On-line surveying and mapping method and system for full-working-condition Stribeck curve of engine friction pair

Abstract

The invention belongs to the technical field of engine testing, and particularly relates to an online surveying and mapping method and system for a full-working-condition Stribeck curve of an engine friction pair. The technical problems that the actual friction performance of an engine in a full working condition range is difficult to accurately reflect and the smoothness and accuracy of a lubricating state transition area are difficult to guarantee in an existing method are solved. The method comprises the following steps: calculating an instantaneous mach number and an instantaneous friction coefficient corresponding to each data point, and calculating a working condition transient suppression factor corresponding to each data point; calculating a width parameter of a lubrication state conversion area according to the density of data points at the junction of the lubrication area; obtaining a prediction variance of each interpolation point; and performing weighted fitting on all the data points including the original data points and the interpolation points to obtain a full-working-condition Stribeck curve. According to the method, the high-fidelity all-working-condition Steribeck curve capable of comprehensively and truly reflecting the friction characteristics of the engine can be obtained.

Description

Technical Field

[0001] This invention belongs to the technical field of engine testing, specifically relating to an online method and system for plotting the Stribek curve of engine friction pairs under all operating conditions. Background Technology

[0002] The Stribeck curve is a tool for characterizing the variation of the friction coefficient with the Hersey number under different lubrication conditions. It is of great significance for evaluating and optimizing the tribological characteristics of engines, reducing energy loss, and pollutant emissions. Traditional Stribeck curve mapping relies on dedicated friction and wear testing machines, which must be performed under strictly controlled steady-state conditions. While this method can obtain highly accurate curves, the test conditions differ from the actual operating conditions experienced by key friction pairs such as piston rings-cylinder liners and bearings within the engine. Test benches cannot fully reproduce the effects of internal combustion pressure, component thermal deformation, and reciprocating inertial forces, making it difficult for the mapping results to accurately reflect the actual frictional performance of the engine across the entire operating range. Furthermore, the high cost and long testing cycle limit its application in rapid engine development and online condition monitoring.

[0003] During actual operation, engines frequently experience transient processes such as acceleration, deceleration, and load changes. Friction torque data under these transient conditions contains dynamic disturbances. If these are indiscriminately mixed with steady-state data, it will result in excessively large data point dispersion, severely distorting the true shape of the Stribeck curve. Furthermore, throughout the engine's entire operating cycle, data points in certain lubrication areas may be very sparse, causing curves to be distorted or impossible to construct in these critical regions.

[0004] Furthermore, traditional methods use a single Hersey number threshold to determine the boundary lubrication, mixed lubrication, and hydrodynamic lubrication zones; and they typically employ piecewise models for curve fitting, making it difficult to guarantee the smoothness and accuracy of the lubrication state transition zone. More importantly, traditional methods fail to reliably differentiate the quality of data points, treating less reliable transient data and interpolated data from sparse regions equally with high-quality steady-state data, thus affecting the accuracy and reliability of the Stribeck curve mapping under all operating conditions. Summary of the Invention

[0005] This invention provides a method and system for online plotting of the Stribek curve of engine friction pairs under all operating conditions, in order to solve the technical problems that existing methods are unable to accurately reflect the actual friction performance of the engine under all operating conditions and are unable to guarantee the smoothness and accuracy of the lubrication state transition zone.

[0006] In a first aspect, the present invention provides a method for online plotting of the Stribek curve of an engine friction pair under all operating conditions, including: The system acquires real-time data on engine speed, load, lubricating oil temperature, and friction torque online. Based on the real-time data, it calculates the instantaneous Hersey number and instantaneous friction coefficient corresponding to each data point, and calculates the transient suppression factor of the operating condition corresponding to each data point based on the time second derivative of the engine speed and load data. Based on the local radius of curvature of the data points in the friction coefficient-Hersey number coordinate system, the boundary lubrication zone, the mixed lubrication zone and the hydrodynamic lubrication zone are divided by spectral clustering analysis. The width parameter of the lubrication state transition zone is calculated based on the data point density at the boundary of the lubrication zone. Determine whether the number of data points in each lubrication zone is lower than the preset data volume threshold. If so, use a Gaussian process regression model to interpolate the data in the lubrication zone and obtain the prediction variance of each interpolation point. A composite friction model representing boundary lubrication and mixed lubrication and an oil film model representing hydrodynamic lubrication are constructed. A smooth transition function is determined using the lubrication state transition zone width parameter to connect the two models. The operating condition transient suppression factor of the original data points and the reciprocal of the prediction variance of the interpolation points are used as their respective fitting weights. A weighted fitting is performed on all data points including the original data points and the interpolation points to obtain the full-condition Stribek curve.

[0007] Furthermore, the instantaneous Hersey number satisfies the following relationship: ; In the formula, Let be the instantaneous Hercy number at time i. Let be the real-time dynamic viscosity at time i, which is calculated based on the lubricating oil temperature using the Vogel viscosity-temperature formula. Let be the engine speed at time i. Let be the load at time i.

[0008] Furthermore, the instantaneous coefficient of friction satisfies the following relationship: ; In the formula, Let be the instantaneous friction coefficient at time i. Let be the frictional torque at time i. Let be the load at time i.

[0009] Furthermore, the transient suppression factor for each data point is calculated based on the time second derivative of the engine speed and load data, including: By performing second-order central difference calculations on time-series engine speed and load data, the second derivatives of speed and load at each data point are obtained; the degree of drastic change in operating conditions is calculated using the following formula: In the formula, As an indicator of the degree of drastic change in operating conditions, The second derivative of the rotational speed. The second derivative of the load; through the exponential decay function The transient suppression factor under operating conditions was calculated. ,in This is the preset attenuation coefficient.

[0010] Furthermore, based on the local radius of curvature of the data points in the friction coefficient-Hersey number coordinate system, spectral clustering analysis was used to divide the boundary lubrication zone, the mixed lubrication zone, and the hydrodynamic lubrication zone, including: Calculate the local radius of curvature of each data point in the friction coefficient-Hersey number coordinate system; construct a similarity matrix between data points based on the local radius of curvature; calculate the Laplacian matrix of the similarity matrix and perform eigenvalue decomposition on the Laplacian matrix, taking the eigenvectors corresponding to the first three smallest non-zero eigenvalues; use these three eigenvectors as new features, and use the k-means clustering algorithm to divide the data points into three categories: boundary lubrication, mixed lubrication, and hydrodynamic lubrication.

[0011] Furthermore, the width parameter of the lubrication state transition zone is calculated based on the data point density at the boundary of the lubrication zone, including: Kernel density estimation is performed on the data points at the boundary between the mixed lubrication zone and the hydrodynamic lubrication zone to determine the instantaneous Hersey value corresponding to the intersection of the probability density function curves of the two lubrication zones. The instantaneous Hersey value is used as the conversion center, and the conversion width is determined according to the distribution characteristics of the data points at the boundary. The lubrication state conversion zone width parameter is defined by the conversion center and the conversion width.

[0012] Furthermore, a Gaussian process regression model is used to interpolate the data in the lubrication zone, including: The instantaneous Hersey number is used as the input to the Gaussian process regression model, and the instantaneous friction coefficient is used as the output. The radial basis function kernel is selected as the covariance function. In the lubrication zone where the number of data points is lower than the preset data volume threshold, several equally spaced instantaneous Hersey numbers are selected as new input points. The trained Gaussian process regression model is used to predict the corresponding instantaneous friction coefficient and prediction variance, thereby performing data interpolation.

[0013] Furthermore, a smooth transition function is determined using the lubrication state transition zone width parameter to connect the two models, including: A hyperbolic tangent function is used as the smooth transition function. The center and width of this function are determined by the width parameter of the lubrication state transition zone, and they satisfy the following relationship: ; in, For smooth transition function, For the instantaneous Hercy number, It is the hyperbolic tangent function. As a conversion center, To convert the width.

[0014] Furthermore, a weighted fit is performed on all data points, including both the original data points and the interpolation points, including: Construct a weighted least squares fitting objective function that satisfies the following relationship: ; In the formula, for the th One original data point, For the transient suppression factor of the operating condition; for the first One interpolation point, It is equal to the reciprocal of the prediction variance; For the first The friction coefficient of each data point For the full-condition Stribek curve model, the instantaneous Hersey number The predicted value at the specified location; the model parameters are determined by minimizing the objective function.

[0015] Secondly, the present invention provides an online mapping system for the full-condition Stribek curve of an engine friction pair, comprising a memory and a processor. The memory stores computer program instructions, and when the computer program instructions are executed by the processor, the above-mentioned online mapping method for the full-condition Stribek curve of an engine friction pair is realized.

[0016] The beneficial effects are as follows: This invention proposes a method to improve the accuracy and reliability of online mapping of Stribek curves under all engine operating conditions. This invention acquires real-time data on engine speed, load, lubricating oil temperature, and friction torque online. Based on the real-time data, it calculates the transient suppression factor corresponding to each data point, thereby characterizing the reliability of the data points under different operating conditions. By extracting the local radius of curvature of the data points in the friction coefficient-Hersey number coordinate system, spectral clustering analysis is used to accurately divide the boundary lubrication zone, mixed lubrication zone, and hydrodynamic lubrication zone. Combined with the data point density at the boundary of each lubrication zone, the width parameter of the lubrication state transition zone is calculated. To address the sparsity problem where the number of data points in some lubrication zones is below a preset threshold, a Gaussian process regression model is used for data interpolation. Simultaneously, the prediction variance of each interpolation point is obtained to evaluate the reliability of the interpolated data. Subsequently, a composite friction model representing boundary lubrication and mixed lubrication, and an oil film model representing hydrodynamic lubrication are constructed. A smooth transition function is determined using the lubrication state transition zone width parameter to connect the two models. The transient suppression factor of the original data points and the reciprocal of the prediction variance of the interpolation points are used as the fitting weights for the corresponding data points. Weighted fitting is performed on all data points including the original data points and the interpolation points to obtain a high-fidelity full-condition Stribek curve that can comprehensively and realistically reflect the friction characteristics of the engine. Attached Figure Description

[0017] Figure 1 A flowchart for the online plotting method of Stribek curves of engine friction pairs under all operating conditions; Figure 2 This is a diagram showing the parameter processing of the engine friction pairs under all operating conditions. Figure 3 This is a scatter plot of the lubrication zone distribution of the instantaneous friction coefficient and instantaneous Hercy number under all operating conditions of the engine friction pair. Detailed Implementation

[0018] An embodiment of the online plotting method for the full-condition Stribek curve of engine friction pairs provided by this invention: like Figure 1 As shown, a method for online plotting of the Stribek curve of an engine friction pair under all operating conditions includes the following steps: S1 acquires real-time data of engine speed, load, lubricating oil temperature and friction torque online, calculates the instantaneous Hercy number and instantaneous friction coefficient corresponding to each data point based on the real-time data, and calculates the transient suppression factor of each data point based on the time second derivative of engine speed and load data.

[0019] Specifically, by installing crankshaft speed sensors, dynamometer load sensors, oil pan temperature sensors, and crankshaft torque sensors on an engine test bench, a data acquisition system is used to synchronously acquire time-series data of engine speed, load, lubricating oil temperature, and friction torque, such as... Figure 2 As shown. For each data point at acquisition time i, the real-time dynamic viscosity of the lubricating oil is calculated using the Vogel viscosity-temperature relationship based on the lubricating oil temperature. The instantaneous Hercy number is obtained through the relationship... The calculation shows that, in the formula, Let be the instantaneous Hercy number at the i-th moment; Let be the real-time dynamic viscosity at time i. Let be the engine speed at time i; Let be the load at time i. The instantaneous friction coefficient is expressed by the formula... The calculation shows that, in the formula, Let be the instantaneous friction coefficient at the i-th moment; Let be the frictional torque at time i. The second time derivative is calculated using the three-point central difference method on the time series data of engine speed and load, and it satisfies the following relationship: ; ; In the formula, Let be the second derivative of the rotational speed at time i; Let be the engine speed at time i; Let be the engine speed at time i+1; Let be the engine speed at time i-1; The time interval between adjacent moments; The second time derivative of the load at time i; Let i be the load at time i; Let i+1 be the load at time i; Let be the load at time i-1.

[0020] In an optional embodiment, the transient suppression factor for each data point is calculated based on the time second derivative of the engine speed and load data, including: By performing second-order central difference calculations on time-series engine speed and load data, the second derivatives of speed and load at each data point are obtained; the degree of drastic change in operating conditions is calculated using the following formula: In the formula, As an indicator of the degree of drastic change in operating conditions, The second derivative of the rotational speed. The second derivative of the load; through the exponential decay function The transient suppression factor under operating conditions was calculated. ,in This is the preset attenuation coefficient.

[0021] In one example, a set of time series data was collected: at time points , , The corresponding engine speeds are 1000 rpm, 1200 rpm, and 1100 rpm, respectively, and the corresponding loads are 50 N, 55 N, and 52 N, respectively. The time interval between adjacent moments is 0.1 s. The second-order central difference formula is used for calculation. Second derivative of rotational speed at time t and the second derivative of the load : , .

[0022] The severity of changes in operating conditions is assessed by summing the absolute values ​​of the calculated second derivatives; the model structure is a linear summation model. Taking the above data as an example... 30800. An exponential decay function model is applied to calculate the transient suppression factor of the operating condition, assuming a preset decay coefficient. If the value is 0.0001, then the transient suppression factor for this data point is 0.046. A transient suppression factor close to 0 indicates that the data point was generated under drastically changing conditions, and its weight in subsequent fitting will be reduced.

[0023] S2, based on the local radius of curvature of the data points in the friction coefficient-Hersey number coordinate system, uses spectral clustering analysis to divide the boundary lubrication zone, mixed lubrication zone and hydrodynamic lubrication zone, and calculates the width parameter of the lubrication state transition zone according to the data point density at the junction of the lubrication zones.

[0024] Specifically, all data points are plotted in a friction coefficient-Hersey number coordinate system and sorted by instantaneous Hersey number from smallest to largest. For each data point in the coordinate system, two adjacent points are selected, and the local radius of curvature is calculated based on the principle that three points are concyclic. The local radii of curvature of all data points are used as feature inputs to construct a similarity matrix based on radial basis functions, and a Laplace transform is performed on the similarity matrix. By calculating the eigenvectors corresponding to the first three smallest non-zero eigenvalues ​​of the Laplace matrix, each data point is mapped to a three-dimensional feature space. Then, the k-means clustering algorithm is used to cluster the mapped points into three categories, corresponding to the boundary lubrication zone, the mixed lubrication zone, and the hydrodynamic lubrication zone, respectively. After clustering, the instantaneous Hersey values ​​at the boundaries between the mixed lubrication zone and the boundary lubrication zone, and between the mixed lubrication zone and the hydrodynamic lubrication zone, are identified. Within a preset Hersey number window near the instantaneous Hersey value at the boundary, the number of data points is counted to calculate the data point density. The width parameter of the lubrication state transition zone is set to be proportional to the reciprocal of the data point density; the denser the data points at the boundary, the narrower the transition zone width.

[0025] In an optional embodiment, based on the local radius of curvature of the data points in the friction coefficient-Hersey number coordinate system, spectral clustering analysis is used to divide the boundary lubrication zone, the mixed lubrication zone, and the hydrodynamic lubrication zone, including: Calculate the local radius of curvature of each data point in the friction coefficient-Hersey number coordinate system; construct a similarity matrix between data points based on the local radius of curvature; calculate the Laplacian matrix of the similarity matrix and perform eigenvalue decomposition on the Laplacian matrix, taking the eigenvectors corresponding to the first three smallest non-zero eigenvalues; use these three eigenvectors as new features, and use the k-means clustering algorithm to divide the data points into three categories: boundary lubrication, mixed lubrication, and hydrodynamic lubrication.

[0026] Specifically, the first step is to extract the core features of the data: In the Stribek curve, the curve bends sharply at the inflection point, with a very small local radius of curvature; while in the smooth part of the hydrodynamic lubrication zone, the radius of curvature is very large. The radius of curvature, as a key indicator characterizing the local morphology of the curve, can be used as the core feature of each data point. The second step is to construct a similarity matrix based on the radius of curvature features, using a Gaussian similarity function as the core model structure: if the radii of curvature of two data points are similar, their similarity value is high, and vice versa.

[0027] Subsequently, a Laplacian matrix is ​​constructed based on the similarity matrix, and eigenvalue decomposition is performed on the Laplacian matrix to extract the eigenvectors corresponding to the three smallest non-zero eigenvalues. These three eigenvectors together constitute a new three-dimensional feature space, mapping the original data points into the new space. This process employs a dimensionality reduction embedding model, revealing the inherent clustering structure among the data points. In the newly generated three-dimensional feature space, a k-means clustering model is applied, setting the number of clusters to three, dividing all data points into three independent clusters. Based on the original positions of the data points on the Stribek curve, these three clusters correspond to the boundary lubrication zone, the mixed lubrication zone, and the hydrodynamic lubrication zone of the curve, respectively. Figure 3 As shown.

[0028] In an optional embodiment, the width parameter of the lubrication state transition zone is calculated based on the data point density at the boundary of the lubrication zone, including: Kernel density estimation is performed on the data points at the boundary between the mixed lubrication zone and the hydrodynamic lubrication zone to determine the instantaneous Hersey value corresponding to the intersection of the probability density function curves of the two lubrication zones. The instantaneous Hersey value is used as the conversion center, and the conversion width is determined according to the distribution characteristics of the data points at the boundary. The lubrication state conversion zone width parameter is defined by the conversion center and the conversion width.

[0029] Specifically, after dividing the data points into two regions—hybrid lubrication and hydrodynamic lubrication—using spectral clustering, the focus is on analyzing the data points at the boundary between these two regions. For the data points in these two regions, kernel density estimation is performed on their instantaneous Hersey numbers. The model structure employs a non-parametric probability density function estimation method, which does not require pre-setting the data distribution form and can better reflect the characteristics of actual data. For example, a Gaussian kernel function is used for estimation: a smooth density distribution curve is generated for the hybrid lubrication region, denoted as... Another density curve is generated for the hydrodynamic lubrication region, denoted as... .

[0030] Two density curves typically intersect at a point where the instantaneous Hersey value represents the location where the data densities of the two regions are equal. This intersection point is defined as the transition center of the lubrication state. For example, calculations show that... The determination of the transformation width is related to the dispersion of data points at the boundary. Two methods can be used: one is to calculate the standard deviation of the instantaneous Hersey number of data points within a preset range near the transformation center; the other is to calculate the distance between the peaks of the two density curves. For example, if the data distribution at the boundary is compact, the calculated transformation width might be 0.2 × If the distribution is sparse, the transformation width may be... The final transition center and transition width together constitute the quantitative representation parameters of the lubrication state transition zone.

[0031] S3. Determine whether the number of data points in each lubrication zone is lower than the preset data volume threshold. If so, use a Gaussian process regression model to interpolate the data in the lubrication zone and obtain the prediction variance of each interpolation point.

[0032] Specifically, a data volume threshold is set, for example, 100 data points. Data points are counted for each of the three defined lubrication zones. If the number of data points in a zone is less than 100, an interpolation program is initiated. The existing sparse data points in that zone are used as the training set to construct a Gaussian process regression model, which uses the squared exponential covariance function as the kernel function. Within the range of instantaneous Hersey numbers in the sparse region, a series of new instantaneous Hersey values ​​are selected at uniform intervals as interpolation points. Using the trained Gaussian process regression model, the new instantaneous Hersey values ​​are predicted to obtain the corresponding friction coefficient values ​​and the prediction variance for each predicted value. The magnitude of the prediction variance reflects the uncertainty of the interpolation point; the farther the location is from the original data point, the larger the prediction variance and the lower the data reliability.

[0033] In an optional embodiment, a Gaussian process regression model is used to interpolate data in the lubrication zone, including: The instantaneous Hersey number is used as the input to the Gaussian process regression model, and the instantaneous friction coefficient is used as the output. The radial basis function kernel is selected as the covariance function. In the lubrication zone where the number of data points is lower than the preset data volume threshold, several equally spaced instantaneous Hersey numbers are selected as new input points. The trained Gaussian process regression model is used to predict the corresponding instantaneous friction coefficient and prediction variance, thereby performing data interpolation.

[0034] Specifically, Gaussian process regression is a nonparametric Bayesian regression model that learns the posterior distribution of a function using existing observational data. In this embodiment, the model takes the instantaneous Hersey number as input and the instantaneous friction coefficient as output. A radial basis function kernel (RBF kernel) is chosen as the covariance function because it fits smooth functions well and matches the characteristics of the Stribek curve. The model is trained using existing data points; for example, the boundary lubrication zone has only 15 data points, which is below the preset data volume threshold.

[0035] After training, within the range of the Hercy number in the sparse region, a series of new, equally spaced instantaneous Hercy values ​​are generated as query points. For example, within the range of the Hercy number in the sparse region... Within this model, 40 new instantaneous Herssey values ​​are generated. For each new instantaneous Herssey value, the trained Gaussian process regression model not only predicts the most probable instantaneous friction coefficient value but also provides a prediction variance, which characterizes the uncertainty of the model's prediction for that point. For example, for a new instantaneous Herssey value... The model predicted a friction coefficient of 0.12 and a prediction variance of 0.0005. Through the above process, a batch of interpolation points with uncertain information were generated in the sparse data region, providing a richer data foundation for subsequent global fitting.

[0036] S4. Construct a composite friction model to represent boundary lubrication and mixed lubrication, and an oil film model to represent hydrodynamic lubrication. Use the lubrication state transition zone width parameter to determine a smooth transition function to connect the two models. Use the transient suppression factor of the original data points and the reciprocal of the prediction variance of the interpolation points as their respective fitting weights. Perform weighted fitting on all data points including the original data points and the interpolation points to obtain the full-condition Stribek curve.

[0037] Specifically, a composite friction model representing boundary lubrication and mixed lubrication is constructed, in the form of: ,in, The instantaneous friction coefficient of the boundary-mixed lubrication zone. , and These are the undetermined parameters for the composite friction model. For the instantaneous Hercy number, In one embodiment, the preset model exponent parameters are used. Construct an oil film model to represent hydrodynamic lubrication, in the form of: ,in, The instantaneous friction coefficient of the hydrodynamic lubrication zone. , These are the undetermined parameters for the oil film model. The two models are connected into a global model using a smooth transition function. ,in, A smooth transition function is used. All data points for fitting are prepared, including original data points and interpolation points: for each original data point, the fitting weight is the corresponding transient suppression factor for the operating condition; for each interpolation point, the fitting weight is the reciprocal of the prediction variance. The Levenberg-Marquardt nonlinear least squares method is employed, aiming to minimize the weighted sum of squared residuals, for the undetermined parameters in the model. , , , , The optimized solution yields a high-precision Stribek curve for all operating conditions.

[0038] In an optional embodiment, a smooth transition function is determined using the lubrication state transition zone width parameter to connect the two models, including: A hyperbolic tangent function is used as the smooth transition function. The center and width of this function are determined by the width parameter of the lubrication state transition zone, and they satisfy the following relationship:

[0039] in, For smooth transition function, For the instantaneous Hercy number, As a conversion center, It is the hyperbolic tangent function. To convert the width.

[0040] Specifically, to construct a full-condition Stribek curve that seamlessly connects the mixed lubrication zone and the hydrodynamic lubrication zone, a smooth transition function is needed to achieve a natural transition between the two types of models. The model structure used in this embodiment is a scaled and translated hyperbolic tangent function, i.e., the tanh function. This function is an S-shaped function with a smooth transition range between 0 and 1, making it suitable as a switching switch between models. The two key parameters of the tanh function, the transition center and the transition width, are determined by the lubrication state transition zone width parameter calculated in the above steps.

[0041] Assuming the transformation center is obtained through kernel density estimation, , convert width to When the instantaneous Hersey number is much smaller than the transformation center, for example, when the instantaneous Hersey number is... ,at this time It is a large negative number. The function value is close to -1, therefore The value is close to 0. When the instantaneous Hersey number is much larger than the transformation center, for example, when the instantaneous Hersey number is... , It is a large positive number. The function value is close to 1, therefore The value is close to 1. When the instantaneous Hersey number equals the transformation center, =0.5. The smooth transition function will be used as a weight to smoothly integrate the hybrid lubrication model and the hydrodynamic lubrication model, ensuring that the first derivative of the curve is continuous in the transition region without sharp inflection points.

[0042] In an optional embodiment, a weighted fit is performed on all data points, including the original data points and the interpolated points, comprising: Construct a weighted least squares fitting objective function that satisfies the following relationship:

[0043] In the formula, for the th One original data point, For the transient suppression factor of the operating condition; for the first One interpolation point, It is equal to the reciprocal of the prediction variance; For the first The friction coefficient of each data point For the full-condition Stribek curve model, the instantaneous Hersey number The predicted value at the specified location; the model parameters are determined by minimizing the objective function.

[0044] Specifically, the final step in constructing the full-condition Stribek curve model is parameter optimization using the weighted least squares method. The model structure of this method is an objective function, with the core objective being to minimize the total error. Here, the total error specifically refers to the cumulative weighted squared error between the model's predicted values ​​and the actual data points. The setting of the weights is crucial in this step, as it integrates the information obtained from the preceding steps to distinguish the importance of different data points.

[0045] In one example, a raw data point collected under steady-state conditions has a transient suppression factor of 0.98, so its weight in the fitting is 0.98, significantly influencing the shape of the final curve. Conversely, a data point collected during rapid acceleration / deceleration might have a suppression factor of only 0.1, resulting in a much smaller weight. For an interpolation point generated by Gaussian process regression, if the prediction variance is small, for example, 0.0004, indicating high model certainty for that interpolation point, its weight is 1 / 0.0004 = 2500, a very large weight. If another interpolation point has a larger prediction variance, for example, 0.01, its weight is 100. By minimizing the objective function, for example using numerical optimization algorithms such as Levenberg-Marquardt, the determined Stribek curve model parameters will make the curve closer to the raw data points under steady-state conditions and the high-confidence interpolation points, thus obtaining a more reliable and accurate lubrication curve across all operating conditions.

[0046] An embodiment of the online mapping system for the full-condition Stribek curves of engine friction pairs provided by this invention: The online mapping system for the full-condition Stribek curve of engine friction pairs includes a processor and a memory. The memory stores computer program instructions, and when the computer program instructions are executed by the processor, the above-mentioned online mapping method for the full-condition Stribek curve of engine friction pairs is realized.

[0047] The online mapping system for the full-condition Stribek curve of the engine friction pair also includes other components well known to those skilled in the art, such as communication interfaces. Their settings and functions are known in the art and will not be described in detail here.

[0048] In addition, in the description of this specification, "multiple" means at least two, such as two, three or more, etc., unless otherwise expressly and specifically defined.

Claims

1. A method for online plotting of Stribek curves of engine friction pairs under all operating conditions, characterized in that, include: The system acquires real-time data on engine speed, load, lubricating oil temperature, and friction torque online. Based on the real-time data, it calculates the instantaneous Hersey number and instantaneous friction coefficient corresponding to each data point, and calculates the transient suppression factor of the operating condition corresponding to each data point based on the time second derivative of the engine speed and load data. Based on the local radius of curvature of the data points in the friction coefficient-Hersey number coordinate system, the boundary lubrication zone, the mixed lubrication zone and the hydrodynamic lubrication zone are divided by spectral clustering analysis. The width parameter of the lubrication state transition zone is calculated based on the data point density at the boundary of the lubrication zone. Determine whether the number of data points in each lubrication zone is lower than the preset data volume threshold. If so, use a Gaussian process regression model to interpolate the data in the lubrication zone and obtain the prediction variance of each interpolation point. A composite friction model representing boundary lubrication and mixed lubrication and an oil film model representing hydrodynamic lubrication are constructed. A smooth transition function is determined using the lubrication state transition zone width parameter to connect the two models. The operating condition transient suppression factor of the original data points and the reciprocal of the prediction variance of the interpolation points are used as their respective fitting weights. A weighted fitting is performed on all data points including the original data points and the interpolation points to obtain the full-condition Stribek curve.

2. The method for online plotting of the Stribek curve of the engine friction pair under all operating conditions according to claim 1, characterized in that, The instantaneous Hercy number satisfies the following relationship: ; In the formula, Let be the instantaneous Hercy number at time i. Let be the real-time dynamic viscosity at time i, which is calculated based on the lubricating oil temperature using the Vogel viscosity-temperature formula. Let be the engine speed at time i. Let be the load at time i.

3. The method for online plotting of the Stribek curve of the engine friction pair under all operating conditions according to claim 1, characterized in that, The instantaneous friction coefficient satisfies the following relationship: ; In the formula, Let be the instantaneous friction coefficient at time i. Let be the frictional torque at time i. Let be the load at time i.

4. The method for online plotting of the Stribek curve of the engine friction pair under all operating conditions according to claim 1, characterized in that, The transient suppression factor for each data point is calculated based on the second time derivative of engine speed and load data, including: By performing second-order central difference calculations on time-series engine speed and load data, the second derivatives of speed and load at each data point are obtained; the degree of drastic change in operating conditions is calculated using the following formula: In the formula, As an indicator of the degree of drastic change in operating conditions, The second derivative of the rotational speed. The second derivative of the load; through the exponential decay function The transient suppression factor under operating conditions was calculated. ,in This is the preset attenuation coefficient.

5. The method for online plotting of the Stribek curve of the engine friction pair under all operating conditions according to claim 1, characterized in that, Based on the local radius of curvature of the data points in the friction coefficient-Hersey number coordinate system, spectral clustering analysis was used to divide the boundary lubrication zone, mixed lubrication zone, and hydrodynamic lubrication zone, including: Calculate the local radius of curvature of each data point in the friction coefficient-Hersey number coordinate system; construct a similarity matrix between data points based on the local radius of curvature; calculate the Laplacian matrix of the similarity matrix and perform eigenvalue decomposition on the Laplacian matrix, taking the eigenvectors corresponding to the first three smallest non-zero eigenvalues; use these three eigenvectors as new features, and use the k-means clustering algorithm to divide the data points into three categories: boundary lubrication, mixed lubrication, and hydrodynamic lubrication.

6. The method for online plotting of the Stribek curve of the engine friction pair under all operating conditions according to claim 5, characterized in that, The width parameter of the lubrication state transition zone is calculated based on the data point density at the boundary of the lubrication zone, including: Kernel density estimation is performed on the data points at the boundary between the mixed lubrication zone and the hydrodynamic lubrication zone to determine the instantaneous Hersey value corresponding to the intersection of the probability density function curves of the two lubrication zones. The instantaneous Hersey value is used as the conversion center, and the conversion width is determined according to the distribution characteristics of the data points at the boundary. The lubrication state conversion zone width parameter is defined by the conversion center and the conversion width.

7. The method for online plotting of the Stribek curve of the engine friction pair under all operating conditions according to claim 6, characterized in that, A Gaussian process regression model was used to interpolate data in the lubrication zone, including: The instantaneous Hersey number is used as the input to the Gaussian process regression model, and the instantaneous friction coefficient is used as the output. The radial basis function kernel is selected as the covariance function. In the lubrication zone where the number of data points is lower than the preset data volume threshold, several equally spaced instantaneous Hersey numbers are selected as new input points. The trained Gaussian process regression model is used to predict the corresponding instantaneous friction coefficient and prediction variance, thereby performing data interpolation.

8. The method for online plotting of the Stribek curve of the engine friction pair under all operating conditions according to claim 7, characterized in that, The smooth transition function is determined using the lubrication state transition zone width parameter to connect the two models, including: A hyperbolic tangent function is used as the smooth transition function. The center and width of this function are determined by the width parameter of the lubrication state transition zone, and they satisfy the following relationship: ; in, For smooth transition function, For the instantaneous Hercy number, It is the hyperbolic tangent function. As a conversion center, To convert the width.

9. The method for online plotting of the Stribek curve of the engine friction pair under all operating conditions according to claim 1, characterized in that, A weighted fit is performed on all data points, including both original and interpolated data points, including: Construct a weighted least squares fitting objective function that satisfies the following relationship: ； In the formula, for the th One original data point, For the transient suppression factor of the operating condition; for the first One interpolation point, It is equal to the reciprocal of the prediction variance; For the first The friction coefficient of each data point For the full-condition Stribek curve model, the instantaneous Hersey number The predicted value at the specified location; the model parameters are determined by minimizing the objective function.

10. An online mapping system for the full-condition Stribek curves of engine friction pairs, characterized in that, It includes a memory and a processor, wherein the memory stores computer program instructions, and when the computer program instructions are executed by the processor, the online measurement method for the full-condition Stribek curve of the engine friction pair as described in any one of claims 1-9 is implemented.

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