A method for modeling and predicting coefficient of friction fluctuation and mean value index layering

Abstract

The application discloses a kind of friction coefficient fluctuation and mean value index layered modeling prediction method, belong to mechanical engineering and intelligent monitoring technical field, including the following steps: step S1, multi-source information acquisition and pre-processing;Step S2, multi-source information feature extraction and correlation analysis;Step S3, based on step S2 carries out friction coefficient fluctuation index prediction;Step S4, based on step S3 carries out friction coefficient mean value index prediction.The application uses the above-mentioned friction coefficient fluctuation and mean value index layered modeling prediction method, by introducing layered modeling mechanism and mixed training strategy, realize the modeling of the physical rationality stronger, higher prediction accuracy of each type of index of friction coefficient, with good physical explainability, applicable popularization and engineering practical value.

Description

Technical Field

[0001] This invention relates to the fields of mechanical engineering and intelligent monitoring technology, and in particular to a hierarchical modeling and prediction method for friction coefficient fluctuation and mean index. Background Technology

[0002] In existing technologies, rotating components such as rotor-bearing and meshing gears, and sliding components such as slide rails and piston-cylinder liners are widely used in industries such as machinery, transportation, and energy. During operation, friction and wear are inevitable, resulting in significant energy consumption and economic losses. Therefore, monitoring the state of the friction interface is of great importance for ensuring the operational stability of mechanical systems and extending their service life.

[0003] In practical applications, direct measurement of friction is challenging due to the difficulty in directly obtaining frictional force at the contact interface and limitations in sensor deployment. Acoustic-vibrational signals derived from sliding friction are closely related to the frictional state and can therefore be used for indirect monitoring of the frictional state; however, the complex nonlinear relationship between acoustic-vibrational characteristics and the friction coefficient remains unclear.

[0004] In recent years, multi-source signal fusion methods have enabled the fusion modeling of acoustic and vibration signals, improving the accuracy and robustness of friction condition monitoring. However, existing methods mostly focus on predicting the mean friction coefficient without distinguishing between its mean and fluctuating components, making it difficult to fully reflect its dynamic evolution and potential fault characteristics. Summary of the Invention

[0005] The purpose of this invention is to provide a hierarchical modeling and prediction method for the fluctuation and mean of friction coefficient. By introducing a hierarchical modeling mechanism and a hybrid training strategy, it achieves modeling with stronger physical rationality and higher prediction accuracy for various friction coefficient indicators, and has good physical interpretability, applicability and engineering practical value.

[0006] To achieve the above objectives, this invention provides a hierarchical modeling and prediction method for friction coefficient volatility and mean index, comprising the following steps:

[0007] Step S1: Multi-source information acquisition and preprocessing;

[0008] Step S2: Multi-source information feature extraction and correlation analysis;

[0009] Step S3: Predict the friction coefficient fluctuation index based on step S2;

[0010] Step S4: Predict the average friction coefficient based on step S3.

[0011] Preferably, step S1 specifically includes the following steps:

[0012] Step S101: Based on the standard friction and wear testing machine, build a multi-source friction information synchronous acquisition system to collect multi-source information, including friction force, friction coefficient, and acoustic vibration information;

[0013] The acoustic vibration information includes vibration in the X direction, vibration in the Y direction, and sound pressure signal; where the vibration in the X direction is vibration along the friction direction, and the vibration in the Y direction is vibration perpendicular to the friction direction on the horizontal plane;

[0014] Step S102: Before the test begins, collect acoustic and vibration signals under no-load conditions as background noise baseline data;

[0015] Step S103: Install the test specimen, set the test load, speed and duration, and then start the friction test;

[0016] Step S104: Collect multi-source data on the dry friction process under set material and working conditions;

[0017] Step S105: Using the excitation threshold detected in the X-direction vibration signal as the time anchor point, timestamp alignment of multi-source information is achieved;

[0018] Step S106: The acquired signal is filtered using a least mean square (LMS) adaptive filter to suppress background noise and obtain filtered multi-source friction information data aligned with the timestamp.

[0019] Preferably, step S2 specifically includes the following steps:

[0020] Step S201: Use the moving average method to extract the time-domain features, frequency-domain features, and time-frequency-domain features of multi-source information;

[0021] Step S202: Calculate the Pearson correlation coefficient between acoustic vibration information and friction coefficient to obtain the correlation matrix between acoustic vibration information and friction coefficient;

[0022] Step S203: Sort the correlation coefficients in the correlation matrix in descending order of absolute value, and select the friction coefficient features that have an absolute correlation coefficient greater than 0.8 with any acoustic vibration signal feature to obtain multiple highly correlated friction features. After analysis, the multiple highly correlated features obtained are all fluctuation features of the friction coefficient.

[0023] Step S204: Among the multiple highly correlated friction features obtained, the five acoustic vibration features with the highest correlation corresponding to each feature are further retained, and a correspondence table between acoustic vibration signal features and friction coefficient fluctuation features is constructed.

[0024] Preferably, step S3 specifically includes the following steps:

[0025] Step S301: Use the basic regression model to perform regression training on the fluctuation of the friction coefficient, and use different fusion algorithms to integrate and fuse the basic regression model;

[0026] Step S302: Use evaluation indicators to assess the fit of the regression model;

[0027] Step S303: Select the model with the highest evaluation index as the prediction model for the friction coefficient fluctuation index, and save it.

[0028] Preferably, step S4 specifically includes the following steps:

[0029] Step S401: Based on the distribution characteristics and statistical laws of the friction coefficient fluctuation index, construct a physical heuristic feature that reflects the relationship between the friction coefficient fluctuation index and the mean index.

[0030] Step S402: Using the extracted volatility index and physical heuristic features as input features, and the mean index of friction coefficient as output variable, construct a dataset for regression modeling.

[0031] Step S403: Adopt a hybrid training strategy and use a random forest regression model to perform regression training and prediction on the mean index of the friction coefficient;

[0032] Step S404: Based on the training results, complete the model fitting and save the trained random forest model as the prediction model for the mean friction coefficient index.

[0033] Preferably, the physically inspired features are specifically:

[0034] Derived predicted mean:

[0035]

[0036] Where peak is the peak value in the volatility index; min is the minimum value in the volatility index;

[0037] Derived predicted root mean square value:

[0038]

[0039] Where std is the standard deviation in the volatility index;

[0040] Derived frequency energy value:

[0041] freq energy =psd mean *hjorth_activity;

[0042] Among them, psd meanhjorth_activity is the mean energy spectral density in the volatility index; hjorth_activity is the signal variance in the volatility index.

[0043] Preferably, in step S201, the time-domain features, frequency-domain features, and time-frequency-domain features of multi-source information are extracted using a moving window method. The width of the moving window is set to the time length corresponding to one rotation of the friction pair, and the step size is one-quarter of this width.

[0044] Preferably, in step 301, different fluctuation indices of the friction coefficient are used as target variables, and corresponding acoustic and vibration characteristics are selected as input variables based on the correspondence table between acoustic and vibration signal characteristics and friction coefficient fluctuation characteristics.

[0045] Preferably, the basic regression model includes a variety of representative regression algorithms, such as linear models (e.g., Linear Regression, Ridge Regression, Lasso Regression), kernel-based support vector regression (SVR), nonparametric model K-nearest neighbor regression (KNN), tree-based ensemble models (Random Forest RF, Gradient Boosting GBDT, Extreme Gradient Boosting XGBoost), Bayesian Ridge, and artificial neural networks (ANN).

[0046] Preferably, the integration and fusion strategy includes:

[0047] The weighted average method assigns weights to each model based on their performance and then performs a weighted fusion of the prediction results.

[0048] Soft voting regression method, which simply averages the output results of each model, can alleviate the overfitting problem;

[0049] Stacking and fusion are used to construct a meta-regressor to relearn the prediction results of the base model in order to capture higher-order nonlinear relationships.

[0050] Therefore, the present invention employs the above-mentioned hierarchical modeling and prediction method for friction coefficient fluctuation and mean index, and the technical effects are as follows:

[0051] By adopting a hierarchical modeling method, the fluctuation and mean of the friction coefficient are modeled and predicted in a hierarchical manner, making the statistical modeling based on acoustic vibration information-friction coefficient fluctuation and fluctuation-mean more physically reasonable and interpretable.

[0052] Based on the basic regression algorithm and the fusion algorithm, an algorithm model that is more suitable for predicting the fluctuation of friction coefficient was selected;

[0053] A physics-inspired wave characteristic is proposed, and a hybrid training method is put forward to meet the statistical modeling requirements of the volatility-mean of the friction coefficient and improve the training speed.

[0054] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0055] Figure 1 This is a flowchart of an embodiment of a hierarchical modeling and prediction method for friction coefficient volatility and mean index according to the present invention;

[0056] Figure 2 This is a framework diagram of an embodiment of the hierarchical modeling and prediction method for friction coefficient volatility and mean index of the present invention;

[0057] Figure 3 This is a table showing the correspondence between acoustic and vibration signal characteristics and friction coefficient fluctuation characteristics in an embodiment of the hierarchical modeling and prediction method for friction coefficient fluctuation and mean index of the present invention. Detailed Implementation

[0058] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0059] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning as understood by one of ordinary skill in the art to which this invention pertains.

[0060] Example 1

[0061] like Figure 1 As shown, this invention provides a hierarchical modeling and prediction method for friction coefficient volatility and mean index. Figure 2 Here is a framework diagram of the prediction method, including the following steps:

[0062] Step S1: Multi-source information acquisition and preprocessing; Based on a standard friction and wear testing machine (hereinafter referred to as the testing machine), and combined with various sensing devices such as force sensors, sound pressure sensors, and acceleration vibration sensors, a multi-source friction information synchronous acquisition system is built. Taking the ball-disc rotational friction test as an example, multi-source information under specified working conditions is acquired synchronously. The multi-source information includes friction force, friction coefficient, and sound vibration information. The sound vibration information includes X-direction vibration, Y-direction vibration, and sound pressure signal; where X-direction vibration is vibration along the friction direction, and Y-direction vibration is vibration perpendicular to the friction direction on the horizontal plane.

[0063] Based on the vibration excitation threshold in the X direction, timestamp alignment of multi-source information is achieved. Vibration signals and sound pressure signals under frictionless conditions are treated as background noise, and their characteristics are statistically modeled to determine an energy-based suppression threshold. A least mean square adaptive filter is then used to suppress the background noise, resulting in filtered, timestamp-aligned multi-source friction information data.

[0064] Step S2: Multi-source information feature extraction and correlation analysis; using a moving window, extract time-domain features (including 16 time-domain features such as mean, root mean square, standard deviation, peak value, maximum and minimum values, peak-to-peak value, energy waveform factor, and sound pressure level), frequency-domain features (including 8 frequency-domain features such as maximum frequency, maximum frequency amplitude, frequency mean, and energy spectrum peak value), and time-frequency-domain features (obtained using the short-time Fourier transform method). The width of the moving window is set to the time length corresponding to one revolution of the friction pair, and the step size is one-quarter of this width, ensuring that the extracted features can characterize the signal characteristics of each revolution of the friction process.

[0065] The Pearson correlation coefficient between acoustic vibration information and the friction coefficient was calculated to obtain the correlation matrix between them. The correlation coefficients in the matrix were sorted in descending order of their absolute values, and friction coefficient features with an absolute correlation coefficient greater than 0.8 with any acoustic vibration signal feature were selected, resulting in 10 highly correlated friction features. Analysis revealed that these highly correlated features all exhibited fluctuation characteristics of the friction coefficient.

[0066] Among the 10 highly correlated frictional fluctuation characteristics mentioned above, the 5 acoustic-vibration characteristics with the highest correlation for each characteristic are further retained, and a correspondence table between acoustic-vibration signal characteristics and friction coefficient fluctuation characteristics is constructed, as follows: Figure 3 As shown, this provides a high-quality feature combination for subsequent modeling and prediction.

[0067] Step S3: Predict the friction coefficient fluctuation index based on step S2;

[0068] Multiple basic regression models were used to train the regression on the volatility of the friction coefficient. Different indicators of the volatility of the friction coefficient were used as target values, and acoustic and vibration characteristics selected according to the relationship table were used as input values. The basic regression models included linear models (such as Linear Regression, Ridge Regression, and Lasso Regression), kernel-based Support Vector Regression (SVR), nonparametric model K-Nearest Neighbor Regression (KNN), tree-based ensemble models (Random Forest, Gradient Boosting GBDT, Extreme Gradient Boosting XGBoost), Bayesian Ridge Regression, and Artificial Neural Networks (ANN), among other representative regression algorithms.

[0069] To improve prediction accuracy and model generalization ability, the prediction results from the above-mentioned multiple basic regression models are integrated and fused. The fusion strategy includes:

[0070] The weighted average method assigns weights to each model based on their performance and then performs a weighted fusion of the prediction results.

[0071] Soft voting regression method, which simply averages the output results of each model, can alleviate the overfitting problem;

[0072] Stacking and fusion are used to construct a meta-regressor to relearn the prediction results of the base model in order to capture higher-order nonlinear relationships.

[0073] Specific evaluation metrics are used to assess the fit of the regression model, such as mean squared error (MSE), root mean squared error (RMSE), and goodness of fit (R²). The dataset is divided into training and test sets using the hold-out method. The test set is not used in the training process but only to validate the trained model. The model with the highest evaluation metric is selected as the prediction model for the friction coefficient volatility index and saved.

[0074] Step S4: Based on step S3, predict the mean value of the friction coefficient; based on the volatility characteristics of the friction coefficient, combined with statistical properties and the distribution characteristics of the friction coefficient, construct three physically inspired derived features from volatility to mean to establish the mapping relationship between volatility indicators and central trend indicators. The central trend indicators include the mean and the root mean square (RMS); construct a dataset with volatility indicators and physically inspired features as inputs and the mean indicator as output.

[0075] The physical heuristic features are as follows:

[0076] Derived predicted mean:

[0077]

[0078] Where peak is the peak value in the volatility index; min is the minimum value in the volatility index;

[0079] Derived predicted root mean square value:

[0080]

[0081] Where std is the standard deviation in the volatility index;

[0082] Derived frequency energy value:

[0083] freq energy =psd mean *hjorth_activity;

[0084] Among them, psd mean hjorth_activity is the mean energy spectral density in the volatility index; hjorth_activity is the signal variance in the volatility index.

[0085] To improve the robustness of the model in real-world deployment scenarios, a hybrid training strategy is introduced: that is, the true values ​​of some intermediate features in the training set are randomly replaced with their corresponding predicted values.

[0086] Based on the constructed physical heuristic features, a random forest regression model was used for training. The evaluation index was the same as that of S3. The model with the highest evaluation index was selected as the prediction model for the friction coefficient volatility index and saved.

[0087] Finally, by combining the most accurate models, we can achieve physically interpretable and accurate predictions of everything from acoustic and vibration characteristics to friction coefficient fluctuation indices, and then to friction coefficient central trend indices.

[0088] Therefore, the present invention adopts the above-mentioned hierarchical modeling and prediction method of friction coefficient fluctuation and mean index. By introducing a hierarchical modeling mechanism and a hybrid training strategy, it achieves accurate modeling of the multidimensional dynamic behavior of friction coefficient, which has good physical interpretability, generalizability and engineering practical value.

[0089] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A hierarchical modeling and prediction method for friction coefficient volatility and mean index, characterized in that, Includes the following steps: Step S1: Multi-source information acquisition and preprocessing; Step S2: Multi-source information feature extraction and correlation analysis; Step S3: Predict the friction coefficient fluctuation index based on step S2; Step S3 specifically includes the following steps: Step S301: Use the basic regression model to perform regression training on the fluctuation of the friction coefficient, and use the fusion algorithm to integrate and fuse the basic regression model; Step S302: Use evaluation indicators to assess the fit of the regression model; Step S303: Select the model with the highest evaluation index as the prediction model for the friction coefficient fluctuation index, and save it; Step S4: Based on step S3, predict the average friction coefficient. Step S4 specifically includes the following steps: Step S401: Based on the distribution characteristics and statistical laws of the friction coefficient fluctuation index, construct a physical heuristic feature that reflects the relationship between the friction coefficient fluctuation index and the mean index. Step S402: Using the extracted volatility index and physical heuristic features as input features, and the mean index of friction coefficient as output variable, construct a dataset for regression modeling. Step S403: Adopt a hybrid training strategy and use a random forest regression model to perform regression training and prediction on the mean index of the friction coefficient; Step S404: Based on the training results, complete the model fitting and save the trained random forest model as the prediction model for the mean friction coefficient index.

2. The hierarchical modeling and prediction method for friction coefficient fluctuation and mean index according to claim 1, characterized in that, Step S1 specifically includes the following steps: Step S101: Based on the standard friction and wear testing machine, build a multi-source friction information synchronous acquisition system to collect multi-source information, including friction force, friction coefficient, and acoustic vibration information; The acoustic vibration information includes vibration in the X direction, vibration in the Y direction, and sound pressure signal; where the vibration in the X direction is vibration along the friction direction, and the vibration in the Y direction is vibration perpendicular to the friction direction on the horizontal plane; Step S102: Before the test begins, collect acoustic and vibration signals under no-load conditions as background noise baseline data; Step S103: Install the test specimen, set the test load, speed and duration, and then start the friction test; Step S104: Collect multi-source data on the dry friction process under set material and working conditions; Step S105: Using the excitation threshold detected in the X-direction vibration signal as the time anchor point, timestamp alignment of multi-source information is achieved; Step S106: The acquired signal is filtered using a minimum mean square adaptive filter to suppress background noise and obtain filtered multi-source friction information data aligned with the timestamp.

3. The hierarchical modeling and prediction method for friction coefficient fluctuation and mean index according to claim 2, characterized in that, Step S2 specifically includes the following steps: Step S201: Use the moving average method to extract the time-domain features, frequency-domain features, and time-frequency-domain features of multi-source information; Step S202: Calculate the Pearson correlation coefficient between acoustic vibration information and friction coefficient to obtain the correlation matrix between acoustic vibration information and friction coefficient; Step S203: Sort the correlation coefficients in the correlation matrix in descending order of absolute value, and select the friction coefficient features that have an absolute correlation coefficient greater than 0.8 with any acoustic vibration signal feature to obtain multiple highly correlated friction features. After analysis, the multiple highly correlated features obtained are all fluctuation features of the friction coefficient. Step S204: Among the multiple highly correlated friction features obtained, the five acoustic vibration features with the highest correlation corresponding to each feature are further retained, and a correspondence table between acoustic vibration signal features and friction coefficient fluctuation features is constructed.

4. The hierarchical modeling and prediction method for friction coefficient fluctuation and mean index according to claim 1, characterized in that, The physical heuristic features are specifically: Derived predicted mean: Where peak is the peak value in the volatility index; min is the minimum value in the volatility index; Derived predicted root mean square value: Where std is the standard deviation in the volatility index. Derived frequency energy value: freq energy =psd mean *hjorth_activity; Among them, psd mean hjorth_activity is the mean energy spectral density in the volatility index; hjorth_activity is the signal variance in the volatility index.

5. The hierarchical modeling and prediction method for friction coefficient fluctuation and mean index according to claim 3, characterized in that, In step S201, the time-domain features, frequency-domain features, and time-frequency-domain features of multi-source information are extracted using a moving window method. The width of the moving window is set to the time length corresponding to one rotation of the friction pair, and the step size is one-quarter of this width.

6. The hierarchical modeling and prediction method for friction coefficient volatility and mean index according to claim 1, characterized in that, In step S301, different fluctuation indices of the friction coefficient are used as target variables. Based on the correspondence table between acoustic and vibration signal characteristics and friction coefficient fluctuation characteristics, the corresponding acoustic and vibration characteristics are selected as input variables.

7. The hierarchical modeling and prediction method for friction coefficient fluctuation and mean index according to claim 6, characterized in that, The basic regression models include a variety of representative regression algorithms, such as linear models, kernel-based support vector regression, nonparametric K-nearest neighbor regression, tree-based ensemble models, Bayesian regression, and artificial neural networks.

8. The hierarchical modeling and prediction method for friction coefficient fluctuation and mean index according to claim 7, characterized in that, The integration and fusion include: The weighted average method assigns weights to each model based on their performance and then performs a weighted fusion of the prediction results. Soft voting regression method, which simply averages the output results of each model, can alleviate the overfitting problem; Stacking and fusion are used to construct a meta-regressor to relearn the prediction results of the base model in order to capture higher-order nonlinear relationships.

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