Aero-engine gear time-varying reliability analysis method based on Gaussian process model

Abstract

The invention discloses an aero-engine gear time-varying reliability analysis method based on a Gaussian process model. The method comprises the steps that S1, a two-failure-mode series reliability model of an aero-engine gear is established; s2, on the basis of the two-failure-mode reliability model, considering tooth surface wear, and establishing a three-failure-mode series reliability model; s3, in combination with the Gaussian process model, establishing an improved single-cycle Gaussian process model considering the first fault moment; s4, performing aeroengine gear time-varying reliability analysis by using the three-failure-mode series reliability model and the improved single-cycle Gaussian process model; compared with other methods, the method is more excellent in precision and efficiency.

Description

Technical Field

[0001] The invention belongs to the field of aircraft engine reliability analysis, and in particular relates to an aircraft engine gear time-varying reliability analysis method based on a Gaussian process model. Background Art

[0002] In the current era of globalization, the aviation field plays an extremely critical role as an important bridge connecting the world. The research objects in the aviation industry are numerous and complex, and the performance of aircraft engines, as the "heart" of aircraft, is directly related to the safety, economy and other indicators of aircraft. Strengthening the research on aircraft engine reliability will help improve the quality of aircraft engine products, improve technical competitiveness, reduce maintenance costs, achieve cost reduction and increase efficiency, and provide impetus for achieving the country's medium- and long-term scientific and technological development goals.

[0003] As the main component of aircraft engines, aircraft engine accessory casing transmits power to various components when the engine is working to maintain the normal operation of various systems of aircraft. The most important component system in aircraft engine accessory casing is the gear transmission system. Most of the functions of the accessory casing are realized by the gear transmission system. Therefore, the performance of the gear transmission system has a direct impact on the overall operation of the aircraft engine. Gears are the core components for transmitting power and adjusting speed. The research on their reliability is crucial to improving the safety and operational performance of aircraft.

[0004] As the performance requirements of aircraft engines continue to upgrade and the number of auxiliary equipment on board increases, the demand for the speed and power input of the accessory casing is also increasing, which puts higher requirements on the design and manufacture of transmission gears. New designs need to take into account factors such as higher loads, more extreme temperature conditions and longer service life. In addition, the pursuit of lighter and thinner-walled aircraft gears poses higher challenges to the gear transmission system in the accessory casing in terms of component design, manufacturing process, and testing technology.

[0005] Traditional reliability analysis is based on the calculation of instantaneous reliability results under time-independent conditions. In this case, only the uncertainty factors of material properties, environmental loads and model errors are usually considered, while time-related factors such as load changes over time, material strength degradation, and component fatigue accumulation process are ignored, resulting in inaccurate reliability analysis results. Therefore, considering incorporating time factors into reliability analysis to complete structural time-varying reliability analysis can better deal with the problem and obtain more accurate results. Summary of the invention

[0006] In view of the above-mentioned deficiencies in the prior art, the Gaussian process model-based time-varying reliability analysis method for aircraft engine gears provided by the present invention solves the problem that the existing time-varying reliability analysis method for aircraft engine gears ignores time-related influencing factors, thereby leading to inaccurate reliability analysis results.

[0007] In order to achieve the above-mentioned purpose of the invention, the technical solution adopted by the present invention is: a time-varying reliability analysis method for aircraft engine gears based on a Gaussian process model, comprising the following steps:

[0008] S1. Establish a two-failure-mode series reliability model for aircraft engine gears;

[0009] Among them, the two failure modes include gear tooth surface pitting and gear breakage;

[0010] S2. Based on the two-failure mode reliability model, a three-failure mode series reliability model is established by considering tooth surface wear;

[0011] S3. Combined with the Gaussian process model, an improved single-loop Gaussian process model considering the first failure moment is established;

[0012] S4. Use the three-failure-mode tandem reliability model and the improved single-cycle Gaussian process model to perform time-varying reliability analysis on aircraft engine gears.

[0013] Furthermore, the step S1 is specifically as follows:

[0014] S11. Based on the gear engineering test data, the comprehensive influence coefficient is introduced to correct the gear contact stress-life curve and bending stress-life curve corresponding to gear tooth surface pitting and gear breakage respectively;

[0015] S12. Establish the gear dynamics model and solve it to obtain the tooth surface contact stress σ H and tooth root bending stress σ F , and then establish the gear tooth surface contact stress load spectrum σ ht0 and tooth root bending stress load spectrum σ ft0 ;

[0016] S13, based on fatigue damage accumulation theory, using Miner's law, according to the load spectrum Load spectrum As well as the modified gear contact stress-life curve and bending stress-life curve, the functional functions of the two failure modes of gear tooth surface pitting and gear breakage are established, and then the reliability model of the two failure modes in series is obtained.

[0017] Furthermore, the step S13 is specifically as follows:

[0018] In the established gear tooth surface contact stress load spectrum and tooth root bending stress load spectrum Based on the rain flow counting method, the load frequency is counted;

[0019] According to the modified gear contact stress-life curve and bending stress-life curve, and based on the fatigue damage accumulation theory, the life limit under multi-level stress is calculated;

[0020] Based on the statistical load frequency and life limit under multi-level stress, according to Miner's law, the cumulative damage corresponding to gear tooth surface pitting and gear tooth fracture is calculated as a functional function, and then a reliability model of two failure modes in series is obtained.

[0021] Furthermore, in step S13, the expression of the reliability model of the two failure modes in series is:

[0022]

[0023] Where D H (X,t) represents the tooth surface pitting function, D F (X,t) represents the gear breaking function, r i represents the linear function of the load spectrum and the solution time, and refers to the load frequency under the load amplitude corresponding to the subscript i, represents the tooth surface contact stress load spectrum, represents the tooth root bending stress load spectrum, t represents the solution time, t0 represents the time when the gear rotates for a fixed period, N i It represents the life limit corresponding to the subscript i, which is obtained from the stress-life curve. The subscript i = 1, 2, 3, …, n represents the number of different load amplitudes.

[0024] Furthermore, the step S2 is specifically as follows:

[0025] S21. Determine the allowable wear amount [h] using the precision method, and establish a relationship model between the normal line wear amount of the contact surface and time based on the solid wear theory and Hertz contact theory as the gear continuous wear model h(t);

[0026] S22, considering the impact wear during the operation of the gear, a segmented processing method is used to establish a relationship model between the impact wear and time as the gear impact wear model D(t);

[0027] S23. Based on the gear continuous wear model h(t) and the gear impact wear model D(t), a wear amount-wear threshold model is constructed as a functional function of tooth surface wear, and combined with the two failure mode series reliability model, a three failure mode series reliability model is established.

[0028] Furthermore, in step S23, the three-failure-mode series reliability model established is:

[0029]

[0030] Furthermore, in step S3, the method for establishing the improved single-loop Gaussian process model is specifically:

[0031] S31. Generate initial sample x using Monte Carlo sampling T0 , and randomly generate the initial time t T0 ;

[0032] S32, combining samples and moments into training sample points X TP , and calculate the response value Y of the time-varying function TP =g(X TP );

[0033] S33. Use X TP and Y TP Constructing Gaussian process models;

[0034] S34, use Monte Carlo to sample from the original distribution to generate N CP samples, and the required time interval [0,t e ] is divided into N T The vector T of the moment e , for each sample x CP and the time vector T e Combine to form X CP ;

[0035] S35. Predict X using Gaussian process model CP The mean and standard deviation of the response and calculate X CP The failure time T of each sample in F and X CP The number of failed samples N F ,judge whether it is established;

[0036] If yes, proceed to step S36;

[0037] If not, change N CP The number of, return to step S34;

[0038] S36, calculate X CP Each sample T F The first contribution value C at each moment before CP1 , the failure time T F The contribution values ​​of the subsequent sample points are all zero, and the first contribution value is calculated from X CP Select a certain number of points to form X SCP;

[0039] S37, calculate X SCP The expected maximum value of the predicted failure probability at all times at each point in the max (P f )=Σmax(C CP1 ) / N SCP , and the maximum value of the standard deviation of the failure probability threshold

[0040] judge whether it is established;

[0041] If not, proceed to step S38;

[0042] If yes, proceed to step S39;

[0043] Among them, δ0 represents the allowable relative error of failure probability, Φ -1 represents the inverse function of the standard normal distribution function, α represents the significance level, and 1-α represents the confidence level;

[0044] S38. Using the learning function in X SCP Select the update point x new , calculate the update point (x new ,t new ) at the response value y new , and (x new ,t new ) and y new Add to X TP and Y TP , return to step S33;

[0045] S39, obtain an improved single-cycle Gaussian process model and use it for the failure probability P f Evaluation calculation.

[0046] Furthermore, the step S4 is specifically as follows:

[0047] S41. Based on the three-failure mode series reliability model, sample points are obtained by sampling and a Gaussian process model is constructed;

[0048] S42, calculating the first failure moment of each sample, updating the sample space using the learning function, and iterating the Gaussian process model until the Gaussian process model converges to obtain an improved single-cycle Gaussian process model;

[0049] S43. Monte Carlo sampling is used to generate samples of the three-failure mode series reliability model, and the samples are substituted as input into the improved single-cycle Gaussian process model to solve the time-varying failure probability of aircraft engine gears and complete the reliability analysis.

[0050] Furthermore, in step S43, the method for improving the single-loop Gaussian process model for time-varying reliability analysis is specifically as follows:

[0051] S43-1. Generate N using Monte Carlo sampling MCS Sample points x MCS ;

[0052] S43-2. ​​Calculate the sample point x using the improved single-cycle Gaussian process model MCS The model response

[0053] S43-3, according to Calculate an estimate of the probability of failure I(·) represents the indicator function. When I(·)=1, When , I(·)=0;

[0054] S43-4. Judgment Is it true? CV(·) represents the coefficient of variation;

[0055] If yes, proceed to step S43-5;

[0056] If not, increase N MCS , and returns to step S43-1;

[0057] S43-5. When the set convergence conditions are met, the calculated estimated failure probability is used as the solved time-varying failure probability of the gear to complete the reliability analysis.

[0058] The beneficial effects of the present invention are:

[0059] (1) Aiming at the problem of time-varying reliability analysis, the present invention considers the instantaneous moment of the first failure and proposes a reliability analysis method based on an improved single-cycle Gaussian process model that considers the moment of the first failure. The proposed method is used for time-varying reliability analysis of aircraft engine gears, and the time-varying failure probability of aircraft engine gears is evaluated. The method is then compared with other methods to demonstrate its high efficiency and accuracy.

[0060] (2) The time-varying reliability analysis method based on the proxy model in the method of the present invention improves the computational efficiency by constructing an approximate model to replace the performance function, which is more advantageous for highly nonlinear implicit performance functions.

[0061] (3) The present invention adopts an improved single-cycle Gaussian process model for reliability analysis. The Gaussian process is a powerful probability model used to describe random processes. Its characteristic is that the joint distribution of any finite number of variables obeys the multidimensional normal distribution. In the proxy model, the Gaussian process is used to model the unknown mapping relationship of the objective function or the system. Based on this, even if the specific form of the objective function is unknown, the potential distribution of the objective function can be inferred through some existing observation data (sample points). BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 A flow chart of the time-varying reliability analysis method for aircraft engine gears based on the Gaussian process model provided by the present invention.

[0063] Figure 2 The present invention provides a gear transmission dynamics model. DETAILED DESCRIPTION

[0064] The specific implementation modes of the present invention are described below so that those skilled in the art can understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific implementation modes. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the attached claims, these changes are obvious, and all inventions and creations utilizing the concept of the present invention are protected.

[0065] The embodiment of the present invention provides a method for analyzing the time-varying reliability of aircraft engine gears based on a Gaussian process model. Figure 1 As shown, the following steps are included:

[0066] S1. Establish a two-failure-mode series reliability model for aircraft engine gears;

[0067] Among them, the two failure modes include gear tooth surface pitting and gear breakage;

[0068] S2. Based on the two-failure mode reliability model, a three-failure mode series reliability model is established by considering tooth surface wear;

[0069] S3. Combined with the Gaussian process model, an improved single-loop Gaussian process model considering the first failure moment is established;

[0070] S4. Use the three-failure-mode tandem reliability model and the improved single-cycle Gaussian process model to perform time-varying reliability analysis on aircraft engine gears.

[0071] Step S1 of the embodiment of the present invention is specifically as follows:

[0072] S11. Based on the gear engineering test data, the comprehensive influence coefficient is introduced to correct the gear contact stress-life curve and bending stress-life curve corresponding to gear tooth surface pitting and gear breakage respectively;

[0073] In an example of this embodiment, taking the material 12Cr2Ni4A as an example, a time-varying reliability analysis is performed; by consulting the literature, the SN curve fitting equation lgN = 51.6567-15.5873lgσ S However, the SN curve of the material is obtained through the tensile fatigue test of the smooth specimen or the notched specimen. The shape and size of the specimen are quite different from the gear. Therefore, the comprehensive influence is introduced in this embodiment, and the modified tooth surface contact stress-life curve expression lgN=50.4567-15.5873lgσ is obtained. h , and the tooth root bending stress-life curve expression lgN = 13.7070-3.4299lgσ f ;

[0074] S12. Establish the gear dynamics model and solve it to obtain the tooth surface contact stress σ H and tooth root bending stress σ F , and then establish the gear tooth surface contact stress load spectrum σ ht0 and tooth root bending stress load spectrum σ ft0 ;

[0075] In one example of this embodiment, the gear dynamics model is as follows: Figure 2 As shown, on this basis, the gear dynamics equation is established to solve the time-varying meshing stiffness and dynamic meshing force of the gear. The dynamic meshing force of the gear is regarded as the loaded tangential force. According to ISO 6336-2 and Hertz contact theory, the tooth surface contact stress σ is calculated. H , calculated according to ISO 6336-3, the tooth root bending stress σ F , and then establish the gear tooth surface contact stress load spectrum σ ht0 and tooth root bending stress load spectrum σ ft0 ;

[0076] S13, based on fatigue damage accumulation theory, using Miner's law, according to the load spectrum σ ht0 , load spectrum σ ft0 As well as the modified gear contact stress-life curve and bending stress-life curve, the functional functions of the two failure modes of gear tooth surface pitting and gear breakage are established, and then the reliability model of the two failure modes in series is obtained.

[0077] Step S13 of this embodiment is specifically as follows:

[0078] In the established gear tooth surface contact stress load spectrum σ ht0and tooth root bending stress load spectrum σ ft0 Based on the rain flow counting method, the load frequency is counted;

[0079] According to the modified gear contact stress-life curve and bending stress-life curve, and based on the fatigue damage accumulation theory, the life limit under multi-level stress is calculated;

[0080] Based on the statistical load frequency and life limit under multi-level stress, according to Miner's law, the cumulative damage corresponding to gear tooth pitting and gear tooth fracture is calculated as a function, and then the reliability model of two failure modes in series is obtained, and its expression is:

[0081]

[0082] Where D H (X,t) represents the tooth surface pitting function, D F (X,t) represents the gear breaking function, r i represents the linear function of the load spectrum and the solution time, and refers to the load frequency under the load amplitude corresponding to the subscript i, represents the tooth surface contact stress load spectrum, represents the tooth root bending stress load spectrum, t represents the solution time, t0 represents the time when the gear rotates for a fixed period, N i It represents the life limit corresponding to the subscript i, which is obtained from the stress-life curve. The subscript i = 1, 2, 3, …, n represents the number of different load amplitudes.

[0083] In one example of this embodiment, the fatigue damage accumulation theory believes that the internal damage of the structure accumulates continuously during operation, and the fatigue failure of the structure occurs when the accumulated damage reaches the damage threshold. In this embodiment, the damage accumulation model is established based on Miner's law. On the basis of establishing the load spectrum, the rainflow function in MATLAB is used to complete the load frequency statistics based on the rainflow counting method. Combined with the modified stress-life curve, the gear cumulative damage is obtained according to the above process, and then the gear tooth surface pitting and gear tooth breakage two failure mode function functions are established. Since the two failure modes are in series, a two-failure mode series reliability model can be obtained.

[0084] Step S2 of the embodiment of the present invention is specifically as follows:

[0085] S21. Determine the allowable wear amount [h] using the precision method, and establish a relationship model between the normal line wear amount of the contact surface and time based on the solid wear theory and Hertz contact theory as the gear continuous wear model h(t);

[0086] In one example of this embodiment, the main basis for judging the occurrence of gear wear failure is considered to be whether the wear amount exceeds the wear threshold, and the precision method is used to determine the allowable wear amount [h]. Based on the solid wear theory and Hertz contact theory, a relationship model between the normal line wear amount of the contact surface and time is established;

[0087] S22, considering the impact wear during the operation of the gear, a segmented processing method is used to establish a relationship model between the impact wear and time as the gear impact wear model D(t);

[0088] In one example of this embodiment, factors causing impact wear include operating conditions and environmental factors;

[0089] In an example of this embodiment, considering that the impact process is a discrete process, a method for establishing a relationship model between impact wear and time by using a segmented processing method is as follows:

[0090] Firstly, the amount of wear caused by each impact is assumed, and the number of impacts is assumed to be a counting function that obeys a Poisson process. The total amount of wear in the time interval is calculated, and then a relationship model between impact wear and time is established.

[0091] S23. Based on the gear continuous wear model h(t) and the gear impact wear model D(t), a wear amount-wear threshold model is constructed as a functional function of tooth surface wear, and combined with the two failure mode series reliability model, a three failure mode series reliability model is established.

[0092] In step S23 of this embodiment, the established three-failure mode series reliability model is:

[0093]

[0094] Specifically, based on the continuous wear model and the impact wear model, this embodiment considers that when the wear amount exceeds the wear threshold, the gear fails due to wear, so a wear amount-wear threshold model G can be constructed. w (t) = [h] - h(t) - D(t). Since tooth surface wear, tooth surface pitting and gear tooth breakage are in series, the reliability model of the two failure modes of gear tooth surface pitting and gear tooth breakage established previously can be combined to obtain the reliability model of the three failure modes of gear tooth surface pitting, gear tooth breakage and wear in series.

[0095] In step S3 of the embodiment of the present invention, before establishing the improved single-loop Gaussian process model, the principle and construction method of the single-loop proxy model are analyzed based on the single-layer loop Kriging model; in this embodiment, the single-loop proxy model refers to completing the time-varying reliability analysis by constructing a single-layer proxy model, which can effectively solve the problem of high computational cost of the double-layer nested loop proxy model. The process of reliability analysis of the loop proxy model is as follows:

[0096] Step 1: Parameter initialization, setting the model maximum error threshold ε th = 0.05, set the time interval of interest and the number of interval divisions N t ;

[0097] Step 2: Use the Quasi Monte Carlo (QMC) technique to sample and obtain N0 initial training samples;

[0098] Step 3: Generate N candidate sample points

[0099] Step 4: Use the training sample point set to build a proxy model, and use the proxy model to calculate the predicted response value and U function value of the candidate sample point set at each moment;

[0100] Step 5: Calculate N f1 and N f1 , and use this to calculate the maximum error ε max , judge ε max Is it less than ε? th , decide whether the model continues to update, if so, find the update point x new Add the training sample point set and go to step 4 to repeat the above operation; if not, go to step 6;

[0101] Step 6: Determine whether the model error reaches the threshold requirement. If so, go to step 7; if not, increase the number of candidate sample points N, go to step 3 and repeat the above operation;

[0102] Step 7: Complete the calculation of failure probability through the proxy model.

[0103] In this embodiment, the common single-layer cyclic proxy model only considers whether the sample fails in the entire time trajectory, but does not consider when the failure occurs in the interval, and cannot obtain the failure probability of any sub-time interval. A proxy model modeling idea that considers the first failure moment is proposed. The Gaussian process model is obtained by training the GPML toolbox in MATLAB, and an improved single-cycle Gaussian process model that considers the first failure moment is established. The method is as follows:

[0104] S31. Generate initial sample x using Monte Carlo sampling T0 , and randomly generate the initial time tT0 ;

[0105] S32, combining samples and moments into training sample points X TP , and calculate the response value Y of the time-varying function TP =g(X TP );

[0106] S33. Use X TP and Y TP Constructing Gaussian process models;

[0107] S34, use Monte Carlo to sample from the original distribution to generate N CP samples, and the required time interval [0,t e ] is divided into N T The vector T of the moment e , for each sample x CP and the time vector T e Combine to form X CP ;

[0108] S35. Predict X using Gaussian process model CP The mean and standard deviation of the response and calculate X CP The failure time T of each sample in F and X CP The number of failed samples N F ,judge whether it is established;

[0109] If yes, proceed to step S36;

[0110] If not, change N CP The number of, return to step S34;

[0111] S36, calculate X CP Each sample T F The first contribution value C at each moment before CP1 , the failure time T F The contribution values ​​of the subsequent sample points are all zero, and the first contribution value is calculated from X CP Select a certain number of points to form X SCP ;

[0112] S37, calculate X SCP The expected maximum value of the predicted failure probability at all times at each point in the max (P f )=Σmax(C CP1 ) / N SCP , and the maximum value of the standard deviation of the failure probability threshold

[0113] judge whether it is established;

[0114] If not, proceed to step S38;

[0115] If yes, proceed to step S39;

[0116] Among them, δ0 represents the allowable relative error of failure probability, Φ -1 represents the inverse function of the standard normal distribution function, α represents the significance level, and 1-α represents the confidence level;

[0117] S38. Using the learning function in X SCP Select the update point x new , calculate the update point (x new ,t new ) at the response value y new , and (x new ,t new ) and y new Add to X TP and Y TP , return to step S33;

[0118] S39, obtain an improved single-cycle Gaussian process model and use it for the failure probability P f Evaluation calculation.

[0119] Step S4 of the embodiment of the present invention is specifically as follows:

[0120] S41. Based on the three-failure mode series reliability model, sample points are obtained by sampling and a Gaussian process model is constructed;

[0121] S42, calculating the first failure moment of each sample, updating the sample space using the learning function, and iterating the Gaussian process model until the Gaussian process model converges to obtain an improved single-cycle Gaussian process model;

[0122] S43. Monte Carlo sampling is used to generate samples of the three-failure mode series reliability model, and the samples are substituted as input into the improved single-cycle Gaussian process model to solve the time-varying failure probability of aircraft engine gears and complete the reliability analysis.

[0123] In step S43 of this embodiment, the method for improving the single-cycle Gaussian process model for time-varying reliability analysis is specifically as follows:

[0124] S43-1. Generate N using Monte Carlo sampling MCS Sample points x MCS ;

[0125] S43-2. ​​Calculate the sample point x using the improved single-cycle Gaussian process model MCS The model response

[0126] S43-3, according to Calculate an estimate of the probability of failure I(·) represents the indicator function. When I(·)=1, When , I(·)=0;

[0127] S43-4. Judgment Is it true? CV(·) represents the coefficient of variation;

[0128] If yes, proceed to step S43-5;

[0129] If not, increase N MCS , and returns to step S43-1;

[0130] S43-5. When the set convergence conditions are met, the calculated estimated failure probability is used as the solved time-varying failure probability of the gear to complete the reliability analysis.

[0131] In the embodiment of the present invention, a specific calculation example of performing reliability analysis using the method of the present invention is provided.

[0132] In this embodiment, the improved single-loop Gaussian process model considering the first failure moment is applied to the time-varying reliability analysis of the research object aircraft engine gear, and the MCS method, the single-loop kriging (Single Loop Kriging, SILK) method, the NewSILK method and the improved Gaussian process model method are used for comparative verification. The error is the relative error of the MCS method result, and the results are shown in Table 1. The results show that the number of function calls using the MCS method is 10,000, the SILK method is 29 times, the NewSILK method is 94 times, and the method proposed in the invention is 39 times, which is second only to the SILK method, but it is the best in terms of calculation accuracy compared to the other two methods. Although the SILK method has a lower calculation cost, its accuracy is the lowest among all methods.

[0133] Table 1

[0134]

[0135] The present invention uses specific embodiments to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core idea. At the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as a limitation on the present invention.

[0136] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific variations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed by the present invention, and these variations and combinations are still within the protection scope of the present invention.

Claims

1. A time-varying reliability analysis method for aircraft engine gears based on a Gaussian process model, characterized in that: The following steps are involved: S1. Establish a two-failure-mode series reliability model for aircraft engine gears; Among them, the two failure modes include gear tooth surface pitting and gear breakage; S2. Based on the two-failure mode reliability model, a three-failure mode series reliability model is established by considering tooth surface wear; S3. Combined with the Gaussian process model, an improved single-loop Gaussian process model considering the first failure moment is established; S4. Use the three-failure-mode tandem reliability model and the improved single-cycle Gaussian process model to perform time-varying reliability analysis on aircraft engine gears.

2. The method for time-varying reliability analysis of aircraft engine gears based on Gaussian process model according to claim 1 is characterized in that: The step S1 is specifically as follows: S11. Based on the gear engineering test data, the comprehensive influence coefficient is introduced to correct the gear contact stress-life curve and bending stress-life curve corresponding to gear tooth surface pitting and gear breakage respectively; S12. Establish the gear dynamics model and solve it to obtain the tooth surface contact stress σ H and tooth root bending stress σ F , and then establish the gear tooth surface contact stress load spectrum σ ht0 and tooth root bending stress load spectrum σ ft0 ; S13, based on fatigue damage accumulation theory, using Miner's law, according to the load spectrum σ ht0 , load spectrum σ ft0 As well as the modified gear contact stress-life curve and bending stress-life curve, the functional functions of the two failure modes of gear tooth surface pitting and gear breakage are established, and then the reliability model of the two failure modes in series is obtained.

3. The method for time-varying reliability analysis of aircraft engine gears based on Gaussian process model according to claim 2 is characterized in that: The step S13 is specifically as follows: In the established gear tooth surface contact stress load spectrum σ ht0 and tooth root bending stress load spectrum σ ft0 Based on the rain flow counting method, the load frequency is counted; According to the modified gear contact stress-life curve and bending stress-life curve, and based on the fatigue damage accumulation theory, the life limit under multi-level stress is calculated; Based on the statistical load frequency and life limit under multi-level stress, according to Miner's law, the cumulative damage corresponding to gear tooth surface pitting and gear tooth fracture is calculated as a functional function, and then a reliability model of two failure modes in series is obtained.

4. The method for time-varying reliability analysis of aircraft engine gears based on Gaussian process model according to claim 2 is characterized in that: In step S13, the expression of the reliability model of the two failure modes in series is: Where D H (X,t) represents the pitting function of the tooth surface, D F (X,t) represents the gear breaking function, r i represents the linear function of the load spectrum and the solution time, and refers to the load frequency under the load amplitude corresponding to the subscript i, represents the tooth surface contact stress load spectrum, represents the tooth root bending stress load spectrum, t represents the solution time, t0 represents the time when the gear rotates for a fixed period, N i It represents the life limit corresponding to the subscript i, which is obtained from the stress-life curve. The subscript i = 1, 2, 3, …, n represents the number of different load amplitudes.

5. The method for time-varying reliability analysis of aircraft engine gears based on Gaussian process model according to claim 4 is characterized in that: The step S2 is specifically as follows: S21. Determine the allowable wear amount [h] using the precision method, and establish a relationship model between the normal line wear amount of the contact surface and time based on the solid wear theory and Hertz contact theory as the gear continuous wear model h(t); S22, considering the impact wear during the operation of the gear, a segmented processing method is used to establish a relationship model between the impact wear and time as the gear impact wear model D(t); S23. Based on the gear continuous wear model h(t) and the gear impact wear model D(t), a wear amount-wear threshold model is constructed as a functional function of tooth surface wear, and combined with the two failure mode series reliability model, a three failure mode series reliability model is established.

6. The method for time-varying reliability analysis of aircraft engine gears based on Gaussian process model according to claim 5 is characterized in that: In step S23, the established three-failure mode series reliability model is:

7. The method for time-varying reliability analysis of aircraft engine gears based on Gaussian process model according to claim 1, characterized in that: In step S3, the method for establishing the improved single-loop Gaussian process model is specifically: S31. Generate initial sample x using Monte Carlo sampling T0 , and randomly generate the initial time t T0 ; S32, combining samples and moments into training sample points X TP , and calculate the response value Y of the time-varying function TP =g(X TP ); S33. Use X TP and Y TP Constructing Gaussian process models; S34, use Monte Carlo to sample from the original distribution to generate N CP samples, and the required time interval [0,t e ] is divided into N T The vector T of the moment e , for each sample x CP and the time vector T e Combine to form X CP ; S35. Predict X using Gaussian process model CP The mean and standard deviation of the response and calculate X CP The failure time T of each sample in F and X CP The number of failed samples N F ,judge whether it is established; If yes, proceed to step S36; If not, change N CP The number of, return to step S34; S36, calculate X CP Each sample T F The first contribution value C at each moment before CP1 , the failure time T F The contribution values ​​of the subsequent sample points are all zero, and the first contribution value is calculated from X CP Select a certain number of points to form X SCP ; S37, calculate X SCP The expected maximum value of the predicted failure probability at all times at each point in the max (P f )=∑max(C CP1 ) / N SCP , and the maximum value of the standard deviation of the failure probability threshold judge whether it is established; If not, proceed to step S38; If yes, proceed to step S39; Among them, δ0 represents the allowable relative error of failure probability, Φ -1 represents the inverse function of the standard normal distribution function, α represents the significance level, and 1-α represents the confidence level; S38. Using the learning function in X SCP Select the update point x new , calculate the update point (x new ,t new ) at the response value y new , and (x new ,t new ) and y new Add to X TP and Y TP , return to step S33; S39, obtain an improved single-cycle Gaussian process model and use it for the failure probability P f Evaluation calculation.

8. The method for time-varying reliability analysis of aircraft engine gears based on Gaussian process model according to claim 1, characterized in that: The step S4 is specifically as follows: S41. Based on the three-failure mode series reliability model, sample points are obtained by sampling and a Gaussian process model is constructed; S42, calculating the first failure moment of each sample, updating the sample space using the learning function, and iterating the Gaussian process model until the Gaussian process model converges to obtain an improved single-cycle Gaussian process model; S43. Monte Carlo sampling is used to generate samples of the three-failure mode series reliability model, and the samples are substituted as input into the improved single-cycle Gaussian process model to solve the time-varying failure probability of aircraft engine gears and complete the reliability analysis.

9. The method for time-varying reliability analysis of aircraft engine gears based on Gaussian process model according to claim 8, characterized in that: In step S43, the method for improving the single-cycle Gaussian process model for time-varying reliability analysis is specifically as follows: S43-1. Generate N using Monte Carlo sampling MCS Sample points x MCS ; S43-2. ​​Calculate the sample point x using the improved single-cycle Gaussian process model MCS The model response S43-3, according to Calculate failure probability estimates I(·) represents the indicator function. When I(·)=1, When , I(·)=0; S43-4. Judgment Is it true? CV(·) represents the coefficient of variation; If yes, proceed to step S43-5; If not, increase N MCS , and returns to step S43-1; S43-5. When the set convergence conditions are met, the calculated estimated failure probability is used as the solved time-varying failure probability of the gear to complete the reliability analysis.

Images