Force-thermal coupling machine learning prediction method for bearing guide surface lubrication state

Abstract

The application discloses a force-heat coupling machine learning prediction method for lubrication state of a bearing guide surface and belongs to the technical field of intelligent manufacturing of high-end equipment and intelligent key mechanical parts. The method comprises the following steps: for a plurality of working condition parameter vectors, a low-fidelity two-dimensional oil film pressure field is obtained by solving the physical baseline model, and a high-fidelity two-dimensional oil film pressure field is obtained by solving a thermo-elastohydrodynamic coupling finite element model considering the temperature-viscosity coupling effect of lubricating oil. The force-heat coupling machine learning prediction method for the lubrication state of the bearing guide surface is suitable for lubrication design optimization and online state evaluation of high-speed rolling bearings.

Description

Technical Field

[0001] This invention relates to the field of intelligent manufacturing of high-end equipment and intelligent key mechanical components, and in particular to the application of data-driven modeling based on machine learning in predicting the lubrication state of the guide surface of high-speed rolling bearings. Background Technology

[0002] During the operation of high-speed rolling bearings, the lubrication state between the cage guide surface and the inner ring interface directly determines the bearing's load-carrying capacity, wear behavior, and operational stability. Traditional engineering analysis typically simplifies this interface to a short sliding bearing model, predicting oil film pressure and load-carrying capacity by solving the Reynolds equation. The short sliding bearing theory is widely used in multibody dynamics simulation and preliminary design due to its high computational efficiency and clear physical concepts. However, this model has two inherent limitations: first, it usually ignores the circumferential pressure gradient, retaining only the axial flow effect; second, it often employs the isoviscosity assumption, assuming that the lubricant viscosity remains constant. More importantly, this method is primarily used to synthesize oil film forces and frictional forces, while the two-dimensional oil film pressure and temperature fields at the cage-inner ring interface are usually not directly solved, thus failing to provide full-field physical information for refined design.

[0003] With the ever-increasing demands of modern industry on bearing speeds, the shear rate within the oil film increases dramatically under ultra-high-speed operation, leading to a significant rise in lubricating oil temperature. This drastic temperature change triggers a nonlinear change in lubricant viscosity (i.e., the temperature-viscosity coupling effect), which in turn alters the load-bearing characteristics and pressure distribution of the oil film. Under these complex conditions of high shear and high temperature rise, traditional short-sliding bearing theory suffers from a significant decrease in prediction accuracy due to its inability to capture dynamic viscosity-temperature changes, making it difficult to meet high-fidelity design requirements.

[0004] To overcome the accuracy limitations of traditional analytical models, high-fidelity thermo-elasto-fluid (TEHD) coupled numerical methods have been introduced into bearing lubrication analysis in recent years. These methods, by simultaneously applying the generalized Reynolds equation, energy equation, and thermal deformation equation, can accurately simulate the temperature, pressure, and viscosity fields of the oil film. However, TEHD models involve complex nonlinear coupling solutions, resulting in enormous computational costs; a single simulation often takes hours or even days. This high computational cost makes them unsuitable for multi-parameter optimization design, real-time condition monitoring, or extreme condition traversal, hindering their engineering applications.

[0005] Meanwhile, data-driven machine learning methods are gradually emerging in the field of lubrication. Existing research often uses algorithms such as neural networks (NNs) and Gaussian process regression (GPR) to establish the mapping relationship between operating parameters and lubrication performance indicators, which have been successfully used to predict thermoelastic hydrodynamic lubrication behavior, sliding bearing pressure fields, maximum temperatures, frictional torques, and oil film thickness. However, existing methods have two prominent problems: First, many methods still focus on scalar output prediction (such as maximum pressure and minimum film thickness), rather than the two-dimensional pressure field distribution across the entire field; second, while other methods attempt to predict the entire field, they usually treat the mapping from operating conditions to target quantities as a black box problem, ignoring the inherent constraints of the lubrication physics equations, resulting in limited model generalization ability and difficulty in interpreting the physical meaning of the prediction results.

[0006] Therefore, how to integrate prior physical knowledge and data-driven advantages to achieve rapid and high-precision prediction of the two-dimensional oil film pressure field on the guide surface of a high-speed rolling bearing cage while ensuring prediction accuracy is a technical problem that urgently needs to be solved in this field. In other words, a rapid prediction method for oil film pressure that takes into account both physical consistency and computational efficiency is urgently needed. Summary of the Invention

[0007] This invention proposes a force-thermal coupling machine learning prediction method for the lubrication state of bearing guide surfaces. This method solves the problems of existing technologies, such as the high shear and high temperature rise of high-speed rolling bearing cage guide surfaces and rings, insufficient prediction accuracy and information dimension due to the use of the isoviscosity assumption and failure to solve the two-dimensional pressure field in short sliding bearing theory, high-fidelity fluid-structure-thermal coupling finite element method is too computationally expensive to meet the needs of engineering design iteration and real-time monitoring, and existing data-driven methods focus on scalar output or black-box mapping and fail to effectively integrate physical prior knowledge to achieve fast and high-precision prediction of the two-dimensional pressure field.

[0008] The training method for the hybrid prediction model described in this invention, wherein the hybrid prediction model is used for force-thermal coupled machine learning prediction of the lubrication state of the bearing guide surface:

[0009] The hybrid prediction model includes a physical baseline model and a data-driven corrector; the physical baseline model is constructed based on the short sliding bearing theory, and the data-driven corrector includes an intrinsic orthogonal decomposition dimensionality reduction module and a Gaussian process regression nonlinear mapping module; the training method includes the following steps:

[0010] Step S1, construct a high-fidelity and low-fidelity joint dataset:

[0011] Define the working condition parameter vector The operating condition parameter vector At least the inner ring speed, cage speed, eccentricity, and initial oil film temperature;

[0012] For multiple sets of operating condition parameter vectors The low-fidelity two-dimensional oil film pressure field is obtained by solving the physical baseline model, and the high-fidelity two-dimensional oil film pressure field is obtained by solving the thermo-elastohydrodynamic coupling finite element model that considers the temperature-viscosity coupling effect of lubricating oil.

[0013] Step S2: Extract the residual pressure field and perform mean removal and dimensionality reduction:

[0014] For each set of operating condition parameter vectors The high-fidelity two-dimensional oil film pressure field and the low-fidelity two-dimensional oil film pressure field are converted into gauge pressures respectively, and the difference is calculated to obtain the residual pressure field. ;

[0015] The residual pressure field under all working condition parameter vectors is constructed as a snapshot matrix D, and the average residual pressure field of all samples is calculated.

[0016] Subtract the average residual pressure field from each residual pressure field in the snapshot matrix D, and then perform mean removal processing to obtain the mean-removed snapshot matrix. ;

[0017] The mean-removed snapshot matrix Perform singular value decomposition to extract the truncated basis function matrices of the first r dominant modes. and the corresponding modal coefficient vector , where r is determined by the cumulative energy ratio criterion;

[0018] Step S3, train the Gaussian process regression surrogate model:

[0019] For the operating condition parameter vector Perform feature engineering to construct extended feature vectors. ;

[0020] With the extended feature vector As input, the modal coefficient vector The modal coefficients of each order are used as outputs, and r independent Gaussian process regression models are established and trained respectively. The set of trained Gaussian process regression models is obtained. ;

[0021] Save the set of trained Gaussian process regression models and the truncated basis function matrix. And the average residual pressure field, to obtain the trained hybrid prediction model.

[0022] The force-thermal coupling machine learning prediction method for the lubrication state of the bearing guide surface described in this invention is based on a hybrid prediction model trained using the aforementioned training method. The method includes the following steps:

[0023] Step P1: Obtain the basic operating condition parameter vector of the test condition, which includes at least the inner ring speed, cage speed, eccentricity and initial oil film temperature;

[0024] Step P2: Solve the physical baseline model to obtain the low-fidelity two-dimensional oil film pressure field corresponding to the test condition;

[0025] Step P3: Perform feature engineering on the basic working condition parameter vector of the working condition to be tested to obtain the extended feature vector of the working condition to be tested, and input the extended feature vector of the working condition to be tested into the trained Gaussian process regression model set to predict the modal coefficient vectors of the working condition to be tested.

[0026] Step P4: Using the modal coefficient vectors of each order of the test condition and the truncated basis function matrix And the average residual pressure field, reconstructing the residual pressure field of the working condition under test;

[0027] Step P5: Superimpose the residual pressure field of the test condition with the low-fidelity two-dimensional oil film pressure field corresponding to the test condition, and restore the ambient atmospheric pressure to obtain the predicted absolute two-dimensional oil film pressure field.

[0028] Furthermore, a preferred embodiment is provided, wherein the short sliding bearing theory is the Ocvirk infinite short bearing approximation, which ignores the circumferential pressure gradient term in the Reynolds equation and simplifies the two-dimensional lubrication problem into a one-dimensional ordinary differential equation along the axial direction for solution.

[0029] Furthermore, a preferred embodiment is provided in which the thermo-elastohydrodynamic coupled finite element model combines the generalized Reynolds equation and the energy equation, and uses the Roelands equation to describe the relationship between the viscosity of the lubricant and the change of pressure and temperature.

[0030] Furthermore, a preferred embodiment is provided, wherein the cumulative energy ratio criterion in step S2 is: selecting the smallest r such that the ratio of the sum of squares of the first r singular values ​​to the sum of squares of all singular values ​​reaches a preset threshold, wherein the preset threshold is 99.99%.

[0031] Furthermore, a preferred embodiment is provided, wherein step S2, which involves converting the high-fidelity two-dimensional oil film pressure field and the low-fidelity two-dimensional oil film pressure field into gauge pressures and then calculating the difference, includes:

[0032] Subtract the ambient atmospheric pressure from the high-fidelity two-dimensional oil film pressure field and the low-fidelity two-dimensional oil film pressure field respectively to obtain the corresponding gauge pressure field.

[0033] The residual pressure field is obtained by calculating the difference between the high-fidelity gauge pressure field and the low-fidelity gauge pressure field. .

[0034] Furthermore, in a preferred embodiment, the feature engineering process in step S3 includes: processing the operating condition parameter vector. Logarithmic transformations were performed on the inner ring speed, cage speed, and ambient viscosity parameters, and dimensionless parameters from lubrication mechanics were introduced to construct an extended eigenvector. .

[0035] Furthermore, a preferred embodiment is provided, wherein step P5 superimposes the residual pressure field of the test condition with the low-fidelity two-dimensional oil film pressure field corresponding to the test condition, and restores the ambient atmospheric pressure, including:

[0036] The residual pressure field of the test condition is superimposed with the gauge pressure form of the low-fidelity two-dimensional oil film pressure field corresponding to the test condition to obtain the predicted gauge pressure field.

[0037] By adding ambient atmospheric pressure to the predicted gauge pressure field, the predicted absolute two-dimensional oil film pressure field is obtained.

[0038] A non-negative physical constraint is applied to the predicted absolute two-dimensional oil film pressure field.

[0039] Furthermore, in a preferred embodiment, the method further includes step P6: post-processing the predicted absolute two-dimensional oil film pressure field by integrating the gauge pressure field over the bearing surface to calculate the oil film force in the y-direction. And extract the maximum oil film pressure. .

[0040] Furthermore, a preferred embodiment is provided, wherein the oil film force in the y-direction... Predicted value The calculation formula is:

[0041] ;

[0042] in, The inner ring radius of the bearing. To maintain the width of the frame on one side, Circumferentially normalized coordinates; This represents the predicted gauge pressure field.

[0043] The present invention has the following beneficial effects:

[0044] 1. The force-thermal coupling machine learning prediction method for the lubrication state of the bearing guide surface described in this invention can significantly improve the physical consistency and computational accuracy of the prediction model by constructing a hybrid prediction framework of "physical baseline + residual correction" (i.e., using short sliding bearing theory as a low-fidelity physical baseline and using high-fidelity finite element results considering temperature-viscosity coupling as a reference).

[0045] Technical means and function: This invention does not abandon the traditional short sliding bearing theory, but uses the analytical pressure field calculated by it as a benchmark, and only uses machine learning to learn the residual pressure field between the "high-fidelity solution" and the "low-fidelity solution".

[0046] Technical benefits: This method fully utilizes the geometric and kinematic physical constraints inherent in the short bearing theory, avoids the risk of physical distortion in the "black box" prediction of pure data-driven models, and at the same time compensates for the short bearing theory's neglect of thermo-viscosity coupling by correcting residuals, thus achieving an optimal balance between accuracy and efficiency.

[0047] 2. The force-thermal coupling machine learning prediction method for the lubrication state of the bearing guide surface described in this invention introduces intrinsic orthogonal decomposition (POD) to reduce the dimensionality of the high-dimensional residual pressure field, and combines Gaussian process regression (GPR) to establish a nonlinear mapping from the operating parameters to the low-dimensional modal coefficients. This can significantly reduce the complexity of model training and inference, and solve the curse of dimensionality problem in the prediction of high-dimensional fluid fields.

[0048] Technical means and functions: The original two-dimensional pressure field snapshot matrix, which is often tens of thousands of dimensions, is reduced to a low-dimensional modal coefficient vector of tens of dimensions through SVD / POD. The GPR model only needs to learn the relationship between the working condition and these tens of coefficients, rather than directly predicting the entire high-dimensional field.

[0049] Technical effects: This not only significantly reduces the amount of data and computing resources required for training, but also improves the model's generalization ability, enabling the model to maintain extremely high predictive stability when faced with unseen operating parameters.

[0050] 3. The force-thermal coupling machine learning prediction method for the lubrication state of the bearing guide surface described in this invention, by explicitly considering the viscosity-temperature relationship and thermo-elastohydrodynamic coupling effect of the lubricant Roelands, and using it as a high-fidelity input for constructing the residual dataset, can effectively capture the real influence of viscosity changes on oil film pressure distribution under high-speed and high-temperature conditions, and overcome the technical bias of the traditional isoviscosity assumption.

[0051] Technical means and functions: The Roelands equation is introduced into the high-fidelity finite element model to describe the change of viscosity with pressure / temperature, which realistically reproduces the "thermal wedge" effect and viscosity softening phenomenon under high-speed operation.

[0052] Technical effect: It corrects the systematic deviation caused by constant viscosity when predicting high pressure peaks in traditional short bearing theory, so that the prediction results remain accurate and reliable under extreme working conditions of high shear and high temperature rise.

[0053] 4. The force-thermal coupling machine learning prediction method for the lubrication state of the bearing guide surface described in this invention can reconstruct the entire field pressure by only one short bearing theoretical solution and simple algebraic superposition operation. It can realize the rapid prediction (second-level prediction) of the two-dimensional oil film pressure field and oil film force, which solves the pain point of traditional TEHD simulation being time-consuming and unable to be applied to real-time design.

[0054] Technical means and functions: In the online prediction stage, it is only necessary to call the trained GPR model to predict a few modal coefficients, and then reconstruct the residual field through simple matrix multiplication and superimpose it with the baseline field.

[0055] Technical benefits: The time required for a single prediction is significantly reduced compared to the finite element method (e.g., from hours to seconds), greatly improving the iterative efficiency of bearing lubrication design. It is very suitable for multi-parameter optimization design, online fault diagnosis, and real-time condition assessment.

[0056] The force-thermal coupling machine learning prediction method for the lubrication state of the bearing guide surface described in this invention is applicable to the lubrication design optimization and online condition assessment of high-speed rolling bearings (especially high-speed bearings such as those used in aero-engines and high-speed rail traction motors). Attached Figure Description

[0057] To more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0058] Figure 1 This is a schematic diagram of the cage-inner ring cross-sectional geometry and coordinate system in one embodiment of the present invention;

[0059] Figure 2 This is a flowchart illustrating a method for rapid prediction of oil film pressure on the cage guide surface and raceway of a high-speed rolling bearing based on machine learning (i.e., a force-thermal coupling machine learning prediction method for the lubrication state of the bearing guide surface).

[0060] Figure 3In one embodiment of the present invention, under specific working conditions of inner ring speed of 25500 r / min, initial oil film temperature of 110℃, and eccentricity of 0.99, the following diagrams are presented: the two-dimensional pressure field of the oil film calculated theoretically for a short sliding bearing (sub-figure a), the two-dimensional pressure field of the oil film calculated by the finite element (FE) method considering fluid-structure-thermal coupling (sub-figure b), the two-dimensional pressure field of the oil film predicted by the present invention (sub-figure c), and the absolute error distribution between the predicted results of the present invention and the calculated results of the finite element method considering fluid-structure-thermal coupling (sub-figure d, i.e., the absolute error after reconstruction).

[0061] Figure 4 In one embodiment of the present invention, on the validation set, the maximum oil film pressure predicted by the present invention ( ) and oil film force in the y direction ( A comparison of scatter plots of results from finite element method (FE) and high-fidelity finite element method (FE) methods;

[0062] Figure 5 In one embodiment of the present invention, under different initial oil film temperatures and inner ring rotation speeds, the predicted relative error of the two-dimensional pressure field ( Line graph showing the variation of eccentricity. Detailed Implementation

[0063] To make the technical solutions and advantages of the present invention clearer, the specific embodiments of the present invention will be described in further detail and completely below with reference to the accompanying drawings. The various embodiments described below are only some preferred embodiments of the present invention, and not all of them; the various embodiments described below are intended to explain the present invention and should not be construed as limiting the present invention; reasonable combinations of the technical features defined in the various embodiments of the present invention, as well as all other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort, are all within the scope of protection of the present invention.

[0064] Implementation Method 1: The geometric model and physical boundaries for bearing lubrication analysis are introduced below:

[0065] (1) Geometric structure and coordinate system:

[0066] Figure 1 This is a two-dimensional cross-sectional geometric model and a three-dimensional rectangular coordinate system for the interface between the cage guide surface and the inner ring of a rolling bearing.

[0067] Coordinate system definition: based on the geometric center of the bearing system. Establish a three-dimensional rectangular coordinate system with the origin. -XYZ. Wherein, the Z-axis is along the axial direction of the bearing, and the X-axis and Y-axis form radial and circumferential planes (the specific directions are indicated by the arrows in the figure).

[0068] Bearing assembly distribution:

[0069] Inner circle: located at the geometric center The internal cavity is shown in purple in the diagram.

[0070] Cage: Located outside the inner ring, it is shown as a gray ring structure in the figure. A lubricating oil film gap is formed between its internal guide surface and the outer surface of the inner ring.

[0071] Lubricating oil: fills the gap between the cage guide surface and the outer surface of the inner ring, marked as the purple area in the figure.

[0072] (2) Kinematic boundary conditions (physical motion boundary):

[0073] The system consists of two rigid bodies around a center. Each component rotates, and each has a different angular velocity of rotation:

[0074] Inner ring rotation: The inner ring revolves around its own center. With angular velocity Rotate. The diagram shows curved arrows and symbols within the inner circle. Its rotation direction and motion state are clearly indicated.

[0075] Cage rotation: Cage around center With angular velocity Rotation is performed. The diagram shows the curved arrows and symbols inside the cage. Its rotation direction and motion state are clearly indicated.

[0076] (Note: The difference in rotation direction and angular velocity between the inner ring and the cage is the direct driving force for shear flow and pressure distribution within the oil film.)

[0077] (3) Calculation of oil film geometric parameters and oil film thickness:

[0078] The thickness (h) of the oil film is not uniformly distributed, but rather a function of spatial angle. Its geometry and calculation depend on several key geometric parameters:

[0079] Eccentricity e: Due to assembly errors, load application, or manufacturing tolerances, the centerline of the cage is offset from the centerline of the inner ring. There exists an offset distance, which is the eccentricity e. It is the core parameter that determines the asymmetry of the oil film thickness distribution.

[0080] Azimuth : Used to describe the polar coordinates of a specific position in the circumferential direction (the angle measured from the positive X-axis in the figure).

[0081] Offset angle : Used to describe the spatial pointing angle of the eccentric direction (the angle between the straight line connecting the centers of the inner and outer circles in the figure and a certain reference axis such as the X-axis), usually used in conjunction with the azimuth angle to determine the extreme position of the oil film thickness in polar coordinates.

[0082] Minimum oil film thickness At a specific eccentricity e and azimuth angle and offset angle Under the combined effect of various factors, the oil film thickness will have a thinnest point in the circumferential direction, and the oil film thickness at this point is defined as... .

[0083] Oil film thickness calculation logic:

[0084] Based on the above geometric parameters, the formula for calculating the oil film thickness h can be abstractly expressed as a spatial angle (azimuth angle). and offset angle And a function of the eccentricity e, i.e. In practical engineering analysis, this geometric clearance is usually simplified to a variable thickness slider bearing model in polar coordinates, and the geometric boundary morphology of the oil film can be accurately described by this function.

[0085] Implementation Method 2: Structure of the Hybrid Prediction Model:

[0086] The hybrid prediction model is a composite model that integrates physical prior knowledge and data-driven correction. Its core architecture consists of two cooperating components, which are used to achieve efficient and high-precision prediction of the two-dimensional oil film pressure field on the bearing guide surface.

[0087] Component 1: Physical Baseline Model (Low-Fidelity Model):

[0088] The physical baseline model is constructed based on the short sliding bearing theory (Ocvirk's infinitely short bearing approximation). This model neglects the circumferential pressure gradient term in the Reynolds equations, simplifying the two-dimensional lubrication problem into a one-dimensional ordinary differential equation along the axial direction for solution. Its input is a vector of operating parameters. (including inner ring speed) Cage speed eccentricity and initial oil film temperature The output is the corresponding two-dimensional oil film pressure field. .

[0089] The model is extremely fast (milliseconds) and can capture the main morphological features of oil film pressure distribution (such as the approximate location of pressure peaks and bearing area). However, due to its use of the isoviscosity assumption and neglect of thermal effects, it has systematic deviations under high shear and high temperature rise conditions.

[0090] Component 2: Data-Driven Corrector (Machine Learning Model):

[0091] The data-driven corrector is a surrogate model based on intrinsic orthogonal decomposition (POD) and Gaussian process regression (GPR) to learn and correct systematic biases between the physical baseline model and the high-fidelity reference solution. Its structure consists of two modules:

[0092] Module 1: POD Dimensionality Reduction Module (or simply POD Module):

[0093] This module uses singular value decomposition (SVD) to analyze the high-dimensional residual pressure field. Dimensionality reduction is performed to extract the basis function matrices of the first r dominant modes. .in, This module is used to calculate a high-fidelity pressure field (high-fidelity reference solution) using a thermo-elastohydrodynamic finite element model that considers the temperature-viscosity coupling effect. Its function is to compress the original two-dimensional pressure field containing tens of thousands of mesh nodes into a low-dimensional modal coefficient vector 'a' of only r dimensions, thereby significantly reducing the complexity of subsequent learning.

[0094] Module 2: GPR Nonlinear Mapping Module (or simply GPR Module):

[0095] This module contains r independent Gaussian process regression models. Each model uses a vector of operating condition parameters. As input, with the corresponding k-th order POD mode coefficients For output, learn the nonlinear mapping relationship from operating parameters to low-dimensional modal coefficients: ,in This is a Gaussian noise term. The function of this module is to establish a mapping relationship between "operating condition parameters" and "low-dimensional features," so that the corresponding modal coefficients can be quickly predicted for any new operating condition.

[0096] The collaborative relationship between the two components:

[0097] During the forecasting phase, the hybrid forecasting model operates according to the following process:

[0098] The physical baseline model is based on the input conditions. Quickly calculate the low-fidelity pressure field .

[0099] The GPR module in the data-driven corrector predicts the corresponding low-dimensional modal coefficient vector. .

[0100] The POD module in the data-driven corrector utilizes and basis function matrix Reconstructing the residual pressure field .

[0101] The low-fidelity pressure field is superimposed with the reconstructed residual pressure field to obtain the final predicted pressure field: .

[0102] The training of the hybrid prediction model relies on a joint dataset (or high- and low-fidelity joint dataset) generated by a high-fidelity finite element model (considering the lubricating oil temperature-viscosity coupling effect) and a low-fidelity physical baseline model (based on short bearing theory). This dataset contains multiple sets of operating condition parameters. and its corresponding and This is used to extract the residual pressure field and train the POD and GPR modules in the data-driven corrector. Once training is complete, the high-fidelity finite element model is no longer involved in the calculations during subsequent online prediction phases.

[0103] It should be noted that the short sliding bearing theory should not be considered merely a low-precision approximation model. It actually captures the main influences of oil film thickness variation, relative sliding velocity, and geometric parameters on pressure, making it a priori model with clear physical meaning. If used as a baseline model, the data-driven component only needs to learn the systematic deviations between the short sliding bearing theory results and the high-fidelity finite element results, thus significantly reducing the learning difficulty and improving prediction efficiency and generalization ability. However, current technologies lack an effective scheme to combine this physical prior with data-driven residual learning for rapid prediction of the two-dimensional oil film pressure field on the guide surface of high-speed rolling bearings.

[0104] Implementation Method 3: Training Method for Hybrid Prediction Models

[0105] The core idea of ​​this method is to train a hybrid prediction model of "physical baseline + data-driven residual correction", which aims to solve the problems of insufficient accuracy of traditional pure physical models and poor generalization ability of pure data-driven models, and achieve efficient and high-precision reconstruction of two-dimensional oil film pressure field.

[0106] The training of the hybrid prediction model is conducted offline. Its goal is to train the POD dimensionality reduction module and the GPR nonlinear mapping module in the data-driven corrector using a pre-built high-fidelity and low-fidelity joint dataset. After training, the trained GPR model set and the POD truncated basis function matrix are saved for use in the subsequent online prediction phase.

[0107] Step 1: Data Generation and Operating Condition Definition

[0108] Define the model input parameter space; based on the short bearing theory and the finite element model considering the temperature-viscosity coupling effect, calculate the two-dimensional oil film pressure field data under the corresponding working conditions, and construct a high-fidelity and low-fidelity joint dataset.

[0109] Specifically as follows:

[0110] 1.1 Definition of operating condition parameter space:

[0111] First, define the model's input parameter space (operating condition parameter vector). In this implementation, define... This is the operating condition parameter vector (or simply operating condition vector), which contains four key variables: inner ring speed. Cage speed eccentricity and initial oil film temperature ,Right now .

[0112] in:

[0113] : Rotational speed of the inner ring (in r / min);

[0114] : Rotational speed of the cage (in r / min);

[0115] Eccentricity, a dimensionless parameter, is defined as the ratio of the eccentricity e to the nominal clearance C, i.e. =e / C, with a value range of 0 to 1;

[0116] Initial oil film temperature (in °C), which is the temperature of the lubricating oil before it enters the bearing clearance.

[0117] These four parameters together determine the boundary conditions and load conditions of the bearing lubrication state.

[0118] 1.2 Sampling Strategy and Dataset Partitioning:

[0119] To construct the training dataset, systematic sampling is required within the aforementioned four-dimensional parameter space. This implementation employs a grid sampling method, which involves taking values ​​at a fixed step size in each parameter dimension to generate all possible parameter combinations. The specific division of the training and validation sets is as follows:

[0120] Training set: initial oil film temperature Within the temperature range of 60 to 140℃, with a step size of 10℃, a total of 9 values ​​were obtained; eccentricity Within the range of 0.92 to 0.99, the value varies in increments of 0.01, resulting in a total of 8 possible values; inner ring speed. and cage speed The combinations are shown in Table 1, with a total of 16 speed combinations.

[0121] Table 1 Training Set Rotation Speed ​​Combination Table

[0122]

[0123] Validation set: Five speed combinations were selected (as shown in Table 2); the initial oil film temperature at each speed combination was... Three values ​​were selected: 80℃, 110℃, and 140℃; eccentricity. Within the range of 0.92 to 0.99, the value varies in increments of 0.01, resulting in a total of 8 possible values.

[0124] Table 2 Validation Set Rotation Speed ​​Combination Table

[0125]

[0126] 1.3 Construction of High-Fidelity and Low-Fidelity Joint Datasets:

[0127] For each set of operating parameters obtained from sampling Two-dimensional oil film pressure field data under corresponding working conditions were calculated using the following two models (a low-fidelity physical baseline model based on short bearing theory and a high-fidelity finite element model considering the temperature-viscosity coupling effect of lubricating oil) to construct a "high-fidelity-low-fidelity" joint dataset (or high-low-fidelity joint dataset).

[0128] (1) Low-fidelity physical baseline model (short sliding bearing theory):

[0129] The Ocvirk infinite short bearing approximation is used as the physical baseline model. This model neglects the circumferential pressure gradient term in the Reynolds equations, simplifying the two-dimensional lubrication problem into a one-dimensional ordinary differential equation along the axial direction for fast analytical solution.

[0130] First, consider the two-dimensional Reynolds equation for the circumferential sliding velocity:

[0131] ;

[0132] In the formula, p is the oil film pressure, h is the oil film thickness, η is the dynamic viscosity of the lubricant, u is the relative sliding speed between the two surfaces, x is the circumferential coordinate, and z is the axial coordinate.

[0133] The short sliding bearing theory neglects the circumferential flow effect (i.e., ignores) The above two-dimensional Reynolds equation is simplified to:

[0134] ;

[0135] The equation can be solved analytically by direct integration, thus obtaining the low-fidelity pressure field. .

[0136] (2) High-fidelity finite element model (TEHD):

[0137] A thermo-elastohydrodynamic lubrication finite element model considering the force-thermal coupling effect is established. This model combines the generalized Reynolds equation and the energy equation, and uses the Roelands equation to describe the nonlinear variation of lubricant viscosity η with pressure p and temperature T.

[0138] Under high-speed operating conditions, pressure and temperature variations can significantly affect lubricant viscosity and should therefore be taken into account. Pressure- and temperature-dependent viscosity is described using the Roelands equation.

[0139] The Roelands equation is expressed as follows:

[0140]

[0141] in:

[0142] This refers to the ambient viscosity (reference viscosity) of the lubricant.

[0143] The pressure-viscosity coefficient of the lubricant;

[0144] The temperature-viscosity coefficient of the lubricant;

[0145] The ambient temperature (or inlet oil temperature, i.e., the initial oil film temperature in the operating parameters) is typically set as a baseline value in bearing lubrication analysis when the lubricating oil just enters the meshing zone (or at the start of the calculation). This is the reference temperature;

[0146] and To and and The relevant parameters.

[0147] The high-fidelity pressure field is obtained by solving the above simultaneous equations using the finite element method. .

[0148] For a given operating condition, the pressure field of the short sliding bearing and the finite element pressure field are respectively expressed as: and .

[0149] Step 2: Construction of pressure field snapshot and extraction of residual field:

[0150] The two-dimensional oil film pressure field p(x,z) under each working condition is discretized and flattened into a vector form to construct a pressure field snapshot matrix; mean field removal is performed on the data to obtain the residual pressure field for subsequent intrinsic orthogonal decomposition.

[0151] Specifically as follows:

[0152] 2.1 Gauge pressure conversion:

[0153] Due to atmospheric pressure This is an invariant constant term that will be canceled out in subsequent residual calculations; therefore, the absolute pressure is first converted to gauge pressure.

[0154] ;

[0155] .

[0156] in, This represents atmospheric pressure, which is the reference pressure of the bearing's external environment. It is usually a known constant (e.g., approximately 101325 Pa or 0.101325 MPa at standard atmospheric pressure). In fluid dynamics calculations, absolute pressure equals gauge pressure plus atmospheric pressure.

[0157] 2.2 Definition of residual pressure field:

[0158] The core learning objective of this method is defined as the (two-dimensional) residual pressure field. That is, the difference between the high-fidelity solution and the low-fidelity solution in the gauge pressure space:

[0159] ;

[0160] The residual pressure field reflects the systematic bias in the short sliding bearing theory caused by neglecting the temperature-viscosity coupling effect, and is an object that subsequent machine learning needs to learn and correct.

[0161] 2.3 Snapshot Matrix Construction:

[0162] All The two-dimensional residual pressure fields of each training sample are discretized, and each residual pressure field contains... Each grid node. The two-dimensional residual pressure field is reconstructed and flattened into a vector form (one-dimensional column vector). , dimension (or vectorized residual pressure field), constructing a "snapshot matrix" D:

[0163] ;

[0164] in, Let D represent the vectorized residual pressure field corresponding to the i-th sample, where D has dimensions of . .

[0165] 2.4 Mean removal processing:

[0166] Before performing intrinsic orthogonal decomposition, the data undergoes mean field removal, i.e., the mean field of all samples is subtracted. We obtain the mean-free fluctuation components:

[0167] ;

[0168] in, The average residual pressure field; The residual pressure field after removing the mean; This is the snapshot matrix after removing the mean.

[0169] The purpose of mean removal is to eliminate the overall bias of the data, allowing subsequent POD analysis to focus on the fluctuation characteristics of the data, thereby improving dimensionality reduction efficiency.

[0170] III. Step 3: Intrinsic Orthogonal Decomposition (POD) Dimensionality Reduction:

[0171] Singular value decomposition is performed on the residual pressure snapshot matrix to extract its orthogonal basis functions and corresponding eigenvalues, obtaining a low-dimensional subspace representation. The dominant modes are selected by energy criteria, and only the first r intrinsic orthogonal decomposition modes are retained. The truncation order r satisfies the cumulative energy ratio reaching a preset threshold (99.99%). The residual pressure field is projected onto the truncated intrinsic orthogonal decomposition basis to obtain the corresponding mode coefficient vector.

[0172] Specifically as follows:

[0173] 3.1 Singular Value Decomposition (SVD):

[0174] Snapshot matrix after removing the mean Perform Singular Value Decomposition (SVD):

[0175] ;

[0176] in:

[0177] It is a left singular vector matrix, and its column vectors are the basis functions (modes) of the orthogonal eigenvalue decomposition (POD), representing the main spatial distribution patterns of the residual pressure field;

[0178] For a diagonal matrix, its diagonal elements The values ​​are singular and are sorted in descending order. , representing the amount of energy contained in each mode;

[0179] It is a right singular vector matrix.

[0180] 3.2 Modal Truncation (Extracting intrinsic orthogonal decomposition and dimensionality reduction of modes / basis functions):

[0181] To significantly reduce data dimensionality while maintaining accuracy, it is necessary to determine how many modes to retain. This implementation uses the cumulative energy ratio criterion to determine the truncation order r:

[0182] ;

[0183] in, For the k-th singular value, This represents the percentage of the cumulative energy of the first r modes relative to the total energy.

[0184] The minimum value of r that satisfies the requirement that the cumulative energy percentage reaches a preset threshold is selected. In this embodiment, the preset threshold is 99.99%, meaning that the retained modes can explain 99.99% of the energy changes in the original data.

[0185] Only the first r dominant modes are retained to form the truncated basis function matrix. (dimension is) ).

[0186] Subsequently, the residual pressure field can be approximated as:

[0187] ;

[0188] The residual pressure field after removing the mean can be approximated as follows:

[0189] ;

[0190] The residual pressure field after removing the mean It can be approximated as a basis function With modal coefficients A linear combination of;

[0191] in, The vector represents the truncated eigenorthogonal decomposition basis function matrix. These are the retained intrinsic orthogonal decomposition mode coefficients.

[0192] 3.3 Modal coefficient extraction (projection):

[0193] The high-dimensional residual pressure field is projected onto a low-dimensional subspace, and the modal coefficient vector corresponding to each sample is extracted. :

[0194] ;

[0195] At this point, the parameters for each operating condition are... The corresponding residual pressure field is compressed into an r-dimensional low-dimensional modal coefficient vector. It has achieved the following: Significant dimensionality reduction from r-dimensional to r-dimensional (usually) ,For example ,and (It could reach tens of thousands).

[0196] IV. Step 4: Training the Gaussian Process Regression (GPR) surrogate model:

[0197] Using operating parameters as input, Gaussian process regression models are established for each intrinsic orthogonal decomposition mode coefficient to learn nonlinear mapping relationships.

[0198] Specifically as follows:

[0199] 4.1 Model Construction:

[0200] Preferably, in order to improve the training efficiency and prediction accuracy of the Gaussian process regression (GPR) model, this embodiment modifies the basic operating condition parameter vector. Feature engineering was performed.

[0201] Known basic operating condition parameter vector It includes four basic physical quantities: inner ring rotation speed Cage speed eccentricity and initial oil film temperature In this embodiment, the basic operating parameters are... As input, key dimensionless parameters from lubrication mechanics (such as bearing speed ratio) are introduced. Viscosity-temperature characteristic coefficient (etc.), and perform logarithmic transformation on some parameters (e.g. , To eliminate dimensional differences and data skewness, an extended high-dimensional feature vector is finally constructed. .

[0202] That is, feature vector Based on basic operating parameters The resulting mapping relationship between the two is specifically expressed as follows:

[0203] ;

[0204] in, This represents the feature transformation function. In the training of the Gaussian process regression (GPR) model described below, this extended high-dimensional feature vector will be used. As input variables for the GPR model.

[0205] The core of this method lies in establishing a nonlinear mapping from operating parameters to low-dimensional modal coefficients. To this end, r independent Gaussian Process Regression (GPR) models are established.

[0206] Each model Using working condition vectors As input, the k-th order POD mode coefficients For the output, learn its nonlinear mapping relationship:

[0207] ;

[0208] in, Let be a Gaussian process function, representing the nonlinear mapping to be learned; For independent and identically distributed Gaussian noise terms, satisfying .

[0209] Gaussian process regression is a nonparametric Bayesian method that assumes the function values ​​follow a multivariate Gaussian distribution. For a given training data... The GPR model can learn the probability mapping from input to output and provide an estimate of the uncertainty of the prediction.

[0210] 4.2 Model Training:

[0211] Specifically, for the k-th mode, the training data is ,in Let be the working condition parameter vector for the i-th sample. is the k-th modal coefficient of this sample.

[0212] The training process optimizes the hyperparameters of GPR (such as the length scale of the kernel function, noise variance, etc.) by maximizing the log marginal likelihood until the model converges.

[0213] The offline model training phase is now complete. Save the following training results:

[0214] The set of trained GPR models ;

[0215] Truncation of basis function matrix ;

[0216] Mean residual pressure field .

[0217] These training results will be used in the subsequent online prediction phase to quickly predict new operating conditions. Once training is complete, the high-fidelity finite element model will no longer be involved in the calculations during the subsequent online prediction phase.

[0218] Implementation Method 4: Force-Heat Coupled Machine Learning Prediction Method for Lubrication State of Bearing Guide Surface

[0219] This embodiment provides a force-thermal coupled machine learning prediction method for the lubrication state of the bearing guide surface based on the aforementioned trained hybrid prediction model, belonging to the online rapid prediction stage. This method utilizes an offline trained GPR model set, a POD truncated basis function matrix, and an average residual pressure field to achieve second-level prediction of the two-dimensional oil film pressure field and key performance indicators under any new operating condition.

[0220] Step 5: Prediction of New Operating Conditions and Reconstruction of Pressure Field

[0221] Under the new operating conditions, the intrinsic orthogonal decomposition coefficients are predicted by the trained Gaussian process regression model. The residual pressure field is reconstructed using the predicted intrinsic orthogonal decomposition coefficients and the truncated basis function, and superimposed with the short bearing reference field to obtain the two-dimensional oil film pressure distribution. At the same time, non-negative physical constraints are applied to calculate the maximum oil film pressure and oil film force.

[0222] Specifically, when it is necessary to address a new, unseen working condition When making a prediction, perform the following steps:

[0223] 5.1 Preprocessing of operating parameters:

[0224] First, obtain the basic operating condition parameter vector of the operating condition to be tested. Following the same feature engineering methods as in the training phase, it is transformed into an extended high-dimensional feature vector. :

[0225] ;

[0226] in, This is a feature transformation function consistent with the training phase.

[0227] Note: yes The extended vector after feature engineering (such as logarithmic transformation and dimensionless transformation) is used by the GPR model. Input; short bearing theory and subsequent pressure field synthesis based on original operating parameters. For input.

[0228] 5.2 Calculate the physical baseline (low-fidelity pressure field):

[0229] Using the short sliding bearing theory (Ocvirk infinite short bearing approximation), the low-fidelity pressure field under this working condition can be quickly calculated. This step is achieved by solving the simplified Reynolds equation, neglecting the circumferential pressure gradient term, with a computation speed in the millisecond range.

[0230] 5.3 Predicted Modal Coefficients:

[0231] The preprocessed extended feature vector Input the set of trained GPR models The corresponding low-dimensional mode coefficient vector is predicted. :

[0232] ;

[0233] in, This represents the predicted value of the k-th order POD mode coefficient. Since the GPR model provides a probabilistic prediction (including mean and variance), the predicted mean is used as the point estimate here (i.e., the Gaussian noise is omitted). Item, because The expected value is 0, and it has been internalized by the model during the training phase.

[0234] 5.4 Reconstructing the residual pressure field:

[0235] Using the predicted modal coefficient vector and the POD truncation basis function matrix saved during the training phase Combined with the average residual pressure field preserved during the training phase The residual pressure field under this working condition is reconstructed:

[0236] ;

[0237] in, The mean residual pressure field (mean field before POD decomposition) is saved during the training phase. Since the POD decomposition during the training phase is performed on the mean-removed data, the mean residual pressure field needs to be added back during reconstruction to restore the complete residual pressure field.

[0238] 5.5 Synthesizing the final pressure field:

[0239] The predicted residual pressure field is superimposed back onto the short bearing theoretical baseline solution (gauge pressure form) under this operating condition, and atmospheric pressure is restored to obtain the final predicted absolute pressure field value:

[0240] (1) Final prediction field in gauge pressure form: (in yes (Reconstructed two-dimensional pressure field);

[0241] (2) Absolute pressure field: ;

[0242] in, The ambient atmospheric pressure.

[0243] To ensure the physical accuracy of the prediction results (non-negative oil film pressure), a non-negative physical constraint is applied to the predicted pressure field:

[0244] ;

[0245] This constraint ensures that the oil film pressure will not become negative, which conforms to the cavitation boundary conditions in fluid lubrication.

[0246] 5.6 Calculate engineering indicators:

[0247] The predicted two-dimensional pressure field is post-processed to calculate key engineering performance indicators:

[0248] (1) Maximum oil film pressure :

[0249] .

[0250] (2) Oil film force in the y direction :

[0251] By analyzing the gauge pressure field Integrating on the bearing surface yields:

[0252] ;

[0253] in, The inner ring radius of the bearing. To maintain the width of the frame on one side, Circumferential normalized coordinates ( ); for The predicted value.

[0254] Step 6: Model Validation and Performance Evaluation

[0255] Error assessment is performed using finite element results.

[0256] Specifically, to quantitatively evaluate the prediction accuracy of the hybrid prediction model on two-dimensional pressure fields and scalar performance indicators, the following error indicators are introduced.

[0257] 6.1 Relative Error Index of Two-Dimensional Field:

[0258] Define the relative error of a two-dimensional field as follows:

[0259] ;

[0260] in:

[0261] The two-dimensional oil film pressure field of the gauge pressure is predicted by the hybrid prediction model of this invention;

[0262] Two-dimensional oil film pressure field of gauge pressure calculated for a high-fidelity finite element model (as a reference standard);

[0263] It represents the Euclidean norm of the vector composed of all discrete grid nodes.

[0264] This index measures the deviation of the predicted pressure field from the high-fidelity finite element pressure field in terms of overall shape. The smaller the value, the higher the prediction accuracy.

[0265] 6.2 Coefficient of Determination for Scalar Indicators:

[0266] To assess maximum oil film pressure And oil film force To improve prediction accuracy, a coefficient of determination is introduced. :

[0267] ;

[0268] in, For high-fidelity finite element results, The prediction results of this invention, This is the average value of the high-fidelity finite element results. The number of samples in the validation set. The closer the value is to 1, the stronger the consistency between the predicted value and the reference value.

[0269] III. Summary of Technical Results:

[0270] In summary, the force-thermal coupling machine learning prediction method for the lubrication state of the bearing guide surface proposed in this invention has the following significant technical effects:

[0271] Effect 1: By constructing a hybrid prediction framework of "short sliding bearing theoretical physical baseline + data-driven residual correction", the physical prior knowledge contained in the short bearing theory is fully utilized, so that the data-driven component only needs to learn the system bias rather than the entire physical field, which greatly reduces the learning difficulty and training data requirements, while ensuring the physical consistency of the prediction results.

[0272] Effect 2: By introducing intrinsic orthogonal decomposition (POD) to reduce the dimensionality of the high-dimensional residual pressure field, the original tens of thousands of dimensions of the pressure field are compressed into low-dimensional modal coefficients of only a dozen dimensions. Combined with Gaussian process regression (GPR) to establish a nonlinear mapping from the working parameters to the modal coefficients, the problem of the curse of dimensionality in the prediction of high-dimensional fluid fields is effectively solved, and the model complexity is significantly reduced.

[0273] Effect 3: By explicitly considering the Roelands viscosity-temperature relationship and thermo-elasto-fluidic coupling effect of the lubricant, and using it as a high-fidelity reference for constructing the residual dataset, the true impact of viscosity changes on oil film pressure distribution under high-speed and high-temperature conditions is effectively captured. This overcomes the technical bias of the isoviscosity assumption in the traditional short bearing theory, making the prediction results accurate and reliable even under extreme conditions of high shear and high temperature rise.

[0274] Effect 4: Through the two-stage design of offline training and online prediction, the online prediction stage only requires one short bearing theoretical solution and simple algebraic operation to reconstruct the pressure of the entire field. The time taken for a single prediction is reduced from hours in finite element method to seconds, which greatly improves the iterative efficiency of bearing lubrication design. It is very suitable for multi-parameter optimization design, online fault diagnosis and real-time status assessment.

[0275] The method described in this invention is applicable to the lubrication design optimization, life prediction, and online health status monitoring system for high-speed rolling bearings (especially high-speed bearings in aircraft engines, high-speed rail traction motors, precision machine tool spindles, etc.).

[0276] Implementation Method 5: Comparative Experimental Examples.

[0277] To verify the effectiveness and prediction accuracy of the hybrid prediction model described in this invention, a comparative experiment was conducted.

[0278] I. Experimental Setup:

[0279] This embodiment uses the training set shown in Table 1 and the validation set shown in Table 2 of the above embodiments for experimental verification. The specific parameter configurations of the training set and validation set have been described in detail in the above embodiments and will not be repeated here.

[0280] According to the training method described in the above implementation, data generation and working condition definition are first performed to construct a high-fidelity and low-fidelity joint dataset; then, snapshot construction and residual field extraction are performed on the calculated pressure field; next, modal truncation and coefficient extraction are performed on the intrinsic orthogonal decomposition (POD); then, modal coefficient modeling and training are performed through Gaussian process regression (GPR); finally, pressure field reconstruction and performance evaluation are performed on the validation set working conditions according to the prediction method described in the above implementation.

[0281] II. Verification Results and Analysis:

[0282] 2.1 Comparative Analysis of Two-Dimensional Oil Film Pressure Fields:

[0283] Figure 3 Comparison of inner circle speeds = 25500 r / min, initial oil film temperature = 110℃, eccentricity ε=0.99, the two-dimensional oil film pressure field obtained by short sliding bearing theory, high-fidelity finite element model and the hybrid prediction model of this invention.

[0284] from Figure 3 It can be seen that the oil film pressure is mainly concentrated in the circumferential coordinate x. Within a narrow high-pressure band around 0.46–0.5, extending axially, the short sliding bearing theory can capture the location of the main load-bearing area, but it significantly overestimates the pressure amplitude in the peak pressure region. This indicates that the analytical short bearing model cannot accurately reflect the pressure field redistribution characteristics caused by the thermoviscosity effect under high eccentricity conditions.

[0285] In contrast, the prediction results of the hybrid prediction model of this invention are highly consistent with the high-fidelity finite element reference solution in both the high-pressure and low-pressure regions. The reconstruction error is mainly concentrated in an extremely narrow high-pressure band, with a maximum error of approximately 0.023 MPa. This indicates that the method of this invention can effectively correct the deviation of the short sliding bearing theory in terms of peak pressure and accurately reproduce the two-dimensional oil film pressure distribution under this operating condition.

[0286] 2.2, Consistency Analysis of Key Engineering Indicators:

[0287] Figure 4 The prediction results of this invention were compared with the high-fidelity finite element reference results in the validation set at maximum oil film pressure. and oil film force Consistency on the above. The dashed red line in the figure represents the ideal prediction, i.e., y = x.

[0288] from Figure 4 It can be seen that, for and The predicted values ​​of this invention are closely distributed around the diagonal within the studied range of initial oil film temperature and inner ring speed. Among them: maximum oil film pressure... Predictive Determination Coefficient Reaching 0.9999645; oil film force Predictive Determination Coefficient It reached 0.999957.

[0289] The above results demonstrate a strong correlation between the predictions obtained in this invention and the high-fidelity finite element analysis results. Although slight deviations can still be observed in the larger pressure and force ranges, the overall consistency remains high. This indicates that, within the scope of the validation study, the method of this invention can accurately predict the maximum oil film pressure and the corresponding oil film force.

[0290] 2.3, Overall Prediction Error Analysis:

[0291] Figure 5The relative error of the two-dimensional field predicted in the validation set is shown. The pattern of change with eccentricity. From Figure 5 It can be seen that the method of this invention maintains a low field-level prediction error throughout the entire eccentricity range ε ​​= 0.92–0.99. For all the initial oil film temperature and inner ring speed conditions studied, The values ​​remained stable at approximately 0.55%, indicating that the hybrid prediction model proposed in this invention can accurately reconstruct the two-dimensional oil film pressure field even without observed operating conditions.

[0292] III. Summary of Implementation Examples:

[0293] Based on the above verification results, the force-thermal coupling machine learning prediction method for the lubrication state of the bearing guide surface described in this invention has the following characteristics:

[0294] (1) High prediction accuracy across the entire field: Under all verification conditions, the relative error of the two-dimensional field is low. All values ​​remained stable below 0.55%. This indicates that the hybrid prediction model can accurately learn and correct the systematic deviation between the short bearing theory and the high-fidelity finite element method results, achieving an accuracy level almost identical to that of the high-fidelity finite element method in predicting the overall pressure distribution.

[0295] (2) Strong consistency of key indicators: maximum oil film pressure Predictive Determination Coefficient The oil film force reached 0.9999645. Predictive Determination Coefficient The result reached 0.999957. Both of these indicators are extremely close to 1, indicating that the predicted values ​​of the method of this invention on key engineering indicators have a very strong correlation with the high-fidelity finite element results.

[0296] (3) Strong generalization ability: The model shows stable predictive ability for unseen speed-temperature combinations (i.e., operating conditions not included in the training set). The error did not increase significantly. This confirms that the proposed method has good generalization ability and can be applied to the variable working conditions in practical engineering.

[0297] (4) High computational efficiency: Thanks to the two-stage design of offline training and online prediction, the single calculation time of this method in the online prediction stage is only in the second range, which is more than three orders of magnitude higher than the traditional high-fidelity finite element method (single calculation time is small), and fully meets the needs of real-time prediction and multi-parameter optimization design.

[0298] The above results demonstrate that the method of the present invention has stable and high-precision field-level prediction capabilities throughout the entire verification range, can effectively learn the residual pressure field structure between short sliding bearing theory and high-fidelity finite element results, and has good generalization ability for unseen speed-temperature combinations.

[0299] The above description of several specific embodiments further details the technical solution provided by the present invention in order to highlight the advantages and benefits of the technical solution provided by the present invention. However, the above-described specific embodiments are not intended to limit the present invention. Any reasonable modifications and improvements to the present invention, reasonable combinations of embodiments, and equivalent substitutions based on the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A training method for a hybrid prediction model, wherein the hybrid prediction model is used for force-thermal coupled machine learning prediction of the lubrication state of a bearing guide surface, characterized in that: The hybrid prediction model includes a physical baseline model and a data-driven corrector; the physical baseline model is constructed based on the short sliding bearing theory, and the data-driven corrector includes an intrinsic orthogonal decomposition dimensionality reduction module and a Gaussian process regression nonlinear mapping module; the training method includes the following steps: Step S1, construct a high-fidelity and low-fidelity joint dataset: Define the working condition parameter vector The operating condition parameter vector At least the inner ring speed, cage speed, eccentricity, and initial oil film temperature; For multiple sets of operating condition parameter vectors The low-fidelity two-dimensional oil film pressure field is obtained by solving the physical baseline model, and the high-fidelity two-dimensional oil film pressure field is obtained by solving the thermo-elastohydrodynamic coupling finite element model that considers the temperature-viscosity coupling effect of lubricating oil. Step S2: Extract the residual pressure field and perform mean removal and dimensionality reduction: For each set of operating condition parameter vectors The high-fidelity two-dimensional oil film pressure field and the low-fidelity two-dimensional oil film pressure field are converted into gauge pressures respectively, and the difference is calculated to obtain the residual pressure field. ; The residual pressure field under all working condition parameter vectors is constructed as a snapshot matrix D, and the average residual pressure field of all samples is calculated. Subtract the average residual pressure field from each residual pressure field in the snapshot matrix D, and then perform mean removal processing to obtain the mean-removed snapshot matrix. ; The mean-removed snapshot matrix Perform singular value decomposition to extract the truncated basis function matrices of the first r dominant modes. and the corresponding modal coefficient vector , where r is determined by the cumulative energy ratio criterion; Step S3, train the Gaussian process regression surrogate model: For the operating condition parameter vector Perform feature engineering to construct extended feature vectors. ; With the extended feature vector As input, the modal coefficient vector The modal coefficients of each order are used as outputs, and r independent Gaussian process regression models are established and trained respectively. The set of trained Gaussian process regression models is obtained. ; Save the set of trained Gaussian process regression models and the truncated basis function matrix. And the average residual pressure field, to obtain the trained hybrid prediction model.

2. A force-thermal coupling machine learning prediction method for the lubrication state of a bearing guide surface, characterized in that, The method is implemented based on the trained hybrid prediction model obtained by the training method of claim 1, and the method includes the following steps: Step P1: Obtain the basic operating condition parameter vector of the test condition, which includes at least the inner ring speed, cage speed, eccentricity and initial oil film temperature; Step P2: Solve the physical baseline model to obtain the low-fidelity two-dimensional oil film pressure field corresponding to the test condition; Step P3: Perform feature engineering on the basic working condition parameter vector of the working condition to be tested to obtain the extended feature vector of the working condition to be tested, and input the extended feature vector of the working condition to be tested into the trained Gaussian process regression model set to predict the modal coefficient vectors of the working condition to be tested. Step P4: Using the modal coefficient vectors of each order of the test condition and the truncated basis function matrix And the average residual pressure field, reconstructing the residual pressure field of the working condition under test; Step P5: Superimpose the residual pressure field of the test condition with the low-fidelity two-dimensional oil film pressure field corresponding to the test condition, and restore the ambient atmospheric pressure to obtain the predicted absolute two-dimensional oil film pressure field.

3. The training method for the hybrid prediction model according to claim 1 or the force-thermal coupled machine learning prediction method for the lubrication state of the bearing guide surface according to claim 2, characterized in that, The short sliding bearing theory is the Ocvirk infinite short bearing approximation, which ignores the circumferential pressure gradient term in the Reynolds equation and simplifies the two-dimensional lubrication problem into a one-dimensional ordinary differential equation along the axial direction for solution.

4. The training method for the hybrid prediction model according to claim 1 or the force-thermal coupling machine learning prediction method for the lubrication state of the bearing guide surface according to claim 2, characterized in that, The thermo-elastohydrodynamic coupled finite element model combines the generalized Reynolds equation and the energy equation, and uses the Roelands equation to describe the relationship between lubricant viscosity and pressure and temperature.

5. The training method for the hybrid prediction model according to claim 1, characterized in that, The cumulative energy ratio criterion in step S2 is: select the smallest r such that the ratio of the sum of squares of the first r singular values ​​to the sum of squares of all singular values ​​reaches a preset threshold, which is 99.99%.

6. The training method for the hybrid prediction model according to claim 1, characterized in that, Step S2, which involves converting the high-fidelity two-dimensional oil film pressure field and the low-fidelity two-dimensional oil film pressure field into gauge pressures and then calculating the difference, includes: Subtract the ambient atmospheric pressure from the high-fidelity two-dimensional oil film pressure field and the low-fidelity two-dimensional oil film pressure field respectively to obtain the corresponding gauge pressure field. The residual pressure field is obtained by calculating the difference between the high-fidelity gauge pressure field and the low-fidelity gauge pressure field. .

7. The training method for the hybrid prediction model according to claim 1, characterized in that, The feature engineering process in step S3 includes: processing the operating condition parameter vector. Logarithmic transformations were performed on the inner ring speed, cage speed, and ambient viscosity parameters, and dimensionless parameters from lubrication mechanics were introduced to construct an extended eigenvector. .

8. The force-thermal coupling machine learning prediction method for the lubrication state of the bearing guide surface according to claim 2, characterized in that, Step P5 involves superimposing the residual pressure field of the test condition with the low-fidelity two-dimensional oil film pressure field corresponding to the test condition, and restoring the ambient atmospheric pressure, including: The residual pressure field of the test condition is superimposed with the gauge pressure form of the low-fidelity two-dimensional oil film pressure field corresponding to the test condition to obtain the predicted gauge pressure field. By adding ambient atmospheric pressure to the predicted gauge pressure field, the predicted absolute two-dimensional oil film pressure field is obtained. A non-negative physical constraint is applied to the predicted absolute two-dimensional oil film pressure field.

9. The force-thermal coupling machine learning prediction method for the lubrication state of the bearing guide surface according to claim 2, characterized in that, The method further includes step P6: post-processing the predicted absolute two-dimensional oil film pressure field, and calculating the oil film force in the y-direction by integrating the gauge pressure field on the bearing surface. And extract the maximum oil film pressure. .

10. The force-thermal coupling machine learning prediction method for the lubrication state of the bearing guide surface according to claim 9, characterized in that, The oil film force in the y direction Predicted value The calculation formula is: ； in, The inner ring radius of the bearing. To maintain the width of the frame on one side, Circumferentially normalized coordinates; This represents the predicted gauge pressure field.

Images