An engine material design allowable value statistical processing method, device and medium

Abstract

This application discloses a statistical processing method, device, and medium for allowable design values ​​of engine materials, belonging to the field of material performance data processing and reliability statistics technology. The method uses the AD test for normality. If the data conforms to a normal distribution, the allowable design value is calculated using conventional methods. If the data does not conform, the cumulative distribution probability of the sample observations and the corresponding standard normal quantiles are determined; the data is truncated by 50%, retaining a subset of low-tailed data; linear regression is performed with quantiles as independent variables and observations as dependent variables to obtain the regression intercept and slope, and the goodness of fit is used as the model fit index; based on a non-central T-distribution, the lower limit coefficient of the one-sided tolerance is calculated according to the specified reliability, confidence level, and sample size; finally, the high-precision allowable design value is calculated using the regression intercept, slope, and this coefficient, effectively eliminating interference from high-tailed data and improving the reliability and lightweighting level of engine structural design.

Description

Technical Field

[0001] This invention relates to the field of material performance data processing and reliability statistics, and in particular to a method, equipment and medium for statistical processing of allowable design values ​​for engine materials. Background Technology

[0002] The allowable static performance design values ​​for engine materials are key parameters in aircraft and engine structural design, and are typically based on reliability. and confidence level The lower limit of tolerance is determined, among which commonly used methods are... and The values ​​(corresponding to reliability levels of 97.72% and 99.87%, respectively). Traditional methods rely on the assumption that the data follows a normal distribution, and calculate the mean by subtracting... The standard deviation is calculated using a "multiple standard deviation" method. However, in actual engineering, material property data often exhibit non-normal characteristics (such as high-tailed data with abnormally large or small dispersion). In such cases, traditional methods are prone to errors due to the standard deviation. Excessive influence from high-tailed data leads to a decrease in the calculated design allowable value. or The value deviates significantly from the true tolerance lower limit. This deviation directly affects the reliability and weight of the engine structural design, potentially leading to an overly conservative (weight increase) or risky (reduced reliability) structure, becoming a pressing statistical processing challenge that needs to be addressed.

[0003] Currently, the engine field generally adopts statistical processing methods based on the normal distribution of complete data, directly using the sample mean. and standard deviation Calculate the lower tolerance limit, i.e. , where the coefficient Based on reliability With confidence level Determined through classical statistical theory (such as the t-distribution). The principle of this method originates from the one-sided tolerance coefficient theory in statistics, which has been widely adopted in aviation standards. Its focus is on ensuring the accuracy of the calculations. , The values ​​have a high level of confidence and reliability under the assumption that the data are normally distributed.

[0004] Although the above-mentioned traditional methods are simple and have a clear theoretical basis, they have two significant drawbacks: Lower limit of tolerance for high-tailed data interference: When the data is not normally distributed, the standard deviation It is often greatly affected by high-tailed values ​​(outliers that are too large or too small), which makes the calculation results unable to truly reflect the low-tailed tolerance characteristics of performance, resulting in systematic bias in the statistical results; Lack of targeted modeling for low-tail data: Engine design focuses on the "low-tail" part of performance (i.e. the lower limit of performance related to safety design), but existing methods only include the overall data under the normality assumption and lack optimized statistical techniques specifically for low-tail data, resulting in unscientific reliability judgments.

[0005] In summary, traditional tolerance lower bound statistical methods based on the overall normal distribution are significantly unsuitable for non-normal datasets. Therefore, there is an urgent need to develop a new processing method that can specifically model the normality of low-tailed data and eliminate interference from high-tailed data, thereby enabling accurate calculation of engine material properties even when the data is non-normal. and This enhances the reliability of the structural design and its potential for lightweighting. Summary of the Invention

[0006] To address the shortcomings of existing technologies, the present invention aims to provide a method, device, and medium for statistical processing of allowable design values ​​for engine materials. This method, when data does not conform to a normal distribution, can significantly improve allowable design values ​​by focusing on low-tailed data related to the lower tolerance limit to construct a statistical model. and The accuracy of value calculations improves the reliability and lightweighting of engine structural design.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows: Firstly, a method for statistically processing allowable design values ​​for engine materials is provided, the method comprising: S1: The sample size is The data samples are arranged in ascending order to obtain ordered sample observations. ,in, Indicates the first Observations of a sample , is a natural number, representing the total number of data samples; S2: Perform an A / D test on the data sample to check whether the data sample conforms to a normal distribution. If it conforms to a normal distribution, then use conventional methods to calculate the allowable design values ​​of the static properties of the engine materials. and ; Furthermore, the normality AD test for the data sample described in S2 is specifically verified by calculating the AD statistic of the normality AD test for the data sample, the expression of which is:

[0008] In the formula, This represents the mean of the observed values ​​in the data sample. This represents the standard deviation of the observed values ​​in the data sample. The cumulative distribution function representing the standard normal distribution; As an intermediate variable; Furthermore, when the test statistic AD value is less than the critical threshold, the data is determined to conform to a normal distribution. In this case, the mean minus... Traditional method for calculating multiple standard deviations , value( For reliability and confidence level (The confidence lower limit coefficients are all relevant). Furthermore, the critical threshold is .

[0009] S3: If the data sample being tested does not conform to a normal distribution, then determine the cumulative probability distribution of each sample observation. And based on this, calculate the corresponding standard normal distribution quantiles. ; Furthermore, the cumulative probability distribution of each sample observation in S3. The calculation expression is,

[0010] In the formula, The unit is % This indicates the sequence number of the observation in the sorted data sample; when there are duplicate data points in the sample, the sequence number of the intermediate data is used for calculation. value.

[0011] Furthermore, the quantile The quantile corresponding to each cumulative probability value is calculated based on a standard normal distribution with a mean of 0 and a variance of 1.

[0012] S4: Perform proportional truncation on the data, removing a predetermined proportion of high-tailed sample observations and retaining low-tailed data to obtain a new sample size. A low-tailed subset of data; Furthermore, in S4, the data is truncated proportionally, removing a predetermined proportion of high-tailed sample observations and retaining low-tailed data. Specifically, the data is truncated by 50%, that is, the largest 50% of sample observations are removed, and the lowest 50% are retained as the low-tailed data subset.

[0013] S5: Based on each data point in the low-tailed data subset Construct a dataset and perform linear regression analysis on it to obtain the regression intercept. With slope ,in, , Indicates the first sub-data set in the low-tailed data set. Observations of a sample Indicates the first sub-data set in the low-tailed data set. quantiles corresponding to the observations of each sample, intercept The mean and slope of the normal distribution representing the low-tailed data constructed. Characterize its standard deviation; Furthermore, S5 also includes: Using least squares for low-tailed data subsets Linear regression was performed on the data points to obtain the regression equation. And calculate the goodness of fit. Among them, quantiles As an independent variable Sample observations As dependent variable .

[0014] S6: Based on the linear regression analysis results and the predetermined judgment criteria, determine the degree of fit between the low-tailed data and the constructed normal distribution model; Furthermore, in S6, the goodness of fit between the low-tailed data and the constructed normal distribution model is determined based on the linear regression analysis results and predetermined judgment criteria, using the goodness of fit as the criterion. As an indicator of consistency, when When the success rate is not less than 90%, the constructed low-tailed data normal distribution model is confirmed to be effective.

[0015] S7: Based on non-centralized Distribution, based on specified reliability With confidence level and the sample size of the low-tailed data subset. Calculate the lower limit coefficient of the one-sided tolerance. ; Furthermore, the calculation of the lower limit coefficient of the one-sided tolerance described in S7... The methods include: S701: Calculation and Reliability Confidence level and the reduced sample size Related one-sided tolerance factor ; S702: Calculate the standard normal distribution quantiles in the low-tailed data subset. mean and total square Among them, the total sum of squares The calculation expression is, ; S703: Calculate the skewness coefficient The expression is, In the formula, As an intermediate variable; S704: Based on confidence level Eccentricity parameter Degrees of freedom Non-center investigation Distribution quantile table or non-centrality obtained through calculation Values ​​of the lower quantile of the distribution Among them, the eccentricity parameter For the standard normal distribution at reliability The quantile value divided by the skewness coefficient Degrees of freedom ; S705: Calculation of the lower limit coefficient of unilateral tolerance The expression is, .

[0016] S8: Regression intercept obtained from S5 With slope And the lower limit coefficient of the one-sided tolerance calculated by S7. Through the expression: Calculate the allowable design values ​​for the static properties of engine materials. and .

[0017] Furthermore, in S8, the design allowable value for calculating the static properties of engine materials is... and middle, Value corresponds to reliability The confidence level is 97.72%. It is 95%; Value corresponds to reliability The confidence level is 99.87%. It is either 50% or 95%.

[0018] In a second aspect, a data processing device is provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the statistical processing method for allowable design values ​​of engine materials as described in the first aspect of the present invention.

[0019] Thirdly, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the method for statistical processing of allowable design values ​​for engine materials as described in the first aspect of the present invention.

[0020] Compared with the prior art, the present invention has the following significant advantages: 1. Highly targeted: This invention innovatively proposes to truncate the high-tail data by 50% and focus on the low-tail data, which plays a decisive role in the design of engine structural reliability, to perform normal distribution modeling, thus avoiding the abnormal influence of the dispersion of high-tail data on the standard deviation.

[0021] 2. High scientific rigor and reliability: It utilizes linear regression fitting and goodness-of-fit assessment, combined with non-center methods specifically designed for truncated samples. Distribution tolerance factor This makes the calculation more efficient when the original data does not conform to a normal distribution. and The values ​​are closer to the actual lower limit of material performance tolerance, significantly improving the scientific nature of statistical processing.

[0022] 3. High engineering practical value: The design allowable values ​​obtained by this method are more accurate, which helps to ensure the design reliability and safety margin of the engine structure, and can also provide a more optimized data basis for structural weight reduction design, thus combining safety and economy.

[0023] Other features and advantages of the invention will be set forth in the description which follows, and will be apparent in part from the description, or may be learned by practicing the invention. The objects and other advantages of the invention may be realized and obtained by means of the structures pointed out in the description, claims and drawings. Attached Figure Description

[0024] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0025] Figure 1 This is a schematic flowchart of a method for statistically processing allowable design values ​​for engine materials in one embodiment of the present invention; Figure 2 This is a schematic diagram of the normal distribution probability plot and the low-tailed 50% data fitting line in one embodiment of the present invention. Detailed Implementation

[0026] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0027] In one embodiment, please refer to Figure 1 A method for statistically processing allowable values ​​for engine material design is provided, the method comprising the following steps: Step S1: Set the sample size to... The data samples are arranged in ascending order to obtain ordered sample observations. ,in, Indicates the first Observations of a sample , is a natural number, representing the total number of data samples; Step S2: Perform an A / D test on the data sample to check whether the data sample conforms to a normal distribution. If it conforms to a normal distribution, calculate the allowable design values ​​of the static performance of the engine materials using conventional methods. and ; Step S3: If the data sample being tested does not conform to a normal distribution, then determine the cumulative probability distribution of each sample observation. And based on this, calculate the corresponding standard normal distribution quantiles. ; Step S4: Thrust the data proportionally, removing a predetermined proportion of high-tailed sample observations and retaining low-tailed data, resulting in a new sample size of [missing value]. A low-tailed subset of data; Step S5: Based on each data point in the low-tailed data subset... Construct a dataset and perform linear regression analysis on it to obtain the regression intercept. With slope ,in, , Indicates the first sub-data set in the low-tailed data set. Observations of a sample Indicates the first sub-data set in the low-tailed data set. quantiles corresponding to the observations of each sample, intercept The mean and slope of the normal distribution representing the low-tailed data constructed. Characterize its standard deviation; Step S6: Based on the linear regression analysis results and the predetermined judgment criteria, determine the degree of fit between the low-tailed data and the constructed normal distribution model; Step S7: Based on non-central Distribution, based on specified reliability With confidence level and the sample size of the low-tailed data subset. Calculate the lower limit coefficient of the one-sided tolerance. ; Step S8: Use the regression intercept obtained in S5 With slope And the lower limit coefficient of the one-sided tolerance calculated by S7. Through the expression: Calculate the allowable design values ​​for the static properties of engine materials. and .

[0028] Furthermore, in this embodiment, the normal distribution AD test performed on the data sample in step S2 is specifically verified by calculating the AD statistic of the normal distribution AD test of the data sample, the expression of which is:

[0029] In the formula, This represents the mean of the observed values ​​in the data sample. This represents the standard deviation of the observed values ​​in the data sample. The cumulative distribution function representing the standard normal distribution; As an intermediate variable; Furthermore, when the test statistic AD value is less than the critical threshold, the data is determined to conform to a normal distribution. In this case, the mean minus... Traditional method for calculating multiple standard deviations , value( For reliability and confidence level (The confidence lower limit coefficients are all relevant). Furthermore, the critical threshold is .

[0030] Furthermore, in this embodiment, the cumulative distribution probability of each sample observation in step S3 is... The calculation expression is,

[0031] In the formula, The unit is % This indicates the sequence number of the observation in the sorted data sample; when there are duplicate data points in the sample, the sequence number of the intermediate data is used for calculation. Values, for example: when the 3rd, 4th, and 5th data points in a sample are exactly the same, then the values ​​corresponding to these three data points... The value is always 4; if there are an even number of identical values ​​in the sample, the average of the two middle data indices is taken as the average of these values. value; The quantile It calculates the quantiles corresponding to each cumulative probability value based on a standard normal distribution with a mean of 0 and a variance of 1; for example: .

[0032] Furthermore, in this embodiment, the step S4 of truncating the data proportionally, removing a preset proportion of high-tailed sample observations and retaining low-tailed data, specifically involves truncating the data by 50%, that is, removing the largest 50% of sample observations and retaining the lowest 50% as a subset of low-tailed data.

[0033] Furthermore, in this embodiment, step S5 further includes: using the least squares method to process the low-tailed data subset. Linear regression was performed on the data points to obtain the regression equation. And calculate the goodness of fit. Among them, quantiles As an independent variable Sample observations As dependent variable .

[0034] Furthermore, in this embodiment, the step S6, which determines the goodness of fit between the low-tailed data and the constructed normal distribution model based on the linear regression analysis results and predetermined judgment criteria, is based on the goodness of fit. As an indicator of consistency, when When the success rate is not less than 90%, the constructed low-tailed data normal distribution model is confirmed to be effective.

[0035] Furthermore, in this embodiment, the calculation of the unilateral tolerance lower limit coefficient in step S7 is... The methods include: Step S701: Calculation and Reliability Confidence level and the reduced sample size Related one-sided tolerance factor ; Step S702: Calculate the standard normal distribution quantiles in the low-tailed data subset. mean and total square Among them, the total sum of squares The calculation expression is, ; Step S703: Calculate the skewness coefficient The expression is, In the formula, As an intermediate variable; Step S704: Based on confidence level Eccentricity parameter Degrees of freedom Non-center investigation Distribution quantile table or non-centrality obtained through calculation Values ​​of the lower quantile of the distribution Among them, the eccentricity parameter For the standard normal distribution at reliability The quantile value divided by the skewness coefficient Degrees of freedom ; Step S705: Calculate the lower limit coefficient of the one-sided tolerance. The expression is, .

[0036] Furthermore, in this embodiment, the design allowable value for calculating the static properties of the engine material in step S8 is... and middle, Value corresponds to reliability The confidence level is 97.72%. It is 95%; Value corresponds to reliability The confidence level is 99.87%. It is either 50% or 95%.

[0037] In one embodiment, such as Figure 2 As shown, Figure 2 This is a schematic diagram of the normal distribution probability plot and the fitting line for the low-tail 50% data, designed to solve the problem of accurately calculating the allowable design values ​​(-2σ, -3σ) of engine materials under non-normal data. Figure 2 It can be seen that: in terms of degrees of freedom (Horizontal axis) and non-central parameters (Horizontal axis or curve parameter) is a variable, and the vertical axis represents the state at a specified confidence level. The lower quantile value Each curve in the graph represents a fixed set of reliability. (e.g., 97.72% or 99.87%) and confidence level (e.g., 95%) combination, corresponding to a specific Value, of which This is the low-tail data skewness adjustment factor. In this invention, Figure 2 For formula Provide verifiable numerical data for the project. When low-tailed data is obtained through linear regression... , Afterwards, the engineer can... Figure 2 Chinese correspondence and The curve can be directly retrieved. This allows for the calculation of final design allowable values ​​that meet 97.72% or 99.87% reliability at a 95% confidence level. This embodiment transforms theoretical statistical distributions into an engineering-operable graphical tool, avoiding complex numerical integration or software dependence. It enables aerospace material designers to complete high-precision statistical inferences by consulting graphs in a non-programming environment, significantly improving the engineering practicality and scalability of the method.

[0038] In one embodiment, a data processing device is provided, including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the statistical processing method for allowable design values ​​of engine materials as described in the first aspect of the present invention.

[0039] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon that, when executed by a processor, implements the method for statistical processing of allowable design values ​​for engine materials as described in the first aspect of the present invention.

[0040] Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A method for statistically processing allowable design values ​​for engine materials, characterized in that, The method includes: S1: The sample size is The data samples are arranged in ascending order to obtain ordered sample observations. ,in, Indicates the first Observations of a sample , is a natural number representing the total number of data samples; S2: Perform an A / D test on the data sample to check whether the data sample conforms to a normal distribution. If it conforms to a normal distribution, then use conventional methods to calculate the allowable design values ​​of the static properties of the engine materials. and ; S3: If the data sample being tested does not conform to a normal distribution, then determine the cumulative probability distribution of each sample observation. And based on this, calculate the corresponding standard normal distribution quantiles. ; S4: Perform proportional truncation on the data, removing a predetermined proportion of high-tailed sample observations and retaining low-tailed data to obtain a new sample size. A low-tailed subset of data; S5: Based on each data point in the low-tailed data subset Construct a dataset and perform linear regression analysis on it to obtain the regression intercept. With slope ,in, , Indicates the first sub-data set in the low-tailed data set. Observations of a sample Indicates the first sub-data set in the low-tailed data set. quantiles corresponding to the observations of each sample, intercept The mean and slope of the normal distribution representing the low-tailed data constructed. Characterize its standard deviation; S6: Based on the linear regression analysis results and the predetermined judgment criteria, determine the degree of fit between the low-tailed data and the constructed normal distribution model; S7: Based on non-centralized Distribution, based on specified reliability With confidence level and the sample size of the low-tailed data subset. Calculate the lower limit coefficient of the one-sided tolerance. ; S8: Regression intercept obtained from S5 With slope And the lower limit coefficient of the one-sided tolerance calculated by S7. Through the expression: Calculate the allowable design values ​​for the static properties of engine materials. and .

2. The method for statistical processing of allowable design values ​​for engine materials as described in claim 1, characterized in that, The aforementioned normal distribution AD test for the data sample is specifically verified by calculating the AD statistic of the normal distribution AD test for the data sample, the expression of which is as follows: In the formula, This represents the mean of the observed values ​​in the data sample. This represents the standard deviation of the observed values ​​in the data sample. The cumulative distribution function represents the standard normal distribution.

3. The method for statistical processing of allowable design values ​​for engine materials as described in claim 2, characterized in that: When the test statistic AD value is less than the critical threshold, the data is determined to conform to a normal distribution. In this case, the mean minus... Traditional method for calculating multiple standard deviations , value; Wherein, the critical threshold is .

4. A method for statistically processing allowable design values ​​of engine materials as described in any one of claims 1 to 3, characterized in that, The method described in S4, which involves truncating the data proportionally by removing a predetermined proportion of high-tailed sample observations and retaining low-tailed data, specifically involves truncating the data by 50%, that is, removing the largest 50% of sample observations and retaining the lowest 50% as a subset of low-tailed data.

5. The method for statistical processing of allowable design values ​​for engine materials as described in claim 1, characterized in that, Cumulative probability distribution of each sample observation in S3 The calculation expression is, In the formula, The unit is % This indicates the sequence number of the observation in the sorted data sample; when there are duplicate data points in the sample, the sequence number of the intermediate data is used for calculation. value.

6. The method for statistical processing of allowable design values ​​for engine materials as described in claim 1, characterized in that: S5 also includes using the least squares method for low-tailed data subsets. Linear regression was performed on the data points to obtain the regression equation. And calculate the goodness of fit. Among them, quantiles As an independent variable Sample observations As dependent variable ; In S6, the goodness of fit between the low-tailed data and the constructed normal distribution model is determined based on the linear regression analysis results and predetermined judgment criteria. As an indicator of consistency, when When the success rate is not less than 90%, the constructed low-tailed data normal distribution model is confirmed to be effective.

7. The method for statistical processing of allowable design values ​​for engine materials as described in claim 1, characterized in that, The calculation of the lower limit coefficient of the one-sided tolerance is described in S7. The methods include: Calculation and Reliability Confidence level and the reduced sample size Related one-sided tolerance factor ; Calculate the standard normal distribution quantiles in the low-tailed data subset. mean and total square Among them, the total sum of squares The calculation expression is, ; Calculate the skewness coefficient The expression is, In the formula, As an intermediate variable; Based on confidence level Eccentricity parameter Degrees of freedom Non-center investigation Distribution quantile table or non-centrality obtained through calculation Values ​​of the lower quantile of the distribution Among them, the eccentricity parameter For the standard normal distribution at reliability The quantile value divided by the skewness coefficient Degrees of freedom ; Calculate the lower limit coefficient of the one-sided tolerance. The expression is, .

8. The method for statistical processing of allowable design values ​​for engine materials as described in claim 1, characterized in that: The design allowable value for calculating the static properties of engine materials as described in S8 and middle, Value corresponds to reliability The confidence level is 97.72%. It is 95%; Value corresponds to reliability The confidence level is 99.87%. It is either 50% or 95%.

9. A data processing device, comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements a statistical processing method for allowable design values ​​of engine materials according to any one of claims 1 to 8.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by the processor, the program implements a statistical processing method for allowable values ​​of engine material design as described in any one of claims 1 to 8.

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