SGEMP damage probability evaluation method and system under small sample constraint

Abstract

The application provides a small sample constraint SGEMP damage probability evaluation method and system, adopts probability characteristics to evaluate the damage of SGEMP to a satellite electronic system, and obtains the damage probability of SGEMP to the satellite electronic system; is more consistent with the randomness of an actual SGEMP source and a space electromagnetic field, and the accuracy of evaluation is improved. The damage evaluation method firstly obtains the probability density function of sample data through parameter estimation; for sample data of a known probability distribution type, the confidence interval of unknown parameters in the probability density function is obtained by adopting an interval estimation method; for sample data of an unknown probability distribution type, multi-parameter optimization is adopted for estimation to obtain the probability density function; and then damage probability calculation is performed. The method can solve the practical problems of lack of a large amount of data in actual engineering application, and can avoid a large amount of tests to reduce the cost.

Description

Technical Field

[0001] This invention relates to a damage probability assessment method and system, specifically to a method and system for assessing the damage probability of a satellite electronic system to a system electromagnetic pulse (SGEMP), belonging to the field of electromagnetic damage technology. Background Technology

[0002] System electromagnetic pulse (SGEMP) is an effect distinct from other electromagnetic environments. Because its effects cannot be suppressed or reduced using traditional electromagnetic shielding methods for high-power microwaves and electromagnetic pulses, it has gained increasing attention and research in recent years. Given the mechanisms of SGEMP generation, its damage to spacecraft is a key focus of SGEMP research.

[0003] Studying the damage caused by SGEMP to satellite electronic systems is a key focus of SGEMP technology development, and practical research involves determining the extent of damage through experiments. However, on the one hand, due to the randomness of space electromagnetic fields and electromagnetic environment effects, as well as the randomness of SGEMP sources, the actual damage caused by SGEMP to satellite electronic systems is not a deterministic value, but rather exhibits probabilistic characteristics. Using deterministic methods cannot accurately assess the damage characteristics of SGEMP to satellite electronic systems; generally, deterministic numerical assessments are only valid for experimental results on the current object. On the other hand, limited by the small sample size of satellite equipment (generally considered to be less than 100 samples), it is difficult to obtain a sufficient number of samples to determine the probability of SGEMP damage to satellite electronic systems. Therefore, determining the probability is a probabilistic determination method under small sample constraints. Finally, since SGEMP is a relatively new research subject, there is currently a lack of sufficiently relevant probability distribution types for its electromagnetic damage probability to electronic systems.

[0004] Therefore, determining the probability of damage under small sample constraints requires not only solving the parameter estimation problem, but also developing a hypothesis testing method suitable for such constraints. These are issues that current damage assessment methods cannot address. Summary of the Invention

[0005] In view of this, the present invention provides a method for assessing the SGEMP damage probability under small sample constraints. The method uses probabilistic characteristics to assess the damage of SGEMP to satellite electronic systems and obtains the damage probability of SGEMP to satellite electronic systems. This method is more consistent with the randomness of actual SGEMP sources and space electromagnetic fields, thus improving the accuracy of the assessment.

[0006] The technical solution of this invention is: a SGEMP damage probability assessment method under small sample constraints, the steps of which are:

[0007] Step 1: Obtain the probability density function of the sample data through parameter estimation;

[0008] For sample data with a known probability distribution type, the confidence interval of the unknown parameter in the probability density function is obtained by using the interval estimation method;

[0009] For sample data with unknown probability distribution types, multi-parameter optimization is used to estimate its probability density function;

[0010] Step 2: Calculation of damage probability

[0011] The formula for calculating the probability of damage to satellite electronic systems by SGEMP is as follows:

[0012]

[0013] Where: P D denoted as , where p(x) is the probability density function of the sample data obtained in step one; and xl and xu are the lower and upper limits of the range of values ​​for the SGEMP damage assessment parameter x to the satellite electronics system, respectively.

[0014] As a preferred embodiment of the present invention: in step one:

[0015] For sample data with a known probability distribution type, the process of obtaining the confidence interval of the unknown parameter in the probability density function using interval estimation is as follows:

[0016] 201: Set the confidence level α based on the accuracy required for the assessment, with the confidence level between 0 and 1;

[0017] 202: Let the number of sample data be n, and the sample data be x′1, x′2, ..., x′ n Its probability density function is P. The confidence intervals (a, b) of the unknown parameters in the probability density function are obtained by solving the following equations:

[0018] P[a <Q(x′1,x′2,…,x′ 12 ;θ) <b]=1-α

[0019] Where: θ is the unknown parameter to be estimated, Q(x′1,x′2,…,x′) n ;θ) is a random variable;

[0020] Substituting the confidence intervals of each unknown parameter into the probability density function yields the interval of the probability density function.

[0021] As a preferred embodiment of the present invention: after obtaining the confidence intervals of each unknown parameter, the maximum likelihood estimate of each unknown parameter in its corresponding confidence interval is substituted into the probability density function to obtain a definite probability density function.

[0022] As a preferred embodiment of the present invention: in step one:

[0023] For sample data with unknown probability distribution types, the process of estimating its probability density function using multi-parameter optimization is as follows:

[0024] 211: Arrange the sample data in ascending order to obtain the order statistic. Let the i-th data in the order statistic be x. i (i = 1, 2, ..., n);

[0025] 212: Reliability R(x) of estimating the i-th sample data using the order statistic i ):

[0026]

[0027] 213: Calculate the probability distribution F(x) of the sample data:

[0028] F(x) = 1 - R(x)

[0029] in

[0030] 214: Perform a logarithmic transformation on F(x):

[0031]

[0032] Where: γ is the position parameter, α is the shape parameter, and m is the scale parameter;

[0033] 215: Perform variable substitution to establish a linear relationship:

[0034] Y = mX + b

[0035]

[0036] Where: Y is the output of the linear transformation, X is the input, and b is the coefficient; let the elements in Y be y i ,

[0037] 216: Perform parameter optimization; given step size t and N, where the choice of N must ensure that the following correlation coefficient ρ exhibits its maximum value, let:

[0038] X i =x i -tk(k=1,2,…,N)

[0039] Calculate the correlation coefficient ρ between X and Y, and determine the location parameter γ:

[0040]

[0041] Therefore, the position parameters are determined.

[0042] 217: The least squares method is used to obtain estimates of the shape parameter α and the scale parameter m:

[0043]

[0044]

[0045] 218: Determine the probability density function p(x) for the sample data:

[0046] The probability density function p(x) of the sample data is:

[0047]

[0048] As a preferred embodiment of the present invention: before performing parameter estimation and obtaining the probability density function of the sample data, preliminary statistical analysis is performed on the sample data to preliminarily determine whether the sample data is sample data of a known probability type.

[0049] As a preferred embodiment of the present invention: before calculating the damage probability, the probability density function obtained in step one is first checked to verify the correctness of the probability density function.

[0050] As a preferred embodiment of the present invention, the process of verifying the probability density function obtained in step one is as follows:

[0051] 301: Arranging the sample data in ascending order yields: x (1) ≤x (2) ≤…≤x (n) ;

[0052] 302: Find the empirical distribution function F n (x):

[0053]

[0054] Among them, v i For sample data x∈[x (i) ,x (i+1) The frequency of ] and ∑v i =n;

[0055] 303: Calculate the test statistic A 2 :

[0056]

[0057] Where F(x) i The probability distribution function is obtained by integrating the probability density function p(x).

[0058] 304: Perform parameter correction: If the number of evaluation data samples > 50, then use A 2 Used as a test parameter; otherwise, the parameter is corrected according to the table below to obtain the correction value A. *2 Then with A *2 As a test parameter;

[0059] If the sample data is normally distributed, then

[0060] If the sample data is log-normally distributed, then

[0061] If the sample data follows a gamma distribution Where m is the scale parameter;

[0062] If the sample data follows a Weibull distribution, then

[0063] If the sample data follows an exponential distribution, then

[0064] 304: Define hypothesis testing criteria:

[0065] If the sample size is ≤10, the criterion value range is [3.5, 4.0];

[0066] If the sample size is greater than 10 and less than or equal to 50, then the criterion value range is [2.2, 2.6].

[0067] If the sample size is greater than 50, the criterion value range is [1.5, 2.1].

[0068] 305: Determine whether the test parameter is within the range of the criterion values. If it is, the test is considered passed, and the damage probability is calculated. If it is not, the test is not passed, and the parameter estimation is performed again.

[0069] Furthermore, this invention also provides a SGEMP damage probability assessment system under small sample constraints, comprising: a parameter estimation module and a probability calculation module; sample data can be called as a global variable in each module;

[0070] The parameter estimation module obtains the probability density function p(x) of the sample data through parameter estimation; and then passes the probability density function p(x) to the probability calculation module.

[0071] In the parameter estimation module, the parameter estimation method is selected first:

[0072] For sample data with a known probability distribution type, the confidence interval of the unknown parameter in the probability density function is obtained by interval estimation; for sample data with an unknown probability distribution type, multi-parameter optimization is used to estimate and obtain its probability density function.

[0073] The probability calculation module is configured with an upper limit xl and a lower limit xu corresponding to the probability to be calculated. The probability calculation module calculates the probability according to the set formula. The probability of damage P within this interval D Perform the calculation.

[0074] As a preferred embodiment of the present invention, it further includes a data processing module;

[0075] Once the system is started, the data processing module is executed first. The data processing module reads sample data, sets the interval numbers, and draws a histogram. After the data processing module completes its task, the parameter estimation module is activated.

[0076] As a preferred embodiment of the present invention, it further includes a hypothesis testing module; after the parameter estimation module completes, the probability density function is first passed to the hypothesis testing module, and the hypothesis testing module is activated at the same time, and the correctness of the probability density function is verified by the hypothesis testing module; only when the hypothesis test passes, the probability density function is passed to the probability calculation module, and the probability calculation module is activated at the same time; otherwise, the parameter estimation module is fed back to re-evaluate the parameters.

[0077] Beneficial effects:

[0078] (1) This invention proposes an evaluation method based on actual sample data to address the damage of new electromagnetic environmental effects such as SGEMP to satellite electronic systems. This method can determine the probability of damage to satellite electronic systems by SGEMP, providing a means of capability and effect evaluation for the research and engineering application of SGEMP technology, as well as a data evaluation method for satellite protection against SGEMP.

[0079] (2) The method of the present invention is designed for small sample constraints of actual sample data, which can solve the practical problem of lack of a large amount of data in actual engineering applications, and avoid conducting a large number of experiments, thereby reducing costs.

[0080] (3) The present invention uses probabilistic characteristics to assess the damage of SGEMP to satellite electronic systems, which is more consistent with the randomness of actual SGEMP sources and space electromagnetic fields, improves the accuracy of assessment, and avoids the problem that the numerical assessment is only valid for the current test results.

[0081] (4) In terms of parameter estimation, this invention designs a multi-parameter optimization method for estimation, which can be used when there is insufficient understanding of the object being evaluated and it is not appropriate to use a known probability distribution type. By determining the probability distribution type through multi-parameter optimization, the evaluation accuracy can be improved. This can solve the problem of not being able to predict the probability distribution type due to insufficient understanding of the SGEMP effect, improve the accuracy of parameter estimation, and is more in line with the current level of understanding of the SGEMP effect.

[0082] (5) In terms of hypothesis testing, this invention proposes hypothesis testing methods, parameter correction methods and criteria for small sample constraints, which can solve the problem that current construction testing is mainly oriented towards large samples and is not suitable for small sample hypothesis testing, and is more suitable for hypothesis testing under small sample constraints. Attached Figure Description

[0083] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0084] Figure 1 This is a flowchart of the damage assessment method of the present invention;

[0085] Figure 2 The statistical histogram drawn in Example 1;

[0086] Figure 3 This is a flowchart of the parameter estimation steps in Example 1;

[0087] Figure 4 This is a flowchart of the multi-parameter optimization estimation step in Example 1;

[0088] Figure 5 This is a flowchart of the hypothesis testing process. Detailed Implementation

[0089] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0090] The embodiments described herein are for illustrative purposes only, but are not limited to, the present invention. To provide the public with a better understanding of the invention, the following description includes specific details.

[0091] Example 1:

[0092] This embodiment provides a method for assessing the probability of damage to satellite electronic systems by SGEMP under small sample constraints. This method can calculate the probability of damage under small sample conditions to solve the problem of assessing the damage of satellite electronic systems by SGEMP. It can be applied to the research on SGEMP systems and technologies, and can also provide a reference for satellite protection and system configuration against SGEMP.

[0093] In terms of parameter estimation, this method employs two approaches: interval estimation using known probability distributions and multi-parameter optimization estimation. In terms of hypothesis testing, it designs testing methods under small sample constraints, as well as parameter correction methods and criteria.

[0094] The following section describes a damage assessment based on experimental results composed of 12 sample data points (sample data of a specific parameter of the satellite electronics system, such as voltage or current, which are random numbers). This method is used to determine the probability of SGEMP damaging this parameter in the satellite electronics system. Figure 1 As shown:

[0095] Step 1: Preliminary Statistical Analysis

[0096] Preliminary analysis involves creating histograms to conduct preliminary statistical analysis of the sample data, aiming to understand its distribution range. This preliminary statistical analysis can help determine whether the sample data falls under a known probability category. The process is as follows:

[0097] 101: Determine the number of intervals. The number of intervals should not be less than 0. In this example, the number of intervals is determined to be 5, that is, the 12 sample data are divided into 5 intervals.

[0098] 102: Draw a statistical histogram of 12 sample data based on the determined interval numbers, such as... Figure 2 As shown, there are 3 sample data in the first interval, 5 sample data in the second interval, 1 sample data in the third interval, and 3 sample data in the fifth interval.

[0099] Step 2: Parameter estimation to obtain the probability density function of the sample data.

[0100] like Figure 3 As shown, parameter estimation is divided into two cases:

[0101] For sample data with a known probability distribution type (preliminarily determined through the preliminary statistical analysis in step one), the confidence interval of the unknown parameter in the probability density function is obtained using interval estimation (for small sample data, the unknown parameter cannot be estimated using general methods to estimate a definite number; instead, a confidence interval of the unknown parameter is obtained). The process is as follows:

[0102] 201: Set the confidence level α based on the accuracy required for the assessment. The confidence level is between 0 and 1. In this example, the assessment requirement is 95% accuracy. Based on this, the confidence level α is set to 95%.

[0103] 202: In this example, the probability distribution of the sample data is known to be a log-normal distribution (for a normal distribution, parameter estimation is to estimate the expectation and variance; given the expectation and variance, and knowing that it is a normal distribution, the probability density function can be obtained). Let the 12 sample data be x′1, x′2…x′ 12 If its probability density function is P, then the confidence intervals (a, b) for the expectation and variance can be obtained by solving the following equations:

[0104] P[a <Q(x′1,x′2,…,x′ 12 ;θ) <b]=1-α

[0105] Where: θ is the unknown parameter to be estimated; in this example, the unknown parameters to be estimated are the expectation and variance of a normal distribution; Q(x′1,x′2,…,x′) 12 ;θ) is a random variable.

[0106] For the expectation and variance, an interval is estimated respectively; in this example, the confidence interval for the expectation is (0.1722, 0.1935) and the confidence interval for the variance is (86.1335, 90.0217).

[0107] After obtaining the interval estimates (i.e., confidence intervals) of the expectation and variance, the maximum likelihood estimates for each interval can be used for subsequent calculations (i.e., substituting the maximum likelihood estimates of the expectation and variance in their respective intervals into the probability density function of the log-normal distribution to determine the probability density function). Alternatively, the upper and lower limits of the interval estimates can be used for calculation. In this case, the probability density function of the sample data is also an interval range. If this method is used, the final probability assessment result will be an interval range.

[0108] If it is initially determined that the sample data simultaneously conforms to multiple probability distribution types, one or more probability distribution types can be selected for parameter estimation to obtain the confidence intervals of the unknown parameters of each probability density function. If multiple probability distribution types are selected simultaneously, the parameter estimation results of each probability distribution type are calculated separately, that is, the confidence intervals of the unknown parameters under different probability distribution types are obtained, and thus different probability density functions (or probability density function intervals) are obtained.

[0109] For sample data with an unknown probability distribution (i.e., whose probability distribution type cannot be determined through the preliminary statistical analysis in step one), multi-parameter optimization is used to estimate and obtain its probability density function, such as... Figure 4 As shown, the process is as follows:

[0110] 211: Arrange the sample data in ascending order to obtain the order statistic. Let the i-th data in the order statistic be x. i (i = 1, 2, ..., n), in this example n = 12;

[0111] 212: Reliability R(x) of estimating the i-th sample data using the order statistic i ):

[0112]

[0113] 213: Calculate the probability distribution F(x) of the sample data:

[0114] F(x) = 1 - R(x)

[0115] in

[0116] 214: Perform a logarithmic transformation on F(x):

[0117]

[0118] Where: γ is the position parameter, α is the shape parameter, and m is the scale parameter;

[0119] 215: Perform variable substitution to establish a linear relationship:

[0120] Y = mX + b

[0121]

[0122] Where: Y is the output of the linear transformation, X is the input, and b is the coefficient; let the elements in Y be y i ,

[0123] 216: Perform parameter optimization; given a step size t and a sufficiently large value N (the choice of N must ensure that the correlation coefficient ρ exhibits its maximum value, i.e., a peak value appears), let:

[0124] X i =x i -tk(k=1,2,…,N)

[0125] Calculate the correlation coefficient ρ between X and Y, and determine the location parameter γ:

[0126]

[0127] The above formula means that when the correlation coefficient ρ exhibits its maximum value ρ max When k is at this time, k is taken as k′ for the position parameter estimation value. The calculation is performed; and then the position parameters are determined accordingly.

[0128] 217: The least squares method is used to obtain estimates of the shape parameter α and the scale parameter m:

[0129]

[0130]

[0131] In this example, the shape parameter α calculated using the above formula is 4.30; the scale parameter m is 1.45.

[0132] 218: Determine the probability density function p(x) for the sample data:

[0133] The probability density function p(x) of the sample data is:

[0134]

[0135] Substituting the calculated location, shape, and scale parameters into the probability density function of the sample data, we obtain:

[0136]

[0137] Step 3: Hypothesis testing (used to verify whether the probability density function of the sample data obtained in Step 2 is correct), such as... Figure 5 As shown, the process is as follows:

[0138] 301: Evaluation data sorting:

[0139] Arranging the sample data in ascending order yields: x (1) ≤x (2) ≤…≤x (n) .

[0140] 302: Find the empirical distribution function F n (x):

[0141]

[0142] Among them, v i For sample data x∈[x (i) ,x (i+1) The frequency of ] and ∑v i =n;v i This can be intuitively obtained through the histogram in step 1.

[0143] 303: Calculate the test statistic A 2 :

[0144]

[0145] Where F(x)i ) is the probability distribution function obtained by integrating the probability density function p(x).

[0146] 304: Perform parameter correction: If the number of evaluation data samples > 50, then use A 2 Used as a test parameter; otherwise, the parameter is corrected according to the table below to obtain the correction value A. *2 Then with A *2 As a test parameter.

[0147]

[0148]

[0149] 304: Define hypothesis testing criteria:

[0150] If the sample size is ≤10, the criterion value range is [3.5, 4.0];

[0151] If the sample size is greater than 10 and less than or equal to 50, then the criterion value range is [2.2, 2.6].

[0152] If the number of samples is greater than 50, the criterion value range is [1.5, 2.1].

[0153] 305: Determine whether the test parameter is within the range of the criterion values. If it is, the test is considered passed, and the next step of probability calculation is performed. If it is not, the test is not passed, and parameter estimation needs to be performed again, i.e., return to step two.

[0154] If multiple probability distributions can all pass the hypothesis test, the probability distribution with the smallest test parameter should be selected for subsequent calculations.

[0155] Step 4: Calculation of damage probability

[0156] Once the probability density function of the sample data is determined, and p(x) is used as the damage probability density function, the damage probability of SGEMP to the satellite electronics system can be calculated using the following formula:

[0157]

[0158] Where: P D denoted as SGEMP, representing the probability of damage to the satellite's electronic system; xl and xu are the lower and upper limits of the range of values ​​for the SGEMP damage assessment parameter x, respectively. xl and xu are given values, usually determined based on the characteristics of the assessment object and the test results.

[0159] In this example, assuming the damage assessment parameter x takes values ​​in the range of [17, +∞], the calculated probability of SGEMP damaging the satellite electronics system is 5.04%.

[0160] Example 2:

[0161] This embodiment provides a SGEMP damage probability determination system under small sample constraints. The system includes: a data processing module, a parameter estimation module, a hypothesis testing module, and a probability calculation module; the four modules are performed in a serial process; the evaluation sample data is used as a global variable and can be called in each module.

[0162] The modules described above can be implemented using general-purpose computing devices. They can be centralized on a single computing device or distributed across a network of multiple computing devices. Optionally, they can be implemented using computer-executable program code, thereby enabling them to be stored in a storage device for execution by the computing device. Alternatively, they can be fabricated as individual integrated circuit modules, or multiple modules or steps can be fabricated as a single integrated circuit module.

[0163] The following sections will introduce each module in the system.

[0164] Once the system starts, the data processing module is executed first. The data processing module reads the evaluation data, sets the interval numbers, and draws a histogram (which will be displayed by a display module).

[0165] After the data processing module completes its task, the parameter estimation module is activated.

[0166] In the parameter estimation module, the parameter estimation method is selected first. If the known probability type is selected for interval estimation, the preset probability type is activated, the corresponding probability type is selected, the confidence level is set, and interval estimation is performed. If the multi-parameter optimization method is selected for parameter estimation, the corresponding multi-parameter optimization estimation processing interface is activated, and parameter estimation is performed.

[0167] After the parameter estimation is completed, select the estimated probability distribution type and parameters to be tested for hypothesis testing, and pass them to the hypothesis testing module, which will then be activated.

[0168] In the hypothesis testing module, select the probability distribution to be tested. The probability distribution type and probability parameters are passed from the data selected in the previous parameter estimation step. After selection, the system automatically matches the test parameter correction amount and criteria based on the sample data and probability distribution type, and performs the hypothesis test.

[0169] Once the hypothesis test passes, select the probability distribution type for which you want to calculate the probability, pass it to the probability calculation module, and activate the probability calculation module.

[0170] In the probability calculation module, set the upper and lower limits of the values ​​corresponding to the probability to be calculated, and calculate the damage probability within the range of that interval.

[0171] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A SGEMP damage probability assessment method under small sample constraints, characterized in that, Includes the following steps: Step 1: Obtain the probability density function of the sample data through parameter estimation; For sample data with a known probability distribution type, the confidence interval of the unknown parameter in the probability density function is obtained by using the interval estimation method; For sample data with unknown probability distribution types, multi-parameter optimization is used to estimate its probability density function; Step 2: Calculation of damage probability The formula for calculating the probability of damage to satellite electronic systems by SGEMP is as follows: in: The probability of SGEMP damaging satellite electronic systems; The probability density function of the sample data obtained in step one; and These are the SGEMP parameters for assessing damage to satellite electronic systems. The lower and upper limits of the value range; In step one: For sample data with a known probability distribution type, the process of obtaining the confidence interval of the unknown parameter in the probability density function using interval estimation is as follows: 201: Set the confidence level according to the accuracy required for the assessment. The confidence level is between 0 and 1; 202: Let the number of sample data be n, and the sample data be as follows: Its probability density function is P. The confidence intervals of the unknown parameters in the probability density function can be obtained by solving the following equations. : in: For the unknown parameters to be estimated, It is a random variable; Substituting the confidence intervals of each unknown parameter into the probability density function yields the interval of the probability density function. In step one: For sample data with unknown probability distribution types, the process of estimating its probability density function using multi-parameter optimization is as follows: 211: Arrange the sample data in ascending order to obtain the order statistic. Let the i-th data in the order statistic be... ,in ; 212: Reliability of estimating the i-th sample data using order statistics : 213: Calculate the probability distribution of the sample data : in , ; 214: Yes Perform a logarithmic transformation: in: For position parameters, For shape parameters, For scale parameters; 215: Perform variable substitution to establish a linear relationship: in: The output is the linear transformation relationship. For input, Let be the coefficient; The elements in are , 216: Perform parameter optimization; given a step size and ,in The selection of [value] must ensure the following correlation coefficients. To exhibit the maximum value, let: in calculate and correlation coefficient Determine position parameters : Therefore, the position parameters are determined. ; 217: Obtaining shape parameters using the least squares method and scale parameters The estimated value: 218: Determine the probability density function of the sample data : probability density function of sample data for: 。 2. The SGEMP damage probability assessment method under small sample constraints as described in claim 1, characterized in that: After obtaining the confidence intervals of each unknown parameter, the maximum likelihood estimate of each unknown parameter in its corresponding confidence interval is substituted into the probability density function to obtain the definite probability density function.

3. The SGEMP damage probability assessment method under small sample constraints as described in claim 1 or 2, characterized in that: Before performing parameter estimation and obtaining the probability density function of the sample data, a preliminary statistical analysis is conducted on the sample data to preliminarily determine whether the sample data is of a known probability type.

4. The SGEMP damage probability assessment method under small sample constraints as described in claim 1 or 2, characterized in that: Before calculating the probability of damage, the probability density function obtained in step one is first checked to verify its correctness.

5. The SGEMP damage probability assessment method under small sample constraints as described in claim 4, characterized in that: The process of testing the probability density function obtained in step one is as follows: 301: Arranging the sample data in ascending order yields: ; 302: Find the empirical distribution function : in, For sample data The frequency of, and ; 303: Calculate the test statistic : in For probability density function The probability distribution function obtained by integration; 304: Perform parameter correction: If the number of evaluation data samples > 50, then... Used as a test parameter; otherwise, the parameter is corrected according to the table below to obtain the correction value. , and then with As a test parameter; If the sample data is normally distributed, then ; If the sample data is log-normally distributed, then ; If the sample data follows a gamma distribution ,in For scale parameters; If the sample data follows a Weibull distribution, then ; If the sample data follows an exponential distribution, then ; 304: Define hypothesis testing criteria: If the sample size is ≤10, the criterion value range is [3.5, 4.0]; If the sample size is greater than 10 and less than or equal to 50, then the criterion value range is [2.2, 2.6]. If the sample size is greater than 50, the criterion value range is [1.5, 2.1]. 305: Determine whether the test parameter is within the range of the criterion values. If it is, the test is considered passed, and the damage probability is calculated. If it is not, the test is not passed, and the parameter estimation is performed again.

6. A SGEMP damage probability assessment system under small sample constraints, characterized in that, include: The module includes parameter estimation and probability calculation; sample data is used as a global variable and can be accessed in various modules. The parameter estimation module obtains the probability density function of the sample data through parameter estimation. ; and the probability density function Passed to the probability calculation module; In the parameter estimation module, the parameter estimation method is selected first: For sample data with a known probability distribution type, the confidence interval of the unknown parameter in the probability density function is obtained by interval estimation; for sample data with an unknown probability distribution type, multi-parameter optimization is used to estimate and obtain its probability density function. The probability calculation module is set with an upper limit on the value corresponding to the probability to be calculated. and lower limit The probability calculation module is based on a set formula. The probability of damage within the interval range Perform the calculation.

7. The SGEMP damage probability assessment system under small sample constraints as described in claim 6, characterized in that, It also includes a data processing module; Once the system is started, the data processing module is executed first. The data processing module reads sample data, sets the interval numbers, and draws a histogram. After the data processing module completes its task, the parameter estimation module is activated.

8. The SGEMP damage probability assessment system under small sample constraints as described in claim 6 or 7, characterized in that, It also includes a hypothesis testing module; after the parameter estimation module completes, it first passes the probability density function to the hypothesis testing module and activates the hypothesis testing module to verify the correctness of the probability density function; only when the hypothesis test passes will the probability density function be passed to the probability calculation module and the probability calculation module be activated; otherwise, it will feed back to the parameter estimation module to re-evaluate the parameters.

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