Mechanical component degradation prediction method and system based on adaptive time-varying weight integrated gaussian process regression

Abstract

The application provides a mechanical component degradation prediction method and system based on adaptive time-varying weight integrated Gaussian process regression, which comprises the following steps: taking the degradation data of the same mechanical component under the same working condition as a prior data set, selecting a polynomial function family as a prior mean function, constructing different mean function predictors based on the Gaussian regression method according to the prior data set and the prior mean function family, and constructing a global base predictor, a health period base predictor, a base predictor in the period of impending degradation and a base predictor in the degradation period through index optimization; in the global, health, impending degradation and degradation periods, the weights of the corresponding base predictors in each period are adaptively updated based on adaptive time-varying weights to construct a final integrated model; and the integrated model is used to predict the degradation trend of a mechanical component to be predicted. Compared with other existing methods, the application has the advantages of using less historical data to realize higher-precision and more adaptable prediction.

Description

Technical Field

[0001] This invention relates to the field of predicting the degradation trend of mechanical components, and specifically to a method and system for predicting the degradation of mechanical components based on adaptive time-varying weighted integrated Gaussian process regression. Background Technology

[0002] Rolling bearings are widely used in rotating machinery, playing a crucial role in the operation of these machines. Once a rolling bearing fails, other adjacent components degrade more rapidly until they fail as well. This can significantly reduce machine productivity and even lead to catastrophic accidents. Regular monitoring and prevention of rolling bearing failure are essential to ensuring the proper functioning of rotating machinery. However, with the increasing complexity of modern machinery, excessive repair and maintenance can lead to high operating and maintenance costs. To strike a balance between high reliability requirements and limited operating and maintenance costs, there is a shift towards condition-based preventative maintenance rather than traditional fail-safe repair. Remaining useful life (RUL) is a key indicator for implementing preventative maintenance strategies and is playing an increasingly important role.

[0003] To estimate the resistance level (RUL) of components and perform preventative maintenance before serious failures occur, several methods for predicting degradation trends have been investigated. These methods can be categorized into two types: parametric and nonparametric methods. Parametric methods primarily assume that physical degradation behavior or potential failure modes follow some probabilistic models or equations and have a fixed set of parameters. The advantage of these methods is that they can provide some high-accuracy estimates with the help of domain knowledge. However, this typically relies on sufficient and detailed degradation history data, as well as a deep understanding of the degradation mechanisms. In the case of bearing degradation, collecting full life-cycle degradation data is both time-consuming and expensive. Furthermore, in practice, the degradation mechanisms of various factors (i.e., roughness, surface quality, assembly clearance, and installation conditions) are highly complex; therefore, constructing the parameter distribution or equations for RUL estimation based on domain knowledge has become a challenging task. Unlike parametric methods, nonparametric methods do not require further assumptions about the parameters of a given complex population and can build models and achieve high-quality estimates with only a small amount of prior information or knowledge. With the rapid development of machine learning, many nonparametric methods related to machine learning have been studied for predicting the RUL of components, and deep learning methods for predicting RUL have been studied on this basis. Therefore, nonparametric methods have become increasingly popular in bearing degradation modeling and RUL prediction.

[0004] One of the most promising nonparametric methods is Gaussian process regression (GPR), which provides a flexible and practical probabilistic approach for learning nonlinear mappings. The advantages of GPR-driven prediction methods include several key aspects. First, these methods can adjust the model complexity based on training data and provide an interval estimate, adapting to scenarios with high security requirements. Second, GPR can be used to build high-precision models with flexible assumptions about distributions or parameters. GPR has been widely applied in many fields, such as consumer electronics, clean energy, and transportation. However, most Gaussian processes currently studied employ a deterministic time-invariant mean function or a non-informative zero-mean function as the prior mean. To achieve satisfactory performance, these models must be trained with a large number of samples to obtain an appropriate posterior mean. Even so, when the test data deviates significantly from the training data, these Gaussian processes based on deterministic time-invariant means still experience a substantial performance drop, hindering larger-scale and more accurate extrapolation predictions. Summary of the Invention

[0005] In order to overcome the defects in the prior art, the purpose of this invention is to provide a method and system for predicting the degradation of mechanical parts based on adaptive time-varying weighted integrated Gaussian process regression.

[0006] To achieve the above-mentioned objectives of this invention, this invention provides a method for predicting the degradation of mechanical components based on adaptive time-varying weighted integrated Gaussian process regression, comprising the following steps:

[0007] Using the degradation data of the same mechanical parts under the same working conditions as the prior dataset, a family of multinomial functions is selected as the prior mean function. Based on the Gaussian regression method, different mean function predictors are constructed using the prior dataset and the family of prior mean functions. Through index optimization, a global base predictor, a base predictor for the healthy period, a base predictor for the period about to degrade, and a base predictor for the degraded period are constructed.

[0008] In the four stages of global, healthy, impending decline, and decline, the weights of the corresponding base predictors in each stage are adaptively updated based on adaptive time-varying weights to construct the final ensemble model.

[0009] This integrated model is used to predict the degradation trend of the mechanical parts to be predicted.

[0010] In a preferred embodiment of the mechanical component degradation prediction method based on adaptive time-varying weighted ensemble Gaussian process regression, the steps for constructing the global base predictor, the healthy period base predictor, the pre-degradation period base predictor, and the degradation period base predictor are as follows:

[0011] Using degradation data of the same mechanical parts under the same working conditions as the prior dataset, the prior data is divided into a healthy stage, a deteriorating stage, and a degradation stage. A family of polynomial functions is used as the prior mean function to construct predictors with different mean functions. Each predictor is used to predict the four stages: global, healthy, deteriorating, and degradation stages.

[0012] The mean absolute error (MAE), mean square error (MSE), Akaike information criterion (AIC), and Bayesian information criterion (BIC) are used to select the best predictor for each stage from the prediction results.

[0013] Based on the optimization results, the predictor with the best prediction performance in each stage is used as the base predictor for that stage, resulting in the global base predictor, the base predictor for the healthy period, the base predictor for the period about to deteriorate, and the base predictor for the deterioration period.

[0014] In a preferred embodiment of the mechanical component degradation prediction method based on adaptive time-varying weighted integrated Gaussian process regression, the mean absolute error (MAE) is calculated using the following formula: Among them, y i Represents the true value. This represents the predicted value, where m is the number of data points in the datasets corresponding to each stage: global, healthy period, impending decline period, and decline period.

[0015] The formula for calculating the mean square error (MSE) is as follows: Among them, y i Represents the true value. Indicates the predicted value;

[0016] The Akaike Information Criterion (AIC) is calculated as follows: AIC = 2k - 2ln(L), where k is the number of independent parameters in the predictor and L is the likelihood function in the predictor.

[0017] The Bayesian Information Criterion (BIC) is calculated as follows: BIC = kln(n) - 2ln(L), where k is the number of independent parameters in the predictor, L is the likelihood function in the predictor, and n is the number of predicted values.

[0018] In each stage, the predictor with the smallest mean of MAE, MSE, AIC, and BIC for that stage is selected as the predictor for that stage.

[0019] In a preferred embodiment of the mechanical component degradation prediction method based on adaptive time-varying weighted ensemble Gaussian process regression, the construction steps for different mean function predictors are as follows:

[0020] The prior dataset is divided into a training dataset and a test dataset. The data in the training dataset are the training input data, and the data in the test dataset are the test input data. x is the training input data, X is a matrix composed of the input vectors of all training samples, and y is a vector of the output scalars of all training samples. * For test input data, X * The input matrix for the test dataset, x′, comes from the test set, and its Gaussian process is:

[0021] g(x)~GP(h(x) T b, k(x, x′) + h(x) T Bh(x′));

[0022] In the formula, g(x) = f(x) + h(x) T β, where f(x)~GP(0,k(x,x′)) is a general Gaussian process, k(x,x′) is the covariance function, h(x) is a family of polynomial functions, and the constants and coefficients in the family of polynomial functions are determined by the prior dataset. The parameter β~N(b,B) is a Gaussian distribution with mean b and covariance B.

[0023] By using training data and a prior Gaussian process g(x), the Gaussian process that the training data follows is obtained; the Gaussian process that the training data follows is tested using a test dataset to obtain predictors with different mean functions;

[0024] When given test input data x * The corresponding output, i.e., the mean of the predicted distribution, is The covariance of the predicted distribution is cov(g) * The expression for its predicted distribution is:

[0025]

[0026]

[0027] Here, the H matrix is ​​composed of all trained h(x) vectors, H * K consists of the h(x) vectors of all tests. f It is the covariance matrix of the f(x) values. Let I be the noise covariance noise, and I be the identity matrix. The noise distribution is as follows: K * Let cov(f) be the covariance matrix of the training and test data. * Let be the predicted covariance distribution of a general Gaussian process, expressed as:

[0028]

[0029] Wherein K(X) * ,X)=K(X,X * ) T K() refers to the covariance matrix, and K(X, X) is the n-order symmetric positive definite covariance matrix of the training dataset. * X * K(X, X) is the covariance matrix of the test input data. * ) = K * , where is the covariance matrix of the training and testing data.

[0030] Preferably, the polynomial function family is: f1(z) = a p z p +a p-1 z p-1 +...+a1z+c, where a is a constant coefficient, c is a constant, and p is a positive integer.

[0031] In a preferred embodiment of the mechanical component degradation prediction method based on adaptive time-varying weighted ensemble Gaussian process regression, the expression for the adaptive time-varying weights is:

[0032] Adaptive Time-Varying Weights In the formula, l i is the distance between the base predictor in this stage and the global base predictor. The distance is the difference between the output values ​​of different base predictors. b is the distance decay coefficient, m is the balance coefficient, and n is the number of base predictors.

[0033] In a preferred embodiment of the mechanical component degradation prediction method based on adaptive time-varying weighted integrated Gaussian process regression: at each stage, the stage base predictor closest to the global base predictor is given the maximum weight through adaptive time-varying weights, while the base predictors of the remaining stages are given the remaining weights, and each base predictor is assigned the maximum weight only in one stage.

[0034] The present invention also proposes a mechanical component degradation prediction system, including a processor and a memory, wherein the processor and the memory are communicatively connected, and the memory is used to store at least one executable instruction, wherein the executable instruction causes the processor to perform the operation corresponding to the mechanical component degradation prediction method based on adaptive time-varying weighted integrated Gaussian process regression described above.

[0035] The beneficial effects of this invention are:

[0036] 1. The advantage of this invention compared with other existing methods is that it can use less historical data, does not require a large amount of training data, and does not require complex network architecture design to achieve more accurate predictions, which reduces the time and resources required for model training.

[0037] 2. The proposed adaptive time-varying weight method is based on ensemble learning, which can effectively integrate the advantages of each basic predictor, take into account the characteristics of each degradation stage, and adaptively update the weights of each model to improve the overall prediction accuracy of the model. It has high adaptability and strong robustness.

[0038] 3. This method is applicable to the prediction of degradation trends of mechanical parts, especially bearings, providing a promising solution for industrial applications.

[0039] 4. The present invention has high accuracy in predicting degradation trends, and can even provide highly accurate prediction results for the degradation trends of mechanical parts under actual complex working conditions.

[0040] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0041] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0042] Figure 1 It is a flowchart of the invention process.

[0043] Figure 2 The root mean square value of the vibration signal from the prior PHM2012 bearing dataset is used in this invention.

[0044] Figure 3 This invention is based on an index-optimized base predictor;

[0045] Figure 4 This is the prediction result of the PHM2012 bearing dataset in this invention;

[0046] Figure 5 This invention addresses the prediction error of the PHM2012 bearing dataset.

[0047] Figure 6 This invention provides the prediction results for offshore wind turbine bearings;

[0048] Figure 7 This invention addresses the prediction error of offshore wind turbine bearings. Detailed Implementation

[0049] Embodiments of the present invention are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0050] In the description of this invention, unless otherwise specified and limited, it should be noted that the terms "installation", "connection" and "linking" should be interpreted broadly. For example, they can refer to mechanical or electrical connections, or internal connections between two components. They can be direct connections or indirect connections through an intermediate medium. Those skilled in the art can understand the specific meaning of the above terms according to the specific circumstances.

[0051] like Figure 1 As shown, this invention provides a method for predicting the degradation of mechanical components based on adaptive time-varying weighted integrated Gaussian process regression, comprising the following steps:

[0052] Using degradation data of identical mechanical parts under the same working conditions as the prior dataset, a family of polynomial functions is selected as the prior mean function. Based on the Gaussian regression method, different mean function predictors are constructed using the prior dataset and the family of prior mean functions. Through index optimization, a global base predictor, a base predictor for the healthy period, a base predictor for the period about to degrade, and a base predictor for the degraded period are constructed.

[0053] When constructing predictors with different mean functions, a family of polynomial functions can be used as the prior mean function. By combining the prior dataset, the coefficients and constants of the family of polynomial functions in the prior Gaussian process can be determined, and the prior mean functions with different means can be obtained. Based on this, predictors with different mean functions can be constructed using existing methods.

[0054] The expression for a family of polynomial functions can be f1(z) = a p z p +a p-1 z p-1 +...+a1z+c, where a is a coefficient, c is a constant, z is a data point in the prior dataset, and p is a positive integer, p = 1, 2, ...

[0055] The following methods can also be used to construct predictors with different mean functions.

[0056] This invention employs a Gaussian process with a prior mean, where the variables represent: the prior dataset is divided into a training dataset and a test dataset; the data in the training dataset are the training input data, and the data in the test dataset are the test input data; x is the training input data, X is a matrix composed of the input vectors of all training samples, and y is a vector of the output scalars of all training samples. * For test input data, X * The input matrix for the test dataset, x′, comes from the test set, and its Gaussian process is:

[0057] g(x)~GP(h(x) Tb, k(x, x′) + h(x) T Bh(x′));

[0058] In the formula, g(x) = f(x) + h(x) T β, where f(x)~GP(0, k(x, x′)) is a general Gaussian process, k(x, x′) is the covariance function, and h(x) is the specified basis function. In this embodiment, the specified basis function is a family of polynomial functions, whose general expression is: f1(z)=a p z p +a p-1 z p-1 +...+a1z+c, where a is a coefficient and c is a constant. At this point, z is x, which is the training input data. p is a positive integer, p = 1, 2, ... The constants and coefficients in the polynomial function family are determined using the prior dataset. The parameter β is determined by the prior dataset, which contains complete degenerate data. By setting a Gaussian process regression with a mean of zero, the Gaussian process of the prior dataset is calculated, yielding the mean b and covariance B. Let β follow N(b, B), and the distribution of the prior dataset be N(b, B), i.e., β ~ N(b, B). N(b, B) is a Gaussian distribution with a mean of b and a covariance of B.

[0059] By using training data and a prior Gaussian process g(x), the Gaussian process that the training data follows is obtained; the Gaussian process that the training data follows is tested using a test dataset to obtain predictors with different mean functions;

[0060] When given test input data x * The corresponding output, i.e., the mean of the predicted distribution, is The covariance of the predicted distribution is cov(g) * The expression for its predicted distribution is:

[0061]

[0062]

[0063] Here, the H matrix is ​​composed of all trained h(x) vectors, H * K consists of the h(x) vectors of all tests. f It is the covariance matrix of the f(x) values. Let I be the noise covariance noise, and I be the identity matrix. The noise distribution is as follows: K * Let cov(f) be the covariance matrix of the training and test data. * Let be the predicted covariance distribution of a general Gaussian process, expressed as:

[0064]

[0065] Wherein K(X) * ,X)=K(X,X * ) T K() refers to the covariance matrix, and K(X, X) is the n-order symmetric positive definite covariance matrix of the training dataset. * X * K(X, X) is the covariance matrix of the test input data. * ) = K * , where is the covariance matrix of the training and testing data.

[0066] In this embodiment, a polynomial basis function is used as the prior mean function through the prior dataset. The mean function of the prior Gaussian process is determined by combining the prior dataset. The basis function in this embodiment is a polynomial function with a p-value of 1 to 7, and predictors with different mean functions are constructed accordingly.

[0067] After constructing predictors with different mean functions, construct a global base predictor, a base predictor for the healthy period, a base predictor for the period about to deteriorate, and a base predictor for the deteriorating period.

[0068] The specific steps are as follows: using degradation data of the same mechanical parts under the same working conditions as the prior dataset, dividing the prior data into a healthy stage, a deteriorating stage and a degradation stage, using a family of polynomial functions as the prior mean function, constructing predictors with different mean functions, and using each predictor to predict the four stages of global, healthy, deteriorating, and degradation respectively.

[0069] The mean absolute error (MAE), mean square error (MSE), Akaike information criterion (AIC), and Bayesian information criterion (BIC) are used to select the best predictor for each stage from the prediction results.

[0070] Based on the optimization results, the predictor with the best prediction performance in each stage is used as the base predictor for that stage, resulting in the global base predictor, the base predictor for the healthy period, the base predictor for the period about to deteriorate, and the base predictor for the deterioration period.

[0071] The specific content of the indicator is as follows:

[0072] The formula for calculating the mean absolute error (MAE) is: Among them, y i Represents the actual value. This represents the predicted value, where m is the number of data points in the datasets corresponding to each stage: global, healthy period, impending decline period, and decline period.

[0073] The formula for calculating the mean squared error (MSE) is: Among them, y i Represents the actual value. This represents the predicted value.

[0074] The AIC criterion comprises two parts: model complexity and model fit. Generally, it can be expressed as:

[0075] AIC = 2k - 21n(L)

[0076] In the formula, k is the number of independent parameters in the predictor, and L is the likelihood function in the predictor.

[0077] The Bayesian Information Criterion (BIC) is calculated as follows: BIC = kln(n) - 2ln(L), where k is the number of independent parameters in the predictor, L is the likelihood function in the predictor, and n is the number of predicted values.

[0078] The smaller the values ​​of MAE, MSE, AIC, and BIC, the better the predictive ability of the model. Based on this, the predictor for each stage is selected: in each stage, the predictor with the smallest mean of MAE, MSE, AIC, and BIC for that stage is selected as the predictor for that stage.

[0079] Then, in the four stages of global, healthy, impending degradation, and degradation, the weights of the corresponding base predictors in each stage are adaptively updated based on adaptive time-varying weights to construct the final ensemble model. In each stage, the predictor that is better than the global base predictor will be assigned the majority of the weights, and the weights of the predictors in each stage will be adaptively updated.

[0080] The expression for the adaptive time-varying weight is:

[0081] Adaptive Time-Varying Weights In the formula, l i is the distance between the base predictor in this stage and the global base predictor. The distance is the difference between the output values ​​of different base predictors. b is the distance decay coefficient, m is the balance coefficient, and n is the number of base predictors, where n = 1, 2, ... In this invention, n is taken as 4.

[0082] The global base predictor has a good predictive effect for the entire running cycle. The predictors at each stage have a better effect than the global base predictor for their respective stages. Based on this, the closer the base predictor at each stage is to the global base predictor, the closer the predictor is to the true value, and therefore it should be given a larger weight.

[0083] Through adaptive time-varying weight formula This allows the base predictors that perform better at each stage to receive the majority of the weights, while other base predictors receive very small weights. Furthermore, as the bearing moves from one stage to the next, the predictors that received the majority of the weights in the previous stage will be assigned very small weights in the next stage because they are far from the global predictor. Meanwhile, the predictors that perform better in the next stage will be assigned the majority of the weights. This achieves adaptive weight updates from one stage to the next, and the final model integrates the advantages of the predictors at each stage.

[0084] This integrated model is used to predict the degradation trend of the mechanical parts to be predicted.

[0085] Specific case: Predicting bearing degradation

[0086] 1. The prior bearings selected for the PHM2012 bearing dataset are as follows: Figure 2 Construct a global base predictor, a healthy stage base predictor, a degenerate stage base predictor, and a degenerate stage base predictor, and optimize them using MAE, MSE, AIC, and BIC, such as... Figure 3 .

[0087] Bearing 1_1 is used as the prior dataset, the truncated portion of bearing 1_3 is used as the training set, and the remaining portion is used as the test set for life prediction. A global predictor, i.e., a general bagging averaging model, is employed. The prediction results are as follows: Figure 4 As shown, the MAE and MSE values ​​of the predicted and actual values ​​are as follows: Figure 5 As shown in the figure, the experimental results indicate that the prediction performance of a single deterministic prior mean function model is inferior to that of a general bagging model. Furthermore, the general bagging model's predictive ability is lower than that of the adaptive time-varying bagging Gaussian process regression model proposed in this invention. The figure shows that the model effectively predicts the 1-3 degradation stages of the bearing, with actual values ​​all within the 95% confidence interval. Adaptive ensemble using the same kernel function but different mean functions provides a good predictive effect on the bearing degradation trend.

[0088] 2. Real-time collection of wind turbine bearing data in 2021 was also used for experimental verification. This dataset collects one data point per day. The construction and optimization of the baseline predictors for each degradation stage are similar to those used in the PHM2012 bearing dataset. Using rolling bearing #1 as the prior dataset, the degradation trend prediction results for rolling bearing #2 are as follows: Figure 6 As shown, the predicted MAE and MSE values ​​are as follows: Figure 7As shown, the true values ​​are contained within the 95% confidence interval, and the prediction results for rolling bearing #2 are highly accurate. The MSE and MAE of the adaptive time-varying bagging Gaussian process regression model are lower than those of the single time-invariant mean function model and the general bagging model. From the prediction results, the adaptive time-varying weighted ensemble Gaussian process regression model can effectively reduce prediction errors and has strong robustness.

[0089] The present invention also proposes a mechanical component degradation prediction system, including a processor and a memory, wherein the processor and the memory are communicatively connected, and the memory is used to store at least one executable instruction, wherein the executable instruction causes the processor to perform the operation corresponding to the mechanical component degradation prediction method based on adaptive time-varying weighted integrated Gaussian process regression described above.

[0090] In the description of this specification, references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0091] Although embodiments of the invention have been shown and described, those skilled in the art will understand that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

Claims

1. A method for predicting the degradation of mechanical components based on adaptive time-varying weighted ensemble Gaussian process regression, characterized in that, Includes the following steps: Using the degradation data of the same mechanical parts under the same working conditions as the prior dataset, a family of multinomial functions is selected as the prior mean function. Based on the Gaussian regression method, different mean function predictors are constructed using the prior dataset and the family of prior mean functions. Through index optimization, a global base predictor, a base predictor for the healthy period, a base predictor for the period about to degrade, and a base predictor for the degraded period are constructed. In the four stages of global, healthy, impending degradation, and degradation, the weights of the corresponding base predictors for each stage are adaptively updated based on adaptive time-varying weights to construct the final ensemble model; the expression for the adaptive time-varying weights is: Adaptive Time-Varying Weights In the formula, This is the distance between the base predictor at this stage and the global base predictor, where the distance is the difference in the output values ​​of the different base predictors. It is the distance attenuation coefficient. It is the balance coefficient. The number of basis predictors; This integrated model is used to predict the degradation trend of the mechanical parts to be predicted.

2. The mechanical component degradation prediction method based on adaptive time-varying weighted ensemble Gaussian process regression according to claim 1, characterized in that, The steps for constructing the global base predictor, the base predictor during the healthy period, the base predictor during the impending degradation period, and the base predictor during the degradation period are as follows: Using degradation data of the same mechanical parts under the same working conditions as the prior dataset, the prior data is divided into a healthy stage, a deteriorating stage, and a degradation stage. A family of polynomial functions is used as the prior mean function to construct predictors with different mean functions. Each predictor is used to predict the four stages: global, healthy, deteriorating, and degradation stages. The mean absolute error (MAE), mean square error (MSE), Akaike information criterion (AIC), and Bayesian information criterion (BIC) are used to select the best predictor for each stage from the prediction results. Based on the optimization results, the predictor with the best prediction performance in each stage is used as the base predictor for that stage, resulting in the global base predictor, the base predictor for the healthy period, the base predictor for the period about to deteriorate, and the base predictor for the deterioration period.

3. The method for predicting mechanical component degradation based on adaptive time-varying weighted integrated Gaussian process regression according to claim 1 or 2, characterized in that, The family of polynomial functions is: ,in, is a constant coefficient, c is a constant, and p is a positive integer.

4. The mechanical component degradation prediction method based on adaptive time-varying weighted integrated Gaussian process regression according to claim 2, characterized in that, The formula for calculating the mean absolute error (MAE) is as follows: ,in, Represents the actual value. This represents the predicted value, where m is the number of data points in the datasets corresponding to each stage: global, healthy period, impending decline period, and decline period. The formula for calculating the mean square error (MSE) is as follows: ,in, Represents the actual value. Indicates the predicted value; The calculation formula for the Akaike Information Criterion (AIC) is as follows: ,in, It is the number of independent parameters included in the predictor. It is the likelihood function in the predictor; The formula for calculating the Bayesian Information Criterion (BIC) is as follows: ,in, It is the number of independent parameters included in the predictor. It is the likelihood function in the predictor. It is the number of predicted values; In each stage, the predictor with the smallest mean of MAE, MSE, AIC, and BIC for that stage is selected as the predictor for that stage.

5. The method for predicting mechanical component degradation based on adaptive time-varying weighted integrated Gaussian process regression according to claim 1 or 2, characterized in that, The steps for constructing different mean function predictors are as follows: The prior dataset is divided into a training dataset and a test dataset. The data in the training dataset serves as the training input data, and the data in the test dataset serves as the test input data. For training input data, It is a matrix composed of the input vectors of all training samples. It is a vector of scalar outputs from all training samples. For test input data, The input matrix for the test dataset, From the test set, its Gaussian process is: ； In the formula, ,in For a typical Gaussian process, Let covariance function be used. Given a family of polynomial functions, determine the constants and coefficients, and parameters of the family of polynomial functions using a prior dataset. , It is a Gaussian distribution with mean b and covariance B; By using training data and a prior Gaussian process g(x), the Gaussian process that the training data follows is obtained; the Gaussian process that the training data follows is tested using a test dataset to obtain predictors with different mean functions; When given test input data The corresponding output, i.e., the mean of the predicted distribution, is The covariance of the predicted distribution is The expression for its predicted distribution is: ； ； in, The matrix consists of all trained Vector composition, By all tests Vector composition, yes The covariance matrix of the values, , , , Let I be the noise covariance noise, and I be the identity matrix. The noise distribution is as follows: , The covariance matrix of the training and test data. The predicted covariance distribution for a general Gaussian process is expressed as: ,in, K() refers to the covariance matrix. It is the training dataset. 1-order symmetric positive definite covariance matrix It is the covariance matrix of the test input data. = , where is the covariance matrix of the training and testing data.

6. The mechanical component degradation prediction method based on adaptive time-varying weighted integrated Gaussian process regression according to claim 1, characterized in that, In each stage, the stage base predictor closest to the global base predictor is given the maximum weight through adaptive time-varying weights, while the base predictors of the remaining stages are given the remaining weights. Each base predictor is assigned the maximum weight only in one stage.

7. A mechanical component degradation prediction system, characterized in that, The system includes a processor and a memory, which are communicatively connected. The memory is used to store at least one executable instruction that causes the processor to perform the operation corresponding to the mechanical component degradation prediction method based on adaptive time-varying weighted integrated Gaussian process regression as described in any one of claims 1-6.

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