Gear pump sliding bearing performance prediction method based on Gaussian process regression

Abstract

The invention discloses a gear pump sliding bearing performance prediction method based on Gaussian process regression. The method comprises the following steps of: 1, collecting performance parameter data of a sliding bearing under different structure parameters and operation conditions, establishing a data sample, randomly disorganizing a sample sequence, dividing the sample into two parts, namely a training sample and a test sample, and preparing for subsequently training a Gaussian process regression model; 2, setting a mean value function, a kernel function, a hyper-parameter and a likelihood function of the Gaussian process regression model as prior distribution; 3, performing hyper-parameter optimization on the kernel function in the step 2 based on the processed training sample data to obtain a trained Gaussian process regression performance prediction model; and 4, performing performance prediction on test sample data by using the Gaussian process regression model trained in the step 3, and giving prediction accuracy. According to the method, the working performance of the gear pump sliding bearing with different structural parameters is predicted, and uncertainty estimation of a prediction result is given, so that the precision of performance prediction is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of hydrodynamic lubrication analysis of sliding bearings for aviation gear fuel pumps, and particularly to a method for predicting the performance of sliding bearings of gear pumps based on Gaussian process regression. Background Art

[0002] Gear pumps are widely used in the fuel control systems of aeroengines due to their simple structure, small size, stable operation, and insensitivity to oil pollution. Among the components of a gear pump, the sliding bearing is a key supporting component for the normal operation of the gear pump, and its working performance greatly affects the working performance of the aviation engine gear fuel pump. The prediction of its performance is of great significance for preventing failures, extending service life, improving production efficiency, and reducing R & D costs.

[0003] Traditional methods for predicting the performance of sliding bearings mostly rely on empirical formulas or simplified models, such as linear regression, polynomial fitting, etc. These methods usually assume that the performance of the sliding bearing is a deterministic function, ignoring the randomness and uncertainty in the performance. Although these methods can provide reasonable prediction results in some cases, they cannot handle complex performance data, and for non-standard working conditions and changing operating conditions, the prediction accuracy is limited, and a large amount of experimental data is required to establish a reliable model. Another common method for performance prediction is the physical model-based method, which simulates the performance by establishing physical equations. Although these methods can better understand the physical principles of the sliding bearing performance, for complex working conditions and non-linear systems, they usually require a large amount of experimental data and complex mathematical modeling, and it is difficult to accurately predict the performance in actual work, so the cost is high and it is not easy to implement. In addition, because physical models are usually deterministic, they are also difficult to handle the randomness and uncertainty in performance data. Therefore, a method for quickly and accurately predicting the performance of sliding bearings of gear pumps is needed. Summary of the Invention

[0004] In order to overcome the above technical problems, the purpose of the present invention is to provide a method for predicting the performance of sliding bearings of gear pumps based on Gaussian process regression. This method focuses on the sliding bearings of aviation gear pumps, and uses the Gaussian process regression method with self-learning ability to predict the working performance of sliding bearings of gear pumps with different structural parameters, and gives an uncertainty estimate of the prediction results, so as to improve the accuracy of performance prediction and reduce the R & D cost.

[0005] The technical solution adopted by the present invention is as follows:

[0006] A method for predicting the performance of sliding bearings of gear pumps based on Gaussian process regression, comprising the following steps;

[0007] Step 1: Collect the performance parameter data of the sliding bearing under different structural parameters and operating conditions, form a certain amount of data samples, randomly shuffle the sample order, and divide them into two parts: training samples and test samples, to prepare for the subsequent training of the Gaussian process regression model;

[0008] Step 2: Set the mean function, kernel function, its hyperparameters, and likelihood function of the Gaussian process regression model as the prior distribution;

[0009] Step 3: Optimize the hyperparameters of the kernel function in Step 2 based on the processed training sample data to obtain the trained Gaussian process regression performance prediction model;

[0010] Step 4: Use the trained Gaussian process regression model in Step 3 to perform performance prediction on the test sample data and give the prediction accuracy.

[0011] The specific content of Step 1 is as follows:

[0012] The input features of the performance parameters of the sliding bearing under different structural parameters and operating conditions collected constitute \(D =\{(x 1 ,y 1 ),...,(x i ,y i ),...,(x n ,y n )\}\), where \(x i \) represents the structural parameters and operating conditions input of the \(i\)-th group of data samples, which is a vector, \(x i =(a i ,b i ,c i ,d i ,e i )\), where \(a i \) is the diameter-to-length ratio of the \(i\)-th group of data, \(b i \) is the eccentricity of the \(i\)-th group of data, \(c i \) is the rotational speed of the gear shaft of the \(i\)-th group of data, \(d i \) is the oil groove width of the \(i\)-th group of data, and \(e i \) is the oil groove depth of the \(i\)-th group of data.

[0013] The specific content of Step 2 is as follows:

[0014] The properties of the Gaussian process are determined by the mean function and the covariance function, and the specific form is expressed as:

[0015] f(x)~GP(m(x),k(x,x'))

[0016] Where, \(m(x)\) is the mean function of the Gaussian process, \(k(x, x')\) is the kernel function of the Gaussian process, \(x\) and \(x'\) are two different input sample data, and the kernel function adopts the Rational Quadratic (RQ) kernel, which is a generalization of the squared exponential kernel (also known as the Gaussian kernel). The RQ kernel function is more flexible than the squared exponential kernel function because it introduces an additional scale mixing parameter \(\alpha\), which controls the mixing degree of different length scales. This makes the shape of the kernel function more diverse and can adapt to a wider range of data patterns;

[0017] The RQ kernel function is formally expressed in the following form:

[0018]

[0019] Where, \(k(x\) i , \(x\) j ) is the covariance of the function between the input points \(x\) i and \(x\) j . \(\|x\) i - \(x\) j \|^2\) 2 is the square of the Euclidean distance between the points \(x\) i and \(x\) j . \(l\) is the length parameter, which controls the smoothness of the function or the scale of change, and \(\alpha\) is the scale mixing parameter, which controls the mixing degree of different length scales. When \(\alpha\) approaches infinity, the RQ kernel approaches the squared exponential kernel function.

[0020] Considering that the actual output of a Gaussian process regression model will contain noise, the GPR problem is modeled as:

[0021] \(y = f(x)+\epsilon\)

[0022] Where, is Gaussian noise, which satisfies a Gaussian distribution with an expectation of 0 and a variance of . The variance of the noise affects the prediction ability and prediction confidence of the GPR model for new data points. A larger variance indicates that the observed data contains more random noise, and the model will be more conservative during prediction, that is, the prediction uncertainty is higher; while a smaller variance indicates less noise in the data, and the model will be more certain during prediction.

[0023] The specific steps of the said step three are as follows:

[0024] The Gaussian process regression automatically performs the optimization process of hyperparameters. The process of autonomously learning these hyperparameters through the Bayesian method is also the solution process of GPR. According to Bayes' theorem, the posterior of the hyperparameters of Gaussian process regression is:

[0025]

[0026] where θ is a hyperparameter, which consists of the hyperparameters and variances of the kernel function p(θ) represents the prior, and p(y|X,θ) represents the likelihood. The likelihood can be obtained from the following formula:

[0027] p(y|X,θ) = ∫p(y|f,X,θ)p(f|X,θ)df

[0028] where f = f(X). According to the derivation process of the model, when the noise satisfies the independent and identically distributed Gaussian distribution, the likelihood of Gaussian process regression follows a normal distribution as: (where K = k(X,X) is an n×n covariance matrix), and it can be solved by maximum likelihood estimation (MLE);

[0029] The MLE method optimizes the hyperparameters by maximizing the likelihood of GPR, and its negative log-likelihood function is:

[0030]

[0031] Solving the maximum value of the GPR likelihood is equivalent to solving the minimum value of the formula. Therefore, taking the partial derivative of the above formula gives:

[0032]

[0033] The mean and variance of the trained Gaussian process are expressed by the following formula:

[0034]

[0035] where, x * is the training sample data of the input of the trained Gaussian process, μ * is the mean of the input of the trained Gaussian process, σ * is the variance of the trained Gaussian process, y * is the performance output corresponding to x * , x' * is the result of the trained Gaussian process, k * (x * , x' * ) is the kernel function of the trained Gaussian process with parameters x * and x' * respectively. At this time, the posterior distribution of y * is

[0036] The specific content of step four is as follows:

[0037] The mean absolute error MAE formula is as follows:

[0038]

[0039] where y * is the predicted value of the target output, and y r is the true value of the target output; n is the number of test samples.

[0040] The formula for the mean squared error MSE is as follows:

[0041]

[0042] The formula for the root mean squared error RMSE is as follows:

[0043]

[0044] The coefficient of determination R 2 The formula is as follows:

[0045]

[0046] where cov(y * , y r ) is the covariance function between the output predicted value and the true value, D(y * ) is the variance of the predicted value, and D(y r ) is the variance of the true value;

[0047] Gaussian process regression gives the prediction error (i.e., the uncertainty of the prediction). Based on the magnitude of the prediction error, the accuracy of the Gaussian process regression model is judged.

[0048] Advantages of the present invention:

[0049] Traditional performance prediction methods often have difficulty coping with the randomness and uncertainty in the performance of the sliding bearings of gear pumps, resulting in inaccurate prediction results. The present invention uses a Gaussian process regression model, which can better capture the randomness and uncertainty in the input performance data. This comprehensive consideration makes the model more suitable for the complex and changeable situations in the actual working state of the sliding bearings of gear pumps, not only improving the prediction accuracy but also enhancing the robustness of the model. Through multiple iterative trainings and Gaussian regression analysis, the obtained prediction results are more reliable, which helps to discover potential problems in advance and optimize the performance. Description of the drawings

[0050] Figure 1 is a schematic structural diagram of a system for a sliding bearing performance prediction method based on a Gaussian process regression method implemented by the present invention.

[0051] Figure 2 is a comparison diagram of the predicted value and the true value of the dimensionless maximum oil film pressure in the embodiment.

[0052] Figure 3 is a comparison diagram of the predicted value and the true value of the dimensionless oil film bearing capacity in the embodiment.

[0053] Figure 4 Comparison chart of predicted and actual friction values for the embodiment

[0054] Figure 5 Comparison chart of predicted and actual end leakage flow rates for the embodiment Detailed implementation manners

[0055] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0056] The object of the present invention is to provide a sliding bearing performance prediction method based on an active learning algorithm of a Gaussian process regression model to improve the accuracy of performance prediction and reduce the R & D cost.

[0057] The present invention takes a sliding bearing of a two-oil-groove gear pump as the object, and two oil grooves are symmetrically arranged at positions 60° after the maximum oil film gap and 120° before the maximum oil film gap of the sliding bearing.

[0058] First part: Collect performance parameter data of the sliding bearing under different structural parameters and operating conditions, form a certain amount of data samples, randomly shuffle the sample order, and divide them into two parts: training samples and test samples to prepare for subsequent training of the Gaussian process regression model.

[0059] The input features of the performance parameters of the sliding bearing collected under different structural parameters and operating conditions constitute D = {(x 1 , y 1 ),...,(x i , y i ),...,(x n , y n )}, where x i represents the input of the structural parameters and operating conditions of the i-th group of data samples, which is a vector, x i = (a i , b i , c i , d i , e i ), where a i is the diameter-to-length ratio of the i-th group of data, b i is the eccentricity of the i-th group of data, c i is the rotational speed of the gear shaft of the i-th group of data, d i is the width of the oil groove of the i-th group of data, e iis the oil sump depth of the i-th group of data. The sample data takes the bearing aspect ratio, gear shaft speed, eccentricity, oil groove width, and dimensionless oil groove depth as the input variables of the sliding bearing structure parameters, and the dimensionless maximum oil film pressure, dimensionless oil film bearing capacity, friction force, and end leakage flow rate as the output of the sliding bearing performance parameters. Among them, the aspect ratio takes 0.4, 0.9, 1.5, 2 respectively, the gear shaft speed takes 1000, 2000, 3000, 8000 r / min respectively, the eccentricity takes 0.1, 0.3, 0.5, 0.7, 0.9 respectively, the oil groove width takes 18°, 24°, 30°, 36° circumferentially respectively, and the dimensionless oil groove depth takes 0.2, 0.4, 0.6, 1.2 respectively. In this embodiment, the total number of samples is 3840 groups. The order of all samples is randomly shuffled to obtain 3840 groups of disordered data samples. The first 3500 groups of data are used as training samples to train the model and find the optimal hyperparameters, and the last 340 groups of data are used as test samples to evaluate the prediction accuracy of the model.

[0060] Part two: Set the mean function, kernel function, its hyperparameters, and likelihood function of the Gaussian process regression model as the prior distribution.

[0061] The Gaussian process is a continuous random process that assumes there is a continuous random function between any two points in the input space. This means that for adjacent time points, the Gaussian process can be used to describe the relationship between them. The Gaussian process is used to establish a performance model that can capture the complex relationship between input features (such as the bearing aspect ratio, eccentricity, gear shaft speed, etc.) and the sliding bearing performance output. This means that the performance of the sliding bearing under different structures and working conditions can be predicted. The Gaussian process not only provides the expected value of the prediction but also provides information about the confidence interval or variance. This allows understanding the credibility of the performance prediction and helps in decision-making and risk management. The performance model based on the Gaussian process can be used to optimize the structure parameters of the sliding bearing to achieve specific performance goals. It can also be used for decision support, such as making trade-offs between different design choices to meet requirements such as performance and cost.

[0062] The Gaussian process is a non-parametric model that does not require assumptions about the specific form of the model, so it is applicable to various types of data and problems. In the performance prediction of sliding bearings of gear pumps, there are usually complex relationships between input features and performance outputs, and these relationships may not be easily modeled by traditional mathematical formulas. The Gaussian process can flexibly adapt to this complexity. The Gaussian process provides an estimate of the uncertainty of the prediction, which is very useful in performance prediction. Since the performance of sliding bearings is affected by various factors, including working temperature, structural parameters, etc., changes in these factors will lead to performance uncertainty. The Gaussian process can not only give a point estimate of the performance, but also provide information about the performance range, which is crucial for decision-making and risk management. In some cases, the performance data of sliding bearings may be limited and not sufficient to support traditional statistical methods or machine learning methods. The Gaussian process performs well on small sample data. It can effectively utilize limited data points to establish a performance model and provide reasonable predictions. The kernel function of the Gaussian process model can adapt to different types of data relationships. This means that an appropriate kernel function can be selected according to the characteristics of the problem to better capture the relationship between input features and performance outputs. This flexibility is particularly important in the performance prediction of sliding bearings. The Gaussian process can effectively utilize historical performance data to establish a prediction model for performance. This is very important for the long-term monitoring and performance maintenance of sliding bearings, because it can perform real-time performance prediction and fault detection based on historical data.

[0063] The properties of the Gaussian process can be determined by the mean function and the covariance function, and the specific form can be expressed as:

[0064] f(x) ∼ GP(m(x), k(x, x'))

[0065] In the formula, m(x) is the mean function of the Gaussian process, k(x, x') is the kernel function of the Gaussian process, x and x' are two different input sample data, and the kernel function adopts the Rational Quadratic (RQ) kernel, which is a generalization of the squared exponential kernel (also known as the Gaussian kernel). The RQ kernel function is more flexible than the squared exponential kernel function because it introduces an additional scale mixing parameter α, which controls the mixing degree of different length scales. This makes the shape of the kernel function more diverse and can adapt to a wider range of data patterns:

[0066]

[0067] In the formula, k(x i , x j ) is the covariance between the function at the input points x i and x j , σ 2 is the scale parameter, which is used to control the amplitude size of the kernel function, ||xi -x j || 2 is the square of the Euclidean distance between point x i and x j where l is a length parameter that controls the smoothness or scale of variation of the function, and α is a scale mixture parameter that controls the degree of mixing of different length scales. When α approaches infinity, the RQ kernel approaches the squared exponential kernel function.

[0068] Considering that the actual output of a Gaussian process regression model will contain noise, the GPR problem is modeled as:

[0069] y = f(x) + ε

[0070] where is Gaussian noise that follows a Gaussian distribution with an expected value of 0 and a variance of . The variance of the noise affects the prediction ability and confidence of the GPR model for new data points. A larger variance indicates that the observed data contains more random noise, and the model will be more conservative in prediction, that is, the prediction uncertainty is higher; while a smaller variance indicates less noise in the data, and the model will be more certain in prediction.

[0071] Part 3: Optimize the hyperparameters of the kernel function in Step 2 based on the processed training sample data to obtain the trained Gaussian process regression performance prediction model.

[0072] Gaussian process regression can automatically perform the optimization process of hyperparameters. The process of autonomously learning these hyperparameters through the Bayesian method is also the solution process of GPR. According to Bayes' theorem, the posterior of the hyperparameters of Gaussian process regression is:

[0073]

[0074] where θ is the hyperparameter, which consists of the hyperparameters of the kernel function and the variance , p(θ) represents the prior, and p(y|X,θ) represents the likelihood. The likelihood can be obtained from the following formula:

[0075] p(y|X,θ) = ∫p(y|f,X,θ)p(f|X,θ)df

[0076] where f = f(X). According to the derivation process of the model, when the noise follows an independent and identically distributed Gaussian distribution, the likelihood of Gaussian process regression follows a normal distribution as: (where K = k(X,X) is an n×n covariance matrix), and it can be solved by maximum likelihood estimation (MLE).

[0077] The MLE method optimizes the hyperparameters by maximizing the likelihood of GPR, and its negative log-likelihood function is:

[0078]

[0079] Solving for the maximum value of the GPR likelihood is equivalent to solving for the minimum value of the equation. Therefore, taking the partial derivative of the above equation gives:

[0080]

[0081] The mean and variance of the trained Gaussian process are expressed by the following formulas:

[0082]

[0083] where x * is the training sample data of the input of the trained Gaussian process, μ * is the mean of the input of the trained Gaussian process, σ * is the variance of the trained Gaussian process, y * is the performance output corresponding to x * x' * is the result of the trained Gaussian process, k * (x * , x' * ) is the kernel function of the trained Gaussian process with parameters x * and x' * ; k(x * , x' * ) is the kernel function of the Gaussian process with parameters x * and x' * . At this time, the posterior distribution of y * is

[0084] Part 4: Use the trained Gaussian process regression model in Step 3 to perform performance prediction on the test sample data and give the prediction accuracy.

[0085] The formula for the mean absolute error MAE is as follows:

[0086]

[0087] In the formula, y * is the predicted value of the target output, and y r is the true value of the target output.

[0088] The formula for the mean square error MSE is as follows:

[0089]

[0090] The formula for the root mean square error RMSE is as follows:

[0091]

[0092] Coefficient of determination R 2 The formula is as follows:

[0093]

[0094] In the formula, cov(y * , y r ) is the covariance function between the output predicted value and the true value, D(y * ) is the variance of the predicted value, and D(y r ) is the variance of the true value.

[0095] Gaussian process regression gives the prediction error (i.e., the uncertainty of the prediction). Based on the magnitude of the prediction error, the accuracy of the Gaussian process regression model can be judged.

[0096] The MATLAB simulation results show that Figure 2-5 The errors of the predicted values of each performance output are as follows: the mean absolute error of the dimensionless maximum oil film pressure of the oil film is 0.20959, the mean square error is 0.83026, the root mean square error is 0.91119, and the coefficient of determination is 0.99788; the mean absolute error of the dimensionless bearing capacity of the oil film is 0.50247, the mean square error is 0.093315, the root mean square error is 0.30547, and the coefficient of determination is 0.9986; the mean absolute error of the friction force is 0.0063984, the mean square error is 0.60986, the root mean square error is 0.78094, and the coefficient of determination is 0.99999; the mean absolute error of the end leakage flow rate is 0.020227, the mean square error is 1.9565e-8, the root mean square error is 0.00013987, and the coefficient of determination is 0.99962. It can be seen that the errors of the Gaussian process regression model for predicting the performance parameters of the sliding bearing after training, the mean absolute error, the mean square error, and the root mean square error of each prediction are all less than one, and the coefficient of determination of each prediction is greater than 0.99. It can be considered that the accuracy of this Gaussian process regression model is relatively high.

[0104] Gaussian Process Regression (GPR), as a powerful non-linear regression tool, is widely used in various prediction fields because it can flexibly handle complex data distributions and relationships, and provide accurate prediction results and uncertainty estimates. Gaussian process regression is based on probability theory, models the function space, uses known data points to predict unknown output values, and can effectively estimate the uncertainty of the prediction results. Compared with traditional linear regression methods, Gaussian process regression has the advantages of non-parametric, flexibility, and uncertainty estimation.

Claims

1. A method for predicting the performance of a gear pump sliding bearing based on Gaussian process regression, characterized in that: The steps include: Step 1: Collect performance parameter data of different structural parameters and operating conditions of sliding bearings, form a certain amount of data samples, and randomly shuffle the sample order to divide them into training samples and test samples, in preparation for the subsequent training of Gaussian process regression model; Step 2: Set the mean function, kernel function and its hyperparameters, and likelihood function of the Gaussian process regression model as the prior distribution; Step 3: Optimize the hyperparameters of the kernel function in step 2 based on the processed training sample data to obtain the trained Gaussian process regression performance prediction model; Step 4: Use the Gaussian process regression model trained in step 3 to predict the performance of the test sample data and give the prediction accuracy.

2. The method for predicting the performance of a gear pump sliding bearing based on Gaussian process regression according to claim 1 is characterized in that: The step 1 is specifically as follows: The collected performance parameters of the sliding bearing under different structural parameters and operating conditions are input into the characteristic structure D = {(x1, y1), ..., (x i ,y i ),...,(x n ,y n )}, where x i represents the structural parameters and operating condition input of the i-th group of data samples, which is a vector, x i =(a i ,b i ,c i ,d i ,e i ), where a i is the aspect ratio of the i-th group of data, b i is the eccentricity of the i-th group of data, c i is the gear shaft speed of the i-th group of data, d i is the oil groove width of the i-th group of data, e i is the oil tank depth of the i-th group of data.

3. The method for predicting the performance of a gear pump sliding bearing based on Gaussian process regression according to claim 1 is characterized in that: The step 2 is specifically as follows: The properties of the Gaussian process are determined by the mean function and the covariance function, which can be expressed in the following form: f(x)~GP(m(x),k(x,x')) Where m(x) is the mean function of the Gaussian process, k(x,x') is the kernel function of the Gaussian process, x and x' are two different input sample data, the kernel function uses the Rational Quadratic (RQ) kernel, and introduces an additional scale mixing parameter α to control the mixing degree of different length scales; The RQ kernel function is formally expressed as follows: In the formula, k(x i ,x j ) is the function at the input point x i and x j The covariance between ||x i -x j || 2 For point x i and x j The square of the Euclidean distance between them, l is the length parameter, which controls the smoothness of the function or the scale of change, α is the scale mixing parameter, which controls the degree of mixing of different length scales. When α tends to infinity, the RQ kernel tends to the square exponential kernel function.

4. The method for predicting the performance of a gear pump sliding bearing based on Gaussian process regression according to claim 3 is characterized in that: Considering that the actual output of a Gaussian process regression model contains noise, the GPR problem is modeled as: y=f(x)+ε In the formula, is Gaussian noise, satisfying the expectation of 0 and the variance of The variance of the noise affects the GPR model’s ability to predict new data points and the confidence level of the prediction. A larger variance means that the observed data contains more random noise, and the model will be more conservative when predicting, that is, the uncertainty of the prediction is higher. A smaller variance means that there is less noise in the data, and the model will be more certain when predicting.

5. The method for predicting the performance of a gear pump sliding bearing based on Gaussian process regression according to claim 1 is characterized in that: The specific steps of step three are: Gaussian process regression automatically optimizes the hyperparameters. The process of autonomous learning of the hyperparameters through the Bayesian method is also the GPR solution process. According to the Bayesian theorem, the hyperparameter posterior of Gaussian process regression is: Where θ is a hyperparameter, which is determined by the kernel function’s hyperparameters and variance Composition, p(θ) represents the prior, p(y|K,θ) represents the likelihood, and the likelihood can be obtained by the following formula: p(y|X,θ)=∫p(y|f,X,θ)p(f|X,θ)df Where f = f(X). According to the derivation process of the model, when the noise satisfies independent and Gaussian distribution, the likelihood of Gaussian process regression obeys normal distribution: (where K = k(X,X) is the n×n covariance matrix), solved by maximum likelihood estimation (MLE); The MLE method optimizes the hyperparameters by maximizing the likelihood of GPR, and its negative log-likelihood function is: Solving the maximum value of the GPR likelihood is equivalent to solving the minimum value of the solution, so taking the partial derivative of the above formula gives: The mean and variance of the trained Gaussian process are expressed as follows: Among them, x * is the training sample data of the input of the trained Gaussian process, μ * is the mean of the input of the trained Gaussian process, σ * is the variance of the Gaussian process after training, y * For x * The corresponding performance output, x' * is the result of the Gaussian process after training, k * (x * ,x' * ) are the parameters x * and x' * The kernel function of the trained Gaussian process; k(x * ,x' * ) are the parameters x * and x' * The kernel function of the Gaussian process, at this time y * The posterior distribution of 6. The method for predicting the performance of a gear pump sliding bearing based on Gaussian process regression according to claim 1, characterized in that: The step 4 is specifically as follows: The mean absolute error MAE formula is as follows: In the formula, y * is the predicted value of the target output, y r is the true value of the target output; n is the number of test samples. The mean square error MSE formula is as follows: The root mean square error RMSE formula is as follows: Coefficient of determination R 2 The formula is as follows: In the formula, cov(y * ,y r ) is the covariance function between the output prediction value and the true value, D(y * ) is the variance of the predicted value, D(y r ) is the variance of the true value; Gaussian process regression gives a prediction error, and based on the size of the prediction error, the accuracy of the Gaussian process regression model is judged.

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