A method for determining the minimum static performance of aircraft engine structural parts

Abstract

The present application provides a method for determining the minimum value of the static performance of an aircraft engine structural component, including: step 1, determining a representation method for the minimum value of the static performance to ensure that a valid minimum value of the static performance of the aircraft engine structural component is obtained, and selecting the lower quantile value of the static performance probability distribution to represent the minimum value of the static performance; step 2, calculating the minimum value of the static performance of the aircraft engine structural component, including: 2.1) confirming the test data used to obtain the static performance of the structural component to ensure that the data source is no less than a predetermined batch; according to the confidence and reliability requirements, confirming that the test pieces used to obtain the static performance of the structural component meet the minimum sample quantity requirements; 2.2) using the maximum normed residual method to check and confirm abnormal data, and the test data that cannot pass the inspection is regarded as abnormal data and eliminated; 2.3) static performance probability distribution curve fitting based on Wilbull distribution, normal distribution, and lognormal distribution, parameter estimation, and minimum value calculation.

Description

Technical Field

[0001] The present application belongs to the technical field of aero-engine structural design, and in particular relates to a method for determining the minimum value of static performance of aero-engine structural parts. Background Art

[0002] The Outline for Structural Integrity of Aero-engines clearly stipulates that the minimum mechanical properties of structural component materials should be used in structural strength design. However, in actual engineering practice, the specific minimum mechanical properties are generally determined directly by drawing on foreign experience. During acceptance, approximately five specimens are selected based on experience for testing. If the lowest mechanical property among the five specimens meets the requirements, the performance is considered to meet the standard; otherwise, it is considered to be substandard. The minimum value determined based on experience is generally conservative, resulting in conservative design, which does not meet the current demand for high performance and high thrust-to-weight ratio, and cannot truly reflect the dispersion of the static performance of the material. Due to the lack of theoretical basis for determining the minimum value, there have been cases in engine model development where the minimum value acceptance was passed, but development failures occurred due to the large dispersion of material properties. Therefore, a method is needed to scientifically and reasonably determine the minimum value of the mechanical properties of structural component materials. Summary of the Invention

[0003] The purpose of this application is to provide a method for determining the minimum static performance of an aircraft engine structural component to solve or alleviate at least one problem in the background technology.

[0004] The technical solution of the present application is: a method for determining the minimum value of static performance of an aircraft engine structural component, the method comprising:

[0005] Step 1: Determine a method for representing the minimum static performance value to ensure that a valid minimum static performance value of the aircraft engine structural component is obtained, wherein the confidence lower limit of the parent percentile value of the static performance is selected to represent the minimum static performance value;

[0006] Step 2: Calculation of minimum static performance of aircraft engine structural components, including:

[0007] 2.1) Confirm the test data used to obtain the static performance of structural parts, ensuring that the data source is no less than the predetermined batch; confirm that the test pieces used to obtain the static performance of structural parts meet the minimum sample quantity requirements based on the confidence and reliability requirements of the parent percentile value;

[0008] 2.2) The maximum normed residual method is used to check and confirm abnormal data. Test data that cannot pass the check are considered abnormal data and eliminated;

[0009] 2.3) First, a Wilbull distribution static performance probability distribution is fitted and parameters are estimated to obtain a Wilbull distribution static performance probability distribution curve. Then, a goodness-of-fit test of the Wilbull distribution static performance probability distribution is performed. If the goodness-of-fit test passes, the minimum static performance value of the structural component is determined based on the Weibull distribution.

[0010] If it fails, the normal distribution is used to fit the static performance probability distribution curve, and then the normal distribution goodness of fit hypothesis test is performed. If it passes, the minimum static performance value of the structural component is determined based on the normal distribution;

[0011] If it fails, the log-normal distribution is used to fit the static performance probability distribution curve, and then the log-normal distribution goodness of fit hypothesis test is performed. If it passes, the minimum static performance of the structural component is calculated based on the log-normal distribution. If it fails, the test sample size is increased and the calculation is repeated according to the above steps.

[0012] Furthermore, the minimum requirement for the sample size n is:

[0013] Where 1-γ represents the significance level, and p represents the failure probability.

[0014] Furthermore, the process of checking and confirming abnormal data using the maximum normed residual method includes:

[0015] Let x1,x2,...,x n is a sample from population X, then the observation x i The corresponding normed residual value is:

[0016]

[0017] Where, is the sample mean, S is the corrected sample standard deviation, and n is the sample size.

[0018] The sample mean and adjusted sample standard deviation are:

[0019]

[0020] The maximum normed residual statistic MNR is: MNR = max{|r i |}, i=1,2,…,n

[0021] The critical value C of the maximum normed residual is: Where, t α is the 1-α / (2n) quantile of the t distribution with n-2 degrees of freedom; α is the significance level;

[0022] When the maximum normed residual statistic MNR is less than the critical value C, the confidence level 1-α is used to believe that there is no abnormal data in the sample; otherwise, the confidence level 1-α is used to believe that the x corresponding to the maximum normed residual statistic MNR is i For abnormal data.

[0023] Furthermore, the process of fitting the static performance probability distribution of the Wilbull distribution and estimating its parameters to obtain the static performance probability distribution curve of the Wilbull distribution includes:

[0024] Assume that the sample (x1, x2, ... x n ) obeys the three-parameter Weibull distribution and is arranged in ascending order. The probability density function f(x) and cumulative distribution function F(x) of the three-parameter Weibull distribution are expressed as follows:

[0025] Where β, η, and γ are the shape parameter, scale parameter, and location parameter of the three-parameter Weibull distribution, respectively, satisfying γ<x1, β>0, η>0.

[0026] First, transform the cumulative distribution function F(x) of the Weibull distribution, and let:

[0027] Y=ln(-ln(1-F(x))), X=ln(x-γ), B=lnη β

[0028] Then the cumulative distribution function F(x) is transformed into a linear equation: Y = βX-B

[0029] The sample data (x i ,F(x i ))Convert to (X i ,Y i ), calculate the correlation coefficient between X and Y:

[0030]

[0031] To find the best estimate of the parameter γ is actually to find the value of γ when the correlation coefficient R(X,Y) is the largest; according to the maximum value method, we only need to find the first-order derivative of the correlation coefficient R(X,Y) with respect to γ, set it to zero, and solve the equation to get the best location parameter estimate; for the three-parameter Weibull distribution, R(X,Y) is always greater than 0, so finding the first-order derivative of R(X,Y) with respect to γ ​​is the same as finding R 2 The first-order derivative of (X, Y) with respect to γ ​​is equivalent. To simplify the formula, we choose to calculate R 2 The first-order derivative of (X, Y) with respect to the parameter γ gives the following transcendental equation:

[0032]

[0033] Where,

[0034] The parameter γ is solved by the bisection method, and finally the shape parameter and scale parameter are obtained by the least square fitting formula, and finally the static performance probability distribution curve of the Wilbu distribution can be obtained.

[0035] Furthermore, the Anderson-Darling method is used to test the goodness of fit of the Wilbull distribution probability distribution of static performance. The process includes:

[0036] The sample distribution function and the sample empirical distribution function are represented by F(x) and F n (x) means that, assuming that the samples x1, x2,…, x n Coming from the same distribution matrix and with the distribution function F(x,θ), where θ is the parameter vector of the distribution function, the quadratic Anderson-Darling distance is as follows:

[0037]

[0038] The Anderson-Darling test method determines whether to accept or reject the distribution hypothesis at the corresponding confidence level by comparing AD with the critical value of each distribution family at the corresponding significance level α;

[0039] Assume that the sample (x1, x2, ... x n ) is a sample from a particular distribution, and its order statistic is x (1) ,x (2) ,…,x (n) , F(x) is a continuous distribution function, let F(x) = F0(x), F0(x) takes three-parameter Weibull distribution, normal distribution or lognormal distribution respectively;

[0040] Anderson-Darling distribution goodness-of-fit test statistic AD is:

[0041]

[0042] The critical value of the Anderson-Darling distribution goodness-of-fit test statistic is:

[0043]

[0044] Where, the critical value of continuous distribution test is Obtained by looking up the table.

[0045] Furthermore, the process of determining the minimum value of the static performance of the structural component based on the Weibull distribution includes:

[0046] According to the definition of minimum value representation, take the one-sided lower confidence limit, and the corresponding median rank formula is:

[0047]

[0048] Where, F 0.05 [2(n-i+1),2i] is the 0.05 quantile of the F distribution with 2(n-i+1),2i degrees of freedom;

[0049] Use the above formula to replace the middle rank formula in the parameter estimation method of the three-parameter Weibull distribution, and use the corresponding method to estimate the parameter γ l , β l and η l , and then we get the one-sided lower confidence limit curve of the parent distribution under the confidence level:

[0050] The inverse function of the one-sided confidence lower limit curve is used to obtain the value of the given confidence level and the given reliability level. According to the given minimum reliability probability R, when the calculation is performed according to the three-parameter Weibull distribution, the calculation formula for the minimum value of the static performance is:

[0051] Furthermore, the process of fitting the static performance probability distribution curve using normal distribution includes:

[0052] The probability density function of the normal distribution is:

[0053]

[0054] In the formula, μ and σ are the population mean and population standard deviation, respectively, and are the parameters to be estimated;

[0055] Assume that the samples x1, x2, ... x n From the population X~N(μ,σ 2 ), the sample mean and sample corrected standard deviation are:

[0056] Obtaining the sample mean and sample corrected standard deviation means obtaining the estimated values ​​of the parent mean and standard deviation of the normal distribution population, completing the static performance probability distribution curve fitting.

[0057] Furthermore, the calculation process of the minimum value of the structural static performance based on the normal distribution includes:

[0058] Let the samples x1,x2,...,x n From the normal distribution N(μ,σ) with unknown parameters of the parent distribution 2 ). Given the reliability R, the population percentile value x P The estimate of is: Population percentile x P This is the minimum value of static performance;

[0059] Where β is the sample standard deviation S x The correction factor,

[0060] Sample mean and the sample standard deviation S x They are:

[0061] The expression of the one-sided tolerance coefficient k with respect to the sample size is:

[0062] Where u p is the lower quantile of a given reliability, u γ is the lower quantile for a given confidence level.

[0063] Furthermore, the calculation process of the minimum value of the structural static performance based on the lognormal distribution is the same as the calculation process of the minimum value of the structural static performance based on the normal distribution, and the logarithm of the sample is taken during the calculation.

[0064] The method of this application integrates statistical theory with engineering experience to systematically and normatively establish a method for characterizing, obtaining, and statistically processing the minimum value of the static performance of structural parts. It standardizes the current status of determining and accepting and evaluating the minimum value of the static performance of structural parts, avoiding the problem of conservative design due to low minimum values ​​in structural design. At the same time, the minimum value calculation method based on statistical theory can more effectively characterize the dispersion of the static performance of materials, avoiding structural strength failures during research and development due to insufficient dispersion control and affecting research and development progress. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] In order to more clearly illustrate the technical solutions provided by this application, the following is a brief introduction to the accompanying drawings. Obviously, the accompanying drawings described below are only some embodiments of this application.

[0066] Figure 1 Schematic diagram of a probability distribution curve of static performance according to an embodiment of the present application.

[0067] Figure 2 Schematic diagram of the process for determining the minimum static performance of structural material in this application. DETAILED DESCRIPTION

[0068] In order to make the purpose, technical solutions and advantages of the implementation of this application clearer, the technical solutions in the embodiments of this application will be described in more detail below in conjunction with the drawings in the embodiments of this application.

[0069] like Figure 1As shown, the method for determining the minimum static performance of an aircraft engine structural component provided in this application includes the following steps:

[0070] Step 1: First, determine the representation method of the minimum static performance value to ensure that the effective minimum static performance value of the aircraft engine structural parts is obtained.

[0071] In order to meet the requirements of probabilistic reliability design, the lower confidence limit of the static performance matrix percentile value is selected in this application to represent the lowest value of static performance, such as Figure 1 shown.

[0072] Therefore, to ensure the credibility of the test results, a confidence level requirement is introduced. The confidence level represents the degree of credibility of a single test and is related to the sample size n. Therefore, the lowest value of the static performance is determined as the lower quantile value of the probability distribution of the static performance with a given reliability at a given confidence level.

[0073] The corresponding minimum reliability probability and confidence requirements are as follows:

[0074] 1) Take the lower quantile value of the static performance probability distribution. The probability of the lower quantile is determined based on the risk analysis of potential failures caused by the static performance of the structure and the minimum probability requirements of the hazard analysis. If both requirements are met, the one with the higher probability value is selected.

[0075] Table 1 shows the specific basis for determining the minimum reliability probability requirement based on criticality analysis in one embodiment of the present application.

[0076] Table 1 Minimum reliability probability requirements based on criticality analysis

[0077]

[0078]

[0079] 2) The introduction of confidence level puts forward requirements for the test sample size. The sample size n used to determine the minimum value of static performance should satisfy the following relationship:

[0080]

[0081] Where 1-γ represents the significance level, and p represents the failure probability (p=1-R). In the aviation field, the confidence level γ is generally selected to be no less than 95%.

[0082] Step 2: Calculation of minimum static performance of aircraft engine structural parts

[0083] In order to fully characterize the statistical characteristics of static performance and select the best distribution fit, the process and calculation method for determining the minimum value of static performance of structural material according to test data and characterization method are as follows: Figure 2As shown, the process includes: data requirement confirmation, abnormal data inspection and confirmation, static performance probability distribution fitting and parameter estimation and minimum benchmark value calculation.

[0084] 2.1) Confirmation of data requirements

[0085] Confirm the test data used to obtain the static properties of structural parts, and ensure that the data comes from no less than 3 furnaces and 3 batches.

[0086] According to the confidence and reliability requirements, confirm that the test pieces used to obtain the static performance of structural parts meet the minimum sample quantity requirements determined by Formula 1.

[0087] 2.2) Abnormal data inspection and confirmation

[0088] The maximum normed residual method is used to check and confirm abnormal data, and those that fail the check are considered abnormal data and eliminated.

[0089] The maximum normed residual method assumes that all sample data, except for outliers, are drawn from a normal distribution. When the absolute deviation of an observation from the sample mean differs significantly from the sample standard deviation, the maximum normed residual method identifies that observation as an outlier. The maximum normed residual method can only detect one outlier at a time and is suitable for determining individual data points. However, it is possible to develop an application that can detect all outliers in one step.

[0090] Let x1, x2, ..., x n is a sample from the population X, then the observation x i The corresponding normed residual value is:

[0091]

[0092] Where, is the sample mean, S is the corrected sample standard deviation, and n is the sample size.

[0093] The sample mean and adjusted sample standard deviation are:

[0094]

[0095]

[0096] The maximum normed residual statistic MNR is:

[0097] MNR=max{|r i |},i=1,2,…,n(5)

[0098] The critical value C of the maximum normed residual is:

[0099]

[0100] Where, t α It is the 1-α / (2n) quantile of the t distribution with n-2 degrees of freedom; α is the significance level, usually α=0.05.

[0101] When the maximum normed residual statistic MNR is less than the critical value C, the confidence level 1-α is used to believe that there is no abnormal data in the sample; otherwise, the confidence level 1-α is used to believe that the x corresponding to the maximum normed residual statistic MNR is i For abnormal data.

[0102] When the sample dispersion is large and the sample size is only 5-6 data, it is very likely that all the data will be judged as abnormal data when the maximum normed residual test method is used. After checking for abnormal data, it is analyzed to determine whether the detected abnormal data is indeed abnormal data.

[0103] 2.3) Static performance probability distribution fitting and parameter estimation of three-parameter Weibull distribution

[0104] The correlation coefficient optimization method is used to fit the probability distribution of static performance of Weibull distribution and estimate its parameters. The process includes:

[0105] Assume that the sample (x1, x2, ... x n ) obeys the three-parameter Weibull distribution and is arranged in ascending order. The probability density function f(x) and cumulative distribution function F(x) of the three-parameter Weibull distribution are expressed as:

[0106]

[0107]

[0108] Where β, η, and γ are the shape parameter, scale parameter, and location parameter of the three-parameter Weibull distribution, respectively, satisfying γ<x1, β>0, η>0.

[0109] First, make appropriate transformations on the cumulative distribution function F(x) of the Weibull distribution, and let:

[0110] Y=ln(-ln(1-F(x))), X=ln(x-γ), B=lnη β

[0111] It can be transformed into a linear equation: Y = βX-B (9)

[0112] The sample data (x i ,F(x i ))Convert to (X i ,Y i ), calculate the correlation coefficient R(X,Y) between X and Y:

[0113]

[0114] To find the best estimate of the parameter γ is actually to find the value of γ when the correlation coefficient R(X,Y) is the largest. According to the maximum value method, we only need to find the first-order derivative of the correlation coefficient R(X,Y) with respect to γ, set it to zero, and solve the equation to get the best location parameter estimate. For the three-parameter Weibull distribution, R(X,Y) is always greater than 0, so finding the first-order derivative of R(X,Y) with respect to γ ​​is the same as finding R 2 The first-order derivative of (X, Y) with respect to γ ​​is equivalent. To simplify the formula, we choose to calculate R 2 The first-order derivative of (X, Y) with respect to the parameter γ gives the following transcendental equation:

[0115]

[0116] Where,

[0117] The parameter γ is solved by the bisection method, and finally the shape parameter and scale parameter are obtained by the least square fitting formula, and finally the static performance probability distribution curve of the Wilbu distribution can be obtained.

[0118] Wherein F(x) is the empirical distribution function, expressed as: F(x) = (i-0.3) / (n+0.4).

[0119] 2.4) Distribution fit goodness test

[0120] The Anderson-Darling method is used to test the goodness of fit of the Wilbull distribution. This method can also be used to test the goodness of fit of the normal distribution and lognormal distribution. The specific test method is as follows:

[0121] When the Anderson-Darling test is used for distribution fit goodness of fit, the quadratic Anderson-Darling distance between the sample distribution function (CDF) and the sample empirical distribution function (EDF) is used to determine whether the sample belongs to a specific distribution family. The sample distribution function and the sample empirical distribution function are represented by F(x) and F n (x) means that, assuming that the samples x1, x2,…, x n Coming from the same distribution matrix and with the distribution function F(x,θ), where θ is the parameter vector of the distribution function, the quadratic Anderson-Darling distance is as follows:

[0122]

[0123] The Anderson-Darling test method determines whether to accept or reject the distribution hypothesis at the corresponding confidence level by comparing AD with the critical values ​​of each distribution family at the corresponding significance level α. α is generally taken as 0.05.

[0124] Assume that the sample (x1, x2, ... x n ) is a sample from a particular distribution, and its order statistic is x (1) ,x (2) ,…,x (n) F(x) is a continuous distribution function. Let F(x) = F0(x). In this paper, F0(x) takes the three-parameter Weibull distribution, normal distribution, or lognormal distribution. The Anderson-Darling distribution goodness-of-fit test statistic AD is:

[0125]

[0126] The critical value of the Anderson-Darling distribution goodness-of-fit test statistic is:

[0127]

[0128] Where, the critical value of continuous distribution test is It can be found from Table 2.

[0129] Table 2 Critical values ​​of continuous distribution test at different confidence levels

[0130]

[0131] 2.5) Determination of the minimum static performance of structural components based on Weibull distribution

[0132] First, we perform parameter estimation and a goodness-of-fit test based on the sample following a three-parameter Weibull distribution. We then calculate the baseline value. We use the rank distribution to determine the three parameters of the lower confidence limit curve for the Weibull distribution. Then, we use the confidence limit curve to determine the value at a given reliability level.

[0133] According to the definition of minimum value representation, take the one-sided lower confidence limit, and the corresponding median rank formula is:

[0134]

[0135] Where, F 0.05 [2(n-i+1),2i] is the 0.05 quantile of the F distribution with 2(n-i+1),2i degrees of freedom.

[0136] Use the above formula to replace the middle rank formula in the parameter estimation method of the three-parameter Weibull distribution, and use the corresponding method to estimate γ l , β l and ηl Then we get the one-sided confidence lower limit curve of the parent distribution when the confidence level is 0.95:

[0137]

[0138] The inverse function of the one-sided confidence lower limit curve can be used to obtain the value of the given confidence level and the given reliability level. According to the minimum reliability probability requirement R determined in step 1, when calculated according to the three-parameter Weibull distribution, the calculation formula for the minimum static performance is:

[0139]

[0140] 2.6) Normal distribution / lognormal distribution fitting and parameter estimation

[0141] If the Anderson-Darling method is used in step 2.4 to perform the distribution fit goodness-of-fit test but fails, the normal distribution / lognormal distribution is used to fit the static performance probability distribution.

[0142] The probability density function of the normal distribution is:

[0143]

[0144] Where μ and σ are the population mean and population standard deviation, respectively, and are the parameters to be estimated.

[0145] Assume that the samples x1, x2, ... x n From the population X~N(μ,σ 2 ), the sample mean and sample corrected standard deviation are:

[0146]

[0147]

[0148] Obtaining the sample mean and sample-adjusted standard deviation gives us estimates of the population mean and standard deviation of the normal distribution. The calculation method for the lognormal distribution is the same, requiring only the logarithm of the random variable.

[0149] 2.7) Calculation of minimum static performance of structures based on normal distribution / lognormal distribution

[0150] Let the samples x1,x2,...,x n From the normal distribution N(μ,σ) with unknown parameters of the parent distribution 2 ). Given the reliability R, the population percentile value x P The estimate of is:

[0151]

[0152] Population percentile x P This is the minimum static performance.

[0153] Where β is the sample standard deviation S x The correction coefficient is calculated as follows:

[0154]

[0155] Sample mean and the sample standard deviation S x They are:

[0156]

[0157]

[0158] The expression of the one-sided tolerance coefficient k with respect to the sample size is as follows:

[0159]

[0160] Among them, u p is the lower quantile of a given reliability, u γ is the lower quantile for a given confidence level.

[0161] The method of this application integrates statistical theory with engineering experience to systematically and normatively establish a method for characterizing, obtaining, and statistically processing the minimum value of the static performance of structural parts. It standardizes the current status of determining and accepting and evaluating the minimum value of the static performance of structural parts, avoiding the problem of conservative design due to low minimum values ​​in structural design. At the same time, the minimum value calculation method based on statistical theory can more effectively characterize the dispersion of the static performance of materials, avoiding structural strength failures during research and development due to insufficient dispersion control, which affects the progress of research and development.

[0162] The above description is merely a specific embodiment of the present application, but the scope of protection of the present application is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in this application should be included in the scope of protection of the present application. Therefore, the scope of protection of the present application should be based on the scope of protection of the claims.

Claims

1. A method for determining the minimum static performance of an aircraft engine structural component, characterized in that: The method comprises: Step 1: Determine a method for representing the minimum static performance value to ensure that a valid minimum static performance value of the aircraft engine structural component is obtained, wherein the confidence lower limit of the parent percentile value of the static performance is selected to represent the minimum static performance value; Step 2: Calculation of minimum static performance of aircraft engine structural components, including: 2.1) Confirm the test data used to obtain the static performance of structural parts, ensuring that the data source is no less than the predetermined batch; confirm that the test pieces used to obtain the static performance of structural parts meet the minimum sample quantity requirements based on the confidence and reliability requirements of the parent percentile value; 2.2) The maximum normed residual method is used to check and confirm abnormal data. Test data that cannot pass the check are considered abnormal data and eliminated; 2.3) First, a Wilbull distribution static performance probability distribution is fitted and parameters are estimated to obtain a Wilbull distribution static performance probability distribution curve. Then, a goodness-of-fit test of the Wilbull distribution static performance probability distribution is performed. If the goodness-of-fit test passes, the minimum static performance value of the structural component is determined based on the Weibull distribution. If it fails, the normal distribution is used to fit the static performance probability distribution curve, and then the normal distribution goodness of fit hypothesis test is performed. If it passes, the minimum static performance value of the structural component is determined based on the normal distribution; If it fails, the log-normal distribution is used to fit the static performance probability distribution curve, and then the log-normal distribution goodness of fit hypothesis test is performed. If it passes, the minimum static performance of the structural component is calculated based on the log-normal distribution. If it fails, the test sample size is increased and the calculation is repeated according to the above steps.

2. The method for determining the minimum static performance of an aircraft engine structural component according to claim 1, wherein: The minimum requirement for the sample size n is: Where 1-γ represents the significance level, and p represents the failure probability.

3. The method for determining the minimum static performance of an aircraft engine structural component according to claim 1, wherein: The process of checking and confirming abnormal data using the maximum normed residual method includes: Let x1,x2,...,x n is a sample from the population X, then the observation x i The corresponding normed residual value is: Where, is the sample mean, S is the corrected sample standard deviation, and n is the sample size; The sample mean and adjusted sample standard deviation are: The maximum normed residual statistic MNR is: MNR = max{|r i |}, i=1,2,…,n The critical value C of the maximum normed residual is: Where, t α is the 1-α / (2n) quantile of the t distribution with n-2 degrees of freedom; α is the significance level; When the maximum normed residual statistic MNR is less than the critical value C, the confidence level 1-α is used to believe that there is no abnormal data in the sample; otherwise, the confidence level 1-α is used to believe that the x corresponding to the maximum normed residual statistic MNR is i For abnormal data.

4. The method for determining the minimum static performance of an aircraft engine structural component according to claim 3, wherein: The process of fitting the static performance probability distribution of the Wilbull distribution and estimating its parameters to obtain the static performance probability distribution curve of the Wilbull distribution includes: Assume that the sample (x1, x2, ... x n ) obeys the three-parameter Weibull distribution and is arranged in ascending order. The probability density function f(x) and cumulative distribution function F(x) of the three-parameter Weibull distribution are expressed as follows: Where β, η, and γ are the shape parameter, scale parameter, and location parameter of the three-parameter Weibull distribution, respectively, satisfying γ<x1, β>0, η>0; First, transform the cumulative distribution function F(x) of the Weibull distribution, and let: Y=ln(-ln(1-F(x))), X=ln(x-γ), B=lnη β Then the cumulative distribution function F(x) is transformed into a linear equation: Y = βX-B The sample data (x i ,F(x i ))Convert to (X i ,Y i ), calculate the correlation coefficient between X and Y: To find the best estimate of the parameter γ is actually to find the value of γ when the correlation coefficient R(X,Y) is the largest; according to the maximum value method, we only need to find the first-order derivative of the correlation coefficient R(X,Y) with respect to γ, set it to zero, and solve the equation to get the best location parameter estimate; for the three-parameter Weibull distribution, R(X,Y) is always greater than 0, so finding the first-order derivative of R(X,Y) with respect to γ ​​is the same as finding R 2 The first-order derivative of (X, Y) with respect to γ ​​is equivalent. To simplify the formula, we choose to calculate R 2 The first-order derivative of (X, Y) with respect to the parameter γ gives the following transcendental equation: Where, The parameter γ is solved by the bisection method, and finally the shape parameter and scale parameter are obtained by the least square fitting formula, and finally the static performance probability distribution curve of the Wilbu distribution can be obtained.

5. The method for determining the minimum static performance of an aircraft engine structural component according to claim 4, characterized in that: The Anderson-Darling method is used to test the goodness of fit of the Wilbull distribution probability distribution of static properties. The process includes: The sample distribution function and the sample empirical distribution function are represented by F(x) and F n (x) means that, assuming that the samples x1, x2,…, x n Coming from the same distribution matrix and with the distribution function F(x,θ), where θ is the parameter vector of the distribution function, the quadratic Anderson-Darling distance is as follows: The Anderson-Darling test method determines whether to accept or reject the distribution hypothesis at the corresponding confidence level by comparing AD with the critical value of each distribution family at the corresponding significance level α; Assume that the sample (x1, x2, ... x n ) is a sample from a particular distribution, and its order statistic is x (1) ,x (2) ,…,x (n) , F(x) is a continuous distribution function, let F(x) = F0(x), F0(x) takes three-parameter Weibull distribution, normal distribution or lognormal distribution respectively; Anderson-Darling distribution goodness-of-fit test statistic AD is: The critical value of the Anderson-Darling distribution goodness-of-fit test statistic is: Where, the critical value of continuous distribution test is Obtained by looking up the table.

6. The method for determining the minimum static performance of an aircraft engine structural component according to claim 5, characterized in that: The process of determining the minimum static performance of structural components based on Weibull distribution includes: According to the definition of minimum value representation, take the one-sided lower confidence limit, and the corresponding median rank formula is: Where, F 0.05 [2(n-i+1),2i] is the 0.05 quantile of the F distribution with 2(n-i+1),2i degrees of freedom; Use the above formula to replace the middle rank formula in the parameter estimation method of the three-parameter Weibull distribution, and use the corresponding method to estimate the parameter γ l , β l and η l , and then we get the one-sided lower confidence limit curve of the parent distribution under the confidence level: The inverse function of the one-sided confidence lower limit curve is used to obtain the value of the given confidence level and the given reliability level. According to the given minimum reliability probability R, when the calculation is performed according to the three-parameter Weibull distribution, the calculation formula for the minimum value of the static performance is:

7. The method for determining the minimum static performance of an aircraft engine structural component according to claim 6, characterized in that: The process of fitting the static performance probability distribution curve using normal distribution includes: The probability density function of the normal distribution is: In the formula, μ and σ are the population mean and population standard deviation, respectively, and are the parameters to be estimated; Assume that the samples x1, x2, ... x n From the population X~N(μ,σ 2 ), the sample mean and sample corrected standard deviation are: Obtaining the sample mean and sample corrected standard deviation means obtaining the estimated values ​​of the parent mean and standard deviation of the normal distribution population, completing the static performance probability distribution curve fitting.

8. The method for determining the minimum static performance of an aircraft engine structural component according to claim 7, characterized in that: The calculation process of the minimum value of structural static performance based on normal distribution includes: Let the samples x1,x2,...,x n From the normal distribution N(μ,σ) with unknown parameters of the parent distribution 2 ) a subsample; given the reliability R, the population percentile value x P The estimate of is: Population percentile x P This is the minimum value of static performance; Where β is the sample standard deviation S x The correction factor, Sample mean and the sample standard deviation S x They are: The expression of the one-sided tolerance coefficient k with respect to the sample size is: Where u p is the lower quantile of a given reliability, u γ is the lower quantile for a given confidence level.

9. The method for determining the minimum static performance of an aircraft engine structural component according to claim 8, characterized in that: The calculation process of the minimum value of the structural static performance based on the lognormal distribution is the same as that based on the normal distribution, and the logarithm of the sample is taken during the calculation.

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