A method for determining a maintenance cycle of a general aviation aircraft based on a Bayes-Bootstrap method

Abstract

The application relates to the field of aircraft maintenance data processing, and particularly discloses a general aviation aircraft maintenance cycle determination method based on a Bayes-Bootstrap method. The method comprises the following steps: measuring characteristic parameters of horizontal measurement elements of each aircraft; constructing a sample data set, and performing normal distribution testing and effective sample point set construction; creating a set containing n data points; determining a probability density function on which virtual augmentation is based; calculating and storing the data points into the augmented sample point set; introducing a parameter, calculating the augmented sample points; repeating step S6 for 6 times to obtain a data point set for the Bayes-Bootstrap method after expansion; calculating a confidence interval of the sample mean under a confidence level; calculating an early warning failure rate; comprehensively considering the service life of the aircraft and the early warning failure rate, querying an aircraft failure curve table to determine the next maintenance time of the aircraft, effectively reducing hidden troubles caused by untimely aircraft maintenance and reducing the manpower and material resources consumed by large-scale maintenance.

Description

Technical Field

[0001] This invention relates to the field of aircraft maintenance data processing, and in particular to a method for determining the maintenance cycle of general aviation aircraft based on the Bayes-Bootstrap method. Background Technology

[0002] During service, aircraft inevitably experience overload due to overflight and other unforeseen factors (such as hard landings). This overload causes permanent deformation to the fuselage, wings, stabilizers, and other airframe surfaces. As the aircraft's service life increases, this permanent deformation accumulates and gradually increases. When the deformation exceeds a certain value, it will significantly affect the aircraft's flight and handling performance, and in severe cases, endanger flight safety. Currently, the regulations governing general aviation maintenance activities in China are mainly CCAR91 "General Operations and Flight Rules" and CCAR43 "General Maintenance and Modification Rules." CCAR91 only requires small aircraft to undergo 100-hour checks or annual checks, or to adopt incremental maintenance; it does not require small piston-engine aircraft to have maintenance plans. Small piston-engine aircraft were mainly designed in the 1960s and 70s, and their maintenance philosophy remains at the level of scheduled maintenance. Therefore, maintenance plans developed based on manufacturer maintenance plans lack economic efficiency, involve a large workload, are difficult to manage, and lack the dynamic characteristics required for reliable maintenance. Currently, some more advanced maintenance management methods adjust maintenance cycles based on the aircraft's service life. However, relying solely on aircraft service life to determine aircraft maintenance cycles is not flexible enough, fails to fully integrate with actual conditions, and cannot scientifically and objectively formulate damage repair plans to balance the relationship between fleet reliability and maintenance manpower and material resources. Therefore, this paper proposes a method for determining maintenance cycles suitable for small-batch, small-sized civil aviation aircraft fleets. Summary of the Invention

[0003] To address the aforementioned problems in determining the maintenance cycle of general aviation aircraft, reduce the potential risks caused by untimely aircraft maintenance, and lower the manpower and material resources consumed in large-scale maintenance, this invention provides a method for determining the maintenance cycle of general aviation aircraft based on the Bayes-Bootstrap method.

[0004] The technical solution adopted by this invention to achieve the above objectives is: a method for determining the maintenance cycle of general aviation aircraft based on the Bayes-Bootstrap method, comprising the following steps:

[0005] S1: Measure the characteristic parameters of the horizontal measurement elements of each aircraft, measure the coordinates of key positions of the aircraft in a fixed coordinate system, and calculate the characteristic parameters of the horizontal measurement elements of each aircraft based on the digital horizontal measurement.

[0006] S2: Construct a sample dataset using the feature parameters obtained in step S1, perform a normality test on the sample data, calculate the sample mean μ and standard deviation σ, and eliminate gross errors according to the Laida criterion to obtain the effective sample point set for each parameter. );

[0007] S3: Determine the augmented data size n based on the Bayes-Bootstrap method and the effective sample data size in step S2, and create a set containing n data points. ( ), where the probability of a single augmented sample point is a constant. ;

[0008] S4: Based on the mean μ and standard deviation σ of the normally distributed samples obtained in step S2 and the probability of a single augmented data point obtained in step S3, determine the probability density function on which the virtual augmentation is based. ;

[0009] S5: Based on the probability density function in step S4 Construct the augmentation formula for the first pair of augmentation points using the probability of a single augmented sample point, and calculate... and The data points are then stored in the brightening sample point set. middle;

[0010] S6: Introducing parameters With probability density function Let be the integrand, let Given the lower bound of integration and the probability of a single augmented data point as the integral value, construct an augmentation iterative formula to inversely calculate the upper bound of integration. ,according to , , The augmented sample points are calculated from the sample mean μ in step S2. Then update = ;

[0011] S7: Repeat step S6 This yields an augmented sample point set containing n sample points. ( ), and the sample set in step S2 The data points were merged to obtain an expanded set for the Bayes-Bootstrap method. ;

[0012] S8: The sample mean estimate of the sample point set is calculated using the Bayes-Bootstrap method. Sample standard deviation estimation This allows us to calculate the sample mean at a confidence level. Confidence interval under the condition ( );

[0013] S9: Calculate the 95% confidence intervals for each characteristic parameter sample of the aircraft level measurement elements. The failure warning range exceeds the specified characteristic parameter. ratio Then, the failure rate of the early warning system is calculated using the weighted method. ;

[0014] S10: Considering the aircraft's service life and the aforementioned early warning failure rate The next maintenance time for the aircraft can be determined by consulting the aircraft failure curve table.

[0015] Preferably, the coordinates of the key aircraft positions in step S1 include: fuselage measurement data points, wing measurement data points, vertical tail stabilizer measurement data points, and horizontal tail stabilizer measurement data points.

[0016] Preferably, the effective interval of the Laida criterion in step S2 is ( ).

[0017] Preferably, the augmented data volume n in step S3 And n is an even number.

[0018] Preferably, the probability density function on which the augmentation is based in step S4 The calculation formula is as follows:

[0019]

[0020] in, and The sample mean μ and standard deviation σ are obtained from the normality test in step S2.

[0021] Preferably, in step S5 and The calculation formula is as follows:

[0022]

[0023] In the formula For integration objects, It is a dimensionless parameter.

[0024] Preferably, in step S6 The calculation formula is as follows:

[0025]

[0026] in, The iteration parameters are known.

[0027] , ... ;

[0028] The calculation formula is as follows:

[0029]

[0030] in, .

[0031] Preferably, the Bayes-Bootstrap method in step S8 requires first constructing a weight distribution that follows a Dirichlet distribution. , ,in is a uniformly distributed random number in the interval (0,1);

[0032] Sample mean estimation Sample standard deviation estimation The calculation formula is as follows:

[0033]

[0034] in, , For data point set Data randomly selected from the data;

[0035] The formula for calculating the confidence interval is as follows:

[0036]

[0037] in, This represents the upper limit of the confidence interval. This is the lower limit of the confidence interval. Normally distributed The quantiles can be obtained by looking up a table. For data point set The total number of samples in the sample.

[0038] Preferably, the early warning failure rate in step S9 The calculation formula is as follows:

[0039]

[0040] In the formula The failure warning rate for the corresponding parameter is calculated using the following formula:

[0041]

[0042] in, This represents the lower limit of the failure warning range for the corresponding parameter. The upper limit of the failure warning range for the corresponding parameter;

[0043] The weight For a certain model The impact of various horizontal measurement elements on the overall aircraft early warning failure rate is reflected, and

[0044]

[0045] in, This represents the failure weight for the corresponding parameter.

[0046] Preferably, the average flight time of the aircraft in step S10 is divided into intervals of 1000 hours.

[0047] Preferably, the next maintenance time for the aircraft in step S10 is determined by combining the remaining time of the cycle obtained from the table lookup and the current date.

[0048] The present invention provides a method for determining the maintenance cycle of general aviation aircraft based on the Bayes-Bootstrap method, which is applicable to the dynamic evaluation of the maintenance cycle of general aviation aircraft and can reduce the hidden dangers caused by untimely aircraft maintenance while reducing the manpower and material resources consumed by large-scale maintenance. Attached Figure Description

[0049] Figure 1 This is a flowchart of the method for determining the maintenance cycle of general aviation aircraft based on the Bayes-Bootstrap method according to an embodiment of the present invention;

[0050] Figure 2 This is a probability distribution diagram of virtual augmented sample data of the dihedral angle on the right wing for the Bayes-Bootstrap method according to an embodiment of the present invention;

[0051] Figure 3 This is the aircraft integrated early warning failure rate - maintenance cycle remaining time schedule of this invention embodiment. Detailed Implementation

[0052] The embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples. The following examples are for illustrative purposes only and should not be construed as limiting the scope of the invention.

[0053] Example 1

[0054] like Figure 1 As shown, the present invention provides a method for determining the maintenance cycle of general aviation aircraft based on the Bayes-Bootstrap method, comprising the following steps:

[0055] S1: Measure the characteristic parameters of the horizontal measurement elements of each aircraft, measure the coordinates of key positions of the aircraft in a fixed coordinate system, and calculate the characteristic parameters of the horizontal measurement elements of each aircraft based on the digital horizontal measurement.

[0056] The coordinates of key aircraft locations include: fuselage measurement data points, wing measurement data points, vertical tail stabilizer measurement data points, and horizontal tail stabilizer measurement data points. Specifically, the locations of the horizontal measurement data points are: point a, the center of the lower fixing screw head of the left door hinge at the front bulkhead of the fuselage door; point b, the center of the lower fixing screw head of the right door hinge at the front bulkhead of the fuselage door; point c, the center of the first rivet head counting from top to bottom on the left side of the fuselage at position FS228.68; point d, the center of the first rivet head counting from top to bottom on the right side of the fuselage at position FS228.68; point u, the center of the upper fixing screw head of the left door latch at the rear bulkhead of the fuselage door; point v, the center of the upper fixing screw head of the right door latch at the rear bulkhead of the fuselage door; and point e, the left wing WS208... Points f, g, h, and i are the rivet heads at the WS208.00 position on the right wing, where the wing rib and the lower surface of the front spar are located. Points j, k, and k are the rivet heads at the WS100.00 position on the left wing, where the wing rib and the lower surface of the rear spar are located. Point l: The center point of the rivet head between the trailing edge rib and the lower surface of the rear spars at the WS100.00 position on the right wing; Point m: The center point of the rivet head between the upper surface of the left front spars of the horizontal stabilizer and the left outer rib; Point n: The center point of the rivet head between the upper surface of the right front spars of the horizontal stabilizer and the right outer rib; Point q: The center point of the rivet head between the upper surface of the left rear spars of the horizontal stabilizer and the left outer rib; Point r: The center point of the rivet head between the upper surface of the right rear spars of the horizontal stabilizer and the right outer rib; Point s: The center point of the rivet head on the upper part of the left front spars of the vertical stabilizer; Point t: The center point of the rivet head on the upper part of the left rear spars of the vertical stabilizer; Point s': The center point of the rivet head on the upper part of the right front spars of the vertical stabilizer; Point t': The center point of the rivet head on the upper part of the right rear spars of the vertical stabilizer.

[0057] S2: Construct a sample dataset using the feature parameters obtained in step S1, perform a normality test on the sample data, calculate the sample mean μ and standard deviation σ, and eliminate gross errors according to the Laida criterion to obtain the effective sample point set for each parameter. );

[0058] Among them, the effective interval of the Laida criterion is ( );

[0059] S3: Determine the augmented data size n based on the Bayes-Bootstrap method and the effective sample data size in step S2, and create a set containing n data points. ( ), where the probability of a single augmented sample point is a constant. ;

[0060] Among them, the augmented data volume n And n is an even number;

[0061] S4: Based on the mean μ and standard deviation σ of the normally distributed samples obtained in step S2 and the probability of a single augmented data point obtained in step S3, determine the probability density function on which the virtual augmentation is based. ;

[0062] The probability density function of the augmentation basis The expression is as follows:

[0063]

[0064] in, and The sample mean μ and standard deviation σ are obtained from the normality test in step S2;

[0065] S5: Based on the probability density function in step S4 Construct the augmentation formula for the first pair of augmentation points using the probability of a single augmented sample point, and calculate... and The data points are then stored in the brightening sample point set. middle;

[0066] and The calculation formula is as follows:

[0067]

[0068] In the formula For integration objects, It is a dimensionless parameter;

[0069] S6: Introducing parameters With probability density function Let be the integrand, let Given the lower bound of integration and the probability of a single augmented data point as the integral value, construct an augmentation iterative formula to inversely calculate the upper bound of integration. ,according to , , The augmented sample points are calculated from the sample mean μ in step S2. Then update = ;

[0070] The following formula is used to derive:

[0071]

[0072] in, The iteration parameters are known.

[0073] , ... ;

[0074] The calculation formula is as follows:

[0075]

[0076] in, ;

[0077] S7: Repeat step S6 This yields an augmented sample point set containing n sample points. ( ), and the sample set in step S2 The data points were merged to obtain an expanded set for the Bayes-Bootstrap method. ;

[0078] S8: The sample mean estimate of the sample point set is calculated using the Bayes-Bootstrap method. Sample standard deviation estimation This allows us to calculate the sample mean at a confidence level. Confidence interval under the condition ( );

[0079] The Bayes-Bootstrap method requires first constructing a weight distribution that follows a Dirichlet distribution. , ,in is a uniformly distributed random number in the interval (0,1);

[0080] Sample mean estimation Sample standard deviation estimation The calculation formula is as follows:

[0081]

[0082] in, , For data point set Data randomly selected from the data;

[0083] The formula for calculating the confidence interval is as follows:

[0084]

[0085] in, This represents the upper limit of the confidence interval. This is the lower limit of the confidence interval. Normally distributed The quantiles can be obtained by looking up a table. For data point set The total number of samples in the sample;

[0086] S9: Calculate the 95% confidence intervals for each characteristic parameter sample of the aircraft level measurement elements. The failure warning range exceeds the specified characteristic parameter. ratio Then, the failure rate of the early warning system is calculated using the weighted method. ;

[0087] Early warning failure rate The calculation formula is:

[0088]

[0089] In the formula The failure warning rate for the corresponding parameter is calculated using the following formula:

[0090]

[0091] in, This represents the lower limit of the failure warning range for the corresponding parameter. The upper limit of the failure warning range for the corresponding parameter;

[0092] The weight For a certain model The impact of various horizontal measurement elements on the overall early warning failure rate of aircraft is reflected in the fact that the weights of each horizontal measurement element differ for different aircraft models, and are all predetermined manually.

[0093]

[0094] in, This represents the failure weight for the corresponding parameter;

[0095] S10: Considering the aircraft's service life and the aforementioned early warning failure rate The next maintenance time for the aircraft can be determined by consulting the aircraft failure curve table.

[0096] The average flight time of an aircraft is divided into intervals of 1000 hours.

[0097] The next maintenance time for the aircraft is determined by combining the remaining time of the cycle obtained from the table lookup and the current date.

[0098] Example 2

[0099] The present invention provides a method for determining the maintenance cycle of general aviation aircraft based on the Bayes-Bootstrap method, comprising the following steps:

[0100] S1: Measure key coordinate points of the aircraft in a fixed coordinate system, and calculate the characteristic parameters of the horizontal measurement elements of each aircraft based on the coordinates. In the example provided by this invention, the dihedral angle of the right wing of a batch of CESSNA 172 aircraft is used as an example for virtual augmentation and analysis of small sample data. The coordinate points of the key aircraft positions include: fuselage measurement data points, wing measurement data points, vertical tail stabilizer measurement data points, and horizontal tail stabilizer measurement data points. The locations of the horizontal measurement data points are as follows: Point a, the center of the lower fixing screw head of the left door hinge at the front bulkhead of the fuselage door; Point b, the center of the lower fixing screw head of the right door hinge at the front bulkhead of the fuselage door; Point c, the center of the first rivet head counted from top to bottom on the left side at the FS228.68 station on the fuselage; Point d, the center of the first rivet head counted from top to bottom on the right side at the FS228.68 station on the fuselage; Point u, the center of the upper fixing screw head of the left door latch at the rear bulkhead of the fuselage door; Point v, the center of the upper fixing screw head of the right door latch at the rear bulkhead of the fuselage door; Point e, the center of the rivet head on the lower surface of the wing rib and front spars at the WS208.00 station on the left wing; Point f, the center of the rivet head on the right wing at the WS208 station. Point g is the center point of the rivet head between the wing rib and the lower surface of the front spar at position WS208.00 on the left wing; point h is the center point of the rivet head between the wing rib and the lower surface of the rear spar at position WS208.00 on the right wing; point i is the center point of the rivet head between the leading edge wing rib and the lower surface of the front spar at position WS100.00 on the left wing; point j is the center point of the rivet head between the leading edge wing rib and the lower surface of the front spar at position WS100.00 on the right wing; point k is the center point of the rivet head between the trailing edge wing rib and the lower surface of the rear spar at position WS100.00 on the left wing; point l is the center point of the rivet head between the trailing edge wing rib and the lower surface of the rear spar at position WS100.00 on the right wing. Point m is the center point of the rivet head between the trailing edge rib and the lower surface of the rear spar; point n is the center point of the rivet head between the upper surface of the left front spar of the horizontal tail and the left outer rib; point q is the center point of the rivet head between the upper surface of the left rear spar of the horizontal tail and the left outer rib; point r is the center point of the rivet head between the upper surface of the right rear spar of the horizontal tail and the right outer rib; point s is the center point of the rivet head at the upper part of the left front spar of the vertical tail; point t is the center point of the rivet head at the upper part of the left rear spar of the vertical tail; point s' is the center point of the rivet head at the upper part of the right front spar of the vertical tail; point t' is the center point of the rivet head at the upper part of the right rear spar of the vertical tail.

[0101] S2: Perform preliminary statistical analysis on the sample data, conduct a normality test, and obtain the characteristics of the normally distributed data. Eliminate gross errors using the Laida criterion to obtain the effective sample point set. ( ); 10 valid sample data were obtained, and the sample mean was... Sample standard deviation .

[0102] S3: Determine the augmented data size n based on the Bayes-Bootstrap method and the actual situation, and create a set containing n data points. ( Let the probability of a single augmented data point be fixed at ). In this example, the augmented data volume is set to n=200, then the probability of a single augmented sample point is... .

[0103] S4: Based on the mean and standard deviation of the normally distributed samples obtained in step S2 and the probability of a single data point obtained in step S3, determine the probability density function upon which the virtual augmentation is based. In this example

[0104]

[0105] S5: According to Construct the augmentation formula for the first pair of augmentations using the probability of a single augmentation point, and calculate... and Store the data points In the middle, Updated to In this example

[0106]

[0107] Using a computer =178.776 ,make .

[0108] S6: Introducing parameters ,by Let be the integrand, let Given the lower bound of integration and the probability of a single augmented point as the integral value, we reconstruct the augmentation iterative formula and inversely calculate the upper bound of integration. .according to , , The augmented sample points are calculated using μ. Then update = In this example, we construct the iterative formula.

[0109]

[0110] Then substitute Find Then according to

[0111] Calculate =178.813, .renew .

[0112] S7: Repeat step S6 This yields an augmented point set containing n sample points. ( The dataset is then merged with the original dataset X to obtain an expanded data point set for the Bayes-Bootstrap method. In this example, step S6 is repeated until the result is found. This yields an augmentation point set consisting of all 200 virtual augmentation data points. ( ), combining measurement data containing 10 data points with The fusion yields a point set containing 210 data points. The probability distribution is shown in the attached figure. Figure 2 As shown.

[0113] S8: The sample mean estimate of the sample point set is calculated using the Bayes-Bootstrap method. Sample standard deviation estimation This allows us to calculate the sample mean at a confidence level. Confidence interval under the condition ( In this example, the Bayes-Bootstrap method is used to calculate the sample mean estimate of the sample point set. Sample standard deviation estimation Thus, the 95% confidence interval for the sample mean is ( );

[0114] S9: Calculate the 95% confidence intervals for each characteristic parameter sample of the aircraft level measurement elements. The failure warning range exceeds the specified characteristic parameter. ratio Then, the failure rate of the early warning system is calculated using the weighted method. In this example, the failure warning range for the dihedral angle on the aircraft is (174, 180), and its warning failure rate is... In this example, the overall early warning failure rate of the sample group is...

[0115]

[0116] S10: Considering the aircraft's service life and early warning failure rate check Figure 3 The aircraft failure curve table shown determines the next maintenance time for the aircraft. In this example, there are a total of 99 aircraft in this batch, and the average flight time is within the range of (12000, 13000). According to the table, the next overall overhaul should be scheduled 57 days after this inspection, so the reasonable time for the next maintenance can be determined.

[0117] The embodiments of the present invention are given for illustrative and descriptive purposes only, and are not intended to be exhaustive or to limit the invention to the forms disclosed. Many modifications and variations will be apparent to those skilled in the art. The embodiments were chosen and described in order to better illustrate the principles and practical application of the invention, and to enable those skilled in the art to understand the invention and to design various embodiments with various modifications suitable for a particular purpose.

Claims

1. A method for determining a service cycle of a civil aircraft based on a Bayes-Bootstrap method, characterized in that, Comprising the following steps: S1: measuring the characteristic parameters of the horizontal measurement elements of each aircraft, measuring the coordinate points of the key positions of the aircraft in the fixed coordinate system, and calculating the characteristic parameters of the horizontal measurement elements of each aircraft according to the digital horizontal measurement; S2: Constructing a sample data set using the characteristic parameters measured in step S1, performing normal distribution test on the sample data, calculating the sample mean μ and standard deviation σ, and removing gross errors according to the Laiyida criterion to obtain an effective sample point set of each parameter ); S3: Determine the augmented data size n according to the Bayes-Bootstrap method and the effective sample size determined in step S2, and create a set containing n data points ( ), wherein the probability of a single augmented sample point is a constant value ; S4: determining the probability density function on which the virtual augmentation is based according to the normal distribution sample mean μ, the standard deviation σ obtained in step S2, and the individual augmented data point probability obtained in step S3 ; S5: According to the probability density function in step S4 And the single augmented sample point probability builds the augmented formula of the first pair of augmented points, calculates And And stores the data points into the augmented sample point set ; S6: Introducing parameters , let be the integrand, let be the lower limit of integration, the probability of a single data augmentation point be the integral value, construct the augmented iteration formula, and back-solve the upper limit of integration , according to , , and the sample mean μ in step S2, calculate the augmented sample point , and then update = ; S7: repeat step S6 second, obtain an augmented sample point set containing n sample points ( ), and fuse with the sample set of step S2 to obtain an expanded data point set for Bayes-Bootstrap method ; S8: The sample mean estimate of the sample point set is calculated using the Bayes-Bootstrap method. Sample standard deviation estimation This allows us to calculate the sample mean at a confidence level. Confidence interval under the condition ( ); S9: calculate the 95% confidence interval of each characteristic parameter sample of the horizontal measurement elements of the airplane , the ratio of the failure pre-warning interval of the characteristic parameter beyond the interval , and then calculate the pre-warning failure rate by the weighted method S10: integrate the aircraft service life and the early warning failure rate determine the next maintenance time of the aircraft by querying the aircraft failure curve table.

2. The method of claim 1, wherein the method is characterized by, The coordinate points of the key positions of the aircraft in step S1 include: fuselage measurement data points, wing measurement data points, vertical tail fin stabilizer measurement data points and horizontal tail fin stabilizer measurement data points.

3. The method of claim 1, wherein the method is characterized by, The Rajar rule in the step S2 has an effective interval of (0, 1). ).

4. The method of claim 1, wherein the method is characterized by, The augmented data quantity n in the step S3 , and n is an even number.

5. The method of claim 1, wherein the method is characterized by, The augmentation in step S4 is based on a probability density function The calculation formula is as follows: ； wherein and are the sample mean and standard deviation obtained in step S2 from the normality test.

6. The method of claim 1, wherein the method is characterized by, The step S5 and The calculation formula is as follows: ； wherein is the integral object, is a dimensionless parameter.

7. The method of claim 1, wherein the method is characterized by, The step S6 Calculation formula: ； wherein is a known iteration parameter; 、 、…… ； The calculation formula is as follows: ； wherein .

8. The method of claim 1, wherein the method is based on a Bayes-Bootstrap method. The Bayes-Bootstrap method in the step S8 needs to construct a weight value subject to Dirichlet distribution , wherein is a random number uniformly distributed in the interval (0, 1); sample mean estimate sample standard deviation estimate The formula is as follows: ； wherein , is a data point set randomly drawn from among the data points The confidence interval calculation formula is as follows: ； where, is the upper limit of the confidence interval, is the lower limit of the confidence interval, is the normal distribution quantile, which can be obtained from a table, is the set of data points is the total number of samples in the set.

9. The method of claim 1, wherein the method is based on a Bayes-Bootstrap method. The pre-alarm failure rate in the step S9 The calculation formula is as follows: ； In the formula The failure warning rate of the corresponding parameter is calculated as follows: ； wherein, a lower limit of a failure warning interval for the corresponding parameter, an upper limit of a failure warning interval for the corresponding parameter; The weight For a certain model A horizontal measurement element reflects the influence of the integrated early warning failure rate of the aircraft, and ； wherein, is the failure weight of the corresponding parameter.

10. The method of claim 1, wherein the method is based on a Bayes-Bootstrap method. The average flight time of the aircraft in step S10 is divided into intervals of 1000h.

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