Reliability evaluation method for aero-engine structure and system related to multiple failure modes

Abstract

The application provides an aero-engine multi-failure mode related structure and system reliability evaluation method, and belongs to the technical field of aero-engines. The method comprises the following steps: determining the working environment conditions of the aero-engine multi-failure mode related structure and system; determining the failure mode, mechanism model and failure number of the engine structure and system; determining the intensity distribution of different failure modes; determining the equivalent load distribution of multiple load actions; calculating the dynamic structure reliability of the multi-failure mode; calculating the dynamic system reliability of the multi-failure mode; and calculating the dynamic system failure rate of the multi-failure mode. The method provided in the application improves the effectiveness and accuracy of the structure and system reliability evaluation results.

Description

Technical Field

[0001] The present application belongs to the field of aero-engine technology, and in particular relates to a method for evaluating the reliability of structures and systems related to multiple failure modes of an aero-engine. Background Art

[0002] Aeroengine structures and systems can experience a variety of failure modes under complex operating conditions, with static strength failure and fatigue failure (such as bending fatigue and creep) being the primary failure modes. However, in practice, to simplify design complexity and simplify calculations, the reliability of each failure mode is typically calculated or evaluated separately. This reliability evaluation employs a stress-strength interference model to calculate the reliability of each failure mode. System reliability is then evaluated using a traditional series model, assuming each failure mode is independent of the others. This evaluation approach fails to consider the correlation between failure modes under the same load conditions, nor does it account for the multiple load cycles that occur during actual operation. Consequently, the evaluation results significantly underestimate the reliability of the structure and system. Therefore, the correlation of multiple failure modes under multiple loads must be considered during the reliability design of engine structures and systems. This research focuses on developing a reliability evaluation method for aeroengine structures and systems that accurately assesses the reliability of structures and systems under multiple loads. This ensures that the design results meet reliability requirements.

[0003] In the prior art, the patent publication "CN108090266A A Method for Calculating the Correlated Reliability of Multiple Failure Modes of Mechanical Parts" establishes a reliability evaluation method for multiple failure modes of mechanical parts based on Copula functions. However, this method simplifies the failure modes into linear correlations and does not reflect the reliability evaluation results under multiple load actions, and cannot accurately reflect the reliability evaluation results of products under multiple load actions. "Gear Reliability Calculation Model Considering the Number of Load Actions" (Yue Yumei, Wang Zheng, Xie Liyang, Journal of Northeastern University, December 2008, Vol. 29, No. 12) introduces conditional reliability and establishes a multiple failure mode reliability evaluation method for gears under multiple load actions based on the maximum order statistics of the load without making failure independence. However, this method is applicable to the same load under multiple failure mode conditions and overestimates the reliability of the structural system. There are limitations in the application of reliability evaluation methods for systems composed of different parts with different loads. None of the above methods can accurately and effectively evaluate the reliability of products. Summary of the Invention

[0004] The purpose of this application is to provide a method for evaluating the structural and system reliability of an aircraft engine with respect to multiple failure modes, so as to solve or alleviate at least one problem in the background technology.

[0005] The technical solution of this application is: a method for evaluating the structural and system reliability of aircraft engines related to multiple failure modes, including:

[0006] Determine the operating environment conditions of structures and systems related to multiple failure modes of aircraft engines, including mechanical properties of components, operating speed and torque, and number of load applications;

[0007] Conduct failure mode impact and criticality analysis of structures and systems, complete failure mechanism analysis for different failure modes of structures and systems, and determine failure mechanism models and sensitive stresses under different failure modes;

[0008] Construct the strength distribution probability density function under different failure modes and determine the strength distribution probability density function under different failure modes based on the fatigue test results of the structure and system;

[0009] Construct an equivalent load distribution function for multiple load actions, obtain the distribution parameters of the strength distribution probability density function under different failure modes based on the failure mechanism model and sensitive stress under different failure modes, and then obtain the equivalent load distribution under multiple load actions based on the distribution parameters;

[0010] Constructing a structural reliability function with multiple loads and multiple failure modes, and obtaining a dynamic structural reliability with multiple failure modes according to the distribution parameters and the equivalent load distribution;

[0011] Construct a system reliability function with multiple loads and multiple failure modes. Based on the system composition and the stress and strength distribution of each component in the system under different failure modes, the system reliability with multiple failure modes under multiple loads is obtained.

[0012] The failure rate calculation function of the structure and system is constructed, and the dynamic system failure rate of multiple loads and multiple failure modes is obtained based on the system reliability function of multiple loads and multiple failure modes and the failure rate calculation function of the structure and system.

[0013] Furthermore, the failure mechanism model includes a fatigue failure mechanism calculation model, a wear life calculation model and an aging life calculation model.

[0014] Furthermore, the three-parameter Weibull distribution is used to fit the strength distribution of different failure modes. The probability density function of the strength distribution under different failure modes is:

[0015]

[0016] Where, α i is the location parameter of the i-th failure mode; β i is the shape parameter of the i-th failure mode; θ i is the scale parameter of the i-th failure mode; fSi (x) is the probability density function of the strength under the condition of the i-th failure mode; W i is the Weibull distribution probability density function of the strength under the failure mode condition in the i-th case; x i is the strength random number that obeys the three-parameter Weibull distribution under the condition of the i-th failure mode.

[0017] Furthermore, the process of constructing the equivalent load distribution function for multiple load actions is as follows:

[0018] When the load s acts n times, the maximum load is actually the load sample (s1, s2, ..., s n ) determined by the maximum order statistic s (n) ;

[0019] Assume that the cumulative distribution function of the load random variable s is F s (s), the probability density function is f s (s), random variable s n For n load samples (s1, s2, ..., s n ), i.e., the equivalent load distribution when the load acts multiple times;

[0020] Reliability equivalent load s when the load acts n times n The probability cumulative distribution function F sn (s):

[0021] F sn (s)=[F(s)] n =F n (s)

[0022] If the load random variable s~W(x,β,α,θ), according to the inverse transformation method of random sampling, set the variable y~U(0,1), let y=F n (s), n is the number of load actions, which is a fixed integer. If we solve s inversely, the distribution function of the random variable s is F n (s) Calculation formula:

[0023] Where s is the load random variable, F(s) is the probability cumulative distribution function of load s; α is the location parameter of the load distribution; β is the shape parameter of the load distribution; θ is the scale parameter of the load distribution; and W is the probability density function of the random load that obeys the three-parameter Weibull distribution.

[0024] Furthermore, the process of constructing the structural reliability function of load multiple failure modes is as follows:

[0025] The reliability of a structure is equivalent to the reliability of a series system composed of its failure mode m. When the load is a certain value s, the failure modes of the components are independent of each other. At this time, the reliability of the structure can be equivalent to the reliability of a series system under independent failure conditions:

[0026] R s (m)=P(S1>s1∩S2>s2∩...∩S m >s m |s)=P(S1>s 1(s) ∩S2>s 2(s) ∩...∩S m >s m(s) |s)

[0027] Where R s (m) is the conditional reliability of the structure with m failure modes when the load s is determined; when the load is subject to the density function f sn When the random variable (s) is a random variable, the total probability formula and the system-level stress-strength interference theory show that the structural reliability R(n,m) of the failure mode m under n loads is:

[0028]

[0029] Where: R(n,m) is the structural reliability of failure mode m under load n times; f sn (s) is the probability density function of the load sn when the load is applied n times; is the probability density function of the strength S of the i-th failure mode; m is the number of failure modes; i(s) is the random number of loads of the i-th failure mode;

[0030] Based on the normalization principle of load, the structural reliability R(n,m) of failure mode m with n loads is obtained:

[0031] Where y is a random number with mean distribution; n is the number of load actions; m is the number of failure modes; is the probability cumulative distribution function of the intensity of the i-th failure mode; α i is the position parameter of the load distribution of the i-th failure mode; β i is the shape parameter of the load distribution of the i-th failure mode; θ i is the scale parameter of the load distribution of the i-th failure mode;

[0032] is the random number of stress load that obeys the maximum order statistics under different failure mode conditions.

[0033] Furthermore, the process of constructing the system reliability function with multiple loads and multiple failure modes is as follows:

[0034] Assume that the system consists of k components. Under deterministic load conditions, the failure of each component is independent of each other. In this case, the reliability of the system is equivalent to the number of different parts k and the number of failure modes of different parts m under independent failure conditions. k The reliability of the series system composed of is constructed based on the stress-strength interference model of the system layer and the reliability function of the system under the load action n times multi-failure mode:

[0035]

[0036] Where R system (n) is the system reliability of the number of parts with m failure modes under n loads; n is the number of loads; m is the number of failure modes; m k is the number of failure modes of the kth component; k is the number of components that make up the system; is the probability density function of the intensity S of the i-th failure mode; f sn (s) is the probability density function of the load sn when the load is applied n times;

[0037] Then we can obtain the system reliability R of the failure mode m under load n times system (n):

[0038]

[0039] Where m k is the number of failure modes of the kth component; k is the number of components that make up the system; is the probability cumulative distribution function of the intensity of the i-th failure mode.

[0040] Furthermore, the failure rate calculation function of the constructed structure and system is:

[0041]

[0042] Where λ(t) is the failure rate of the structure and system; R(t) is the reliability of the structure and system at time t; R(t+1) is the reliability of the structure and system at time t+1; Δt=1;

[0043] According to the system reliability function of multiple loads and multiple failure modes and the failure rate calculation function of the structure and system, the failure rate of the dynamic system with multiple loads and multiple failure modes is obtained as follows:

[0044]

[0045] Where λ system (n) is the system failure rate when the load is applied n times; R(n) is the system reliability when the load is applied n times; R(n+1) is the system reliability when the load is applied n+1 times; m kis the number of failure modes of the kth component; k is the number of components that make up the system; is the probability cumulative distribution function of the intensity of the i-th failure mode.

[0046] Compared with the existing technology, the structure and system reliability assessment method of this application has the following advantages:

[0047] 1) It avoids the problem of underestimating the inherent reliability level of structures and systems caused by traditional reliability evaluation models. It has wide applicability and is suitable for quantitative evaluation of the structural reliability of various types of turbojet and turbofan military and civilian aircraft engines.

[0048] 2) It is highly versatile and applicable to structural and system reliability assessments of various types of stress and strength distributions. It establishes a structural reliability evaluation method related to multiple load actions and multiple failure modes under different load conditions on different parts, achieving scientific and reasonable determination of reliability evaluation results and providing technical support for the reliability design and improvement of complex engine structures.

[0049] 3) A system reliability assessment method for multiple failure modes under different load conditions and multiple loads on different parts was established, which improved the effectiveness and accuracy of the system reliability evaluation results;

[0050] 4) A method for calculating the system failure rate under multiple load actions and multiple failure modes on different parts under different load conditions was established, and the variation pattern of the system failure rate with the number of load actions was obtained. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] 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.

[0052] Figure 1 Schematic diagram of the structure and system reliability evaluation method of this application.

[0053] Figure 2 Schematic diagram of the gear structure reliability evaluation results according to one embodiment of the present application.

[0054] Figure 3 Schematic diagram of the reliability evaluation results of the gearbox transmission system according to one embodiment of the present application.

[0055] Figure 4 Schematic diagram of the gearbox transmission system failure rate evaluation results according to an embodiment of the present application. DETAILED DESCRIPTION

[0056] 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.

[0057] The purpose of this application is to provide a structural and system reliability assessment method related to multiple failure modes of aircraft engines, so as to effectively evaluate the reliability level of structures and systems and provide guidance for improving product design and enhancing product reliability.

[0058] like Figure 1 As shown, the structure and system reliability assessment method related to multiple failure modes of an aircraft engine provided by this application includes the following steps:

[0059] Step S1: Determine the operating environment conditions of the aircraft engine structure and system, including the mechanical properties of components, operating speed and torque, load application times, etc.

[0060] For example, in this embodiment of the present application, the aircraft engine structure is a mechanical gear structure, and its operating conditions include: engine gear transmission power P = 28 ± 5KW, pinion speed n1 = 970r / min, tooth width b = 35mm, gear ratio u = 3, number of teeth z1 = 25, module m = 3mm, large and small gears are both made of 40Cr steel, and the surface hardness HB = 400 ± 15Mpa.

[0061] Step S2: Determine the failure mode, mechanism model, and failure quantity of the engine structure and system:

[0062] Complete product failure mode impact and criticality analysis in accordance with the "GJB / Z1391-2006 Failure Mode Effect and Criticality Analysis Guide"; at the same time, complete product failure mechanism analysis for different failure modes, determine failure mechanism models and sensitive stresses under different failure modes, and complete the compilation of failure mechanism and sensitive stress tables for typical failure modes.

[0063] Among them, failure mechanism models include fatigue failure mechanism calculation models (Baquin model, TK model, Coffin-Manson model, etc.), wear life calculation models (Archard model, Rabinowicz model, Halling-Finkin model, etc.) and aging life calculation models (Kinetic model, Maxwell model, etc.).

[0064] For example, in this embodiment of the present application, based on the FMECA (Failure Mode, Effects and Criticality Analysis) analysis results of the gear and combined with the engine usage, it is determined that the failure modes of the gear mainly include two failure modes: tooth surface contact failure and tooth root fracture. The failure mechanism model machine sensitive stress of each failure mode is shown in Table 2.

[0065] Table 2 Failure mechanism and sensitive stress of typical failure modes

[0066]

[0067] Step S3: Determine the strength distribution of different failure modes:

[0068] Due to the wide application of Weibull distribution and the fact that the Weibull probability density function can be fitted into different distribution types depending on the shape parameters, this application uses a three-parameter Weibull distribution to fit the strength distribution of different failure modes. Based on the fatigue test results of the product, the shape parameter, location parameter, and scale parameter of the Weibull distribution are obtained using the correlation coefficient method, maximum likelihood estimation method, etc., thereby determining the probability density function of the strength distribution under different failure mode conditions, as shown in Formula 1:

[0069]

[0070] Where, α i is the location parameter of the i-th failure mode; β i is the shape parameter of the i-th failure mode; θ i is the scale parameter of the i-th failure mode; f Si (x) is the probability density function of the strength under the condition of the i-th failure mode; W i is the Weibull distribution probability density function of the strength under the failure mode condition in the i-th case; x i is the strength random number that obeys the three-parameter Weibull distribution under the condition of the i-th failure mode.

[0071] For example, in this embodiment of the present application, based on the fatigue test results of the gear, the distribution parameters of the gear contact and bending fatigue strength are obtained as shown in Table 3.

[0072] Table 3 Distribution parameters of gear contact and bending fatigue strength

[0073]

[0074] Step S4: Determine the equivalent load distribution of multiple load actions:

[0075] When the load s acts n times, the maximum load is actually the load sample (s1, s2, ..., s n ) determined by the maximum order statistic S (n) Assume that the cumulative distribution function of the load random variable s is F s (s), the probability density function is f s (s), random variable s n For n load samples (s1, s2, ..., s n) (i.e., the equivalent load distribution when the load acts multiple times). Reliability equivalent load s when the load acts n times n The cumulative distribution function F sn (s) See Formula 2:

[0076] F sn (s)=[F(s)] n =F n (s) (2)

[0077] If the load random variable s~W(x,β,α,θ), according to the inverse transformation method of random sampling, set the variable y~U(0,1), let y=F n (s) (n is a fixed integer), the inverse solution of s is the distribution function of the random variable s is F n (s) is calculated as shown in Formula 3:

[0078]

[0079] Where s is the load random variable, F(s) is the probability cumulative distribution function of load s; α is the location parameter of the load distribution; β is the shape parameter of the load distribution; θ is the scale parameter of the load distribution; and W is the probability density function of the random load that obeys the three-parameter Weibull distribution.

[0080] For example, in this embodiment of the present application, according to the failure mechanism model in Table 2, the distribution parameters of the gear tooth surface contact and tooth root stress can be obtained as shown in Table 4.

[0081] Table 4 Load distribution parameters of different failure modes

[0082]

[0083] The equivalent load distribution of gear tooth surface contact and tooth root stress under multiple load actions is obtained according to Formula 3, as shown in Table 5.

[0084] Table 5 Equivalent load distribution of multiple load actions

[0085]

[0086] Step S5: Calculate the dynamic structural reliability of multiple failure modes:

[0087] The occurrence of any failure mode during the product's operation will lead to product failure. Therefore, the structural reliability can be equivalent to the reliability of the series system composed of its failure mode m. When the load is a certain value s, the failure modes of the components are independent of each other. At this time, the reliability of the structure can be equivalent to the reliability of the series system under independent failure conditions, as shown in Formula 4:

[0088] R s(m)=P(S1>s1∩S2>s2∩...∩S m >s m |s)=P(S1>s 1(s) ∩S2>s 2(s) ∩...∩S m >s m(s) |s) (4)

[0089] Formula 4 is the conditional reliability of the structure with m failure modes when the load is a certain value s. sn When the random variable (s) is a random variable, the total probability formula and the system-level stress-strength interference theory can be used to determine the structural reliability R(n,m) of the failure mode m under n loads, as shown in Formula 5:

[0090]

[0091] Where: R(n,m) is the structural reliability of failure mode m under load n times; f sn (s) is the probability density function of the load sn when the load is applied n times; is the probability density function of the intensity S of the i-th failure mode; m is the number of failure modes; i(s) is the random number of loads of the i-th failure mode.

[0092] Based on the load normalization principle, Formulas 1 to 3 are substituted into Formula 5 to obtain the structural reliability R(n,m) of failure mode m under load n times, as shown in Formula 6:

[0093]

[0094] Where y is a random number with mean distribution; n is the number of load actions; m is the number of failure modes; is the probability cumulative distribution function of the intensity of the i-th failure mode; α i is the position parameter of the load distribution of the i-th failure mode; β i is the shape parameter of the load distribution of the i-th failure mode; θ i is the scale parameter of the load distribution of the i-th failure mode.

[0095] is the random number of stress load that obeys the maximum order statistics under different failure mode conditions.

[0096] For example, in this embodiment of the present application, the calculation results of Table 3 and Table 5 are substituted into Formula 6 to obtain the gear reliability evaluation results of multiple failure modes under multiple loads. The calculation results are shown in Figure 2 shown.

[0097] Step S6: Calculate the dynamic system reliability of multiple failure modes:

[0098] Assuming that the system consists of k parts, under deterministic load conditions, the failure of each part is independent of each other. At this time, the reliability of the system can be equivalent to the number of different parts k and the number of failure modes of different parts m under failure independence. k The reliability of the series system composed of the components is evaluated by constructing a reliability evaluation formula for the system under the load action n times multi-failure mode based on the system layer stress-strength interference model, as shown in Formula 7:

[0099]

[0100] Where R system (n) is the system reliability of the number of parts with m failure modes under n loads; n is the number of loads; m is the number of failure modes; m k is the number of failure modes of the kth component; k is the number of components that make up the system; is the probability density function of the intensity S of the i-th failure mode; f sn (s) is the probability density function of load sn when the load acts n times.

[0101] Substituting formulas 1 to 3 into formula 7, we can obtain the system reliability R under load n failure mode m. system (n), see Formula 8:

[0102]

[0103] Where m k is the number of failure modes of the kth component; k is the number of components that make up the system; is the probability cumulative distribution function of the intensity of the i-th failure mode.

[0104] For example, in this embodiment of the present application, a certain type of engine gearbox is composed of a transmission system consisting of two different gears. The stress and strength distribution of each gear under different failure modes are shown in Table 6. According to Formula 8, the reliability evaluation results of the transmission system with multiple failure modes under multiple loads can be obtained, such as Figure 3 shown.

[0105] Table 6 Stress and strength distribution parameters of components of gearbox transmission system

[0106] System components Positional parameters Shape parameters scale parameter Contact stress distribution of gear 1 556.7 3.2 190.2 Contact stress distribution of gear 2 420.5 3.1 150.59 Contact strength distribution of gear 1 756.7 3.4 272.5 Contact strength distribution of gear 2 507.4 3.3 198.2 Bending stress distribution of gear 1 268.37 3.5 221.5 Bending stress distribution of gear 2 184.44 3.25 263.6 Bending strength distribution of gear 1 472.1 3.35 152.93 Bending strength distribution of gear 2 572.68 3.45 171.93

[0107] from Figure 3 It can be seen that as the number of loads increases, the reliability of the system gradually decreases; at the same time, compared with the traditional system reliability evaluation results (dashed line) assuming independent failures, the evaluation results of this application are higher than the calculation results of independent failures. Obviously, the traditional calculation model underestimates the reliability of the system.

[0108] Step S7: Calculate the failure rate of the dynamic system with multiple failure modes:

[0109] According to the calculation formula 9 of the product failure rate, the reliability evaluation calculation formula 8 of the system under the load action n-times multiple failure mode is substituted into formula 9 to obtain the dynamic system failure rate λ under the load action n-times multiple failure mode system (n), see formula 10:

[0110]

[0111] Where λ(t) is the failure rate of the structure and system; R(t) is the reliability of the structure and system at time t; R(t+1) is the reliability of the structure and system at time t+1; Δt=1.

[0112]

[0113] Where λ system (n) is the system failure rate when the load is applied n times; R(n) is the system reliability when the load is applied n times; R(n+1) is the system reliability when the load is applied n+1 times; m k is the number of failure modes of the kth component; k is the number of components that make up the system; is the probability cumulative distribution function of the intensity of the i-th failure mode.

[0114] For example, in this embodiment of the present application, according to formula 10, the failure rate calculation results of the gearbox transmission system with multiple failure modes under multiple loads can be obtained, such as Figure 4 As shown. Figure 4 It can be seen that with the increase of load times, the failure rate of the gearbox transmission system gradually decreases, and it is obviously consistent with the early failure and accidental failure characteristics of the bathtub curve of mechanical products, which verifies the effectiveness of the calculation model.

[0115] Compared with the existing technology, the structure and system reliability assessment method of this application has the following advantages:

[0116] 1) It avoids the problem of underestimating the inherent reliability level of structures and systems caused by traditional reliability evaluation models. It has wide applicability and is suitable for quantitative evaluation of the structural reliability of various types of turbojet and turbofan military and civilian aircraft engines.

[0117] 2) It is highly versatile and applicable to structural and system reliability assessments of various types of stress and strength distributions. It establishes a structural reliability evaluation method related to multiple load actions and multiple failure modes under different load conditions on different parts, achieving scientific and reasonable determination of reliability evaluation results and providing technical support for the reliability design and improvement of complex engine structures.

[0118] 3) A system reliability assessment method for multiple failure modes under different load conditions and multiple loads on different parts was established, which improved the effectiveness and accuracy of the system reliability evaluation results;

[0119] 4) A method for calculating the system failure rate under multiple load actions and multiple failure modes on different parts under different load conditions was established, and the variation pattern of the system failure rate with the number of load actions was obtained.

[0120] 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 evaluating the structural and system reliability of aircraft engines with respect to multiple failure modes, characterized by: include: Determine the operating environment conditions of structures and systems related to multiple failure modes of aircraft engines, including mechanical properties of components, operating speed and torque, and number of load applications; Conduct failure mode impact and criticality analysis of structures and systems, complete failure mechanism analysis for different failure modes of structures and systems, and determine failure mechanism models and sensitive stresses under different failure modes; The strength distribution probability density functions under different failure modes are constructed and determined based on the fatigue test results of the structure and system. The three-parameter Weibull distribution is used to fit the strength distribution of different failure modes. The probability density functions of the strength distribution under different failure modes are: Where, α i is the location parameter of the i-th failure mode; β i is the shape parameter of the i-th failure mode; θ i is the scale parameter of the i-th failure mode; f Si (x) is the probability density function of the strength under the condition of the i-th failure mode; W i is the Weibull distribution probability density function of the strength under the failure mode condition in the i-th case; x i is the strength random number that obeys the three-parameter Weibull distribution under the condition of the i-th failure mode; Construct the equivalent load distribution function of multiple load actions, obtain the distribution parameters of the strength distribution probability density function under different failure modes according to the failure mechanism model and sensitive stress under different failure modes, and then obtain the equivalent load distribution under multiple load actions according to the distribution parameters. The process is as follows: When the load s acts n times, the maximum load is actually the load sample (s1, s2, ..., s n ) determined by the maximum order statistic s (n) ; Assume that the cumulative distribution function of the load random variable s is F s (s), the probability density function is f s (s), random variable s n For n load samples (s1, s2, ..., s n ), i.e., the equivalent load distribution when the load acts multiple times; Reliability equivalent load s when the load acts n times n The probability cumulative distribution function F sn (s): F sn (s)=[F(s)] n =F n (s) If the load random variable s~W(x,β,α,θ), according to the inverse transformation method of random sampling, set the variable y~U(0,1), let y=F n (s), n is the number of load actions, which is a fixed integer. If we solve s inversely, the distribution function of the random variable s is F n (s) Calculation formula: Where s is the load random variable, F(s) is the probability cumulative distribution function of load s; α is the location parameter of the load distribution; β is the shape parameter of the load distribution; θ is the scale parameter of the load distribution; W is the probability density function of the random load that obeys the three-parameter Weibull distribution; Constructing a structural reliability function with multiple loads and multiple failure modes, and obtaining a dynamic structural reliability with multiple failure modes according to the distribution parameters and the equivalent load distribution; Construct a system reliability function with multiple loads and multiple failure modes. Based on the system composition and the stress and strength distribution of each component in the system under different failure modes, the system reliability with multiple failure modes under multiple loads is obtained. The failure rate calculation function of the structure and system is constructed, and the dynamic system failure rate of multiple loads and multiple failure modes is obtained based on the system reliability function of multiple loads and multiple failure modes and the failure rate calculation function of the structure and system.

2. The method for evaluating the reliability of structures and systems related to multiple failure modes of an aircraft engine according to claim 1, wherein: The failure mechanism model includes a fatigue failure mechanism calculation model, a wear life calculation model and an aging life calculation model.

3. The method for evaluating the reliability of structures and systems related to multiple failure modes of an aircraft engine according to claim 2, wherein: The process of constructing the structural reliability function of multiple failure modes under load is: The reliability of a structure is equivalent to the reliability of a series system composed of its failure mode m. When the load is a certain value s, the failure modes of the components are independent of each other. At this time, the reliability of the structure can be equivalent to the reliability of a series system under independent failure conditions: R s (m)=P(S1>s1∩S2>s2∩...∩S m >s m |s)=P(S1>s 1(s) ∩S2>s 2(s) ∩...∩S m >s m(s) |s) Where R s (m) is the conditional reliability of the structure with m failure modes when the load s is determined; when the load is subject to the density function f sn When the random variable (s) is a random variable, the total probability formula and the system-level stress-strength interference theory show that the structural reliability R(n,m) of the failure mode m under n loads is: Where: R(n,m) is the structural reliability of failure mode m under load n times; f sn (s) is the probability density function of the load sn when the load is applied n times; is the probability density function of the strength S of the i-th failure mode; m is the number of failure modes; i(s) is the random number of loads of the i-th failure mode; Based on the normalization principle of load, the structural reliability R(n,m) of failure mode m with n loads is obtained: Where y is a random number with mean distribution; n is the number of load actions; m is the number of failure modes; is the probability cumulative distribution function of the intensity of the i-th failure mode; α i is the position parameter of the load distribution of the i-th failure mode; β i is the shape parameter of the load distribution of the i-th failure mode; θ i is the scale parameter of the load distribution of the i-th failure mode; is the random number of stress load that obeys the maximum order statistics under different failure mode conditions.

4. The method for evaluating the reliability of structures and systems related to multiple failure modes of an aircraft engine according to claim 3, wherein: The process of constructing a system reliability function with multiple loads and multiple failure modes is as follows: Assume that the system consists of k components. Under deterministic load conditions, the failure of each component is independent of each other. In this case, the reliability of the system is equivalent to the number of different parts k and the number of failure modes of different parts m under independent failure conditions. k The reliability of the series system composed of is constructed based on the stress-strength interference model of the system layer and the reliability function of the system under the load action n times multi-failure mode: Where R system (n) is the system reliability of the number of parts k in failure mode m under n load actions; n is the number of load actions; m is the number of failure modes; m k is the number of failure modes of the kth component; k is the number of components that make up the system; is the probability density function of the intensity S of the i-th failure mode; f sn (s) is the probability density function of the load sn when the load is applied n times; Then we can obtain the system reliability R of the failure mode m under load n times system (n): Where m k is the number of failure modes of the kth component; k is the number of components that make up the system; is the probability cumulative distribution function of the intensity of the i-th failure mode.

5. The method for evaluating the reliability of structures and systems related to multiple failure modes of an aircraft engine according to claim 4, wherein: The failure rate calculation function of the constructed structure and system is: Where λ(t) is the failure rate of the structure and system; R(t) is the reliability of the structure and system at time t; R(t+1) is the reliability of the structure and system at time t+1; Δt=1; According to the system reliability function of multiple loads and multiple failure modes and the failure rate calculation function of the structure and system, the failure rate of the dynamic system with multiple loads and multiple failure modes is obtained as follows: Where λ system (n) is the system failure rate when the load is applied n times; R(n) is the system reliability when the load is applied n times; R(n+1) is the system reliability when the load is applied n+1 times; m k is the number of failure modes of the kth component; k is the number of components that make up the system; is the probability cumulative distribution function of the intensity of the i-th failure mode.

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