Method for predicting friction coefficient of oil lubricated sliding bearing, electronic device and medium

Abstract

The application discloses a kind of oil lubrication sliding bearing friction coefficient prediction method, electronic equipment and medium, method includes: the friction experimental data of oil lubrication sliding bearing is collected and preprocessed, and the dynamic data of measured friction coefficient and working condition parameter are obtained;Based on physical information neural network, the prediction submodel of fusion stryker curve theory is constructed;Dynamic data of working condition parameter is input into prediction submodel, and dynamic physical hidden variable is output;Based on mean and standard deviation, dynamic data of working condition parameter is transformed reversely, and normalized stryker number is calculated;Dynamic physical hidden variable and normalized stryker number are substituted into Stryker index attenuation equation, and predicted friction coefficient is calculated;Prediction submodel is iteratively trained, and optimal prediction model is obtained;The dynamic data of working condition parameter to be measured are input into optimal prediction model, and the friction coefficient of oil lubrication sliding bearing under the working condition to be measured is output.The prediction precision, generalization ability and stability of the model are improved.

Description

Technical Field

[0001] This invention belongs to the interdisciplinary field of tribology and artificial intelligence deep learning, specifically involving a method for predicting the friction coefficient of oil-lubricated sliding bearings, electronic equipment, and media. Background Technology

[0002] Oil-lubricated sliding bearings are core supporting components of various industrial equipment. Accurate prediction of the bearing friction coefficient is of significant engineering value for assessing equipment operating conditions, optimizing lubrication systems, and predicting service life. The Stribeck curve, a classic lubrication theory, can intuitively reflect the variation of the friction coefficient with operating parameters such as speed, load, and lubricant viscosity. It clearly distinguishes three operating states: boundary lubrication, mixed lubrication, and hydrodynamic lubrication, and is widely used in the field of bearing friction characteristic analysis.

[0003] In related technologies, bearing friction coefficient prediction is mainly divided into two categories: traditional physical modeling methods and pure data-driven deep learning methods. Traditional physical models rely on theories such as the Stribek empirical equation and the Reynolds equation for calculation. These physical models are highly interpretable, but they depend on parameters such as viscosity and surface roughness, which are difficult to measure accurately in real time, and they generally adopt static parameter assumptions, thus limiting prediction accuracy. Pure data-driven deep learning models have strong nonlinear fitting capabilities; however, in small-sample scenarios with scarce training samples, or in extrapolation scenarios where the prediction range exceeds the distribution of the training dataset, they are prone to overfitting and divergence of prediction results. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of existing technologies, such as the difficulty of adapting traditional physical models to time-varying working conditions, the poor extrapolation ability of pure data-driven models with small samples and working conditions, and the lack of physical interpretability. This invention provides a method, electronic device, and medium for predicting the friction coefficient of oil-lubricated sliding bearings under small sample conditions.

[0005] Firstly, to achieve the above objectives, this invention proposes a method for predicting the friction coefficient of oil-lubricated sliding bearings, comprising: collecting friction test data of the oil-lubricated sliding bearing and preprocessing it to obtain measured friction coefficient and dynamic data of operating condition parameters; the friction test data includes torque time-series data and slowly varying operating condition time-series data, and the dynamic data of operating condition parameters includes load, speed, temperature, contact radius, and time; constructing a prediction sub-model based on a physical information neural network that integrates Stricker curve theory; inputting the dynamic data of operating condition parameters into the prediction sub-model, and outputting dynamic physical latent variables within a preset lubrication physical constraint range, wherein the dynamic physical latent variables... The parameters include equivalent viscosity, boundary friction coefficient, fluid friction coefficient, and attenuation factor. The dynamic data of the operating conditions are inversely transformed based on the mean and standard deviation to calculate the normalized Stribek number. The dynamic physical latent variables and the normalized Stribek number are substituted into the Stribek exponential decay equation to calculate the predicted friction coefficient. Using the mean square error as the loss function, and combining an adaptive weight decay optimizer, a learning rate decay strategy, and an early stopping mechanism, the prediction sub-model is iteratively trained until convergence to obtain the optimal prediction model. The dynamic data of the operating conditions to be tested are input into the optimal prediction model, and the friction coefficient of the oil-lubricated sliding bearing under the tested operating conditions is output.

[0006] In one optional implementation, friction test data of oil-lubricated sliding bearings are collected and preprocessed to obtain measured friction coefficients and dynamic data of operating parameters. Specifically, this includes: performing wavelet three-level decomposition on the original torque time-series signal to extract corresponding wavelet detail coefficients; estimating the noise level based on the median absolute deviation algorithm and determining a general threshold based on the noise level; performing noise reduction processing on the wavelet detail coefficients based on the general threshold to reconstruct the noise-reduced torque data; performing polynomial smoothing filtering on the load and speed in the slowly varying operating condition time-series data to obtain processed operating parameters; calculating the measured friction coefficient at the corresponding time based on the noise-reduced torque data, load, and the gyration radius of the friction pair; and filtering the validity of all experimental samples based on a preset parameter value range, removing abnormal samples to obtain dynamic data of operating parameters.

[0007] In one optional implementation, the sample selection criteria for the dynamic data of the operating condition parameters are: the measured friction coefficient corresponding to the sample is within a first preset value range, the rotational speed is greater than a first set threshold, and the load is greater than a second set threshold.

[0008] In one optional implementation, the prediction sub-model includes a dynamic physical parameter prediction multilayer sensor sub-network. The dynamic physical parameter prediction multilayer sensor sub-network takes normalized operating parameters as input and applies range constraints to the dynamic physical latent variables based on two different nonlinear activation functions, so that the output dynamic physical latent variables always satisfy the bearing lubrication physical boundary conditions.

[0009] In one optional implementation, the Stribek exponential decay equation includes a reference friction term and an exponential decay term; the reference friction term is characterized by the boundary friction coefficient and the fluid friction coefficient, and is used to describe the steady-state basic friction characteristics; the exponential decay term is constructed by the decay factor and the normalized Stribek number, and is used to describe the dynamic evolution of the lubrication state; the predicted friction coefficient is obtained by solving the system of the reference friction term and the exponential decay term.

[0010] In one optional implementation, the normalized Stribek number is calculated by inversely transforming the dynamic data of the operating parameters based on the mean and standard deviation saved in the standardization process. Specifically, this includes: calling the mean and standard deviation to perform an inverse transformation on the dynamic data of the operating parameters to restore the true operating parameters; calculating the actual contact area and contact pressure of the bearing friction pair based on the circular contact surface model and the true operating parameters; normalizing the speed parameters and the contact pressure respectively, and combining them with the predicted equivalent viscosity to jointly calculate the normalized Stribek number.

[0011] In one optional implementation, the mean squared error is used as the loss function, and the optimal prediction model is obtained through iterative training based on an adaptive weight decay optimizer, a learning rate decay strategy, and an early stopping mechanism. Specifically, this includes: using an adaptive weight decay optimizer, a learning rate decay strategy, and an early stopping mechanism to perform multiple rounds of iterative training on the prediction sub-model to obtain a primary prediction model; using an independent validation set to verify the generalization performance of the primary prediction model, and retaining the model weights with the minimum validation loss and the best prediction accuracy as the optimal prediction model.

[0012] In one optional implementation, during iterative training, the batch size of training samples per session is dynamically adjusted based on the current total number of training samples, and a fixed initial learning rate and a fixed weight decay coefficient are configured. During training, if the validation loss does not decrease for a preset number of consecutive rounds, the learning rate is automatically reduced. If the validation set prediction effect does not improve for a preset number of consecutive rounds, an early stopping mechanism is triggered to terminate iterative training.

[0013] In a second aspect, the present invention also provides an electronic device comprising: at least one processor;

[0014] A memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to perform any of the oil-lubricated sliding bearing friction coefficient prediction methods described above.

[0015] Thirdly, the present invention also proposes a computer storage medium storing a computer program, which, when executed by a processor, implements the method for predicting the friction coefficient of oil-lubricated sliding bearings as described in any one of the claims.

[0016] The beneficial effects of this invention are as follows: This invention ensures data reliability through multi-dimensional data acquisition and preprocessing. Relying on the network structure of fusion theory, it achieves an organic combination of physical mechanisms and data-driven approaches, dynamically solving various lubrication physical parameters and applying physical constraints. This ensures that the prediction results always conform to the objective laws of tribology, solving the problems of high difficulty in parameter measurement, lack of physical logic in pure data-driven models, and easy divergence in predictions under out-of-domain conditions in traditional methods. Simultaneously, this invention employs multiple optimization strategies to complete model training, significantly improving the model's prediction accuracy, generalization ability, and stability. It can achieve effective predictions under normal operating conditions, small sample scenarios, and high-speed extreme operating conditions. Attached Figure Description

[0017] Figure 1 A flowchart of a method for predicting the friction coefficient of an oil-lubricated sliding bearing provided in an embodiment of the present invention;

[0018] Figure 2 A schematic diagram of the PINN network structure of the fused friction lubrication theory model for the oil-lubricated sliding bearing friction coefficient prediction method provided in an embodiment of the present invention;

[0019] Figure 3a A rotational speed-friction coefficient diagram for a method of predicting the friction coefficient of an oil-lubricated sliding bearing provided in an embodiment of the present invention;

[0020] Figure 3b A load-friction coefficient diagram for a method of predicting the friction coefficient of an oil-lubricated sliding bearing provided in an embodiment of the present invention;

[0021] Figure 4 A schematic diagram of the training process loss curve of the oil-lubricated sliding bearing friction coefficient prediction method provided in an embodiment of the present invention;

[0022] Figure 5a This is one of the small-sample ablation experiment comparison diagrams of the oil-lubricated sliding bearing friction coefficient prediction method provided in an embodiment of the present invention;

[0023] Figure 5b This is the second small-sample ablation experiment comparison diagram of the oil-lubricated sliding bearing friction coefficient prediction method provided in an embodiment of the present invention;

[0024] Figure 6 A comparison diagram of high-speed blind zone extrapolation prediction results of the oil-lubricated sliding bearing friction coefficient prediction method provided in an embodiment of the present invention;

[0025] Figure 7The OOD (Obstruction Delay) dynamic attenuation factor K of the oil-lubricated sliding bearing friction coefficient prediction method provided in an embodiment of the present invention. dynamic Evolution curve with rotational speed. Detailed Implementation

[0026] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0027] like Figure 1 As shown, according to an embodiment of the present invention, in one aspect, a method for predicting the friction coefficient of an oil-lubricated sliding bearing is provided, comprising the following steps:

[0028] Step S101: Collect friction test data of oil-lubricated sliding bearings and preprocess them to obtain measured friction coefficient and dynamic data of operating conditions. The friction test data includes torque time series data and slow-changing operating condition time series data. The dynamic data of operating conditions includes load, speed, temperature, contact radius and time.

[0029] Complete collection of time-series and operating parameters reflecting the bearing's operating status, along with preprocessing to filter out invalid information and standardize the data format, can effectively reduce interference items in the original data, ensure the quality of input data, and provide a reliable data source for model training and friction coefficient prediction.

[0030] Step S102: Construct a prediction sub-model based on physical information neural network that integrates the Stribek curve theory.

[0031] By incorporating classical lubrication mechanisms as physical priors into neural networks, and combining the nonlinear fitting capabilities of deep learning with the tribological laws of the Stribek curve, the model's data learning ability and physical interpretability are taken into account. This approach overcomes the shortcomings of weak fitting capabilities of single physical models and the lack of theoretical support for pure data models.

[0032] Step S103: Input the dynamic data of the operating condition parameters into the prediction sub-model, and output the dynamic physical latent variables within the preset lubrication physical constraint range. The dynamic physical latent variables include equivalent viscosity, boundary friction coefficient, fluid friction coefficient and attenuation factor.

[0033] By dynamically solving key physical parameters in the lubrication process through a network and defining reasonable ranges for parameter values ​​with the help of physical constraints, abnormal values ​​that violate the lubrication mechanism can be prevented from being output by the network, ensuring that the parameter output conforms to the physical operating law of oil-lubricated bearings throughout the process.

[0034] Step S104: Perform an inverse transformation on the dynamic data of the operating parameters based on the mean and standard deviation to calculate the normalized Stribek number.

[0035] By accurately reproducing real physical working parameters and optimizing the distribution of parameter values ​​through normalization, the network gradient propagation effect can be improved, the stability of the Stribek number calculation results can be enhanced, and the computational characteristics of neural networks can be adapted.

[0036] Step S105: Substitute the dynamic physical hidden variables and the normalized Stribek number into the Stribek exponential decay equation to calculate the predicted friction coefficient.

[0037] By using the exponential decay equation to characterize the dynamic evolution of lubrication state and correlating multiple physical parameters to achieve quantitative calculation of friction coefficient, the nonlinear friction characteristics of oil-lubricated bearings in different lubrication ranges can be accurately matched.

[0038] Step S106: Using mean squared error as the loss function, and combining an adaptive weight decay optimizer, a learning rate decay strategy, and an early stopping mechanism, the prediction sub-model is iteratively trained, and the optimal prediction model is obtained after convergence.

[0039] By employing multiple training strategies in synergy, the network training process can be effectively controlled, and the loss curve during training is shown in the figure. Figure 4 As shown. This accelerates model convergence, suppresses overfitting, improves model generalization ability, and ultimately selects the model with the best prediction performance.

[0040] Step S107: Input the dynamic data of the working condition parameters to be tested into the optimal prediction model and output the friction coefficient of the oil-lubricated sliding bearing under the working condition to be tested.

[0041] This technology enables rapid and automated prediction of friction coefficients under unknown operating conditions. It is easy to operate, has a fast response speed, and facilitates bearing condition testing and performance evaluation in industrial settings.

[0042] This invention ensures data reliability through multi-dimensional data acquisition and preprocessing. Relying on a network structure based on fusion theory, it organically combines physical mechanisms with data-driven approaches, dynamically solving various lubrication physical parameters and applying physical constraints. This ensures that the prediction results always conform to the objective laws of tribology, solving the problems of traditional methods such as high difficulty in parameter measurement, lack of physical logic in purely data-driven models, and easy divergence in predictions under out-of-domain conditions. Simultaneously, this invention employs multiple optimization strategies to complete model training, significantly improving the model's prediction accuracy, generalization ability, and stability. It can achieve effective predictions under normal operating conditions, small sample scenarios, and high-speed extreme conditions. The overall solution has strong physical interpretability and high engineering applicability, providing accurate data for sliding bearing lubrication optimization, operational status monitoring, and equipment life assessment.

[0043] Further, based on step S101, friction test data of the oil-lubricated sliding bearing is collected and preprocessed to obtain the measured friction coefficient and dynamic data of operating parameters, specifically including the following steps:

[0044] Step S1011: Perform wavelet three-level decomposition on the original torque time series signal and extract the corresponding wavelet detail coefficients.

[0045] Step S1012: Estimate the noise level based on the median absolute deviation algorithm, and determine a general threshold based on the noise level.

[0046] Step S1013: Denoise the wavelet detail coefficients based on a general threshold and reconstruct the denoised torque data.

[0047] Step S1014: Perform polynomial smoothing filtering on the load and speed in the time series data of the slow-changing operating condition to obtain the processed operating condition parameters.

[0048] Step S1015: Calculate the measured friction coefficient at the corresponding moment based on the torque data after noise reduction, load, and the gyration radius of the friction pair.

[0049] Step S1016: Based on the preset parameter value range, all experimental samples are screened for validity, abnormal samples are removed, and dynamic data of operating parameters are obtained.

[0050] In this embodiment, five features are extracted: load, rotational speed, temperature, contact radius, and time. Wavelet denoising is performed on the original torque signal, and Savitzky-Golay smoothing filtering is applied to the load and rotational speed. The friction coefficient is calculated as the target variable, and valid samples are selected according to the physical reasonable range.

[0051] The five features of load, rotational speed, temperature, contact radius, and time are used as input features and standardized preprocessed. The global training pool and test set are divided proportionally, and the validation set is further divided within the training pool.

[0052] The original signal processing employs a two-stage denoising scheme: first, the torque time series is decomposed into db4 wavelet three-level decomposition, and the noise level is estimated using the median absolute deviation (MAD). , This represents the highest frequency detail coefficients of the first layer in the db4 wavelet three-level decomposition, used for robust estimation of the noise standard deviation of the torque signal; a general threshold is applied. Perform soft thresholding denoising, where The signal length is given, and then Savitzky-Golay polynomial smoothing (window length ≤ 51, third-order polynomial) is applied to slowly varying signals such as load and rotation speed to preserve physical trends while suppressing high-frequency noise.

[0053] A two-stage denoising scheme is adopted for signals with different characteristics: for torque time-series signals, wavelet decomposition combined with noise estimation based on median absolute deviation and soft threshold denoising is used to effectively remove high-frequency noise and retain the transient characteristics of the friction process; for slow-changing operating condition signals such as load and speed, Savitzky-Golay polynomial smoothing filtering is used to suppress noise while accurately retaining the physical change trend of operating condition parameters, providing high signal-to-noise ratio and high realism basic data support for subsequent friction coefficient calculation.

[0054] Standardizing the extracted torque time series data and slow-varying operating condition time series data can eliminate the dimensional differences between different features. Dividing the training set and test set proportionally, and further dividing the training set into a validation set, can effectively avoid model overfitting, facilitate real-time monitoring of model performance during training, and ensure the stability, convergence efficiency, and generalization ability of model training.

[0055] Furthermore, the sample selection criteria for dynamic data of operating parameters are as follows: the measured friction coefficient corresponding to the sample is within the first preset value range, the rotational speed is greater than the first set threshold, and the load is greater than the second set threshold.

[0056] The target friction coefficient μ is given by the formula Calculate, where, This refers to the frictional torque; For bearing normal load; The contact radius of the friction pair; a valid sample must simultaneously satisfy: Rotational speed n>0.5 r / min, load F>1.0 N.

[0057] The validity of experimental samples is verified by pre-set multi-dimensional screening conditions (friction coefficient, rotational speed, load threshold). Only valid samples that simultaneously meet the physical reasonable range are retained, and invalid data caused by experimental errors, abnormal working conditions or noise interference are removed. This can avoid abnormal samples from interfering with subsequent model training and prediction, significantly improve the overall quality of the dataset, and ensure the physical consistency and engineering applicability of the data.

[0058] The friction coefficient calculation formula is directly based on experimental physical quantities. The measured friction coefficient is calculated by using the denoised torque data, load parameters and the gyration radius of the friction pair. The calculation process has clear physical meaning and is traceable, avoiding the additional errors caused by indirect estimation.

[0059] Furthermore, the prediction sub-model includes a dynamic physical parameter prediction multilayer sensor sub-network. The dynamic physical parameter prediction multilayer sensor sub-network takes the normalized operating parameters as input and applies range constraints to the dynamic physical latent variables based on two different nonlinear activation functions, so that the output dynamic physical latent variables always satisfy the bearing lubrication physical boundary conditions.

[0060] The hard constraint mapping relationship of the four physical hidden variables in the PINN network architecture incorporating Stribeck curve theory is as follows:

[0061] (1) Equivalent dynamic viscosity coefficient : The constraint range is [0.1, 1.6].

[0062] (2) Boundary lubrication friction coefficient : The constraint range is [0.08, 0.28].

[0063] (3) Fluid lubrication friction coefficient : The constraint range is [0.01, 0.06].

[0064] (4) Stribeck attenuation factor : The constraint range is [1, +∞).

[0065] The first three factors are mapped to a bounded interval by the Sigmoid function, and α is strictly greater than 1.0 by the Softplus function (a smooth version of ReLU). These hard constraints ensure that the network satisfies physical consistency in the early stage of training, avoiding physical incompatibility during the optimization process.

[0066] The Sigmoid function is used to map the value range of the equivalent dynamic viscosity coefficient, boundary lubrication friction coefficient, and fluid lubrication friction coefficient, strictly constraining the network output within the physical range that conforms to bearing lubrication theory. At the same time, the Softplus function is used to constrain the Stribeck decay factor to ensure that it is always greater than 1, so that the network can meet the lubrication physical boundary conditions in the early stage of training, avoiding physical incompatibility during the optimization process, and improving the engineering effectiveness and credibility of the model prediction results.

[0067] To suit the characteristics of different physical parameters, the Sigmoid and Softplus activation functions are selected differently: the bounded output characteristics of the Sigmoid function are adapted to the finite physical range of friction coefficient and viscosity coefficient, while the non-negative and smooth characteristics of the Softplus function are adapted to the unbounded physical constraint of the decay factor being strictly greater than 1. This achieves precise constraint of parameters and avoids the gradient vanishing or gradient exploding problems caused by activation functions, ensuring the stability and convergence efficiency of the model training process.

[0068] Furthermore, the Stribek exponential decay equation includes a baseline friction term and an exponential decay term;

[0069] The baseline friction term is characterized by both the boundary friction coefficient and the fluid friction coefficient, and is used to describe the steady-state basic friction characteristics;

[0070] The exponential decay term is constructed by the decay factor and the normalized Stribek number, and is used to describe the dynamic evolution of the lubrication state.

[0071] By combining the baseline friction term and the exponential decay term, the predicted friction coefficient can be obtained.

[0072] In this embodiment, the actual physical quantities are calculated from the standardized input, the normalized Stribeck number is calculated, and the dynamic physical latent variables are substituted into the structured Stribeck exponential decay equation to forward calculate and predict the friction coefficient.

[0073] The neural network structure includes an input layer, hidden layers, and an output layer, such as... Figure 2 As shown, the input data for the input layer includes load (in Newtons), rotational speed (in revolutions per minute), temperature (in degrees Celsius), contact radius (in meters), and time (in seconds). Hidden layer 1 is a fully connected layer with 64 neurons, using the Mish activation function. Hidden layer 2 is a fully connected layer with 32 neurons, also using the Mish activation function. The output layer is a fully connected layer with 4 neurons, no activation function, and outputs four intermediate feature values:

[0074] The first feature is activated by the Sigmoid function, which outputs the equivalent viscosity, with a value range limited to 0.1 to 1.6.

[0075] The second feature is activated by the Sigmoid function, which outputs the upper limit of the friction coefficient, with the value range limited to between 0.08 and 0.28.

[0076] The third feature is activated by the Sigmoid function, which outputs the lower limit of the fluid friction coefficient, with a value range limited to 0.01 to 0.06.

[0077] The fourth feature is activated by the Softplus function, which outputs a decay factor with a value range limited to 1.0 and above.

[0078] By substituting the dynamic physical latent variables output by the neural network into the structured Stribeck exponential decay equation for forward computation, a deep integration of the data-driven model and tribological theory is achieved. The prediction process strictly follows the physical laws of the Stribeck curve, with the boundary friction term, fluid friction term, and exponential decay term jointly characterizing the bearing friction characteristics. Compared with a pure black-box neural network model, this significantly improves the interpretability and physical consistency of the prediction results, while ensuring dynamic adaptability to complex working conditions.

[0079] A neural network structure with two fully connected hidden layers is adopted. The Mish activation function is used to extract deep nonlinear features from multiple working condition inputs such as load, rotation speed, temperature, contact radius and time. The output layer uses differential activation functions to constrain the range of different physical parameters: the sigmoid function realizes the bounded mapping of equivalent viscosity, boundary friction coefficient and fluid friction coefficient, and the Softplus function realizes the non-negativity constraint of the decay factor. This not only ensures the rationality of physical parameters, but also avoids the gradient vanishing or exploding problem, and improves the model training stability and convergence efficiency.

[0080] By back-calculating actual physical quantities and calculating the normalized Stribeck number, operating parameters are mapped to lubrication state characteristics. At the same time, the dynamic physical latent variables output by the network represent the changes in tribological parameters under different operating conditions in real time. Combined with the exponential decay term of the Stribeck equation, the dynamic evolution process of oil-lubricated sliding bearings from boundary lubrication to fluid lubrication can be accurately described, achieving high-precision prediction of friction coefficients under different lubrication conditions and effectively improving the model's prediction performance and generalization ability over a wide range of operating conditions.

[0081] Further, in step S104, the dynamic data of the operating parameters are inversely transformed based on the mean and standard deviation saved in the standardization process to calculate the normalized Stribek number, which specifically includes the following steps:

[0082] Step S1041: Use the mean and standard deviation to perform an inverse transformation on the dynamic data of the operating parameters and restore the true operating parameters;

[0083] Step S1042: Based on the circular contact surface model, calculate the actual contact area and contact pressure of the bearing friction pair according to the actual working conditions.

[0084] Step S1043: Normalize the rotation speed parameters and contact pressure respectively, and calculate the normalized Stribek number by combining the predicted equivalent viscosity.

[0085] In this embodiment, as Figure 2 As shown, the process of predicting the friction coefficient through forward calculation using the Stribeck physics equations module is as follows:

[0086] S01. Speed ​​normalization: Divide the actual speed by 100 to obtain the normalized speed.

[0087] S02. Contact pressure normalization: Divide the actual pressure in megapascals by 10 and add 0.1 to obtain the normalized pressure.

[0088] S03. Reverse calculation of actual physical quantity: Multiply the normalized value by the standard deviation and add the mean to restore the actual physical quantity.

[0089] S04. Calculate the Stribek number: Multiply the equivalent viscosity output by the neural network by the normalized rotational speed, and then divide by the normalized pressure to obtain the normalized Stribek number.

[0090] S05. Stribek exponential decay equation:

[0091] Predicted friction coefficient = lower limit of fluid friction coefficient + (upper limit of friction coefficient - lower limit of fluid friction coefficient) × exp(-attenuation factor × normalized Stribek number).

[0092] The predicted friction coefficient is ultimately obtained, and its value is physically constrained between the lower limit and the upper limit of the fluid friction coefficient.

[0093] Among them, from the standardized input X scaled When calculating the actual physical quantities, the StandardScaler parameters (mean μ) saved during the training phase are used. feat Standard deviation σ feat Perform the inverse transformation using the following formula:

[0094] X real =X scaled σ feat μ feat ;

[0095] Among them, X scaled Standardized feature values ​​as input to the model; X real This is the original, true physical quantity obtained through inverse calculation.

[0096] The contact area is approximated as A = πr² for a circular contact surface; the contact pressure... (Unit: MPa), ε is the area correction margin.

[0097] To make the Stribeck number S norm To avoid gradient vanishing and to keep the gradient at the O(1) level, normalization is used: , ,final S norm Being within a favorable gradient propagation range ensures stable network convergence. Where P... norm is the normalized contact pressure; n is the relative sliding speed of the contact surface. For the normalized Strybeck number; This is the equivalent dynamic viscosity of the lubricating oil; This is the scaled rotational speed feature.

[0098] This method constructs a high-quality training dataset by differentially denoising torque signals and slowly varying operating condition signals, and by performing full-process data quality control and standardization. By combining multi-stage dataset partitioning with a physically hard-constrained PINN network, the Stribeck curve theory is deeply integrated with the neural network, enabling physically interpretable prediction of the friction coefficient. This effectively avoids gradient vanishing and physically incomprehensible interpretations, improves model training stability, convergence efficiency, and generalization ability across a wide range of operating conditions, and provides reliable technical support for the analysis of friction characteristics of oil-lubricated sliding bearings.

[0099] Furthermore, based on step S106, using the mean squared error as the loss function, the optimal prediction model is obtained through iterative training based on an adaptive weight decay optimizer, a learning rate decay strategy, and an early stopping mechanism. This specifically includes the following steps:

[0100] Step S1061: Using an adaptive weight decay optimizer, a learning rate decay strategy, and an early stopping mechanism, the prediction sub-model is trained in multiple rounds to obtain a primary prediction model.

[0101] Step S1062: Use an independent validation set to verify the generalization performance of the primary prediction model, and retain the model weights with the minimum validation loss and the best prediction accuracy as the optimal prediction model.

[0102] In this embodiment, the mean square error (MSE) loss function is used to calculate the average of the squares of the difference between the predicted friction coefficient and the actual friction coefficient. The formula is as follows:

[0103] Loss value = (1 / total number of samples) × Σ(predicted friction coefficient - actual friction coefficient)².

[0104] For a comparison of the actual value of the friction coefficient with the predicted value of PINN, see [link to relevant documentation]. Figure 3a and Figure 3b As shown.

[0105] Backpropagation training was performed using the AdamW optimization algorithm, with a learning rate of 0.005 and weight decay of 0.001.

[0106] Using mean squared error as the loss function, the AdamW optimizer is used in conjunction with the ReduceLROnPlateau learning rate scheduling strategy to train the network, and the optimal model weights on the validation set are saved through an early stopping mechanism.

[0107] By employing the AdamW optimization algorithm combined with the ReduceLROnPlateau learning rate scheduling strategy and early stopping mechanism, and using mean squared error as the loss function to train the network, the adaptive weight decay effectively suppresses model overfitting, while the dynamic adjustment of the learning rate ensures convergence stability in the later stages of training. At the same time, the early stopping mechanism preserves the optimal model weights on the validation set, ensuring that the final model has both low training error and good generalization performance, further improving the accuracy and reliability of predicting the friction coefficient of oil-lubricated sliding bearings.

[0108] Furthermore, during iterative training, the batch size of training samples per session is dynamically adjusted based on the total number of training samples, and a fixed initial learning rate and a fixed weight decay coefficient are configured. During training, if the validation loss does not decrease for a preset number of consecutive rounds, the learning rate is automatically reduced. If the prediction effect on the validation set does not improve for a preset number of consecutive rounds, an early stopping mechanism is triggered to terminate iterative training.

[0109] In this embodiment, IID (Independent and Identically Distributed) small-sample ablation experiments were conducted by gradually reducing the training data ratio from 100% to 0.01%. The PINN model and the pure data-driven BASELINE model were trained at each data ratio gradient, and the R², MAE, and MAPE metrics were compared on a unified test set. The approximate sample sizes for each data ratio in the IID ablation experiment were as follows: 100% corresponds to approximately 500,000 data points, 10% to approximately 50,000 data points, 1% to approximately 5,000 data points, 0.1% to approximately 500 data points, and 0.01% to approximately 50 data points. Random sampling with a fixed random seed (random_state=42) was used for each ratio to ensure reproducibility. The BatchNorm layer in the BASELINE model structure helps stabilize the activation distribution with small samples, and Dropout(0.1) provides lightweight regularization. Both models used the same hyperparameter settings (learning rate, batch size, early stopping) at each ratio to ensure fairness in the comparison.

[0110] OOD extrapolation was performed using 85% of the rotational speed characteristics as the segmentation threshold. High-speed interval data was used as the blind zone test set. After training the PINN model, extrapolation performance was evaluated on the blind zone data. In the OOD extrapolation experiment, the physical background of the OOD scenario in the training set was: when the oil-impregnated bearing operates above the rated speed, the oil film state changes drastically from mixed lubrication to hydrodynamic lubrication. Pure data-driven models, lacking physical understanding of the Stribeck curve, are prone to prediction divergence (a sharp increase or negative change in μ) in the high-speed blind zone. The PINN model uses hard constraints to control μ... pred Always constrained to (μ) fl , μ boundWithin the physically reasonable range, the structure eliminates unreasonable physical extrapolation, ensuring the stability of prediction in high-speed blind zones.

[0111] Generate synthetic scan data covering the entire speed range and extract the attenuation factor K dynamically predicted by the model. dynamic The nonlinear evolution curve of the PINN model with increasing rotational speed is visualized and compared with the traditional static assumption to verify the physical adaptive extrapolation capability of the PINN model. In the synthetic scan data, the other four features are fixed as the mean values ​​of the features in the training set, with only the rotational speed within [n...] being... min ,n max Interpolate 200 points uniformly within the range; n min The minimum operating speed, n max The maximum speed under operating conditions; the baseline for the traditional static assumption is K. dynamic The predicted value at the lowest speed is used as a constant horizontal line; the PINN model uses a dynamic sub-network to provide different K values ​​for the synthetic scan data. dynamic The predicted values ​​show a monotonically decreasing or nonlinear evolution trend with increasing rotational speed, which physically corresponds to the shear-thinning effect, that is, the physical phenomenon that the equivalent viscosity of the oil film decreases and the friction coefficient decreases at high speed under shear.

[0112] Example 1: Small sample ablation experiment of IID, comparison of prediction results is shown in [link to example]. Figure 5a and Figure 5b .

[0113] S1: Collect experimental data files from the bearing test bench. Convert the numerical feature columns (load F (N), rotational speed n (r / min), temperature T (°C), contact radius r (m), time t (s), and torque M (N·m)) to float32 type, delete rows with missing values, and filter outliers with rotational speed ≤0.5 r / min and load ≤1.0 N. Apply db4 wavelet three-layer soft thresholding denoising to the torque column, and apply Savitzky-Golay smoothing (maximum window of 51 points, 3rd order polynomial) to the load and rotational speed columns. Target friction coefficient. We retain the valid samples with 0.001 < μ < 0.6, and obtain a total of valid datasets D.

[0114] S2: Standardize the input features using StandardScaler to obtain X. scaled The complete dataset is split into 80% training pool and 20% test set with random_state=42, resulting in (X) pool X test , y pool , y test ), where X pool For the training set; X testFor the test set; y pool For the training pool truth labels; y test For the test set ground truth labels; the ablation experiments used 5 training data scales: 100%, 10%, 1%, 0.1%, and 0.01%, with values ​​from X at each scale. pool The current training pool X is obtained by random sampling. curr Validation set ratio This ensures that there is still a valid validation set even with small samples.

[0115] S3: Construct the PINN model, a dynamic physics parameter prediction sub-network (Physics-Net), characterized by comprising a cascaded input layer, two hidden layers, and an output layer. Its information processing flow is as follows: First feature mapping unit: receives 5-dimensional input data, maps it to a 64-dimensional feature space through a fully connected network, and performs non-linear activation using the Mish activation function; Second feature mapping unit: reduces the dimensionality of the 64-dimensional features, maps them to 32 dimensions through a fully connected network, and processes them again using the Mish activation function; Parameter output unit: directly maps the 32-dimensional features to a 4-dimensional output through a fully connected layer, using this as the predicted value of the dynamic physics parameters in the current state. Hard constraints are applied to the 4-dimensional output to obtain the dynamic physics hidden variable (η). eq , μ bound , μ fl (α). Simultaneously, a BASELINE pure data-driven model is constructed as a control. This module comprises an input layer, three hidden layers, and an output layer connected sequentially. Specifically: the first hidden layer maps 5-dimensional input features to 128 dimensions, then processes them sequentially using the Mish activation function and Batch Normalization (BN); the second hidden layer reduces the features from 128 dimensions to 64 dimensions, then processes them sequentially using the Mish activation function and a Dropout layer with a dropout rate of 0.1; the third hidden layer reduces the features from 64 dimensions to 32 dimensions and processes them using the Mish activation function; the output layer, through a fully connected mapping, outputs the 32-dimensional hidden features as a 1-dimensional prediction result.

[0116] S4: In the forward inference of the PINN model, the saved StandardScaler parameters are used to scale X... scaled Inverse calculation to X real Extract columns F, n, and r, and calculate P sequentially. MPa P norm n scaled S norm Finally, calculate μ. pred The BASELINE model's forward inference is directly output by the fully connected network μ. pred .

[0117] S5: Both models use AdamW ( , (Optimizer, ReduceLROnPlateau scheduler), early stopping patience=20, maximum 150 epochs of training; batch size After training, load the historical best weights and place them in X. test Calculate R², MAE, and MAPE.

[0118] S6: S2~S5 were executed iteratively at 5 proportional gradients, and the ablation experiment results are summarized in Table 1. The experimental results show that, under full data (100%) conditions, both the PINN and BASELINE models achieved high R² values. R² is an accuracy evaluation metric used to quantify the proportion of true friction coefficient fluctuations that the model can explain. As the proportion of training data decreases, the R² of the BASELINE model drops sharply, approaching random prediction levels at 0.01% of the data. The PINN model, with its physical hard constraints, significantly outperforms BASELINE at 0.01% of the data and maintains similar predictive performance to BASELINE at 0.1% of the data, verifying the effectiveness of physical embedding in improving stability and generalization ability in small samples. Training results are shown in Table 1.

[0119] Table 1 Training Results

[0120]

[0121] Example 2: OOD High-Speed ​​Blind Zone Extrapolation Experiment

[0122] S10~S20: Same as S1~S2 in Example 1, using all the filtered valid datasets.

[0123] S30~S50: Same as Example 1, train the PINN model; generate a comparison chart of extrapolation prediction results, such as... Figure 6 As shown in the figure. Experimental results show that PINN can maintain physically consistent predictions even in the high-speed blind zone, and the predicted friction coefficient is always within the physically reasonable range without divergence.

[0124] S70: Listed in X based on speed characteristics scaled The 85th percentile of the corresponding column is used as the threshold; n scaled Samples ≥threshold are included in the OOD blind zone test set X. test (Approximately 15% of the total samples) constitute the training and validation pool; within the training and validation pool, 20% of the samples are randomly selected for validation, and the remainder are used for training. This segmentation simulates the real-world scenario where high-speed operating data is scarce and model extrapolation is necessary in practical applications.

[0125] S80: Synthetic data is generated using the sweep speed `sweep_var = linspace(n_min, n_max, 200)`, with other features fixed as the mean of the corresponding column in `scaler_X.mean`. The synthesized data is then standardized and input into the trained PINN model. In the `torch.no_grad()` context, the dynamic physics parameter prediction subnetwork extracts the attenuation factor α after Softplus and proportional translation constraints, and plots K... dynamic (n) Evolution curve, such as Figure 7 As shown; with K dynamic The predicted value is a static baseline, compared with the dynamic curve; K dynamic The PINN model shows a continuous decreasing trend in the OOD range, which is consistent with the physical mechanism of the thickening of the lubricating film and the reduction of the effective damping coefficient in oil-impregnated bearings at high speeds, proving that the PINN model has successfully achieved generalized extrapolation guided by physical knowledge.

[0126] The present invention also proposes an electronic device, comprising: at least one processor; a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to perform any of the methods for predicting the friction coefficient of an oil-lubricated sliding bearing.

[0127] This invention proposes a PINN-based method for predicting the friction coefficient of oil-lubricated sliding bearings, which integrates the Stribeck curve theory model. By embedding the friction and lubrication theory as prior physical knowledge into the neural network, stable predictions are achieved under small sample conditions, and good extrapolation ability is demonstrated in the high-speed blind zone of OOD (Out-of-Depth) beyond the training speed range. The specific beneficial technical effects are as follows:

[0128] 1. The PINN architecture proposed in this invention, which integrates Stribeck curve theory, abandons the assumption of global static physical parameters in traditional PINN. It dynamically predicts four physical latent variables through deep sub-networks, endowing the network with strong nonlinear fitting ability while retaining Stribeck's physical prior knowledge, thus fundamentally solving the underfitting problem caused by physical over-constraint under small sample conditions.

[0129] 2. This invention uses Sigmoid / Softplus hard constraints to force the dynamically predicted latent variables to be limited to a physically reasonable range, so that the model can still maintain physical consistency under small sample conditions, which significantly improves the generalization ability of the relative pure data-driven baseline model, especially in the case of scarce data.

[0130] 3. The S of the present invention norm The normalization strategy (on the order of O(1)) effectively solves the engineering problem of gradient vanishing in PINN, ensuring stable convergence of the network under different operating conditions.

[0131] 4. The OOD extrapolation evaluation framework and latent variable evolution visualization method proposed in this invention provide a quantitative verification means for the physical interpretability of the PINN model, and the dynamic decay factor K shown is... dynamic The nonlinear evolution characteristics are highly consistent with the physical mechanism of shear thinning, laying a theoretical foundation for the application of oil-lubricated bearings in high-end equipment.

[0132] The present invention also proposes a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the method for predicting the friction coefficient of oil-lubricated sliding bearings as described in any one of the claims.

[0133] Those skilled in the art will understand that implementing all or part of the processes in the above embodiments can be accomplished by a computer program instructing related hardware. The program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments described above. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory may include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as Static RAM (SRAM), Dynamic RAM (DRAM), Synchronous DRAM (SDRAM), Dual Data SDRAM (DDRSDRAM), Enhanced SDRAM (ESDRAM), Synchlink DRAM (SLDRAM), Rambus Direct RAM (RDRAM), Direct Memory Bus Dynamic RAM (DRDRAM), and Memory Bus Dynamic RAM (RDRAM). The various embodiments described in this specification are presented in a progressive manner, and similar or identical parts between embodiments can be referred to interchangeably. Each embodiment focuses on describing the differences from other embodiments. In particular, for embodiments of apparatus, devices, and non-volatile computer storage media, since they are substantially similar to the method embodiments, the description is relatively simple, and relevant parts can be referred to the description of the method embodiments.

[0134] The above embodiments are merely illustrative examples and are not intended to limit the implementation. Those skilled in the art will recognize that various variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations. However, obvious variations or modifications derived therefrom remain within the scope of this invention.

Claims

1. A method for predicting the friction coefficient of an oil-lubricated sliding bearing, characterized in that, include: Friction test data of oil-lubricated sliding bearings were collected and preprocessed to obtain dynamic data of measured friction coefficient and operating parameters; The friction test data includes torque time-series data and slow-changing working condition time-series data, and the dynamic data of working condition parameters includes load, speed, temperature, contact radius and time; A prediction sub-model based on physical information neural network and incorporating Stribek curve theory is constructed. The prediction sub-model includes a dynamic physical parameter prediction multilayer perceptron sub-network. The dynamic physical parameter prediction multilayer perceptron sub-network takes normalized operating parameters as input and applies range constraints to the dynamic physical latent variables based on two different nonlinear activation functions, so that the output dynamic physical latent variables always satisfy the bearing lubrication physical boundary conditions. The two different nonlinear activation functions include the Sigmoid function and the Softplus function. The dynamic data of the operating condition parameters are input into the prediction sub-model, and dynamic physical latent variables are output within the preset lubrication physical constraint range. The dynamic physical latent variables include equivalent viscosity, boundary friction coefficient, fluid friction coefficient and attenuation factor. The dynamic data of the operating parameters are inversely transformed based on the mean and standard deviation to calculate the normalized Stribek number, specifically including: The mean and standard deviation are used to perform an inverse transformation on the dynamic data of the operating condition parameters to restore the true operating condition parameters. Based on the circular contact surface model, the actual contact area and contact pressure of the bearing friction pair are calculated according to the actual working condition parameters. The rotational speed parameter and the contact pressure were normalized respectively, and the normalized Stribek number was calculated by combining the predicted equivalent viscosity. Substituting the dynamic physical latent variables and the normalized Stribek number into the Stribek exponential decay equation, the predicted friction coefficient is calculated, specifically including: The Stribek exponential decay equation includes a baseline friction term and an exponential decay term. The reference friction term is characterized by both the boundary friction coefficient and the fluid friction coefficient, and is used to describe the steady-state basic friction characteristics; The exponential decay term is constructed by the decay factor and the normalized Stribek number, and is used to describe the dynamic evolution of the lubrication state. By combining the aforementioned baseline friction term and the exponential decay term, the predicted friction coefficient can be obtained; Using mean squared error as the loss function, and combining an adaptive weight decay optimizer, a learning rate decay strategy, and an early stopping mechanism, the prediction sub-model is iteratively trained, and the optimal prediction model is obtained after convergence. The dynamic data of the operating conditions to be tested are input into the optimal prediction model, and the friction coefficient of the oil-lubricated sliding bearing under the operating conditions to be tested is output.

2. The method for predicting the friction coefficient of oil-lubricated sliding bearings according to claim 1, characterized in that, Friction test data of oil-lubricated sliding bearings were collected and preprocessed to obtain dynamic data of measured friction coefficient and operating parameters, specifically including: The original torque time-series signal is decomposed into three wavelet levels to extract the corresponding wavelet detail coefficients. The noise level is estimated based on the median absolute deviation algorithm, and a general threshold is determined based on the noise level. The wavelet detail coefficients are denoised based on the general threshold, and the denoised torque data is reconstructed. The load and speed in the slow-changing operating condition time series data are respectively subjected to polynomial smoothing filtering to obtain the processed operating condition parameters. The measured friction coefficient at the corresponding moment is calculated based on the torque data after noise reduction, the load, and the gyration radius of the friction pair. Based on the preset parameter value range, all experimental samples are screened for validity, and abnormal samples are removed to obtain dynamic data of operating parameters.

3. The method for predicting the friction coefficient of oil-lubricated sliding bearings according to claim 2, characterized in that, The sample selection criteria for the dynamic data of the operating condition parameters are: the measured friction coefficient corresponding to the sample is in the first preset value range, the rotational speed is greater than the first set threshold, and the load is greater than the second set threshold.

4. The method for predicting the friction coefficient of oil-lubricated sliding bearings according to claim 1, characterized in that, Using mean squared error as the loss function, the optimal prediction model is obtained through iterative training based on an adaptive weight decay optimizer, a learning rate decay strategy, and an early stopping mechanism. Specifically, this includes: An adaptive weight decay optimizer, a learning rate decay strategy, and an early stopping mechanism are used to perform multiple rounds of iterative training on the prediction sub-model to obtain a primary prediction model. The generalization performance of the primary prediction model is verified using an independent validation set. The model weights with the minimum validation loss and the best prediction accuracy are retained as the optimal prediction model.

5. The method for predicting the friction coefficient of oil-lubricated sliding bearings according to claim 4, characterized in that, During iterative training, the batch size of training samples per session is dynamically adjusted based on the total number of training samples, and a fixed initial learning rate and a fixed weight decay coefficient are configured. During training, if the validation loss does not decrease for a preset number of consecutive rounds, the learning rate is automatically reduced. If the prediction effect on the validation set does not improve for a preset number of consecutive rounds, an early stopping mechanism is triggered to terminate iterative training.

6. An electronic device, characterized in that, include: At least one processor; A memory that is communicatively connected to the at least one processor; The memory stores instructions that can be executed by the at least one processor, which are executed by the at least one processor to enable the at least one processor to perform the oil-lubricated sliding bearing friction coefficient prediction method as described in any one of claims 1 to 5.

7. A computer storage medium, characterized in that, The system contains a computer program that, when executed by a processor, implements the method for predicting the friction coefficient of an oil-lubricated sliding bearing as described in any one of claims 1 to 5.

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