A model updating method for aviation gear pump sliding bearings

Abstract

The present invention discloses a model updating method for an aviation gear pump sliding bearing, comprising the following steps: Step 1: determining unknown parameters of a bearing lubrication model; Step 2: determining a prior distribution of the unknown parameters; Step 3: determining a measurable lubrication performance value of the aviation gear pump sliding bearing; Step 4: measuring a performance value y based on the measurable bearing lubrication model performance determined in Step 3; Step 5: determining a likelihood function of the measured performance value of the sliding bearing lubrication model based on the performance value y; and Step 6: updating the unknown model parameters based on the likelihood function of the measured lubrication performance value of the sliding bearing and the prior distribution of the unknown model. This method has the characteristics of low computational cost and strong global convergence.

Description

Technical Field

[0001] The present invention relates to the technical field of aviation fuel pumps, and in particular to a model updating method for a sliding bearing of an aviation gear pump. Background Art

[0002] The aviation fuel pump sliding bearing is a key supporting component of the fuel pump, and its model parameters greatly affect the lubrication characteristics of the sliding bearing; however, existing analysis methods, such as the patent number: 202110177933.8 provided by inventors Guo Qiang and others, and the patent name: "Method and device for obtaining the oil film pressure distribution of dynamic and static pressure bearings" and the patent number: 202110633857.7 provided by inventors Li Baotong and others, and the patent name: "Simulation method of oil film characteristics of multi-oil chamber dynamic and static pressure sliding bearings based on high-order isogeometry", all assume that the lubrication model parameters are known, and calculate the lubrication characteristics of the bearing based on the known model parameters.

[0003] However, in actual service, the load of the sliding bearing may change, and during operation, some model parameters change accordingly and cannot be directly measured.

[0004] In summary, the defect of the existing technology is that it does not take into account the problem that the lubrication parameters of the sliding bearing are unmeasurable during operation, but simply sets all parameters to fixed values, which is often inconsistent with the actual situation. Summary of the Invention

[0005] In order to overcome the above technical defects, the purpose of the present invention is to provide a model updating method for aviation gear pump sliding bearings, which has the characteristics of low computational cost and strong global convergence.

[0006] In order to achieve the above object, the technical solution adopted by the present invention is:

[0007] A model updating method for a sliding bearing of an aviation gear pump comprises the following steps:

[0008] Step 1: Determine the unknown parameters of the bearing lubrication model;

[0009] Step 2: Determine the prior distribution of unknown parameters;

[0010] Step 3: Determine the measurable lubrication performance value of the aviation gear pump sliding bearing;

[0011] Step 4: Measure the performance value based on the measurable bearing lubrication model performance determined in step 3

[0012] Step 5: Based on performance value Determine the likelihood function for performance measurements of a journal bearing lubrication model;

[0013] Step 6: Based on the likelihood function of the lubrication performance measurement value of the sliding bearing and the prior distribution of the unknown model, the unknown model parameters are updated.

[0014] Step 1 determines the bearing lubrication model parameters θ, which cannot be directly measured, such as eccentricity and offset angle. This process is primarily based on experimental experience, engineering experience, and experimental conditions. The bearing lubrication model is a user-defined model based on actual application needs.

[0015] The second step is to determine the prior distribution information p(θ) of the model based on prior knowledge or expert guidance.

[0016] In step three, the lubrication performance of the sliding bearing is affected by unknown parameters of the model. It is necessary to determine which lubrication performance parameters can be measured based on the user's experimental experience, engineering experience and experimental conditions in order to facilitate model updating. For example, temperature can be measured by a temperature sensor, oil film thickness can be measured by ultrasonic technology, and pressure can be measured by a piezoelectric film sensor.

[0017] The step five is specifically as follows:

[0018] Based on the performance measurement value obtained in step 4, assuming that the error between the measurement value and the lubrication simulation model M(θ) obeys Gaussian white noise, the likelihood function of the measurement value is It is defined as the probability density function of the measured value, that is

[0019]

[0020] Where N is the number of measurements, Σ ε is the covariance matrix of Gaussian white noise.

[0021] Step 6

[0022] The posterior distribution of the unknown model parameters can be obtained by the Bayesian formula, that is,

[0023]

[0024] in represents the regularization constant.

[0025] Since the calculation of the sliding bearing lubrication simulation model M(θ) is time-consuming, the variational Bayesian inference method is used to calculate the posterior distribution of the unknown model parameters, and q ξ (θ) represents the variational distribution, where ξ is the distribution parameter, then the lower bound of the evidence of the variational distribution can be expressed as

[0026]

[0027] in

[0028] Therefore, the optimal variational distribution is determined by the distribution parameter ξ that maximizes the lower bound of the evidence. The process of optimizing ξ is as follows:

[0029] 1) Randomly generate a sample size of N θ The same number of unknown parameters θ obeys the variational distribution q ξ A random sample set u of (θ) i，i =1,...,N θ ;

[0030] 2) Randomly generate a set of training samples Θ with unknown parameters and calculate the corresponding value of f(Θ);

[0031] 3) Based on the training sample set generated in 2), train the Gaussian process regression model

[0032] 4) Based on the samples generated in 1), calculate Estimated value of and the estimated standard deviation

[0033] 5) Use Bayesian integral inference integral The posterior mean of and the posterior variance

[0034] 6) Due to and The estimated values ​​of all obey Gaussian distribution, so we can get the lower bound of evidence It also obeys the Gaussian process, and its distribution mean is The distribution variance is

[0035] 7) Use Bayesian optimization to obtain the current optimal distribution parameter ξ + ;

[0036] 8) For the result obtained in 7) + , use Bayesian integration to infer μ F (ξ + )The parameter value θ with the largest error + ;

[0037] 9) Calculate θ + The corresponding f(θ + ) value and add it to the training set;

[0038] 10) Repeat 3) to 9) until the Bayesian integral and optimization error meet the requirements and output ξ + , and determine the optimal variational distribution is the posterior distribution of the unknown model parameters θ.

[0039] Beneficial effects of the present invention.

[0040] This invention provides a model updating method for aviation fuel pump sliding bearings. This method leverages measurable bearing lubrication performance data and prior knowledge to update the probability distribution of unknown lubrication model parameters, generating a posterior distribution. This calculation method, based on this application, can update the designer's distribution information for the unknown parameters of the sliding bearing lubrication model, providing theoretical support for subsequent reliability analysis and optimized design.

[0041] This invention fills the gap in the domestic determination of unknown parameters of sliding bearings through model updating technology, and the established model updating technology has the advantages of low computational cost and strong global convergence. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 Schematic diagram of the comparison between the posterior distribution of unknown bearing parameters and the TMCMC method.

[0043] Figure 2 Schematic diagram of the impact of unknown bearing parameters on the joint posterior distribution. DETAILED DESCRIPTION

[0044] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0045] A model updating method for a sliding bearing of an aviation gear pump comprises the following steps:

[0046] Step 1: Determine the unknown parameters of the bearing lubrication model.

[0047] Determine the sliding bearing lubrication model parameters θ that cannot be directly measured, such as eccentricity and offset angle.

[0048] The above steps give the model parameters that need to be updated for the sliding bearing.

[0049] Step 2: Determine the prior distribution of unknown parameters

[0050] Based on prior knowledge or expert guidance, the prior distribution information p(θ) of the model is determined.

[0051] The above steps give the model parameters that need to be updated for the sliding bearing.

[0052] Step 3: Determine the measurable values ​​of the sliding bearing lubrication performance.

[0053] The lubrication performance of sliding bearings is affected by unknown parameters of the model, so it is necessary to determine which performance parameters can be measured to facilitate model updating.

[0054] The above steps give the performance parameters that can be measured for sliding bearings.

[0055] Step 4: Measure the lubrication performance value of the sliding bearing

[0056] Based on the measurable bearing lubrication model performance determined in step 3, some performance values ​​are measured

[0057] The above steps give the measured values ​​of the lubrication performance of the sliding bearing.

[0058] Step 5: Determine the likelihood function for the performance measurements of the sliding bearing lubrication model

[0059] Based on the performance measurement value obtained in step 4, assuming that the error between the measurement value and the lubrication simulation model M(θ) obeys Gaussian white noise, the likelihood function of the measurement value can be expressed as It is defined as the probability density function of the measured value, that is

[0060]

[0061] Where N is the number of measurements, Σ ε is the covariance matrix of Gaussian white noise.

[0062] The above steps give the likelihood function of the measured values ​​of the lubrication performance of the sliding bearing.

[0063] Step 6: Update the unknown model parameters based on the likelihood function of the lubrication performance measurement value of the sliding bearing and the prior distribution of the unknown model

[0064] The posterior distribution of the unknown model parameters can be obtained by the Bayesian formula, that is,

[0065]

[0066] in represents the regularization constant.

[0067] Since the calculation of the sliding bearing lubrication simulation model M(θ) is time-consuming, the variational Bayesian inference method is used to calculate the posterior distribution of the unknown model parameters, and q ξ (θ) represents the variational distribution, where ξ is the distribution parameter, then the lower bound of the evidence of the variational distribution can be expressed as

[0068]

[0069] in

[0070] Therefore, the optimal variational distribution is determined by the distribution parameter ξ that maximizes the lower bound of the evidence.

[0071] The process of optimizing ξ is as follows:

[0072] 1) Randomly generate a sample size of N θ The same number of unknown parameters θ obeys the variational distribution q ξ A random sample set u of (θ) i , i=1,…,N θ ;

[0073] 2) Randomly generate a set of training samples Θ with unknown parameters and calculate the corresponding value of f(Θ);

[0074] 3) Based on the training sample set generated in 2), train the Gaussian process regression model

[0075] 4) Based on the samples generated in 1), calculate Estimated value of and the estimated standard deviation

[0076] 5) Use Bayesian integral inference integral The posterior mean of and the posterior variance

[0077] 6) Due to and The estimated values ​​of all obey Gaussian distribution, so we can get the lower bound of evidence It also obeys the Gaussian process, and its distribution mean is The distribution variance is

[0078] 7) Use Bayesian optimization to obtain the current optimal distribution parameter ξ + ;

[0079] 8) For the result obtained in 7) + , use Bayesian integration to infer μ F (ξ + )The parameter value θ with the largest error + ;

[0080] 9) Calculate θ + The corresponding f(θ + ) value and add it to the training set;

[0081] 10) Repeat 3) to 9) until the Bayesian integral and optimization error meet the requirements and output ξ + , and determine the optimal variational distribution is the posterior distribution of the unknown model parameters θ.

[0082] The above steps provide the posterior distribution inference process of the unknown parameters of the sliding bearing lubrication model.

[0083] Experimental case: The advantages of the present invention can be further illustrated by the following simulation experiment:

[0084] 1. Set the unknown model parameters of the sliding bearing lubrication model to eccentricity, offset angle, speed and initial viscosity, and set the prior distribution to N (0.4, 0.1 2 ),N(0,0.2 2 ),N(6000,100 2 ) and N(9.5×10 -4 , (2×10 -4 ) 2 ).

[0085] 2. The measured values ​​of the lubrication performance of the sliding bearing are the maximum values ​​of the pressure and temperature distribution, which are 527499 Pa and 40.04 degrees Celsius respectively.

[0086] 3. The covariance matrix of Gaussian white noise is

[0087] 4. Results Analysis

[0088] Conclusion 1: From Figure 1 It can be seen that the inferred posterior distribution of the unknown parameters of the sliding bearing is accurate.

[0089] Conclusion 2: From Figure 1 It can be seen that the eccentricity has the greatest impact on the maximum values ​​of pressure and temperature, while the offset angle has almost no effect.

[0090] Conclusion 3: From Figure 2 It can be seen that the results of sensitivity analysis are consistent with Figure 1 same.

[0091] Conclusion 4: The above results show that the theory and method proposed in this patent can accurately and efficiently update the model of sliding bearings.

Claims

1. A model updating method for aviation gear pump sliding bearing, characterized in that: The following steps are included: Step 1: Determine the unknown parameters of the bearing lubrication model; Step 2: Determine the prior distribution of unknown parameters; Step 3: Determine the measurable lubrication performance value of the aviation gear pump sliding bearing; Step 4: Measure the performance value based on the measurable bearing lubrication model performance determined in step 3 ; Step 5: Based on performance value Determine the likelihood function for performance measurements of a journal bearing lubrication model; Step 6: Based on the likelihood function of the lubrication performance measurement value of the sliding bearing and the prior distribution of the unknown model, update the unknown model parameters; Step 6 The posterior distribution of the unknown model parameters can be obtained by the Bayesian formula, that is, in represents the regularization constant; Since the calculation of sliding bearing lubrication simulation model It is time-consuming, so the variational Bayesian inference method is used to calculate the posterior distribution of the unknown model parameters. represents the variational distribution, where is the distribution parameter, then the lower bound of the evidence of the variational distribution is expressed as in , , the optimal variational distribution is the distribution parameter that maximizes the lower bound of the evidence Sure.

2. The model updating method of an aviation gear pump sliding bearing according to claim 1, characterized in that: The first step is to determine the sliding bearing lubrication model parameters that cannot be directly measured. , such as eccentricity and deflection angle.

3. The model updating method of an aviation gear pump sliding bearing according to claim 1, characterized in that: The second step is to determine the prior distribution information of the model based on prior knowledge or expert guidance. .

4. The model updating method for an aviation gear pump sliding bearing according to claim 1, characterized in that: In step three, the lubrication performance of the sliding bearing is affected by unknown parameters of the model. It is necessary to determine which lubrication performance parameters to measure based on the user's experimental experience, engineering experience and experimental conditions in order to facilitate model updating. For example, temperature can be measured by a temperature sensor, oil film thickness can be measured by ultrasonic technology, and pressure can be measured by a piezoelectric film sensor.

5. The model updating method for a sliding bearing of an aviation gear pump according to claim 1, characterized in that: The step five is specifically as follows: Based on the performance measurements obtained in step 4, it is assumed that the measurements and the lubrication simulation model The error between them obeys Gaussian white noise, then the likelihood function of the measured value is It is defined as the probability density function of the measured value, that is in is the number of measured values, is the covariance matrix of Gaussian white noise.

6. The method for updating the model of an aviation gear pump sliding bearing according to claim 1, characterized in that: optimization The process is as follows: 1) Randomly generate sample size and unknown parameters The same number of them follow the variational distribution A random sample set ; 2) Randomly generate a set of training samples with unknown parameters , calculate the corresponding The value of 3) Based on the training sample set generated in 2), train the Gaussian process regression model ; 4) Based on the samples generated in 1), calculate Estimated value of and the estimated standard deviation ; 5) Use Bayesian integral inference integral The posterior mean of and the posterior variance ; 6) Due to and The estimated values ​​of all obey Gaussian distribution, so we can get the lower bound of evidence It also obeys the Gaussian process, and its distribution mean is , the distribution variance is ; 7) Use Bayesian optimization to obtain the current optimal distribution parameters ; 8) Based on the results of 7) , using Bayesian integral inference The parameter value with the largest error ; 9) Calculation Corresponding , add it to the training set; 10) Repeat 3) to 9) until the Bayesian integral and optimization error meet the requirements and output , and determine the optimal variational distribution is the unknown model parameter The posterior distribution of .

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