Creep load characteristic modeling method in aero-engine load spectrum

Abstract

The invention discloses a creep load characteristic modeling method in an aero-engine load spectrum, and relates to the technical field of aero-engine load spectrum modeling, and the method comprises the steps: extracting steady-state points of rotating speed and temperature in an actual measurement load spectrum of an aero-engine, and forming a rotating speed-temperature two-dimensional time distribution matrix; least square nonlinear regression is carried out on the steady state points of the rotating speed and the temperature, and a rotating speed-temperature regression relation is established; selecting logarithmic normal distribution as a basic function, selecting mixed distribution as a distribution type, adopting an EM algorithm to estimate parameters of creep load characteristics, determining the number of optimal basic functions through an AIC method, and establishing a rotating speed one-dimensional mixed distribution model; and combining the rotating speed-temperature regression relationship with the rotating speed one-dimensional mixed distribution model to construct a creep load characteristic model. According to the method, a high-precision mathematical model of creep load characteristics is finally obtained, and a load basis is provided for predicting the service life of a high-precision aero-engine.

Description

Technical Field

[0001] The invention relates to the technical field of aircraft engine load spectrum modeling, in particular to an aircraft engine creep load characteristic modeling method. Background Art

[0002] The load spectrum of aircraft engines is an important basis for evaluating the stress, life and reliability of their components. The actual load spectrum of aircraft engines is complex, and the load characteristics are closely related to the damage form of the components, especially the hot end components such as turbine blades and turbine disks, which are subjected to high temperatures and huge centrifugal forces during service, as well as long-term creep loads. This creep load is a key factor in shortening the life of components, especially in high temperature stress environments.

[0003] The existing load spectrum compilation method mainly obtains the speed steady-state point by analyzing the speed-time matrix. However, the complexity of creep load characteristics increases the difficulty of compiling the task spectrum. The traditional method is limited to the direct analysis of sample data and fails to accurately infer the parent distribution from the sample data. The limitations of this method are reflected in the following points:

[0004] Traditional methods usually perform statistical analysis by sampling each steady-state point in the load spectrum, but this method fails to establish an effective parameterized model, resulting in the description of the load spectrum characteristics being too dependent on the data itself, making it difficult to use for predictions and extrapolations under different conditions. Existing technologies usually use a single statistical method to deal with creep load characteristics, and fail to combine the appropriate probability distribution type, especially for load characteristics under different speeds and temperatures. There is a lack of reasonable distribution modeling methods, which limits the accurate prediction of creep damage. The diversity and frequent changes in flight missions lead to an increase in the dispersion of different creep load characteristics. Existing sampling methods are difficult to cope with the changes in creep characteristics under multi-mission conditions, and cannot effectively establish an accurate load spectrum model. Summary of the invention

[0005] In view of the problems such as lack of parameterized modeling means, insufficient recognition of distribution types, and mixed frequency influence of flight missions, the present invention provides a method for modeling creep load characteristics of an aero-engine. By extracting the speed and temperature steady-state points in the measured load spectrum of the aero-engine, a speed-temperature two-dimensional time allocation matrix is ​​constructed; a speed-temperature two-dimensional time regression model is established by using the least squares nonlinear regression method, a log-normal distribution is used as a basic function, and the EM algorithm is used to estimate the parameters of the creep load characteristics, and the optimal number of basic functions is determined by the AIC criterion, and finally a high-precision creep load characteristic mathematical model is constructed.

[0006] In order to achieve the above object, the present invention is implemented by the following technical solutions:

[0007] A method for modeling creep load characteristics in an aero-engine load spectrum, comprising:

[0008] Step S1, extracting the steady-state points of the speed and temperature in the measured load spectrum of the aircraft engine to form a speed-temperature two-dimensional time distribution matrix;

[0009] Step S2, performing least squares nonlinear regression on the steady-state points of the rotation speed and temperature to establish a two-dimensional time regression relationship between rotation speed and temperature;

[0010] Step S3, selecting lognormal distribution as a basic function, selecting mixed distribution as a distribution type, using EM algorithm to estimate the parameters of creep load characteristics, and determining the optimal number of basic functions by AIC method to establish a one-dimensional mixed distribution model of rotation speed;

[0011] Step S4, combining the rotation speed-temperature regression relationship with the rotation speed one-dimensional mixed distribution model to construct a creep load characteristic model.

[0012] As a preferred embodiment of the present invention, in step S1, extracting the steady-state points of the rotation speed and temperature in the measured load spectrum of the aircraft engine specifically comprises the following steps:

[0013] The high pressure speed N2 is used as the speed representative value, and the exhaust temperature T5 is used as the temperature representative value;

[0014] The determination of the steady-state point starts from the third sampling point of the speed spectrum, and the absolute value k5 of the slope of the line connecting the i+2th sampling point and the i-2th sampling point in the speed spectrum is calculated. The calculation formula of the absolute value k5 of the slope is:

[0015]

[0016] Among them, N i+2 and N i-2 are the speeds of the i+2th sampling point and the i-2th sampling point, t i+2 and t i-2 are the time of the i+2th sampling point and the i-2th sampling point respectively;

[0017] Set the slope judgment threshold k cr , if the absolute value k5 of the slope is less than the slope determination threshold k cr When , the i-th sampling point is taken as the speed steady-state point, and the i-th sampling point in the temperature spectrum corresponding to the speed steady-state point is taken as the temperature steady-state point;

[0018] The speed steady point and the temperature steady point form a speed-temperature two-dimensional time distribution matrix according to the speed N2 and the temperature steady point T5, and the creep load characteristic is expressed as (N2, T5).

[0019] As a preferred solution of the present invention, in step S2, establishing a two-dimensional time regression relationship between rotation speed and temperature specifically includes the following steps:

[0020] S2.1, using the least squares nonlinear regression method, the measured high-pressure speed N2 and exhaust temperature T5 are fitted to establish the speed-temperature two-dimensional time regression relationship. The regression model is expressed as: T5 = f reg (N2);

[0021] S2.2, by Pearson correlation coefficient R pearson Verify the validity of the established regression model. pearson When >0.9, the regression relationship is considered valid.

[0022] As a preferred solution of the present invention, in step S3, the basic function selection includes the following steps:

[0023] Selecting the lognormal distribution as the basic function, the probability density function of the lognormal distribution is expressed as:

[0024]

[0025] Where N2 is the high-pressure speed, μ is the logarithmic mean of the high-pressure speed, σ is the logarithmic standard deviation of the high-pressure speed, π is the circumference of the circle, e is a natural constant, and f j (N2μ,σ) is the probability density function of the jth basic function.

[0026] As a preferred solution of the present invention, in step S3, the distribution type selection includes the following steps:

[0027] Select mixed distribution as the distribution type. The probability density function of the mixed distribution is expressed as:

[0028]

[0029] Among them, f(N2;θ) is the probability density function of the mixed distribution, f j (N2;θ j ) is the probability density function of the jth basic function, θ=[θ1,θ2,...,θ k ] is the set of all unknown parameters of the mixed distribution, w j is the weight of the jth basic function, satisfying the condition:

[0030] 0<w j <1 and

[0031] Where k is the number of basic functions in the mixed distribution model.

[0032] As a preferred solution of the present invention, the EM algorithm is used to implement parameter estimation of the mixed distribution, including the following operations:

[0033] Step 1: Randomly initialize the mixed distribution parameters θ 0 ;

[0034] Step 2: Start the EM algorithm iteration and set θ for the first run. t =θ 0 ;

[0035] Step 3, calculate the conditional expectation of the log-likelihood function LogL(θ);

[0036] Step 4: Solve for the model parameters and calculate the maximum likelihood estimate by maximizing LogL(θ) Get θ t+1 ;

[0037] Step 5: Determine θ t+1 Whether it converges, if it satisfies ||θ t+1 -θ t When ||<δ, the iteration stops, δ is the residual value of parameter iteration, which is taken as 1×10 -7 , then the output θ t+1 , otherwise repeat step 2.

[0038] As a preferred solution of the present invention, in step S3, the optimal number of basic functions c is determined by the AIC method, and the calculation expression of AIC is:

[0039]

[0040] Where c is the number of basic functions, is the number of parameters in the creep load characteristic model when there are c basic functions,

[0041] LogL(c) is the value of the maximum log-likelihood function when there are c basic functions. When the AIC value is at an inflection point, continuing to increase the number of basic functions has little effect on improving the fitting effect. At this time, the number of basic functions c is the optimal value.

[0042] As a preferred solution of the present invention, in step S4, the rotational speed-temperature regression relationship and the rotational speed one-dimensional mixed distribution model together constitute a creep load characteristic model.

[0043] As a preferred solution of the present invention, in step S1, the constructed speed-temperature two-dimensional time distribution matrix includes multiple speed and temperature intervals, and the time distribution of each interval is in seconds. The matrix is ​​used to statistically calculate the distribution of steady-state points (N2, T5) in the creep load characteristics, and the speed interval is between 70.0% and 100.0%, and the temperature interval is between 360°C and 780°C.

[0044] As a preferred solution of the present invention, in step S3, the lognormal distribution is selected as the basic function, the EM algorithm is used for parameter estimation, and the optimal number of basic functions of the mixed distribution is determined to be 3. The parameters of the mixed distribution model include:

[0045] The weights of the basic functions are: w1 = 0.701, w2 = 0.122, w3 = 0.176;

[0046] The logarithmic means are: μ1=4.485, μ2=4.422, μ3=4.564;

[0047] The logarithmic standard deviations are: σ1=0.028, σ2=0.059, σ3=0.016.

[0048] Compared with the prior art, the beneficial effects of the present invention are as follows: the present invention uses the lognormal distribution as the basic function, and combines the mixed distribution model, and adopts the EM algorithm to estimate the parameters of the creep load characteristics. Compared with the traditional single distribution model, this method can more accurately reflect the creep load characteristics under complex flight missions, and greatly improves the modeling accuracy of the load spectrum. Through the AIC method, the present invention can automatically determine the optimal number of basic functions, avoid the uncertainty caused by the complexity of the model manually selected in the traditional method, ensure the applicability and accuracy of the model under complex mission conditions, and avoid overfitting or underfitting. The model of the present invention is not only suitable for a single mission spectrum, but also can effectively deal with the creep load dispersion problem caused by the flight mission mixing, can be widely used in the load characteristic prediction under different flight mission conditions, and has a strong practical value. The creep load characteristic model constructed by the present invention has high accuracy and robustness, provides a more reliable load basis for the life prediction of aircraft engines, significantly improves the accuracy and reliability of life prediction, and thus improves the maintenance and management efficiency of aircraft engines. The present invention can effectively infer the parent distribution through mixed distribution model and regression analysis, reduce the spectrum coding error, and greatly improve the prediction ability of the model under complex working conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying creative labor.

[0050] in:

[0051] Figure 1 A schematic diagram of a creep load characteristic modeling method according to an embodiment of the present invention;

[0052] Figure 2 A schematic diagram of creep load feature extraction according to an embodiment of the present invention;

[0053] Figure 3 A two-dimensional time distribution histogram diagram of creep load characteristics according to an embodiment of the present invention;

[0054] Figure 4 A schematic diagram of the regression relationship between high pressure rotation speed and exhaust temperature in an embodiment of the present invention;

[0055] Figure 5 This is a schematic diagram of the variation of AIC with the number of basic functions in an embodiment of the present invention;

[0056] Figure 6 It is a probability density function diagram of the one-dimensional mixed distribution of rotation speeds according to an embodiment of the present invention. DETAILED DESCRIPTION

[0057] In order to make the purpose, technical solution and advantages of the embodiment of the present invention clearer, the technical solution of the embodiment of the present invention will be clearly and completely described below in conjunction with the drawings of the embodiment of the present invention. Obviously, the described embodiment is a part of the embodiment of the present invention, not all of the embodiments. Based on the described embodiment of the present invention, all other embodiments obtained by ordinary technicians in this field belong to the scope of protection of the present invention.

[0058] like Figure 1 FIG. 1 is an embodiment of the present invention, which provides a method for modeling creep load characteristics in an aircraft engine load spectrum, including:

[0059] Step S1, extracting the steady-state points of the speed and temperature in the measured load spectrum of the aircraft engine to form a speed-temperature two-dimensional time distribution matrix;

[0060] Specifically, in step S1, the extraction of the steady-state points of the rotation speed and temperature in the measured load spectrum of the aircraft engine specifically includes the following steps:

[0061] The high pressure speed N2 is used as the speed representative value, and the exhaust temperature T5 is used as the temperature representative value;

[0062] The determination of the steady-state point starts from the third sampling point of the speed spectrum, and the slope k5 of the line connecting the i+2th sampling point and the i-2th sampling point in the speed spectrum is calculated. The calculation formula of the slope k5 is:

[0063]

[0064] Among them, N i+2 and N i-2 are the speeds of the i+2th sampling point and the i-2th sampling point, ti+2 and t i-2 are the time of the i+2th sampling point and the i-2th sampling point respectively;

[0065] Set the slope judgment threshold k cr If the slope k5 is less than the slope determination threshold k cr When , the i-th sampling point is taken as the speed steady-state point, and the i-th sampling point in the temperature spectrum corresponding to the speed steady-state point is taken as the temperature steady-state point;

[0066] The speed steady point and the temperature steady point form a speed-temperature two-dimensional time distribution matrix according to the speed N2 and the temperature steady point T5, and the creep load characteristic is expressed as (N2, T5).

[0067] Among them, the speed and temperature steady-state points in the measured load spectrum of the aircraft engine are extracted as the creep load characteristics, and the slope judgment threshold k is taken cr =1% / s, creep load feature extraction diagram, such as Figure 2 As shown in Table 1, the steady-state points (N2, T5) in all creep load characteristics are statistically formed into a speed-temperature two-dimensional time distribution matrix, as shown in Table 1. The two-dimensional time distribution histogram of the creep load characteristics is shown in Table 1. Figure 3 As shown;

[0068] Table 1 Speed-temperature two-dimensional time allocation matrix (unit: seconds)

[0069]

[0070] Furthermore, in step S2, least squares nonlinear regression is performed on the steady-state points of the rotation speed and temperature to establish a two-dimensional time regression relationship between rotation speed and temperature;

[0071] Specifically, in step S2, the establishment of the rotation speed-temperature two-dimensional time regression relationship specifically includes the following steps:

[0072] S2.1, using the least squares nonlinear regression method, the measured high-pressure speed N2 and exhaust temperature T5 are fitted to establish the speed-temperature two-dimensional time regression relationship. The regression model is expressed as: T5 = f reg (N2);

[0073] S2.2, by Pearson correlation coefficient R pearson Verify the validity of the established regression model. pearson When >0.9, the regression relationship is considered valid.

[0074] Among them, the least squares nonlinear regression of speed and temperature is as follows: Figure 4 As shown, the speed-temperature regression relationship is:

[0075]

[0076] Verify the speed-temperature correlation coefficient, Pearson correlation coefficient R pearson =0.95>0.9, the speed-temperature regression relationship is valid.

[0077] Further, in step S3, the lognormal distribution is selected as the basic function, the mixed distribution is selected as the distribution type, the parameters of the creep load characteristics are estimated by the EM algorithm, and the optimal number of basic functions is determined by the AIC (Akaike Information Criterion) method to establish a one-dimensional mixed distribution model of the rotation speed;

[0078] Specifically, in step S3, the basic function selection includes the following steps:

[0079] Selecting the lognormal distribution as the basic function, the probability density function of the lognormal distribution is expressed as:

[0080]

[0081] Where N2 is the high-pressure speed, μ is the logarithmic mean of the high-pressure speed, σ is the logarithmic standard deviation of the high-pressure speed, and f j (N2μ,σ) is the probability density function of the jth basic function.

[0082] The distribution type selection includes the following steps:

[0083] Select mixed distribution as the distribution type. The probability density function of the mixed distribution is expressed as:

[0084]

[0085] Among them, f(N2;θ) is the probability density function of the mixed distribution, f j (N2;θ j ) is the probability density function of the jth basic function, θ=[θ1,θ2,...,θ k ] is the set of all unknown parameters of the mixed distribution, w j is the weight of the jth basic function, satisfying the condition:

[0086] 0<w j <1 and

[0087] Where k is the number of basic functions in the mixed distribution model.

[0088] Among them, the EM algorithm is used to realize the parameter estimation of the mixed distribution, including the following operations:

[0089] Step 1: Randomly initialize the mixed distribution parameters θ 0 ;

[0090] Step 2: Start the EM algorithm iteration and set θ for the first run. t =θ 0 ;

[0091] Step 3, calculate the conditional expectation of the log-likelihood function LogL(θ);

[0092] Step 4: Solve for the model parameters and calculate the maximum likelihood estimate by maximizing LogL(θ) Get θ t+1 ;

[0093] Step 5: Determine θ t+1 Whether it converges, if it satisfies ||θ t+1 -θ t When ||<δ, the iteration stops, δ is the residual value of parameter iteration, which is taken as 1×10 -7 , then the output θ t+1 , otherwise repeat step 2.

[0094] Specifically, the optimal number of basic functions c is determined by the AIC method, and the calculation expression of AIC is:

[0095]

[0096] Where c is the number of basic functions, is the number of parameters in the creep load characteristic model when there are c basic functions,

[0097] LogL(c) is the value of the maximum log-likelihood function when there are c basic functions. When the AIC value is at an inflection point, continuing to increase the number of basic functions has little effect on improving the fitting effect. At this time, the number of basic functions c is the optimal value.

[0098] Specifically, we select lognormal distribution as the basic function, select mixed distribution as the distribution type, use EM algorithm for parameter estimation, and use AIC method to determine the optimal number of basic functions. The variation of AIC with the number of basic functions is as follows: Figure 5 As shown in the figure, it can be seen that in this implementation case, the AIC value is at the inflection point when the number of basic functions is 3. Therefore, the number of basic functions is 3 as the optimal solution. At this time, AIC(3)=2.6124×10 6 When the number of basic functions is 3, the parameter estimation results of the one-dimensional mixed distribution model of speed are shown in Table 2.

[0099] Table 2 Parameter estimation results of one-dimensional mixed distribution model of speed

[0100]

[0101] By analyzing the measured high-voltage speed data, the creep load characteristics were modeled using a mixed log-normal distribution. Figure 6 As shown in the figure, the probability density distribution of the measured data (represented by a histogram) and the fitting results of the mixed log-normal distribution model (red curve) are shown. It can be seen from the figure that the mixed log-normal distribution model captures the distribution trend of the measured data well, especially in the 85% to 95% speed range, the fitting effect is significant, indicating that the selected model can accurately reflect the actual creep load characteristics.

[0102] Furthermore, in step S4, the rotational speed-temperature regression relationship is combined with the rotational speed one-dimensional mixed distribution model to construct a creep load characteristic model.

[0103] Among them, the speed-temperature regression relationship The creep load characteristic model is composed of the one-dimensional mixed distribution model of speed (Table 2).

[0104] In addition, in step S1, the constructed speed-temperature two-dimensional time distribution matrix includes multiple speed and temperature intervals, and the time distribution of each interval is in seconds. The matrix is ​​used to statistically analyze the distribution of steady-state points in the creep load characteristics. The speed interval is between 70.0% and 100.0%, and the temperature interval is between 360°C and 780°C.

[0105] Among them, the lognormal distribution is selected as the basic function, the EM algorithm is used for parameter estimation, and the optimal number of basic functions of the mixed distribution is determined to be 3. The parameters of the mixed distribution model include:

[0106] The weights of the basic functions are: w1 = 0.701, w2 = 0.122, w3 = 0.176;

[0107] The logarithmic means are: μ1=4.485, μ2=4.422, μ3=4.564;

[0108] The standard deviations are: σ1=0.028, σ2=0.059, σ3=0.016 respectively.

[0109] In summary, the present invention achieves high-precision modeling of the creep load characteristics of aircraft engines by constructing a mixed distribution model based on lognormal distribution, combining least squares nonlinear regression and EM algorithm. This model can not only accurately describe the creep load characteristics under different flight mission conditions, but also automatically optimize the model complexity to ensure the adaptability and accuracy of the model. The present invention greatly improves the accuracy and reliability of aircraft engine life prediction, provides a more scientific basis for engine service life assessment, and has significant practical application value and promotion prospects.

[0110] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present application. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine different embodiments or examples described in this specification and the features of different embodiments or examples, unless they are contradictory.

[0111] Any process or method description in the flow chart or otherwise described herein can be understood to represent a module, fragment or portion of a code including one or more executable instructions for implementing the steps of a specific logical function or process. And the scope of the preferred embodiment of the present application includes other implementations, in which the functions may not be performed in the order shown or discussed, including in a substantially simultaneous manner or in a reverse order according to the functions involved.

[0112] The above is only a specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any technician familiar with the technical field can easily think of various changes or substitutions within the technical scope disclosed in the present application, which should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

Claims

1. A method for modeling creep load characteristics in an aero-engine load spectrum, characterized in that: The following steps are involved: Step S1, extracting the steady-state points of the speed and temperature in the measured load spectrum of the aircraft engine to form a speed-temperature two-dimensional time distribution matrix; Step S2, performing least squares nonlinear regression on the steady-state points of the rotation speed and temperature to establish a rotation speed-temperature regression relationship; Step S3, selecting lognormal distribution as a basic function, selecting mixed distribution as a distribution type, using EM algorithm to estimate the parameters of creep load characteristics, and determining the optimal number of basic functions by AIC method to establish a one-dimensional mixed distribution model of rotation speed; Step S4, combining the rotation speed-temperature regression relationship with the rotation speed one-dimensional mixed distribution model to construct a creep load characteristic model.

2. The method for modeling creep load characteristics in an aero-engine load spectrum according to claim 1, characterized in that: In step S1, the steady-state points of the rotation speed and temperature in the measured load spectrum of the aircraft engine are extracted. The following steps are involved: The high pressure speed N2 is used as the speed representative value, and the exhaust temperature T5 is used as the temperature representative value; The determination of the steady-state point starts from the third sampling point of the speed spectrum, and the absolute value k5 of the slope of the line connecting the i+2th sampling point and the i-2th sampling point in the speed spectrum is calculated. The calculation formula of the absolute value k5 of the slope is: Among them, N i+2 and N i-2 are the speeds of the i+2th sampling point and the i-2th sampling point, t i+2 and t i-2 are the time of the i+2th sampling point and the i-2th sampling point respectively; Set the slope judgment threshold k cr , if the absolute value k5 of the slope is less than the slope determination threshold k cr When , the i-th sampling point is taken as the speed steady-state point, and the i-th sampling point in the temperature spectrum corresponding to the speed steady-state point is taken as the temperature steady-state point; The speed steady point and the temperature steady point form a speed-temperature two-dimensional time distribution matrix according to the speed N2 and the temperature steady point T5, and the creep load characteristic is expressed as (N2, T5).

3. The method for modeling creep load characteristics in an aero-engine load spectrum according to claim 1, characterized in that: In step S2, the establishment of the rotation speed-temperature regression relationship includes the following steps: S2.1, using the least squares nonlinear regression method, the measured high-pressure speed N2 and exhaust temperature T5 are fitted to establish the speed-temperature two-dimensional time regression relationship. The regression model is expressed as: T5 = f reg (N2); S2.2, by Pearson correlation coefficient R pearson Verify the validity of the established regression model. pearson When >0.9, the regression relationship is considered valid.

4. The method for modeling creep load characteristics in an aircraft engine load spectrum according to claim 1, characterized in that: In step S3, the basic function selection includes the following steps: Selecting the lognormal distribution as the basic function, the probability density function of the lognormal distribution is expressed as: Where N2 is the high-pressure speed, μ is the logarithmic mean of the high-pressure speed, σ is the logarithmic standard deviation of the high-pressure speed, π is the circumference of the circle, e is a natural constant, and f j (N2|μ,σ) is the probability density function of the jth basic function.

5. The method for modeling creep load characteristics in an aero-engine load spectrum according to claim 1, characterized in that: In step S3, the distribution type selection includes the following steps: Select mixed distribution as the distribution type. The probability density function of the mixed distribution is expressed as: Among them, f(N2;θ) is the probability density function of the mixed distribution, f j (N2;θ j ) is the probability density function of the jth basic function, θ=[θ1,θ2,...,θ k ] is the set of all unknown parameters of the mixed distribution, w j is the weight of the jth basic function, satisfying the condition: 0<w j <1 and Where k is the number of basic functions in the mixed distribution model.

6. The method for modeling creep load characteristics in an aero-engine load spectrum according to claim 1, characterized in that: The EM algorithm is used to estimate the parameters of the mixed distribution, including the following operations: Step 1: Randomly initialize the mixed distribution parameters θ 0 ; Step 2: Start the EM algorithm iteration and set θ for the first run. t =θ 0 ; Step 3, calculate the conditional expectation of the log-likelihood function LogL(θ); Step 4: Solve for the model parameters and calculate the maximum likelihood estimate by maximizing LogL(θ) Get θ t+1 ; Step 5: Determine θ t+1 Whether it converges, if it satisfies ||θ t+1 -θ t When ||<δ, the iteration stops, δ is the residual value of parameter iteration, which is taken as 1×10 -7 , then the output θ t+1 , otherwise repeat step 2.

7. The method for modeling creep load characteristics in an aircraft engine load spectrum according to claim 1, characterized in that: In step S3, the optimal number of basic functions c is determined by the AIC method, and the calculation expression of AIC is: Where c is the number of basic functions, is the number of parameters in the creep load characteristic model when there are c basic functions, and LogL(c) is the value of the maximum log-likelihood function when there are c basic functions. When the AIC value is at an inflection point, continuing to increase the number of basic functions has little effect on improving the fitting effect, and the number of basic functions c is the optimal value at this time.

8. The method for modeling creep load characteristics in an aero-engine load spectrum according to claim 1, characterized in that: In step S4, the speed-temperature regression relationship and the speed one-dimensional mixed distribution model together constitute a creep load characteristic model.

9. The method for modeling creep load characteristics in an aircraft engine load spectrum according to claim 1, characterized in that: In step S1, the constructed speed-temperature two-dimensional time distribution matrix includes multiple speed and temperature intervals, and the time distribution of each interval is in seconds. The matrix is ​​used to statistically calculate the distribution of steady-state points (N2, T5) in the creep load characteristics. The speed interval is between 70.0% and 100.0%, and the temperature interval is between 360°C and 780°C.

10. According to the method for modeling creep load characteristics in an aircraft engine load spectrum as described in claim 1, in step S3, a lognormal distribution is selected as a basic function, an EM algorithm is used for parameter estimation, and the optimal number of basic functions of the mixed distribution is determined to be 3, and the parameters of the mixed distribution model include: The weights of the basic functions are: w1 = 0.701, w2 = 0.122, w3 = 0.176; The logarithmic means are: μ1=4.485, μ2=4.422, μ3=4.564; The logarithmic standard deviations are: σ1=0.028, σ2=0.059, σ3=0.016.

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