A method and system for equivalent conversion of equipment test sample size

Abstract

This application relates to the field of equipment performance testing and evaluation technology, and provides a method and system for equivalent reduction of equipment test sample size. By constructing a data fusion evaluation model based on actual and numerical test data, the fidelity of actual test response estimation under small sample conditions is improved. An equivalent measure is designed and calculated by fusing the mean square error of the evaluation model from a single data source with a preset test confidence level, and a box plot of the equivalent measure from a single data source is obtained. By connecting the lower quartile and upper quartile of each obtained box plot, equivalent composite confidence intervals for actual and numerical simulation tests are plotted. Based on these equivalent composite confidence intervals, the theoretically required actual test sample size is equivalently reduced to the numerical simulation test sample size, achieving an equivalent reduction of the actual test sample size by the numerical simulation test, thus solving the problem of equipment performance evaluation under insufficient actual test samples.

Description

Technical Field

[0001] This application belongs to the field of equipment performance testing and evaluation technology, and relates to a method and system for equivalent conversion of equipment test sample size. Background Technology

[0002] Equipment performance verification testing is an indispensable and crucial step in the research, development, production, and deployment of modern equipment. Its core objective is to obtain sufficient and reliable performance data through scientifically designed testing activities to verify whether the equipment meets predetermined technical specifications and usage requirements. However, with the increasing demand for equipment, traditional testing methods face multiple challenges, including high testing costs, long cycles, limited sample sizes, and difficulty in testing boundary indicators.

[0003] In reality, resources and samples for actual equipment testing are often very limited. If the minimum sample size required for verification testing exceeds the available sample size, it will be difficult to conduct equipment performance evaluation. Currently, there is a lack of quantitative "numerical-real equivalence" models for actual equipment testing and digital simulation testing samples. There is no reliable equivalent mapping from actual equipment testing to digital simulation testing, thus making it impossible to effectively and objectively convert the sample sizes of digital simulation testing and actual equipment testing.

[0004] Therefore, a technical solution is urgently needed to solve the above problems. Summary of the Invention

[0005] Therefore, it is necessary to provide a method and system for equivalent conversion of equipment test sample size to address the above-mentioned technical problems.

[0006] A method for equivalent conversion of equipment test sample size includes the following steps:

[0007] Acquire data and construct a data fusion evaluation model based on the data, wherein the data includes digital simulation test sample space data and actual test sample space data;

[0008] Using data from repeated sampling with different sample sizes within the actual experimental factor space as input, the predicted value of the fusion evaluation model of the actual experimental data is calculated. The actual experimental factor space data from each sampling and the corresponding predicted value constitute the expanded actual experimental data. The data from repeated sampling with different sample sizes within the digital simulation experimental sample space is used as the digital simulation experimental data.

[0009] Construct a single data source evaluation model and calculate the mean squared error of the single data source evaluation model;

[0010] The mean square error of the evaluation model is evaluated based on the digital simulation test data with different sample sizes as input. The confidence level of the digital simulation test is preset, the equivalent measure of the digital simulation test is calculated, and the equivalent measure of the digital simulation test and the box plot of different sample sizes are plotted.

[0011] The mean square error of the evaluation model and the preset reliability of the actual test are evaluated based on the expanded experimental data corresponding to different sample sizes of the single data source. The equivalent measure of the actual test is calculated, and the equivalent measure of the actual test and the box plot of different sample sizes are drawn.

[0012] Obtain box plots of the equivalent measures of the actual test and the equivalent measures of the digital simulation test for different sample sizes. For each box plot obtained, connect the lower quartile and the upper quartile to draw the equivalent composite confidence interval of the actual test and the equivalent composite confidence interval of the digital simulation test.

[0013] Based on the equivalent composite confidence interval of the actual test and the equivalent composite confidence interval of the digital simulation test, the sample size of the actual test that is theoretically required but exceeds the actual supply capacity is equivalently converted into the sample size of the digital simulation test.

[0014] In one embodiment, the single data source evaluation model is:

[0015] ;

[0016] in, Evaluate the model response value for a single data source; The residual term has a mean of 0 and a variance of . Gaussian process; A vector of unknown mean parameters; It is a vector of mean functions; Input for the model.

[0017] In one embodiment, the mean squared error of the single data source evaluation model is calculated according to the following formula:

[0018] ;

[0019] in, The mean squared error of the model is evaluated for a single data source; For process variance, and For training data; The input for the model is The single data source is used to evaluate the model response value; The input for the model is The single data source is used to evaluate the model response estimate; For design points and The correlation vector between them; For designing the matrix; D The correlation matrix between design points; for The regression basis function vector at that point.

[0020] In one embodiment, the equivalent measure of the digital simulation test and the equivalent measure of the actual test are calculated according to the following formula:

[0021] ;

[0022] Where ET is the equivalent measure; To assess the reliability of the experiment.

[0023] In one embodiment, the data constructs a data fusion evaluation model for real-world experiments as follows:

[0024] ;

[0025] in, The response value of the evaluation model is determined by the fusion of experimental data; The response estimate of the model is used to evaluate the data from the digital simulation test. This is the scaling factor; It is a Gaussian random process.

[0026] In one embodiment, the predicted value of the data fusion evaluation model is calculated according to the following formula:

[0027] ;

[0028] in, The predicted values ​​are from the data fusion evaluation model of the experimental data. For containing elements The relevant vectors, For actual test data, This refers to the i-th experimental factor in the actual experimental data; H For containing elements The correlation matrix; This is a vector composed of the predicted values ​​of the digital simulation test data evaluation model at the actual sample location; For actual test data The corresponding response value.

[0029] In one embodiment, the sample size of the actual experiment is equivalently converted to the sample size of the digital simulation experiment based on the equivalent composite confidence interval of the actual experiment and the equivalent composite confidence interval of the digital simulation experiment, including:

[0030] The required sample size to find the theoretical value on the equivalent composite confidence interval of the practical experiment. Corresponding experimental equivalent measure value and ;

[0031] Search within the equivalent composite confidence interval of the digital simulation experiment and The corresponding sample size of the digital simulation experiment, of which, The sample size of the equivalent measure of the upper quartile curve in the equivalent composite confidence interval of the corresponding digital simulation experiment is: The sample size for the equivalent measure of the lower quartile curve is ; The sample size of the equivalent measure of the upper quartile curve in the equivalent composite confidence interval of the corresponding digital simulation experiment is: The sample size for the equivalent measure of the lower quartile curve is ;

[0032] Take respectively and as well as and Mean:

[0033] ;

[0034] ;

[0035] in, for and The mean; for and The mean; Round the result up;

[0036] Pick and The mean was used as the sample size for the actual test. Equivalent reduced digital simulation test sample size.

[0037] In one embodiment, the The calculation is performed using the Gaussian correlation function:

[0038] ;

[0039] in, The Gaussian correlation function is... This is the experimental point; For unknown related parameters; k The value ranges from 1 to m , corresponding to the first dimension to the second dimension of the input space mDimension, used to iterate through all dimensions of the factor.

[0040] In one embodiment, the method further includes:

[0041] The digital simulation test data and the actual test data are preprocessed;

[0042] Based on the preprocessed data, a multi-factor fusion method was used to calculate the initial... value;

[0043] Setting the nonlinearity of experimental factor data based on preprocessed data Value optimization boundary.

[0044] An equipment test sample size equivalent conversion system includes:

[0045] The fusion model construction module is used to acquire data and construct a fusion evaluation model of digital simulation test data based on the data. The data includes digital simulation test sample space data and actual test sample space data.

[0046] The actual data expansion module is used to calculate the predicted value of the data fusion evaluation model by taking data repeatedly sampled from different sample sizes in the actual experimental factor space as input. The expanded actual experimental data consists of the actual experimental factor space data sampled each time and the corresponding predicted value. The digital simulation experimental data consists of data repeatedly sampled from different sample sizes in the digital simulation experimental sample space.

[0047] The mean squared error calculation module is used to construct a single data source evaluation model and calculate the mean squared error of the single data source evaluation model.

[0048] The simulation test calculation module is used to evaluate the mean square error of the model and the preset digital simulation test credibility based on a single data source with digital simulation test data corresponding to different sample sizes as input, calculate the equivalent measure of the digital simulation test, and draw box plots of the equivalent measure of the digital simulation test with different sample sizes.

[0049] The experimental setup calculation module is used to evaluate the mean square error of the model and the preset experimental setup confidence level based on a single data source with expanded experimental setup data corresponding to different sample sizes as input, calculate the equivalent measure of the experimental setup, and draw box plots of the equivalent measure of the experimental setup with different sample sizes.

[0050] The equivalent composite confidence interval plotting module is used to obtain box plots of equivalent measures of actual experiments and equivalent measures of digital simulation experiments for different sample sizes. For each obtained box plot, the lower quartile and the upper quartile are connected to plot the equivalent composite confidence intervals of actual experiments and equivalent composite confidence intervals of digital simulation experiments.

[0051] The equivalent conversion module is used to convert the sample size of the actual test, which is theoretically required but exceeds the actual supply capacity, into the sample size of the digital simulation test based on the equivalent composite confidence interval of the actual test and the equivalent composite confidence interval of the digital simulation test.

[0052] The aforementioned method and system for equivalent sample size conversion of equipment tests improves the fidelity of response estimation under small sample conditions in actual equipment tests by constructing a data fusion evaluation model based on numerical and actual test data. Based on digital simulation test data and expanded actual equipment test data composed of predicted values ​​from the data fusion evaluation model and actual test factor space data, single-source evaluation models were constructed. Furthermore, by fusing the mean square error of the single-source evaluation model with a preset test confidence level, equivalent measures were designed and calculated. Multiple sampling was conducted to obtain box plots of the single-source equivalent measures. By connecting the lower and upper quartiles of each obtained box plot, equivalent composite confidence intervals for actual equipment tests and digital simulation tests were plotted, thereby enhancing statistical robustness, focusing on the main part of the data, and effectively avoiding the influence of equipment test sample location selection on its equivalence. Furthermore, based on the equivalent composite confidence intervals of actual testing and digital simulation testing, the theoretically required but physically unavailable sample size for actual testing is equivalently converted into the sample size for digital simulation testing. This achieves an equivalent conversion of the sample size of actual testing to that of digital simulation testing, solving the problem of equipment performance evaluation under conditions of insufficient actual testing samples and effectively reducing the cost of equipment performance evaluation testing. This invention significantly reduces the sample size required for actual testing in equipment testing and evaluation. Attached Figure Description

[0053] Figure 1 This is a flowchart illustrating the method for equivalent conversion of equipment test sample size in one embodiment;

[0054] Figure 2 This is a graph showing the relationship between the MSE of a single data source evaluation model and the sample size in one embodiment.

[0055] Figure 3 This is a graph showing the relationship between equivalent measure and sample size in one embodiment, where, Figure 3 (a) represents credibility. A graph showing the relationship between equivalent measure and sample size. Figure 3 (b) Credibility A graph showing the relationship between equivalent measure and sample size;

[0056] Figure 4 Here is a contour plot of experimental data functions in one embodiment, where, Figure 4 (a) is a contour plot of the actual test data function. Figure 4 (b) is a contour plot of the digital simulation test data function;

[0057] Figure 5 This is a mean square error diagram of a data fusion evaluation model that uses real-world experimental sample space data as model input in one embodiment.

[0058] Figure 6 This is an equivalent composite confidence interval diagram of an actual test in one embodiment.

[0059] Figure 7 This is an equivalent composite confidence interval diagram of an evaluation model based on a single data source when no data fusion evaluation model is constructed in one embodiment.

[0060] Figure 8 This is a schematic diagram illustrating the equivalent reduction of the test sample size based on the equivalent composite confidence interval in one embodiment;

[0061] Figure 9 This is a structural block diagram of an embodiment of an equipment test sample size equivalent conversion system. Detailed Implementation

[0062] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0063] In one embodiment, such as Figure 1 As shown, an equivalent conversion method for equipment test sample size is provided, including the following steps:

[0064] Step 201: Acquire data and construct a data fusion evaluation model based on the data, wherein the data includes digital simulation test sample space data and actual test sample space data.

[0065] Step 202: Using data from repeated sampling with different sample sizes in the actual experimental factor space as input, calculate the predicted value of the fusion evaluation model of the actual experimental data. The actual experimental factor space data from each sampling and the corresponding predicted value constitute the expanded actual experimental data. The data from repeated sampling with different sample sizes in the digital simulation experimental sample space are used as the digital simulation experimental data.

[0066] It should be noted that the experimental sample space data is composed of experimental factors. The experimental factor space is the space formed by all experimental factors in the experimental sample space data. Data from repeated sampling with different sample sizes within the experimental factor space is used as input to calculate the predicted values ​​of the experimental data fusion evaluation model. Specifically, first, a fixed sample size is used for multiple samplings, and the sampled data is used as input to calculate the predicted values ​​of the experimental data fusion evaluation model. Then, the sample size is gradually increased, and the sampling and prediction calculations are repeated. For obtaining digital simulation experimental data, specifically, a fixed sample size is first used for multiple samplings, and then the sample size is gradually increased and the sampling is repeated to obtain the digital simulation experimental data.

[0067] Step 203: Construct a single data source evaluation model and calculate the mean square error of the single data source evaluation model.

[0068] It should be noted that, correspondingly, when different sample sizes of digital simulation test data and actual test data are used as inputs, the constructed single-source evaluation model also corresponds to the sample size and data type. Similarly, the mean squared error of the single-source evaluation model also corresponds to the input.

[0069] Step 204: Based on the single data source of digital simulation test data corresponding to different sample sizes, evaluate the mean square error of the model and the preset credibility of the digital simulation test, calculate the equivalent measure of the digital simulation test, and draw the box plot of the equivalent measure of the digital simulation test with different sample sizes.

[0070] It is understandable that the mean square error of the evaluation model based on a single data source with digital simulation test data corresponding to different sample sizes as input is the mean square error of the evaluation model constructed with digital simulation test data corresponding to different sample sizes as input.

[0071] Step 205: Based on the single data source evaluation model with expanded experimental data corresponding to different sample sizes as input, calculate the equivalent measure of the experimental test and plot the equivalent measure of the experimental test with different sample sizes.

[0072] Step 206: Obtain box plots of the equivalent measures of the actual test and the equivalent measures of the simulation test for different sample sizes. For each box plot obtained, connect the lower quartile and the upper quartile to draw the equivalent composite confidence interval of the actual test and the equivalent composite confidence interval of the digital simulation test.

[0073] Step 207: Based on the equivalent composite confidence interval of the actual test and the equivalent composite confidence interval of the digital simulation test, the sample size of the actual test that is theoretically required but exceeds the actual supply capacity is equivalently converted into the sample size of the digital simulation test.

[0074] It should be noted that the theoretically required but actual supply capacity exceeds the actual supply capacity of the actual test sample size, i.e., the theoretically required actual test sample size minus the actual supply capacity of the actual test sample size.

[0075] In the aforementioned method for equivalent sample size reduction of equipment tests, the fidelity of response estimation under small sample conditions in actual equipment tests is improved by constructing a data fusion evaluation model based on numerical and actual test data. Based on digital simulation test data and expanded actual equipment test data composed of predicted values ​​from the data fusion evaluation model and actual test factor space data, single-source evaluation models were constructed respectively. Furthermore, by fusing the mean square error of the single-source evaluation model with a preset test confidence level, equivalent measures were designed and calculated. Multiple sampling was conducted to obtain box plots of the single-source equivalent measures. By connecting the lower and upper quartiles of each obtained box plot, equivalent composite confidence intervals for actual equipment tests and digital simulation tests were plotted, thereby enhancing statistical robustness, focusing on the main part of the data, and effectively avoiding the influence of equipment test sample location selection on its equivalence. Furthermore, based on the equivalent composite confidence interval of the actual test and the equivalent composite confidence interval of the digital simulation test, the sample size of the actual test, which is theoretically required but exceeds the actual supply capacity, is equivalently converted into the sample size of the digital simulation test. This achieves the equivalent conversion of the sample size of the actual test and the digital simulation test, solves the problem of equipment performance evaluation under the condition of insufficient actual test samples, and effectively reduces the cost of equipment performance evaluation tests.

[0076] In one embodiment, for obtaining n Group of test samples ,in This indicates that each group of test samples contains m One experimental factor, n Test response values ​​corresponding to the test samples The single data source evaluation model is as follows:

[0077] ;

[0078] in, Evaluate the model response value for a single data source; The residual term has a mean of 0 and a variance of . Gaussian processes, i.e. , indicating a local deviation of the model; For an unknown mean parameter vector, ; Let them be the mean function vectors. ; Input for the model. As a regression term in the single data source evaluation model.

[0079] for n Any two sets of test inputs in a group experiment , The covariance corresponding to the response value of the single data source evaluation model is , To calculate the correlation function corresponding to the response, without loss of generality, the Gaussian correlation function is chosen:

[0080] ;

[0081] in, These are unknown related parameters.

[0082] For any unknown input The corresponding single data source evaluation model response estimate for:

[0083] ;

[0084] in, For design points and The correlation vector between them; For designing the matrix; D The correlation matrix between design points;

[0085] And due to The unknown, further derived from the above formula, yields:

[0086] ;

[0087] Assumption Satisfying no-information prior, i.e. The constant can be further obtained:

[0088] ;

[0089] ;

[0090] ;

[0091] in, Let Variance be the variance.

[0092] Using the formula for the multivariate normal distribution, we can further derive... The posterior distribution:

[0093] ;

[0094] in, For process variance; It follows a multivariate normal distribution, with its mean vector and covariance matrix as follows: and .

[0095] Will Substituting the mean, we get:

[0096] ;

[0097] ;

[0098] in, for The mean.

[0099] In one embodiment, the mean squared error of the single data source evaluation model is calculated according to the following formula:

[0100] ;

[0101] in, To evaluate the mean squared error of the model for a single data source. and For training data; For process variance, It is estimated by the generalized least squares method; The input for the model is The single data source is used to evaluate the model response value; The input for the model is The single data source is used to evaluate the model response estimate; For design points and The correlation vectors between them reflect the sample information; To design the matrix, , For regression basis functions; D To design the correlation matrix between points, ; for The regression basis function vector at the location; This indicates the deviation between the regression model and the relevant vector.

[0102] It is evident that MSE can reflect the response relationship and also contains information about the test sample points, thus possessing information completeness.

[0103] In one embodiment, the equivalence measure of the digital simulation test and the equivalence measure of the actual test are calculated according to the following formula:

[0104] ;

[0105] Where ET is the equivalent measure; To ensure the credibility of the experiment, it reflects the authenticity of the digital simulation test and the actual test method.

[0106] It should be noted that the equivalent measure of the digital simulation test and the equivalent measure of the actual test are both calculated using this formula. When calculating the equivalent measure of the digital simulation test, the test confidence is the preset digital simulation test confidence. When calculating the equivalent measure of the actual test, the test confidence is the preset actual test confidence.

[0107] In this embodiment, experimental credibility and MSE are combined to design an equivalent measure, which comprehensively considers experimental credibility and MSE, thereby realizing a scientific and quantitative equivalent conversion of physical test samples to digital simulation test samples.

[0108] In one embodiment, the confidence level of the preset practical test is set. The preset credibility of the digital simulation experiment is 1. , , n This represents the sample size. Follow n The value increases with increasing sample size and asymptotically approaches 1, indicating that the larger the sample size, the greater the contribution to accuracy. This is related to experimental reliability. After multiplication, ET will asymptotically approach... , equivalent to The credibility of the corresponding type of experiment. And it is understandable that even if the number of digital simulation experiment samples is infinite, its ultimate credibility cannot exceed the inherent credibility of its model itself.

[0109] Construct equivalent models of real-world experiments with different experimental samples and different confidence levels:

[0110] ;

[0111] in, Represents the equivalent measure of digital simulation experiments; Represents the equivalent measure of the actual test; The sample size for the digital simulation experiment; This refers to the sample size of the actual test. For model test data; Sample information for digital simulation experiments; This is sample information from the actual test.

[0112] In one embodiment, the data construction and evaluation model of the experimental data fusion is as follows:

[0113] ;

[0114] in, The response value of the evaluation model is determined by the fusion of experimental data; The response estimate of the model is used to evaluate the data from the digital simulation test. This is the scaling factor; It is a Gaussian random process.

[0115] The mean is zero, and the covariance is:

[0116] ;

[0117] in, For process variance; It is a spatial correlation function that depends on the two experimental points. , The distance between them.

[0118] In one embodiment, for the obtained sample space data of the actual test setup The corresponding response is The predicted values ​​of the data fusion evaluation model for the experimental data are:

[0119] ;

[0120] in, The predicted values ​​are from the data fusion evaluation model of the experimental data.

[0121] The mean square error of the evaluation model based on the fusion of numerical and experimental data is calculated using the following formula:

[0122] ;

[0123] in, The mean square error of the evaluation model for the fusion of experimental data; For containing elements The relevant vectors, To provide spatial data for actual experimental samples, This refers to the i-th experimental factor in the actual experimental sample space data; H For containing elements The correlation matrix; This is a vector composed of the predicted values ​​of the digital simulation test data evaluation model at the actual sample location; For the actual test sample space data The corresponding response value.

[0124] In one embodiment, The calculation is performed using the Gaussian correlation function:

[0125] ;

[0126] in, It is the Gaussian correlation function; For unknown related parameters; kThe value ranges from 1 to m , corresponding to the first dimension to the second dimension of the input space m Dimension, used to iterate through all dimensions of the factor.

[0127] In the data fusion evaluation model of numerical and real experiments Training can be performed by maximizing the likelihood function:

[0128] ;

[0129] in, .

[0130] In one embodiment, step 205, which involves equivalently converting the sample size of the actual experiment to the sample size of the digital simulation experiment based on the equivalent composite confidence interval of the actual experiment and the equivalent composite confidence interval of the digital simulation experiment, includes:

[0131] The required sample size to find the theoretical value on the equivalent composite confidence interval of the practical experiment. Corresponding experimental equivalent measure value and .

[0132] Search within the equivalent composite confidence interval of the digital simulation experiment and The corresponding sample size of the digital simulation experiment, of which, The sample size of the equivalent measure of the upper quartile curve in the equivalent composite confidence interval of the corresponding digital simulation experiment is: The sample size for the equivalent measure of the lower quartile curve is ; The sample size of the equivalent measure of the upper quartile curve in the equivalent composite confidence interval of the corresponding digital simulation experiment is: The sample size for the equivalent measure of the lower quartile curve is .

[0133] Take respectively and as well as and Mean:

[0134] ;

[0135] ;

[0136] in, for and The mean; for and The mean; Round the result up.

[0137] Pick and The mean of the sample size is used as the equivalent digital simulation sample size of the actual test sample size.

[0138] It is important to note that and .

[0139] In this embodiment, by simultaneously utilizing the upper and lower quartile curves of the equivalent measure to construct a composite confidence interval, the statistical distribution characteristics of the equivalent measure are fully considered. A sample-weighted average is adopted to integrate information from different quartiles, making the conversion result more representative.

[0140] In one embodiment, the method for equivalent conversion of equipment test sample size further includes:

[0141] Preprocessing is performed on digital simulation test data and actual test data.

[0142] Based on the preprocessed data, a multi-factor fusion method was used to calculate the initial... value.

[0143] Setting the nonlinearity of experimental factor data based on preprocessed data Value optimization boundary.

[0144] Specifically, data preprocessing includes processing experimental samples. Normalization and output response Standardization:

[0145] ;

[0146] in, The mean of the test response data, The variance of the test response data.

[0147] Based on the preprocessed data, an intelligent initialization method using multi-factor fusion is employed to calculate the initial... value:

[0148] ;

[0149] in, , , These are the weighting coefficients. Based on experience, set to This is to emphasize the impact of the relevance and scope of the experimental data. For the initial value; , , These are obtained by considering three statistical characteristics of the data: factor data range, factor response correlation, and data variability.

[0150] for , , Specifically, it is obtained using the following method:

[0151] for The initialization is obtained based on the data range of the test samples. Value. Test sample. X have m There are 1 factor, and the range of data variation for each factor is... Due to the fact that each factor The value is inversely proportional to the data range of the factor, that is... To avoid data ranging from 0, set when season Furthermore, to ensure it remains on a reasonable order of magnitude, Normalization to interval get :

[0152] ;

[0153] in, By all The vector formed by these vectors.

[0154] for The setting is based on the correlation strength between factors and responses in each sample. For the first j Each factor is used to calculate its relationship with the response. y correlation coefficient :

[0155] .

[0156] Based on the absolute value of the correlation coefficient, a piecewise function is used to determine... value:

[0157] ;

[0158] For factors that are strongly correlated with the response, assign a smaller value. A higher value is assigned to factors that are less correlated, allowing the model to capture the more complex effects of that factor; for factors with weak correlations, a higher value is assigned. The value is adjusted to make the model smoother in that factor direction.

[0159] for Values ​​are initialized based on the coefficient of variation (CV) of each sample. The coefficient of variation is defined as the ratio of the standard deviation of each factor to the absolute value of the mean.

[0160] ;

[0161] in, They are the first j The mean and standard deviation of each factor are used. If the mean is zero, the standard deviation is used directly as a measure of variability. Then, the variance is calculated based on the magnitude of the coefficient of variation. Set to three levels:

[0162] ;

[0163] Factors with large coefficients of variation indicate relatively large fluctuations, thus requiring more complex (smaller) models. ) to capture its changes; conversely, variables with small coefficients of variation are captured using larger coefficients. The value makes it smoother in the model.

[0164] Will Constrained to Inside:

[0165] .

[0166] The nonlinearity of the experimental factor data based on the data was set. Value optimization boundary, specifically, dynamically designing based on the factor data complexity estimation results in the experimental samples. Value optimization boundaries (upper and lower bounds). Factor data complexity is calculated by evaluating the nonlinearity of the factor data. To estimate, specifically, a linear model is used to fit the data, and the ratio of the mean squared error to the output variance is calculated:

[0167] ;

[0168] Based on nonlinear error The size of the algorithm divides the complexity into three levels and adjusts them adaptively. The lower and upper bounds are shown in Table 1 below:

[0169] Table 1. Complexity Corresponding to Boundary table

[0170]

[0171] To verify the effectiveness of the method described in this invention, the fitted model was used to calculate the predicted values, and the root mean square error (NRMSE) and coefficient of determination (R²) were calculated to evaluate the model quality. A value of 0.7 or NRMSE > 0.3 indicates poor model quality, triggering a re-initialization mechanism and using randomization. The values ​​were re-optimized.

[0172] The effectiveness of the proposed method is verified by using the following ternary continuous function as a case study in equipment testing.

[0173] ;

[0174] in, .

[0175] First, within the range of values, Latin hypercube sampling was used, with sample sizes of 10, 20, 30, 40, 50, and 60 respectively, to construct a single data source evaluation model. The prediction variance of the model was calculated, and the mean squared error surface of the constructed model was observed. Since there are three variables, they were fixed sequentially for visualization purposes. , and The value is the corresponding sample mean. From Figure 2 It can be seen that as the sample size increases, the corresponding MSE value gradually decreases.

[0176] To further verify the relationship between the equivalent measure ET and the sample size, multiple samplings were performed for each sample size to show the impact of different sample locations, and confidence levels were calculated for each. , This yields the relationship between the equivalent measure and the sample size, such as... Figure 3 (a) and Figure 3 As shown in (b). From Figure 3 As can be seen from the sample size n As the value increases, the equivalent measure value continuously increases, eventually converging to the confidence value. and In addition, sample size n Under the same conditions, different locations of experimental samples will affect the construction of the model, and the equivalent measure will also be different, with its value fluctuating within a certain range.

[0177] The following ternary continuous function is used as a numerical simulation example for equipment testing.

[0178] ;

[0179] from Figure 4 It can be seen that the functions of the two experimental data have similar trends but some differences.

[0180] Due to the limited number of actual samples in the live-fire experiment, 20 sample points were selected from the Latin hypercube sampling within the range for the live-fire experiment, and 120 sample points were selected for the digital simulation experiment. A single-source evaluation model for the digital simulation experiment and a data fusion evaluation model for the live-fire experiment were constructed respectively, and cross-validation was performed on the experimental samples. The results are shown in Table 1. As shown in the table, the constructed single-source evaluation model for the digital simulation experiment (i.e., the single-source evaluation model with digital simulation experiment data as input) and the data fusion evaluation model for the live-fire experiment both exhibit small mean absolute error (MAE) and root mean square error (RMSE) in their predicted responses, verifying the effectiveness of both models and demonstrating their ability to reflect the true responses of the simulation and live-fire experiments.

[0181] Table 2 Comparison of Experimental Data Evaluation Model Response Validation Results

[0182]

[0183] Take the sample size of the digital simulation test respectively Sample size of actual test Furthermore, each sample size was sampled 100 times to account for information differences caused by different sample point locations. Based on different sample sizes of the actual and digital simulation experiments, a data fusion evaluation model for the actual and digital experiments was constructed to obtain the mean square error (MSE) and equivalent composite confidence interval of the extended sample of the actual experiment. Figure 5 , Figure 6 As shown. Figure 5 , Figure 6 With the same sample size, both MSE and ET values ​​fluctuate within a certain range. As the sample size increases, MSE decreases and ET increases. Figure 6 The area formed by the upper and lower blue curves is the equivalent composite confidence interval.

[0184] When the live-fire samples do not undergo data fusion evaluation and modeling for both digital simulation and live-fire experiments, and both are calculated using a single data source evaluation model, equivalent composite confidence intervals for the sample sizes of the digital simulation and live-fire experiments are constructed respectively, as follows: Figure 7 As shown, when the actual sample size requiring equivalent conversion exceeds 20, the equivalent composite confidence interval of the actual experiment is empty, making it impossible to determine its equivalent measure range, and consequently, the equivalent digital simulation experiment sample size cannot be determined. Therefore, based on existing digital simulation experiment data and actual experiment data, we obtain... Figure 8 A schematic diagram illustrating the equivalent sample size reduction over the equivalent composite confidence interval. Setting the confidence value for the digital simulation experiment. Set the reliability of the actual test. When an equivalent sample size for a live test is required. At that time, the equivalent composite confidence interval corresponds to the upper quartile curve. Aand lower quartile curve B Points, respectively, corresponding to the equivalent indicators of the actual test. and Equivalent index On the equivalent composite confidence interval of the corresponding digital simulation sample and (The sample size values ​​in the calculations below are all rounded up from the decimal point.) The corresponding digital simulation sample size is calculated as follows: , The equivalent digital simulation test sample size was calculated at this time. Similarly, On the equivalent composite confidence interval of the corresponding digital simulation sample and The corresponding digital simulation sample size is calculated as follows: , The equivalent digital simulation test sample size was calculated at this time. Ultimately, a practical test can be obtained. The equivalent sample size of each sample is: .

[0185] It should be understood that, although Figure 1 The steps in the flowchart are shown sequentially as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified in this document, there is no strict order in which these steps are executed, and they can be performed in other orders. Figure 1 At least some of the steps in the process may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily executed at the same time, but may be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but may be executed in turn or alternately with other steps or at least some of the sub-steps or stages of other steps.

[0186] In one embodiment, such as Figure 9 As shown, an equivalent reduction system for equipment test sample size is provided, comprising:

[0187] The fusion model construction module 901 is used to acquire data and construct a fusion evaluation model of digital and real experimental data based on the data. The data includes digital simulation test sample space data and actual test sample space data.

[0188] The actual data expansion module 902 is used to calculate the predicted value of the actual experimental data fusion evaluation model by taking the data repeatedly sampled multiple times with different sample sizes in the actual experimental factor space as input, and to use the actual experimental factor space data sampled each time and the corresponding predicted value to form the expanded actual experimental data; and to use the data repeatedly sampled multiple times with different sample sizes in the digital simulation experimental sample space as the digital simulation experimental data.

[0189] The mean squared error calculation module 903 is used to construct a single data source evaluation model and calculate the mean squared error of the single data source evaluation model.

[0190] The simulation test calculation module 904 is used to evaluate the mean square error of the model and the preset digital simulation test credibility based on a single data source with digital simulation test data corresponding to different sample sizes as input, calculate the equivalent measure of the digital simulation test, and draw box plots of the equivalent measure of the digital simulation test with different sample sizes.

[0191] The experimental calculation module 905 is used to evaluate the mean square error of the model and the preset experimental confidence level based on the expanded experimental data corresponding to different sample sizes from a single data source, calculate the equivalent measure of the experimental test, and draw the equivalent measure of the experimental test and box plots of different sample sizes.

[0192] The equivalent composite confidence interval plotting module 906 is used to obtain box plots of equivalent measures of actual experiments and equivalent measures of digital simulation experiments corresponding to different sample sizes. For each obtained box plot, the lower quartile and the upper quartile are connected to plot the equivalent composite confidence intervals of actual experiments and equivalent composite confidence intervals of digital simulation experiments.

[0193] The equivalent conversion module 907 is used to convert the sample size of the actual test, which is theoretically required but exceeds the actual supply capacity, into the sample size of the digital simulation test based on the equivalent composite confidence interval of the actual test and the equivalent composite confidence interval of the digital simulation test.

[0194] Specific limitations regarding the equivalent conversion system for equipment test sample sizes can be found in the limitations on the equivalent conversion method for equipment test sample sizes described above, and will not be repeated here. Each module in the aforementioned equivalent conversion system for equipment test sample sizes can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device, or stored in the memory of a computer device as software, so that the processor can call and execute the corresponding operations of each module.

[0195] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0196] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.

Claims

1. A method for equivalent conversion of equipment test sample size, characterized in that, Includes the following steps: Acquire data and construct a data fusion evaluation model based on the data, wherein the data includes digital simulation test sample space data and actual test sample space data; Using data from repeated sampling with different sample sizes within the actual experimental factor space as input, the predicted value of the fusion evaluation model of the actual experimental data is calculated. The actual experimental factor space data from each sampling and the corresponding predicted value constitute the expanded actual experimental data. The data from repeated sampling with different sample sizes within the digital simulation experimental sample space is used as the digital simulation experimental data. Construct a single data source evaluation model and calculate the mean squared error of the single data source evaluation model; The mean square error of the evaluation model is evaluated based on the digital simulation test data with different sample sizes as input. The confidence level of the digital simulation test is preset, the equivalent measure of the digital simulation test is calculated, and the equivalent measure of the digital simulation test and the box plot of different sample sizes are plotted. The mean square error of the evaluation model and the preset reliability of the actual test are evaluated based on the expanded experimental data corresponding to different sample sizes of the single data source. The equivalent measure of the actual test is calculated, and the equivalent measure of the actual test and the box plot of different sample sizes are drawn. The equivalent measure of the digital simulation test and the equivalent measure of the actual test are calculated according to the following formula: Where ET is the equivalent measure; To ensure the credibility of the experiment; To evaluate the mean squared error of the model for a single data source. and For training data; Obtain box plots of the equivalent measures of the actual test and the equivalent measures of the digital simulation test for different sample sizes. For each box plot obtained, connect the lower quartile and the upper quartile to draw the equivalent composite confidence interval of the actual test and the equivalent composite confidence interval of the digital simulation test. Based on the equivalent composite confidence interval of the actual test and the equivalent composite confidence interval of the digital simulation test, the sample size of the actual test that is theoretically required but exceeds the actual supply capacity is equivalently converted into the sample size of the digital simulation test.

2. The method for equivalent conversion of equipment test sample size according to claim 1, characterized in that, The single data source evaluation model is as follows: in, Evaluate the model response value for a single data source; The residual term has a mean of 0 and a variance of . Gaussian process; A vector of unknown mean parameters; It is a vector of mean functions; Input for the model.

3. The method for equivalent conversion of equipment test sample size according to claim 2, characterized in that, The mean squared error of the single data source evaluation model is calculated according to the following formula: in, To evaluate the mean squared error of the model for a single data source. and For training data; For process variance; The input for the model is The single data source is used to evaluate the model response value; The input for the model is The single data source is used to evaluate the model response estimate; For design points and The correlation vector between them; For designing the matrix; D The correlation matrix between design points; for The regression basis function vector at that point.

4. The method for equivalent conversion of equipment test sample size according to claim 1, characterized in that, The data is used to construct a data fusion and evaluation model for experimental data: in, The response value of the evaluation model is determined by the fusion of experimental data; The response estimate of the model is used to evaluate the data from the digital simulation test. This is the scaling factor; It is a Gaussian random process.

5. The method for equivalent conversion of equipment test sample size according to claim 4, characterized in that, The predicted value of the data fusion evaluation model is calculated according to the following formula: in, The predicted values ​​are from the data fusion evaluation model of the experimental data. For containing elements The relevant vectors, For actual test data, This refers to the i-th experimental factor in the actual experimental data; H For containing elements The correlation matrix; This is a vector composed of the predicted values ​​of the digital simulation test data evaluation model at the actual sample location; For actual test data The corresponding response value.

6. The method for equivalent conversion of equipment test sample size according to claim 1, characterized in that, The sample size of the actual experiment is equivalently converted to the sample size of the digital simulation experiment based on the equivalent composite confidence interval of the actual experiment and the equivalent composite confidence interval of the digital simulation experiment, including: The required sample size to find the theoretical value on the equivalent composite confidence interval of the practical experiment. Corresponding experimental equivalent measure value and ; Search within the equivalent composite confidence interval of the digital simulation experiment and The corresponding sample size of the digital simulation experiment, of which, The sample size of the equivalent measure of the upper quartile curve in the equivalent composite confidence interval of the corresponding digital simulation experiment is: The sample size for the equivalent measure of the lower quartile curve is ; The sample size of the equivalent measure of the upper quartile curve in the equivalent composite confidence interval of the corresponding digital simulation experiment is: The sample size for the equivalent measure of the lower quartile curve is ; Take respectively and as well as and Mean: in, for and The mean; for and The mean; Round the result up; Pick and The mean was used as the sample size for the actual test. Equivalent reduced digital simulation test sample size.

7. The method for equivalent conversion of equipment test sample size according to claim 5, characterized in that, The The calculation is performed using the Gaussian correlation function: in, The Gaussian correlation function is... This is the experimental point; For unknown related parameters; k The value ranges from 1 to m , corresponding to the first dimension to the second dimension of the input space m Dimension, used to iterate through all dimensions of the factor.

8. The method for equivalent conversion of equipment test sample size according to claim 7, characterized in that, The method further includes: The digital simulation test data and the actual test data are preprocessed; Based on the preprocessed data, a multi-factor fusion method was used to calculate the initial... value; Setting the nonlinearity of experimental factor data based on preprocessed data Value optimization boundary.

9. A system for equivalent conversion of equipment test sample size, characterized in that, include: The fusion model construction module is used to acquire data and construct a fusion evaluation model of digital simulation test data based on the data. The data includes digital simulation test sample space data and actual test sample space data. The actual data expansion module is used to calculate the predicted value of the actual experimental data fusion evaluation model by taking the data repeatedly sampled multiple times with different sample sizes in the actual experimental factor space as input, and to form the expanded actual experimental data with the actual experimental factor space data sampled each time and the corresponding predicted value. Digital simulation test data are data obtained by repeatedly sampling different sample sizes within the sample space of a digital simulation test. The mean squared error calculation module is used to construct a single data source evaluation model and calculate the mean squared error of the single data source evaluation model. The simulation test calculation module is used to evaluate the mean square error of the model and the preset digital simulation test credibility based on a single data source with digital simulation test data corresponding to different sample sizes as input, calculate the equivalent measure of the digital simulation test, and draw box plots of the equivalent measure of the digital simulation test with different sample sizes. The experimental setup calculation module is used to evaluate the mean square error of the model and the preset experimental setup confidence level based on a single data source with expanded experimental setup data corresponding to different sample sizes as input, calculate the equivalent measure of the experimental setup, and draw box plots of the equivalent measure of the experimental setup with different sample sizes. The equivalent measure of the digital simulation test and the equivalent measure of the actual test are calculated according to the following formula: Where ET is the equivalent measure; To ensure the credibility of the experiment; To evaluate the mean squared error of the model for a single data source. and For training data; The equivalent composite confidence interval plotting module is used to obtain box plots of equivalent measures of actual experiments and equivalent measures of digital simulation experiments for different sample sizes. For each obtained box plot, the lower quartile and the upper quartile are connected to plot the equivalent composite confidence intervals of actual experiments and equivalent composite confidence intervals of digital simulation experiments. The equivalent conversion module is used to convert the sample size of the actual test, which is theoretically required but exceeds the actual supply capacity, into the sample size of the digital simulation test based on the equivalent composite confidence interval of the actual test and the equivalent composite confidence interval of the digital simulation test.

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