Aero-engine gear reliability evaluation method based on multi-fidelity Gaussian process

Abstract

The invention discloses an aero-engine gear reliability evaluation method based on a multi-fidelity Gaussian process, and the method comprises the steps: taking an aero-engine gear as an object, combining a gear test working condition, and building a high-fidelity finite element model considering the test working condition and a low-fidelity model based on ISO for the tooth surface contact fatigue of the aero-engine gear; and information of the high-fidelity model and information of the low-fidelity model are fused to form a multi-fidelity agent model of the aero-engine gear. And meanwhile, an active learning framework is combined, multi-high-low fidelity model information is combined with an improved learning function, and finally an active learning reliability analysis method based on a multi-fidelity agent model is formed, so that aero-engine gear reliability evaluation is completed. Compared with a classic AK-MCS method, the method provided by the invention has the advantages that the model calculation cost is reduced by 65.57%, the model error is reduced from 0.0394 to 0.004149, and the reliability evaluation precision is relatively high.

Description

Technical Field

[0001] The present invention belongs to the technical field of reliability analysis, and in particular relates to a reliability evaluation method for aircraft engine gears based on a Multi-Fidelity Gaussian Process (MFGP). Background Art

[0002] The degradation evolution mechanism of aircraft engine gears is complex, and reliability assessment is time-consuming and often requires field test data and a large number of finite element simulations, which significantly increases the computational cost of reliability analysis. Limited analysis resources require us to find new methods to achieve a balance between computational cost and reliability assessment accuracy.

[0003] The core idea of ​​the multi-fidelity surrogate model is to integrate the information of the high-fidelity (HF) model and the low-fidelity (LF) model to reduce the modeling cost and improve the modeling accuracy in the process of complex model construction. The active learning reliability method combining Kriging and Monte Carlo Simulation (AK-MCS) is a classic method that can accurately perform reliability assessment and reduce the number of calls to the limit state function. However, classic methods such as AK-MCS only use the mean and variance of Kriging prediction. Summary of the invention

[0004] In view of the above-mentioned deficiencies in the prior art, the invention provides an aircraft engine gear reliability assessment method based on a multi-fidelity Gaussian process to improve the accuracy and efficiency in reliability assessment.

[0005] In order to achieve the above-mentioned purpose of the invention, the technical solution adopted by the present invention is: an aircraft engine gear reliability evaluation method based on a multi-fidelity Gaussian process, comprising the following steps:

[0006] S1, generate a Monte Carlo sample pool and construct training samples based on it;

[0007] S2. Establish a high-fidelity finite element model considering the test conditions and a low-fidelity model based on ISO for the contact fatigue of the gear tooth surface of the aircraft engine, and use them to evaluate the response values ​​of the training samples respectively to construct a multi-fidelity sample response data set;

[0008] S3, using a multi-fidelity sample response data set to form a training set, and constructing a mixed-scale based multi-fidelity Gaussian process model based on the training set;

[0009] S4, randomly sampling in the Monte Carlo sample pool to construct a candidate sample point set, and constructing a sample point set based on the candidate sample point set;

[0010] S5. Using a multi-fidelity Gaussian process model to learn each candidate sample point in the sample point set, constructing a multi-assurance learning function, and using the multi-fidelity learning function to update the multi-fidelity Gaussian process model;

[0011] S6. Use the updated multi-fidelity Gaussian process model to calculate the sample response prediction value of the sample pool, evaluate the failure probability, and complete the reliability assessment.

[0012] Furthermore, in step S1, the method for constructing training samples is specifically as follows:

[0013] Using nested sampling in Monte Carlo sample pooling S MCS Extract N HF high-fidelity samples and N LF low-fidelity samples as training samples, and the experimental sample point set X of the HF model and the LF model H and X L Design meets Among them, X H and X L are the point sets corresponding to high-fidelity samples and low-fidelity samples respectively.

[0014] Furthermore, in step S2:

[0015] Using the high-fidelity finite element model and high-fidelity numerical analysis, we can obtain the response values ​​of the high-fidelity data sample points in the training samples, and then obtain the high-fidelity data response Y H ;

[0016] The low-fidelity model is used to obtain the response value of the low-fidelity data sample point in the training sample by using low-fidelity numerical analysis, and then the low-fidelity data response Y is obtained. L ;

[0017] The high-fidelity data response Y H and low-fidelity data response Y L Composing multi-fidelity sample response datasets.

[0018] Furthermore, in step S3, in the constructed mixed-scaling-based multi-fidelity Gaussian process model MFGP:

[0019] Low-fidelity proxy modelf L (X) and the variance term δ(X) are independent Gaussian processes and satisfy:

[0020] f H (X) = ρf L(X)+δ(X)

[0021] f L (X)~GP(0,k1(X,X′;θ))

[0022] δ(X)~GP(0,k2(X,X′;θ))

[0023]

[0024] in:

[0025] k LL (X,X′;θ1)=k1(X,X′;θ1)

[0026] k LH (X,X′;θ1,ρ)=k HL (X,X′;θ1,ρ)=ρk1(X,X′;θ1)

[0027] k HH (X,X′;θ1,θ2,ρ)=ρ 2 k1(X,X′;θ1)+k2(X,X′;θ1)

[0028] In the formula, f L (X) represents the low-fidelity proxy model, f H (X) represents the high-fidelity proxy model, k(·|θ) is the kernel function, ρ, θ1 and θ2 represent the hyperparameters in the kernel function, GP(·) represents the Gaussian process, and X and X' represent the input samples of the kernel function.

[0029] Furthermore, the sample response prediction value f obtained by the multi-fidelity Gaussian process model is H (X * ) is expressed as:

[0030] f H (X * )|y~N(q T K -1 Y,k HH (X * ,X * )-q T K -1 q)

[0031] Where: q T =[k HL (X * ,X L ;θ1,ρ)k HH (X * ,X H ;θ1,θ2,ρ)]

[0032]

[0033] k HH (X * , X * ) = ρ 2 k1(X * , X * ; θ1) + k2(X * , X * ; θ1)

[0034] In the formula, N(·) represents the normal distribution, y = [y L , y H T represents the set of training output samples, and X * represents the predicted sample input.

[0035] Furthermore, the specific steps of step S4 are as follows:

[0036] S41. Extract a candidate sample point set CP with a quantity of N CP from the Monte Carlo sample pool, predict the response values of the candidate sample point set CP using the multi-fidelity Gaussian process model, and calculate the number N FP of failure points in the candidate sample point set CP and the failure ratio r of the number N SCP of the candidate sample point set to be selected SCP;

[0037] S42. Determine whether P ≤ r ≤ Q holds;

[0038] If so, go to step S43;

[0039] If not, when r < P, increase the extraction quantity of the candidate sample points and return to step S41;

[0040] When r > Q, decrease the extraction quantity of the candidate sample points and return to step S41;

[0041] Among them, when the candidate sample point set increases to the preset value, use the multi-fidelity Gaussian process model to predict the response values of the candidate sample point set, calculate the number of failure sample points, and if the number of failure sample points is greater than N SCP , go to step S43;

[0042] When the candidate sample point set decreases to the preset value, go to step S44;

[0043] S43. Select N SCP sample points from the candidate sample point set as the candidate sample points to be selected SCP, and construct the SCP point set;

[0044] The SCP point set includes all the failure sample points in the candidate sample point set and the sample points with an approximate variance contribution value greater than the set threshold;​

[0045] S44, clearing the candidate sample point set, and using 5σ-criterion uniform sampling to directly extract a candidate sample point set with the same number as the set number of sample point sets, and the candidate sample point set directly constructs the SCP point set;

[0046] The SCP point set includes all failed sample points in the candidate sample point set.

[0047] Furthermore, the step S5 is specifically as follows:

[0048] S51. Use the high-fidelity data and low-fidelity data in the training set T to construct a high-fidelity Gaussian regression model and low-assurance Gaussian regression models Based on and Calculate the cross-correlation function r(x i ,t), where x i Represents a sample point in the Monte Carlo sample pool;

[0049] S52. Use the multi-fidelity Gaussian process model to calculate the sample response prediction value g of each SCP point MFGP (x i ), x i The variance of the estimated failure probability Var(P f )'s contribution value c i And the sampling density function ρ(X,t), combined with the cross-correlation function r(x i ,t), and then construct a multi-fidelity learning function D(x i );

[0050] S53, based on the multi-guarantee learning function D(x i ) Select sample points for updating the multi-fidelity Gaussian process model to update the model, and determine whether the accuracy of the updated model meets the requirements through the learning stop criterion;

[0051] If so, an updated multi-fidelity Gaussian process model is obtained;

[0052] If not, the updated sample points of the selected multi-fidelity Gaussian process model are added to the high-fidelity data sample points, and the process returns to step S2.

[0053] Furthermore, in step S52, the constructed multi-fidelity learning function D(x i ) is expressed as:

[0054] D(x i )=c i *g MFGP (x i )ρ(xi ,t)r(x i ,t),t=L,H

[0055] Where t represents the high-fidelity or low-fidelity model.

[0056] Furthermore, in step S53, the sample points updated by the multi-fidelity Gaussian process model satisfy:

[0057]

[0058] In the formula, x new represents the updated sample point, and i represents any point in the set of candidate sample points to be selected.

[0059] Further, in step S53, the learning judgment criterion is expressed as:

[0060]

[0061] In the formula, Var(P f ) represents the variance of failure probability, E(P f ) represents the expected failure probability, ε0(P f ) represents the allowable relative error of failure probability, Φ represents the cumulative distribution function of standard normal distribution, and α is the confidence level.

[0062] The beneficial effects of the present invention are:

[0063] (1) In view of the difficulty of existing reliability analysis methods in balancing accuracy and efficiency, the method of the present invention proposes a reliability analysis method based on a multi-fidelity proxy model. In view of the active learning problem of the multi-fidelity model, an adaptive active learning strategy for the multi-fidelity model combined with an improved D learning function is proposed, which can be applied to the reliability analysis of aircraft engine gear transmission systems.

[0064] (2) Based on the analysis of the final results, it can be seen that the method proposed in the present invention reduces the model calculation cost by 65.57% compared with the classic AK-MCS method, and the model error is reduced from 0.0394 to 0.004149, which has a higher reliability assessment accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] Figure 1 This is a flow chart of the aircraft engine gear reliability assessment method based on multi-fidelity Gaussian process in this embodiment.

[0066] Figure 2 This is a fatigue simulation model of a certain type of aircraft engine gear in this embodiment.

[0067] Figure 3 Schematic diagram of the change of the predicted value of failure probability in this embodiment. DETAILED DESCRIPTION

[0068] 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.

[0069] The embodiment of the present invention provides a method for evaluating the reliability of aircraft engine gears based on a multi-fidelity Gaussian process. Figure 1 As shown, the following steps are included:

[0070] S1, generate a Monte Carlo sample pool and construct training samples based on it;

[0071] S2. Establish a high-fidelity finite element model considering the test conditions and a low-fidelity model based on ISO for the contact fatigue of the gear tooth surface of the aircraft engine, and use them to evaluate the response values ​​of the training samples respectively to construct a multi-fidelity sample response data set;

[0072] S3, using a multi-fidelity sample response data set to form a training set, and constructing a mixed-scale based multi-fidelity Gaussian process model based on the training set;

[0073] S4, randomly sampling in the Monte Carlo sample pool to construct a candidate sample point set, and constructing a sample point set based on the candidate sample point set;

[0074] S5. Using a multi-fidelity Gaussian process model to learn each candidate sample point in the sample point set, constructing a multi-assurance learning function, and using the multi-fidelity learning function to update the multi-fidelity Gaussian process model;

[0075] S6. Use the updated multi-fidelity Gaussian process model to calculate the sample response prediction value of the sample pool, evaluate the failure probability, and complete the reliability assessment.

[0076] In step S1 of the embodiment of the present invention,

[0077] The Monte Carlo sample pool is generated using the nested Latin hypercube sampling method; the sample pool consists of N MCS The sample pool is composed of samples, and the sample pool is used by the adaptive learning process to select the next update sample point, and the samples that need to be updated in each step are obtained from the sample pool until the convergence condition is met.

[0078] The specific method of constructing training samples is as follows:

[0079] Using nested sampling in Monte Carlo sample pooling S MCS Extract NHF high-fidelity samples and N LF low-fidelity samples as training samples, and the experimental sample point set X of the HF model and the LF model H and X L Design meets Among them, X H and X L are the point sets corresponding to high-fidelity samples and low-fidelity samples respectively.

[0080] The low-discrepancy sequence sampling method and the nested sampling method used in this embodiment are commonly used methods in the field of reliability and multi-fidelity modeling. Low-discrepancy Monte Carlo sampling can avoid a large number of random repetitions during the simulation process, making the algorithm more efficient, with smaller errors and faster convergence. The nested sampling method can ensure that the low-fidelity data set is a subset of the high-fidelity data set and the overall sample space is evenly filled.

[0081] In step S2 of the embodiment of the present invention:

[0082] Using the high-fidelity finite element model and high-fidelity numerical analysis, we can obtain the response values ​​of the high-fidelity data sample points in the training samples, and then obtain the high-fidelity data response Y H ;

[0083] The low-fidelity model is used to obtain the response value of the low-fidelity data sample point in the training sample by using low-fidelity numerical analysis, and then the low-fidelity data response Y is obtained. L ;

[0084] The high-fidelity data response Y H and low-fidelity data response Y L Composing multi-fidelity sample response datasets.

[0085] In step S3 of the embodiment of the present invention, in the constructed mixed-scaling-based multi-fidelity Gaussian process model MFGP:

[0086] Low-fidelity proxy modelf L (X) and the variance term δ(X) are independent Gaussian processes and satisfy:

[0087] f H (X) = ρf L (X)+δ(X)

[0088] f L (X)~GP(0,k1(X,X′;θ))

[0089] δ(X)~GP(0,k2(X,X′;θ))

[0090]

[0091] in:

[0092] k LL (X,X′;θ1)=k1(X,X′;θ1)

[0093] k LH (X,X′;θ1,ρ)=k HL (X,X′;θ1,ρ)=ρk1(X,X′;θ1)

[0094] k HH (X,X′;θ1,θ2,ρ)=ρ 2 k1(X,X′;θ1)+k2(X,X′;θ1)

[0095] In the formula, f L (X) represents the low-fidelity proxy model, f H (X) represents the high-fidelity proxy model, k(·θ) is the kernel function, ρ, θ1 and θ2 represent the hyperparameters in the kernel function, GP(·) represents the Gaussian process, and X and X' represent the input samples of the kernel function.

[0096] Among them, the hyperparameters θ1, θ2, ρ and the noise variance parameter σ 2 L , σ 2 H It can be trained by minimizing the log-marginal likelihood function:

[0097]

[0098] Then, we can infer that the sample response prediction value f obtained by using the multi-fidelity Gaussian process model is H (X * ) is expressed as:

[0099] f H (X * )|y~N(q T K -1 Y,k HH (X * ,X * )-q T K -1 q)

[0100] Where: q T =[k HL (X * ,X L ;θ1,ρ)k HH (X * ,X H ;θ1,θ2,ρ)]

[0101]

[0102] k HH (X * ,X * ) = ρ 2 k1(X * ,X * ; θ1) + k2(X * ,X * ; θ1)

[0103] In the formula, N(·) represents the normal distribution, y = [y L , y H T represents the set of training output samples, and X * represents the predicted sample input.

[0104] Step S4 in the embodiment of the present invention is specifically as follows:

[0105] S41. Extract a candidate sample point set CP with the number of N CP from the Monte Carlo sample pool, use the multi-fidelity Gaussian process model to predict the response values of the candidate sample point set CP, and calculate the number of failure points N FP in the candidate sample point set CP and the failure ratio r of the number of candidate sample point sets SCP to be selected N SCP ;

[0106] S42. Determine whether P ≤ r ≤ Q holds;

[0107] If so, go to step S43;

[0108] If not, when r < P, increase the extraction quantity of the candidate sample points and return to step S41;

[0109] When r > Q, decrease the extraction quantity of the candidate sample points and return to step S41;

[0110] Among them, when the candidate sample point set increases to the preset value, use the multi-fidelity Gaussian process model to predict the response values of the candidate sample point set, calculate the number of failure sample points, and if the number of failure sample points is greater than N SCP , go to step S43;

[0111] When the candidate sample point set decreases to the preset value, go to step S44;

[0112] Optionally, in this embodiment, the values of P and Q are 0.25 and 0.75 respectively, and this value can improve the algorithm efficiency;

[0113] S43. Select N SCP sample points from the candidate sample point set as the candidate sample points SCP to be selected, and construct the SCP point set; ​

[0114] The SCP point set includes all failed sample points in the candidate sample point set and sample points whose variance contribution approximate value is greater than a set threshold;

[0115] S44, clearing the candidate sample point set, and using 5σ-criterion uniform sampling to directly extract a candidate sample point set with the same number as the set number of sample point sets, and the candidate sample point set directly constructs the SCP point set;

[0116] The SCP point set includes all failed sample points in the candidate sample point set.

[0117] In this embodiment, step S5 is specifically as follows:

[0118] S51. Use the high-fidelity data and low-fidelity data in the training set T to construct a high-fidelity Gaussian regression model and low-assurance Gaussian regression models Based on and Calculate the cross-correlation function r(x i ,t), where x i Represents a sample point in the Monte Carlo sample pool;

[0119] S52. Use the multi-fidelity Gaussian process model to calculate the sample response prediction value g of each SCP point MFGP (x i ), x i The variance of the estimated failure probability Var(P f )'s contribution value c i And the sampling density function ρ(X,t), combined with the cross-correlation function r(x i ,t), and then construct a multi-fidelity learning function D(x i );

[0120] S53, based on the multi-guarantee learning function D(x i ) Select sample points for updating the multi-fidelity Gaussian process model to update the model, and determine whether the accuracy of the updated model meets the requirements through the learning stop criterion;

[0121] If so, an updated multi-fidelity Gaussian process model is obtained;

[0122] If not, the updated sample points of the selected multi-fidelity Gaussian process model are added to the high-fidelity data sample points, and the process returns to step S2.

[0123] Specifically, in step S52 of this embodiment, the constructed multi-fidelity learning function D(x i ) is expressed as:

[0124] D(x i)=c i *g MFGP (x i )ρ(x i ,t)r(x i ,t),t=L,H

[0125] Where t represents the high-fidelity or low-fidelity model.

[0126] Specifically:

[0127]

[0128] in, is the mean value [μ j ,μ k ], standard deviation is [σ j ,σ k ], the correlation is r jk Define the cumulative distribution function (CDF) of the bivariate normal distribution.

[0129]

[0130] In step S53 of this embodiment, the sample points updated by the multi-fidelity Gaussian process model satisfy:

[0131]

[0132] In the formula, x new represents the updated sample point, and i represents any point in the set of candidate sample points to be selected.

[0133] In step S53 of this embodiment, the learning judgment criterion is expressed as:

[0134]

[0135] In the formula, Var(P f ) represents the variance of failure probability, E(P f ) represents the expected failure probability, ε0(P f ) represents the allowable relative error of failure probability, Φ represents the cumulative distribution function of standard normal distribution, and α is the confidence level.

[0136] This embodiment provides a specific example based on the above reliability evaluation method.

[0137] In this embodiment, the material used for a certain type of aircraft engine gear is 17CrNiMo6. Under the test conditions, the gear transmission power is input by the input shaft, the input speed is determined according to the characteristics of the test machine, the input torque range is 90-190N·m, oil injection lubrication is adopted, and multi-level stress input is adopted during the test. According to the finite element tooth surface contact model of the gear pair established in ANSYS ADPL, it is corrected by reasonably setting the working condition parameters, stiffness and penetration tolerance, and a high-fidelity gear finite element model with little difference from the test data is obtained as shown in the figure. Figure 2 As shown. Its allowable contact stress σ HP It can be expressed as the gear module m n The function σ HP (m n ) The actual contact stress between gears is obtained through gear finite element simulation and is denoted as σ H-APDL The input parameter types of finite element simulation are gear shape parameters, material parameters and motion parameters, corresponding to the module m n , working tooth width b, elastic modulus E, Poisson's ratio ν and pinion torque T1, the simulation can be regarded as an implicit function of the five input variables, that is, σ H-APDL (m n ,b,E,ν,T1). The low-fidelity model is based on the formula proposed in ISO 6336-2 (Calculation of load capacity of spur and helical gears-Part 2: Calculation of surface durability (pitting)), and the gear contact fatigue failure limit state function is established using the stress intensity interference theory. Finally, the multi-fidelity limit state function constructed based on this engineering example is:

[0138] g H (X) = g1(m n ,b,E,ν,T1)=σ HP (m n )-σ H-APDL (m n ,b,E,ν,T1)

[0139] g L (X) = σ HP (m n )-σ H-ISO (m n ,b,E,ν,T1)

[0140] In the formula, σ H-APDL and σ H-ISOThey are respectively a high-fidelity gear finite element model obtained based on finite element simulation and a low-fidelity model calculated based on ISO formula. The input variable distribution parameters are shown in Table 1:

[0141] Table 1

[0142]

[0143] According to the above method, the generated sample size is N MCS Sample pool S MCS , a dataset of 12 initial high-fidelity samples and 36 low-fidelity samples of aircraft engine gears was established using nested Latin hypercube sampling, and the sample dataset was evaluated using multi-fidelity limit state functions. An initial multi-fidelity surrogate model g was established based on the evaluation results of the gear multi-fidelity data samples. MFGP And form a selected sample point set SCP. Then calculate the learning function value of each point in SCP, and it is required to satisfy when the calculation converges

[0144]

[0145] Among them, ε0(P f ) is taken as 0.01, and α is taken as 0.02.

[0146] Since each call of the limit state function involves a finite element analysis with a large amount of calculation, the reliability assessment cost and reliability assessment error are selected as the evaluation indicators of the method. In order to verify the accuracy of the method, the overconvergent AK-MCS method is used as the benchmark, and AK-MCS-U, Co-Kriging-U and the proposed method are compared. The comparison results are shown in Table 2.

[0147] Table 2

[0148]

[0149] like Figure 3 As shown in the figure, when the model adds more than 1000 points, the failure probability prediction value tends to converge, with very small fluctuations. Subsequent additions all show over-convergence, so it can be used as a reference for the true failure probability. The error of the results of the proposed MFGP evaluation of the failure probability prediction value is the smallest, and the error of MFGP combined with the learning function D is within 1%, and the model accuracy is much higher than that of the Kriging and Co-Kriging models. This reflects the effectiveness of the proposed method in reducing the active learning cost and improving the accuracy and efficiency of reliability assessment.

[0150] 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.

[0151] 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. The reliability evaluation method of aircraft engine gear based on multi-fidelity Gaussian process is characterized by: It includes the following steps: S1. Generate a Monte Carlo sample pool and construct training samples based on it; S2. Establish a high-fidelity finite element model considering test conditions and a low-fidelity model based on ISO for the tooth surface contact fatigue of aero-engine gears, and use them to evaluate the response values of the training samples respectively, and construct a multi-fidelity sample response data set; S3. Use the multi-fidelity sample response data set to form a training set, and construct a multi-fidelity Gaussian process model based on hybrid scales based on the training set; S4. Randomly sample in the Monte Carlo sample pool to construct a candidate sample point set, and construct a sample point set based on the candidate sample point set; S5. Use the multi-fidelity Gaussian process model to learn each candidate sample point in the sample point set, construct a multi-guarantee learning function, and use the multi-fidelity learning function to update the multi-fidelity Gaussian process model; S6. Use the updated multi-fidelity Gaussian process model to calculate the sample response prediction value of the sample pool and evaluate the failure probability to complete the reliability assessment.

2. The aircraft engine gear reliability assessment method based on multi-fidelity Gaussian process according to claim 1 is characterized in that: In the step S1, the method for constructing training samples is specifically as follows: Using nested sampling in Monte Carlo sample pooling S MCS Extract N HF high-fidelity samples and N LF low-fidelity samples as training samples, and the experimental sample point set X of the HF model and the LF model H and X L Design meets Among them, X H and X L are the point sets corresponding to high-fidelity samples and low-fidelity samples respectively.

3. The aircraft engine gear reliability assessment method based on multi-fidelity Gaussian process according to claim 1 is characterized in that: In the step S2: Using the high-fidelity finite element model and high-fidelity numerical analysis, we can obtain the response values ​​of the high-fidelity data sample points in the training samples, and then obtain the high-fidelity data response Y H ; The low-fidelity model is used to obtain the response value of the low-fidelity data sample point in the training sample by using low-fidelity numerical analysis, and then the low-fidelity data response Y is obtained. L ; The high-fidelity data response Y H and low-fidelity data response Y L Composing a multi-fidelity sample response dataset.

4. The aircraft engine gear reliability assessment method based on multi-fidelity Gaussian process according to claim 1 is characterized in that: In the step S3, in the constructed multi-fidelity Gaussian process model MFGP based on hybrid scales: Low-fidelity proxy modelf L (X) and the variance term δ(X) are independent Gaussian processes and satisfy: f H (X)=ρf L (X)+δ(X) f L (X)~GP(0,k1(X,X′;θ)) δ(X)~GP(0,k2(X,X′;θ)) Where: k LL (X,X′;θ1)=k1(X,X′;θ1) k LH (X,X′;θ1,ρ)=k HL (X,X′;θ1,ρ)=ρk1(X,X′;θ1) k HH (X,X′;θ1,θ2,ρ)=ρ 2 k1(X,X′;θ1)+k2(X,X′;θ1) In the formula, f L (X) represents the low-fidelity proxy model, f H (X) represents the high-fidelity proxy model, k · (·|θ) is the kernel function, ρ, θ1 and θ2 represent the hyperparameters in the kernel function, GP(·) represents the Gaussian process, and X and X' represent the input samples of the kernel function.

5. The aircraft engine gear reliability assessment method based on multi-fidelity Gaussian process according to claim 4 is characterized in that: The sample response prediction value f obtained using the multi-fidelity Gaussian process model H (X * ) is expressed as: f H (X * )|y~N(q T K -1 Y,k HH (X * ,X * )-q T K -1 q) Among them: q T =[k HL (X * ,X L ;θ1,ρ)k HH (X * ,X H ;θ1,θ2,ρ)] k HH (X * ,X * )=ρ 2 k1(X * ,X * ;θ1)+k2(X * ,X * ;θ1) In the formula, N(·) represents normal distribution, y=[y L ,y H ] T represents the training output sample set, X * Represents the prediction sample input.

6. The aircraft engine gear reliability assessment method based on multi-fidelity Gaussian process according to claim 1 is characterized in that: The step S4 is specifically as follows: S41. Extract N from the Monte Carlo sample pool CP The number of candidate sample point sets CP is used to predict the response value of the candidate sample point set CP using the multi-fidelity Gaussian process model, and the number of failure points N in the candidate sample point set CP is calculated. FP and the number of candidate sample points to be selected SCP N SCP The failure rate r; S42. Judge whether P≤r≤Q holds; If so, go to step S43; If not, when r<P, increase the extraction quantity of candidate sample points and return to step S41; When r>Q, decrease the extraction quantity of candidate sample points and return to step S41; When the candidate sample point set increases to a preset value, the multi-fidelity Gaussian process model is used to predict the response value of the candidate sample point set, and the number of failed sample points is calculated. If the number of failed sample points is greater than N SCP When , go to step S43; When the candidate sample point set is reduced to a preset value, go to step S44; S43, select N from the candidate sample point set SCP Sample points are selected as candidate sample points SCP to construct the SCP point set; The SCP point set includes all failed sample points in the candidate sample point set and sample points with an approximate variance contribution value greater than a set threshold; S44. Clear the candidate sample point set, and directly extract a candidate sample point set with the same number as the set number of the sample point set by uniform sampling using the 5σ-criterion, and the candidate sample point set directly constructs the SCP point set; The SCP point set includes all failed sample points in the candidate sample point set.

7. The aircraft engine gear reliability assessment method based on multi-fidelity Gaussian process according to claim 1 is characterized in that: The step S5 is specifically as follows: S51. Use the high-fidelity data and low-fidelity data in the training set T to construct a high-fidelity Gaussian regression model and low-assurance Gaussian regression models Based on and Calculate the cross-correlation function r(x i ,t), where x i Represents a sample point in the Monte Carlo sample pool; S52. Use the multi-fidelity Gaussian process model to calculate the sample response prediction value g of each SCP point MFGP (x i ), x i The variance of the estimated failure probability Var(P f )'s contribution value c i And the sampling density function ρ(X,t), combined with the cross-correlation function r(x i ,t), and then construct a multi-fidelity learning function D(x i ); S53, based on the multi-guarantee learning function D(x i ) Select sample points for updating the multi-fidelity Gaussian process model to update the model, and determine whether the accuracy of the updated model meets the requirements through the learning stop criterion; If so, obtain the updated multi-fidelity Gaussian process model; If not, add the sample points updated by the selected multi-fidelity Gaussian process model to the high-fidelity data sample points and return to step S2.

8. The aircraft engine gear reliability assessment method based on multi-fidelity Gaussian process according to claim 7 is characterized in that: In step S52, the constructed multi-fidelity learning function D(x i ) is expressed as: D(x i )=c i *g MFGP (x i )ρ(x i ,t)r(x i ,t),t=L,H In the formula, t represents a high-fidelity or low-fidelity model.

9. The aircraft engine gear reliability assessment method based on multi-fidelity Gaussian process according to claim 7, characterized in that: In the step S53, the sample points updated by the multi-fidelity Gaussian process model satisfy: In the formula, x new represents the updated sample point, and i represents any point in the set of candidate sample points to be selected.

10. The aircraft engine gear reliability assessment method based on multi-fidelity Gaussian process according to claim 7, characterized in that: In the step S53, the learning judgment criterion is expressed as: In the formula, Var(P f ) represents the variance of failure probability, E(P f ) represents the expected failure probability, ε0(P f ) represents the allowable relative error of failure probability, Φ represents the cumulative distribution function of standard normal distribution, and α is the confidence level.

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