked data obtained in step 3 to obtain several pairs of principal component features and corresponding weights of the test and simulation; Step 5, second-layer feature extraction: Use the FSV method to evaluate the difference between each pair of principal component features obtained in step 4 and the simulation, obtain the global difference measure GDM index of each pair of principal component features, and perform weighted average according to the weight obtained in step 4 to obtain the principal component difference measure PCDM index. The smaller the PCDM index, the smaller the difference between the two data sets. Step 6: Statistical analysis: After all data sample pairs have completed data difference evaluation, this step is performed: statistical analysis is performed on the PCDM indicators of all data sample pairs to obtain the uncertainty description of the PCDM indicators and the final U-PCDM indicators.

2. A multi-dimensional correlation response system confirmation measurement method based on PCA and FSV double-layer feature extraction as claimed in claim 1, characterized in that: In step 1, the specific method of distinguishing the responses by correlation type is: dividing the response correlation into field correlation and physical correlation, wherein the field correlation indicates the correlation in time or space, and there is a clear relative position between the responses, and the trend of the response change needs to be considered during the analysis, and the physical correlation indicates the mutual correlation caused by the same physical mechanism, and there is no clear order requirement between the responses.

3. A multi-dimensional correlation response system confirmation measurement method based on PCA and FSV double-layer feature extraction as claimed in claim 1, characterized in that: In step 1, the multi-dimensional correlation response system refers to a system in which responses have both field correlation and physical correlation as defined in claim 2.

4. A multi-dimensional correlation response system confirmation measurement method based on PCA and FSV double-layer feature extraction as claimed in claim 1, characterized in that: In step 2, the acquisition For data sample pairs, the first For the data sample alignment, ; Simulation data sample Recorded in the following format: in, Data representing different physical quantities in the response, with physical correlation, Represents the total number of physical quantities, each column is The vector represents the data of the physical quantity in the time or space field and has field correlation. Indicates the length of the field; Test number sample Recorded in the following format: in, The data representing different physical quantities in different columns as responses have physical relevance, Represents the total number of physical quantities, each column is The vector represents the data of the physical quantity in the time or space field and has field correlation. Indicates the length of the field.

5. A multi-dimensional correlation response system confirmation measurement method based on PCA and FSV double-layer feature extraction as claimed in claim 1, characterized in that: In step 3, the pre-processing steps are: Step 3.1: Stack the simulation data samples and the test data samples vertically, that is: ； Step 3.2: Calculate stacking data The mean of each column of data ; Step 3.3: Centering and de-dimensionalization: Stacking data After subtracting the mean of the corresponding column from each column of data, divide it by the mean of the corresponding column to obtain the preprocessed data .

6. A multi-dimensional correlation response system confirmation measurement method based on PCA and FSV double-layer feature extraction as claimed in claim 1, characterized in that: In step 4, the steps of using the joint PCA method are: Step 4.1: Calculate the covariance matrix between different columns of the preprocessed stacked data obtained in step 3; Step 4.2: Perform eigenvalue decomposition on the covariance matrix in step 4.1 to obtain the eigenvalues and its corresponding eigenvector , each eigenvector is A vector of Step 4.3: Sort the eigenvalues ​​from large to small, and add up the percentage of each eigenvalue to all eigenvalues ​​from large to small. When the accumulated value exceeds 90%, stop adding up and only keep the eigenvalues ​​involved in the accumulation and their corresponding eigenvectors. The eigenvectors at this time constitute the eigenvector set , recalculate the percentage of each retained eigenvalue to all retained eigenvalues ; Step 4.4: Stack the preprocessed data obtained in step 3 With the feature vector set in step 4.3 Do the dot product to get the data projected into the feature space : ； Step 4.5: Project the data obtained in step 4.4 into the feature space Before The rows are the simulated data after being projected into the feature space , each column is called a principal component feature of the simulation data; Will After The rows are the test data after projection into the feature space , each column is called a principal component feature of the test data.

7. A multi-dimensional correlation response system confirmation measurement method based on PCA and FSV double-layer feature extraction as claimed in claim 1, characterized in that: In step 5, the specific steps of second-layer feature extraction are: Step 5.1: Perform FSV on each pair of principal component features obtained in step 4.5 between the simulation and the test to obtain the global difference measure for each pair of principal component features. ; Step 5.2: Add the As obtained in step 5.1 The weights of the principal components are averaged to obtain the principal component difference measure ,Right now: 。 8. A multi-dimensional correlation response system confirmation measurement method based on PCA and FSV double-layer feature extraction as claimed in claim 1, characterized in that: In step 6, the process of statistical analysis of the PCDM indicators of all data sample pairs is as follows: For the PCDM index of the data sample pair, construct the matrix , Each row in represents the PCDM index value of a data sample pair consisting of a set of simulation data samples and different experimental data samples. Find the minimum value of the PCDM index in each row and calculate the mean of all minimum values. and standard deviation , with interval As the uncertainty interval of the PCDM indicator, the upper bound of the uncertainty interval is As the ultimate metric; is the control factor, the default value is 1.

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