Physically data double-driven adaptive fusion method for tire longitudinal force estimation

Abstract

The application relates to a physical data double-driving adaptive fusion tire longitudinal force estimation method, and belongs to the technical field of vehicle dynamics modeling and tire force estimation. Tire state data is acquired and a data set is constructed, and the data set is divided into a training verification set, a weight calibration set, a test set and a generalization data set. A slip rate and a vertical load input data driving model and a relative slip speed and a vertical load input dynamic friction physical driving model are used to obtain two types of prediction values respectively. Then, the prediction errors of the two types of prediction values under different local working conditions are calculated based on the weight calibration data set, and a continuous error function is fitted. In the test stage, the fusion weight is adaptively calculated according to the inverse error principle, and weighted summation is performed to output the final estimated value. The method adaptively complements the local nonlinear fitting capability of the data driving model and the dynamic physical trend constraint of the dynamic friction physical driving model, effectively improving the estimation accuracy, stability and physical rationality of the tire longitudinal force in the whole working condition range.

Description

Technical Field

[0001] This application relates to the field of vehicle dynamics modeling and tire force estimation technology, and in particular to a method for estimating tire longitudinal force by dual-drive adaptive fusion of physical data. Background Technology

[0002] Tire longitudinal force is an important variable describing tire longitudinal slip behavior, directly affecting vehicle braking stability, traction control performance, and longitudinal motion control performance. Under high longitudinal slip ratio conditions such as emergency braking, the tire-road contact interface exhibits frictional hysteresis, stick-slip transition, and nonlinear decay after the peak value, causing the tire longitudinal force to show obvious nonlinear and time-varying characteristics.

[0003] Existing tire longitudinal force modeling methods mainly include empirical models, mechanistic models, and data-driven models. Empirical models, represented by the magic formula, can describe the steady-state relationship between tire longitudinal force and slip ratio; Dugoff models, brush models, and LuGre friction models describe tire forces from the perspective of tire contact and friction mechanisms; multilayer perceptrons, long short-term memory networks, and convolutional neural networks learn the nonlinear mapping relationship between input variables and tire forces through sample data.

[0004] Empirical and mechanistic models typically rely on fixed analytical structures, idealized contact assumptions, or pre-defined model parameters, making it difficult to fully describe the unsteady establishment process of tire longitudinal forces and their strong local nonlinear variations under high-slip emergency braking conditions. While purely data-driven models possess strong nonlinear fitting capabilities, they lack explicit physical mechanism constraints and are prone to predictive oscillations, peak shifts, and insufficient physical consistency when sample coverage is insufficient or operating conditions change.

[0005] Existing hybrid methods combining physical and data-driven models typically employ physical model residual compensation, physical constraint loss functions, or observer-assisted network training, resulting in coupling between the physical and data-driven models during the training phase. When the physical model contains parameter errors or structural biases, directly using it as training constraints may cause the data-driven model's predictions to tend towards the biased physical output. Furthermore, most existing hybrid tire force models use steady-state empirical models as physical priors, failing to adequately consider the dynamic friction establishment process under high-slip emergency braking conditions; fixed fusion weights also cannot adapt to changes in the predictive reliability of the two types of models within different slip ratios and vertical load regions.

[0006] Therefore, a method for predicting tire longitudinal force is needed that can leverage the roles of data-driven models and dynamic physical models respectively, and adaptively adjust the contribution ratio of the two types of prediction results based on the current tire operating conditions. Summary of the Invention

[0007] The embodiment of this application provides a tire longitudinal force estimation method based on dual-drive adaptive fusion of physical data, which can simultaneously describe the dynamic friction establishment process and local strong nonlinearity under high slip emergency braking conditions, solve the problem of insufficient physical consistency, and solve the problem that fixed fusion weights cannot adapt to changes in model prediction reliability within different slip ratios and vertical load regions.

[0008] To achieve the above objectives, this application provides a tire longitudinal force estimation method based on dual-drive adaptive fusion of physical data, comprising the following steps:

[0009] S100. Obtain tire status data, construct a straight-line emergency braking dataset, and divide the straight-line emergency braking dataset into a training and validation dataset, a weight calibration dataset, a test dataset, and a working condition generalization dataset.

[0010] S200, The tire slip ratio from the tire condition data... and vertical load As input, the improved artificial neural network is trained using the training and validation dataset. After training, the network parameters of the improved artificial data network are fixed, and the output data drives the prediction of longitudinal force.

[0011] S300: Using the relative slip velocity and vertical load in the tire condition data as input, the dynamic friction physical driving model with internal bristle deformation state is used to obtain the prediction of the physical driving longitudinal force.

[0012] S400: Input the independent calibration sets into the improved artificial neural network (i.e., the wavelet-KAN data-driven model and the dynamic friction physics-driven model with fixed parameters) and the dynamic friction physics-driven model (i.e., the LuGre dynamic friction physics-driven model), respectively, and calculate the local prediction error relative to the reference longitudinal force, and establish the data-driven continuous local error function and the physics-driven continuous local error function.

[0013] S500. Substitute the current slip ratio and current vertical load of the test sample into the data-driven continuous local error function and the physical-driven continuous local error function to obtain the data-driven estimation error and the physical-driven estimation error. Calculate the data-driven fusion weight and the physical-driven fusion weight according to the inverse error principle, and perform a weighted summation of the data-driven longitudinal force prediction and the physical-driven longitudinal force prediction to obtain the tire longitudinal force estimation result.

[0014] In some embodiments, the output function of the improved artificial neural network is:

[0015]

[0016] in, For tire slip ratio, For vertical loads, To improve the network parameters of artificial neural networks;

[0017] The output function of the dynamic tribological driving model is:

[0018]

[0019] in, The relative slip velocity, For vertical loads, These are the parameters of the dynamic friction physics driving model.

[0020] In some embodiments, the improved artificial neural network includes an input layer, two hidden layers, and an output layer. The input layer includes two nodes corresponding to the slip ratio and vertical load. Each hidden layer includes five nodes. The output layer includes one node corresponding to the prediction of the tire's longitudinal force. A univariate wavelet side function is configured between the layers. Each node in the two hidden layers and the output layer performs an addition operation. The univariate wavelet side function is:

[0021]

[0022] in, The coefficients of the linear residual term, For input variables, This represents the number of wavelet basis functions in a single-sided function. For the first The magnitude parameters of the wavelet basis functions, For the mother wavelet function, For the first Translation parameters of wavelet basis functions For the first The scaling parameters of the wavelet basis functions; the mother wavelet function is the second-order Gaussian derivative:

[0023]

[0024] in, This represents an exponential function with the natural constant e as its base.

[0025] In some embodiments, the dynamic tribological driving model is based on internal state variables. and relative slip velocity and the description of the Stribek friction function To update the internal bristle deformation state, the internal state equation is:

[0026]

[0027] The Stribek friction function is:

[0028]

[0029] in, For bristle stiffness, The coefficient of friction is Coulomb. The static friction coefficient is The critical velocity, The static friction coefficient is the velocity exponent. According to road adhesion coefficient set up.

[0030] In some embodiments, the dynamic friction physical driving model updates the internal state in a discrete-time manner, and the discrete state update formula is as follows:

[0031]

[0032] The derivative of the internal bristle deformation state is:

[0033]

[0034] The predicted longitudinal force driven by physics is:

[0035]

[0036] in, This is the bristle damping coefficient. The coefficient of viscous friction is... For the first The internal bristle deformation state at each sampling time This represents the internal bristle deformation state at the previous sampling time. For time step, It is a positive constant.

[0037] In some embodiments, establishing the continuous local error function includes: constructing a two-dimensional working space based on the absolute value of the slip ratio and the normalized vertical load; segmenting the two-dimensional working space along the slip ratio direction and uniformly dividing it along the vertical load direction to obtain multiple local regions. Calculate the mean square error of the data-driven longitudinal force prediction and the physical-driven longitudinal force prediction relative to the reference longitudinal force in each local region. The data-driven local mean square error and the physical-driven local mean square error are respectively:

[0038]

[0039]

[0040] in, For local areas The number of samples in The sample number. For data-driven models in the first Predicted longitudinal force values ​​for each sample. For the dynamic friction physical driving model in the first Predicted longitudinal force values ​​for each sample. For the first The true value of the reference longitudinal force for each sample;

[0041] Set a sample size threshold to include local areas. Number of samples When the number of samples in a local region is insufficient, it is merged with the adjacent local regions by comparing it with the sample size threshold.

[0042] In some embodiments, the data-driven continuous local error function and the physical drive continuous local error function They are represented as follows:

[0043]

[0044]

[0045] in, For tire slip ratio, , For vertical loads, the normalized vertical load is calculated using the maximum-minimum normalization method. Mapping vertical loads to a uniform scale ; , These are the minimum and maximum vertical loads in the calibration set, respectively. The fitting coefficients are the data-driven error function. These are the fitting coefficients for the physics-driven error function.

[0046] In some embodiments, the corresponding sample data drives the estimation error. and the corresponding physical driving estimation error under the sample They are respectively:

[0047]

[0048]

[0049] in, To avoid the fitted function having extremely small positive numbers that are not positive in the boundary region, For the first Data-driven model estimation error for each sample For the first Estimation error of the physics-driven model for each sample;

[0050] The data-driven fusion weight and the physical drive fusion weights They are respectively:

[0051]

[0052]

[0053] The final tire longitudinal force estimation result is as follows:

[0054]

[0055] in, To finally integrate the tire longitudinal force estimation results, The longitudinal force prediction value is output by the data-driven model. This represents the predicted longitudinal force output by the dynamic friction physics-driven model.

[0056] In some embodiments, for the road adhesion coefficient that was not involved in the improved artificial neural network training and local error function calibration Based on the calibrated low-adhesion road adhesion coefficient and high adhesion road adhesion coefficient Linear interpolation is performed on the corresponding continuous local error function to obtain the error function under the current attachment condition;

[0057] linear interpolation coefficients The calculation formula is as follows:

[0058]

[0059] Data-driven interpolation error function under current attachment conditions Interpolation error function with physical drive They are respectively:

[0060]

[0061]

[0062] in, For low-adhesion roads, the data-driven continuous local error function is... For physical driving continuous local error functions, and These are the data-driven continuous local error function and the physics-driven continuous local error function corresponding to high-adhesion roads, respectively.

[0063] This application has the following beneficial effects:

[0064] The tire longitudinal force estimation method based on dual-driven adaptive fusion of physical data in this application has strong local nonlinear expression capability: it adopts the Wavelet-KAN data-driven model and sets the wavelet function with local support and multi-scale expression capability as the network side function. It can perform local nonlinear fitting for the high curvature change near the peak value of the tire longitudinal force and the post-peak attenuation in the high slip region, thus improving the peak shift and prediction fluctuation problem caused by the insufficient expression of local features by the traditional global activation function.

[0065] Good consistency with dynamic physics: The LuGre dynamic friction physics driving model is introduced, which describes the dynamic friction establishment, stick-slip transition and speed-related friction changes during the tire-road contact process through the deformation state of the internal bristles. This provides dynamic physical trend constraints for tire longitudinal force estimation and enhances the physical rationality of the prediction results.

[0066] The fusion weights can change with the working conditions: the local prediction errors of the Wavelet-KAN data-driven model and the LuGre dynamic friction physics-driven model in different slip ratios and vertical load regions are statistically analyzed using an independent calibration set, and a continuous local error function is fitted. The fusion weights are calculated according to the inverse error principle based on the estimation errors of the two models under the current working conditions, so that the model with smaller prediction error can make a larger contribution and overcome the problem that fixed weights cannot adapt to different working conditions.

[0067] The model exhibits good robustness: Instead of directly using the LuGre dynamic friction physics-driven model as the training constraint for the Wavelet-KAN data-driven model, error-driven fusion is performed after the two models make independent predictions, reducing the impact of parameter errors or structural deviations of the LuGre dynamic friction physics-driven model on the training results of the Wavelet-KAN data-driven model; when the parameters of the LuGre dynamic friction physics-driven model are perturbed, the prediction error of the fused model changes more smoothly;

[0068] Strong adaptability across working conditions: For road adhesion conditions that have not participated in training and error function calibration, the model obtains the error estimate and fusion weight under the current working condition by linearly interpolating the continuous local error function under different adhesion conditions, so that the model can adapt to unseen load and slip combinations and intermediate road adhesion conditions.

[0069] The overall estimation performance is good: the data fitting ability of Wavelet-KAN is adaptively complemented by the dynamic trend constraints of the LuGre dynamic friction physics driving model. While improving the accuracy of tire longitudinal force estimation, it also improves the predictive stability in high slip regions, which can provide technical support for tire force estimation in vehicle braking control, longitudinal stability control and active safety systems.

[0070] Other features and advantages of this application will be described in detail in the following detailed description section. Attached Figure Description

[0071] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0072] To gain a more complete understanding of this application and its beneficial effects, the following description will be provided in conjunction with the accompanying drawings, wherein the same reference numerals in the following description denote the same parts.

[0073] Figure 1 This is a flowchart illustrating the overall process of a tire longitudinal force estimation method based on dual-drive adaptive fusion of physics and data, as provided in an embodiment of the present invention.

[0074] Figure 2 This is a schematic diagram of the CarSim emergency braking simulation dataset partitioning provided in an embodiment of the present invention;

[0075] Figure 3 This is a schematic diagram of the Wavelet-KAN data-driven model structure provided in an embodiment of the present invention;

[0076] Figure 4 A schematic diagram of the dynamic friction mechanism between LuGre tires and road surface and the Stribeck friction function provided in this embodiment of the invention;

[0077] Figure 5 This is a schematic diagram of the local prediction error and adaptive weight distribution of two types of models under different road surface adhesion conditions provided in an embodiment of the present invention;

[0078] Figure 6 This is a schematic diagram of the final fused longitudinal force estimation result and the working condition generalization result provided in the embodiments of the present invention. Detailed Implementation

[0079] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application.

[0080] In the description of this application, it should be understood that the terms "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "top," "bottom," "inner," and "outer," etc., indicating orientation or positional relationships based on the orientation or positional relationships shown in the accompanying drawings, are only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of this application. Unless otherwise expressly specified and limited, the terms "connected" and "linked" should be interpreted broadly. For example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection, an electrical connection, or a connection that allows communication; it can be a direct connection or an indirect connection through an intermediate medium; it can be a connection within two elements or an interaction relationship between two elements. For those skilled in the art, the specific meaning of the above terms in this application can be understood according to the specific circumstances. Furthermore, although the terms "first," "second," etc., may be used herein to describe various components, these components should not be limited by these terms. These terms are used to distinguish one component from another. Therefore, the first component discussed below may be referred to as the second component without departing from the teachings of this application. As used herein, the term "and / or" includes all combinations of any one and more of the associated listed items.

[0081] In the description of this application, "multiple" means two or more, and "at least one" means one, two, or more, unless otherwise explicitly specified. In the description of this application, "perpendicular" means completely perpendicular to 90° or nearly completely perpendicular, for example, an angle of 80° to 100° is considered perpendicular. Similarly, "parallel" means completely parallel or nearly completely parallel, for example, a perfectly parallel angle of 10° is considered parallel.

[0082] The following disclosure provides many different implementations or examples for carrying out different structures of this application. To simplify the disclosure of this application, the components and arrangements of specific examples are described below. Of course, these are merely examples and are not intended to limit this application.

[0083] Please see Figures 1 to 6This embodiment provides a tire longitudinal force estimation method based on dual-driven adaptive fusion of physical data. It obtains tire longitudinal force prediction results using both a Wavelet-KAN data-driven model and a LuGre dynamic friction physics-driven model. Then, it calculates adaptive fusion weights using the prediction errors of the two models under different local working conditions, outputting the final tire longitudinal force estimate. This embodiment of the physical data-driven adaptive fusion tire longitudinal force estimation method exhibits strong local nonlinearity expression capability: employing a Wavelet-KAN data-driven model, it sets wavelet functions with local support and multi-scale expression capabilities as network side functions. This enables local nonlinear fitting for high curvature changes near the peak value of the tire longitudinal force and post-peak attenuation in high slip regions, improving the peak shift and prediction fluctuation problems caused by insufficient local feature expression in traditional global activation functions.

[0084] The above-mentioned dual-drive adaptive fusion method for estimating tire longitudinal force based on physical data includes the following steps:

[0085] S100. Tire state data is obtained through the CarSim vehicle dynamics simulation platform to construct a straight-line emergency braking dataset, which is then divided into a training and validation dataset, a weight calibration dataset, a test dataset, and a working condition generalization dataset.

[0086] It should be noted that tire condition data includes vehicle longitudinal velocity, effective wheel radius, wheel angular velocity, tire slip ratio, vertical load, tire longitudinal force, wheel radius, road adhesion coefficient, relative slip velocity, and reference longitudinal force. The training and validation datasets are used to train the Wavelet-KAN data-driven model; the weight calibration dataset is used to statistically analyze the local prediction errors of the two models (Wavelet-KAN data-driven model and LuGre dynamic friction physics-driven model) under different operating conditions; the test dataset is used to evaluate the final fusion model; and the operating condition generalization dataset is used to evaluate the model's estimation performance under operating conditions that were not involved in training and weight calibration.

[0087] The straight-line emergency braking dataset is represented as follows:

[0088]

[0089] in, The reference longitudinal force output by the CarSim vehicle dynamics simulation platform.

[0090] S200, The tire slip ratio from the tire condition data... and vertical load As input, the improved artificial neural network is trained using the training and validation dataset. After training, the network parameters of the improved artificial data network are fixed, and the output data drives the prediction of longitudinal force.

[0091] Specifically, the improved artificial neural network is the Wavelet-KAN data-driven model. This incorporates tire slip ratio... and vertical load As input to the Wavelet-KAN data-driven model.

[0092] S300: Using the relative slip velocity and vertical load in the tire condition data as input, the dynamic friction physical driving model with internal bristle deformation state is used to obtain the prediction of the physical driving longitudinal force.

[0093] Specifically, the relative slip velocity between the tire and the road surface is calculated based on the vehicle's longitudinal velocity, wheel angular velocity, and wheel radius. The relative slip velocity and vertical load The input is a LuGre dynamic friction physics-driven model with internal brush deformation state, and the output is a prediction of the physical driving longitudinal force. That is, the dynamic physical consistency of this implementation scheme is good: the LuGre dynamic friction physics-driven model is introduced, and the dynamic friction establishment, stick-slip transition and velocity-related friction changes during the tire-road contact process are described by the internal brush deformation state, which provides dynamic physical trend constraints for tire longitudinal force estimation and enhances the physical rationality of the prediction results.

[0094] S400. Input the independent calibration sets into the improved artificial neural network (i.e., Wavelet-KAN data-driven model) and the dynamic friction physics-driven model (i.e., LuGre dynamic friction physics-driven model) with fixed parameters, respectively, and calculate the local prediction error relative to the reference longitudinal force, and establish the data-driven continuous local error function and the physics-driven continuous local error function.

[0095] Specifically, independent calibration sets are input into the Wavelet-KAN data-driven model and the LuGre dynamic friction physics-driven model with fixed parameters, respectively. The prediction results of the two models are compared with the CarSim reference longitudinal force. The prediction errors of the two models in local regions under different slip ratios and vertical loads are statistically analyzed, and the data-driven continuous local error function and the physics-driven continuous local error function are fitted respectively.

[0096] S500: Substitute the current slip ratio and current vertical load of the test sample into the data-driven continuous local error function and the physical-driven continuous local error function to obtain the data-driven estimation error and the physical-driven estimation error. Calculate the data-driven fusion weight and the physical-driven fusion weight according to the inverse error principle, and perform a weighted summation of the data-driven longitudinal force prediction and the physical-driven longitudinal force prediction to obtain the tire longitudinal force estimation result. That is, the fusion weight in this implementation scheme can change with the working condition: using an independent calibration set to statistically analyze the local prediction errors of the Wavelet-KAN data-driven model and the LuGre dynamic friction physical-driven model in different slip ratio and vertical load regions, and fitting the continuous local error function, the fusion weight is calculated according to the inverse error principle based on the estimation errors of the two models under the current working condition, so that the model with the smaller prediction error receives a larger contribution, overcoming the problem that fixed weights cannot adapt to different working conditions.

[0097] In other words, tire state data under emergency braking conditions is obtained through the CarSim vehicle dynamics simulation platform. This data is preprocessed to obtain a straight-line emergency braking dataset. This dataset is then divided into training and validation datasets, weight calibration datasets, test datasets, and generalization datasets. During model calculations, tire slip ratio... and vertical load Inputting the Wavelet-KAN data-driven model yields data-driven longitudinal force predictions and relative slip velocity. and vertical load Inputting the LuGre dynamic friction physics-driven model yields predicted values ​​of the physical driving longitudinal force. The prediction results of the two models in the weight calibration dataset are compared with the CarSim reference longitudinal force. Local mean square errors are calculated in different slip ratios and vertical load regions, and a continuous local error function is fitted. During the testing phase, adaptive fusion weights are calculated based on the estimation errors of the two models corresponding to the current working condition. The longitudinal force prediction results of the two models are then weighted and summed to obtain the final estimated tire longitudinal force value. The model exhibits good robustness: the LuGre dynamic friction physics-driven model is not directly used as a training constraint for the Wavelet-KAN data-driven model. Instead, error-driven fusion is performed after the two models make independent predictions, reducing the impact of parameter errors or structural deviations in the LuGre dynamic friction physics-driven model on the training results of the Wavelet-KAN data-driven model. When the parameters of the LuGre dynamic friction physics-driven model are disturbed, the prediction error of the fused model changes more smoothly.

[0098] It should be noted that the reference longitudinal force is used for Wavelet-KAN data-driven model training, local error calibration, and test performance evaluation. The input vector of the Wavelet-KAN data-driven model is:

[0099]

[0100] in, For tire slip ratio, This is a vertical load.

[0101] The output function of the improved artificial neural network described above, namely the longitudinal force prediction value driven by the output data of the Wavelet-KAN data-driven model:

[0102]

[0103] in, These are the network parameters for improving artificial neural networks, specifically the trainable parameters of the Wavelet-KAN data-driven model.

[0104] Specifically, Figure 2 This diagram illustrates the acquisition and dataset partitioning of emergency braking data provided in this embodiment of the invention. This embodiment uses the CarSim vehicle dynamics simulation platform to construct emergency braking simulation data. The simulated vehicle uses 205 / 55R16 tires, the sampling frequency is set to 100 Hz, the initial vehicle speed is set to 40 km / h, the tire inflation pressure is set to 230 kPa, the tire slip angle is set to 0, the peak road adhesion coefficients are set to 0.85 and 0.35 respectively, the vertical loads are set to 7 kN, 9 kN, and 11 kN respectively, and the longitudinal slip ratio range is set to [-1, 0].

[0105] To simulate an emergency braking process, a braking pressure ramp input is used. The braking pressure remains zero before braking begins, increases linearly to the maximum braking pressure after braking begins, and remains constant after reaching the maximum braking pressure. Its expression is:

[0106]

[0107] in, For simulation time, The moment when the braking pressure begins to increase. The moment when the braking pressure reaches its maximum value. This represents the maximum braking pressure. The CarSim vehicle dynamics simulation platform outputs the vehicle's longitudinal velocity. Wheel angular velocity Tire slip ratio Vertical load longitudinal force of tires Effective radius of wheels In addition to time-series data such as the road surface adhesion coefficient, the LuGre dynamic friction physics driving model calculates the relative slip velocity between the tire and the road surface based on the vehicle's longitudinal velocity, wheel angular velocity, and effective wheel radius.

[0108] .

[0109] In some embodiments, the improved artificial neural network (i.e., the Wavelet-KAN data-driven model) includes an input layer, two hidden layers (a first hidden layer and a second hidden layer, respectively), and an output layer. The input layer includes two nodes corresponding to slip ratio and vertical load, the first and second hidden layers each include five nodes, and the output layer includes one node corresponding to tire longitudinal force prediction, used to output the predicted tire longitudinal force value. The edges between layers are configured with learnable univariate wavelet side functions (i.e., the edges between the input layer and the first hidden layer, the first hidden layer and the second hidden layer, and the second hidden layer and the output layer are configured with learnable univariate wavelet side functions). Each node in the two hidden layers and the output layer performs addition operations (i.e., each node in the two hidden layers and the output layer acts as an independent computational unit, performing a summation operation on its received input signal). The side functions are in the form of a superposition of linear residual terms and multiple wavelet basis functions. The univariate wavelet side function (i.e., the side function of the Wavelet-KAN data-driven model) is:

[0110]

[0111] in, The coefficients of the linear residual term, For input variables, This represents the number of wavelet basis functions in a single-sided function. For the first The magnitude parameters of the wavelet basis functions, For the mother wavelet function, For the first Translation parameters of wavelet basis functions For the first The scaling parameters of the wavelet basis functions.

[0112] In this embodiment, the second-order Gaussian derivative is used as the mother wavelet function:

[0113]

[0114] in, This represents an exponential function with the natural constant e as its base.

[0115] Substituting the mother wavelet function into the side function, we obtain a univariate wavelet function based on the second derivative of Gauss, with the following expression:

[0116]

[0117] The linear residual term in the first part of the formula To preserve the linear trend of the input variables, it can effectively improve the predictive stability of the model in the low slip rate linear region; the wavelet terms in the latter half of the formula are obtained by superposition. Each with different translation parameters and scale parameters The wavelet basis function can adaptively form multi-scale local responses in different tire slip regions. The design of this wavelet edge function greatly enhances the ability of the improved artificial neural network to characterize complex dynamic features such as local high curvature abrupt changes in tire longitudinal force, peak nonlinearity, and high slip rate decay.

[0118] During training, the slip ratio and vertical load from the training and validation datasets are input into the Wavelet-KAN data-driven model, and the corresponding CarSim reference longitudinal force is used as the supervision output to update the side function parameters and network parameters in the Wavelet-KAN data-driven model. After training, fix it. The Wavelet-KAN data-driven model with fixed parameters is used for subsequent error calibration and testing. This implementation scheme has good overall estimation performance. It adaptively complements the data fitting capability of Wavelet-KAN with the dynamic trend constraints of the LuGre dynamic friction physics-driven model, improving the accuracy of tire longitudinal force estimation while enhancing the predictive stability in high slip regions. This provides technical support for tire force estimation in vehicle braking control, longitudinal stability control, and active safety systems.

[0119] Figure 4 This is a schematic diagram of the LuGre physics-driven model structure provided in an embodiment of the present invention. The input feature vector of the LuGre dynamic friction physics-driven model is:

[0120]

[0121] in, The relative slip speed between the tire and the road surface. The load is vertical. The LuGre dynamic friction physics driving model equates the microscopic contact relationship between the tire tread rubber and the road surface to a bristle system with elastic and damping characteristics. At low relative slip speeds, the bristle deformation is small; as the relative slip speed increases, the bristles gradually bend, and the friction level at the tire contact interface gradually transitions from static friction to Coulomb friction.

[0122] The LuGre dynamic tribology physics-driven model uses the Stribeck friction function to describe the change in friction level with relative slip velocity:

[0123]

[0124] in, The coefficient of friction is Coulomb. The static friction coefficient is This is the critical velocity (i.e., the Stribeck characteristic velocity). The velocity index (i.e., Stribeck index) is the coefficient of static friction. According to road adhesion coefficient set up.

[0125] The LuGre dynamic tribology physics-driven model is based on internal state variables. and relative slip velocity Update the internal bristle deformation state. The internal bristle deformation state of the LuGre dynamic friction physics-driven model is denoted as... Its continuity equation is:

[0126]

[0127] in, This represents the average deformation state of the internal bristles. This is the equivalent bristle stiffness.

[0128] Since CarSim simulation data is a discrete-time series, the LuGre dynamic friction physics driving model updates the internal state in a discrete-time form. The discrete state update formula is:

[0129]

[0130] in, For the first The internal bristle deformation state at each sampling time This represents the internal bristle deformation state at the previous sampling time. The sampling time interval, To prevent positive constants with a denominator of zero.

[0131] The derivative of the internal bristle deformation state is calculated using the finite difference method:

[0132] .

[0133] The above-mentioned predicted value of the physical driving longitudinal force consists of the bristle elastic deformation term, the bristle damping term, and the viscous friction term, specifically:

[0134]

[0135] in, This is the equivalent bristle damping coefficient. is the coefficient of viscous friction. In this embodiment, , , , , , , Static friction coefficient Based on the current road surface adhesion conditions, the Coulomb friction coefficient is set. Set it to a value lower than the static friction coefficient.

[0136] In some embodiments, a continuous local error function is established, that is, the local prediction errors of the two types of models are calculated based on the independent weight calibration dataset, and a continuous error function is fitted, specifically including:

[0137] A two-dimensional working space is constructed based on the absolute value of the slip ratio and the normalized vertical load;

[0138] The two-dimensional working space is segmented along the slip ratio direction and then uniformly divided along the vertical load direction to obtain multiple local regions. ;

[0139] Calculate the mean square error of the data-driven longitudinal force prediction and the physical-driven longitudinal force prediction relative to the reference longitudinal force in each local region.

[0140] Specifically, in the weight calibration process, the absolute slip ratio and normalized vertical load are defined, that is, the slip ratio and vertical load in the weight calibration dataset are processed:

[0141]

[0142]

[0143] in, , These are the minimum and maximum vertical loads in the calibration set, respectively.

[0144] The prediction residuals of the Wavelet-KAN data-driven model and the dynamic tribological physics-driven model relative to the reference longitudinal force are as follows:

[0145]

[0146]

[0147] in, For data-driven models in the first Prediction error on a single sample For the physics-driven model in the first Prediction error on a single sample For the first Each sample is a longitudinal force prediction value output by the physics-driven model. For the first The longitudinal force prediction value of each sample is output by the physics-driven model.

[0148] By directly calculating the absolute prediction deviation of the Wavelet-KAN data-driven model and the LuGre dynamic friction physics-driven model at each specific operating point, the most basic data source is provided for subsequently statistically analyzing the local MSE (Mean Square Error) of each local region in the two-dimensional working space. Based on this residual statistical data, this data-physics adaptive fusion method can fit a continuous local error function. Thus, in the final fusion stage, according to the local error performance of the Wavelet-KAN data-driven model and the LuGre dynamic friction physics-driven model under the current working condition, the prediction weights of the Wavelet-KAN data-driven model and the LuGre dynamic friction physics-driven model can be dynamically and adaptively allocated according to the inverse error principle.

[0149] The two-dimensional working space is divided into Local area (That is, dividing the area into multiple intervals along the direction of absolute slip ratio and uniformly dividing it along the direction of normalized vertical load to obtain multiple local working condition regions.) The mean square error in each local region (i.e., in the local operating condition region) Within the model, the local mean square errors of the Wavelet-KAN data-driven model and the LuGre dynamic tribology physics-driven model relative to the CarSim reference longitudinal force are as follows:

[0150]

[0151]

[0152] in, For local areas The number of samples in The sample number. For data-driven models in the first Predicted longitudinal force values ​​for each sample. For the dynamic friction physical driving model in the first Predicted longitudinal force values ​​for each sample. For the first The reference longitudinal force true value for each sample. A sample size threshold is set to select local areas. Number of samples When the number of samples in a local region is insufficient, it is merged with the adjacent local regions by comparing it with the sample size threshold.

[0153] Figure 5This invention provides local error functions and adaptive fusion weight distribution diagrams for high-adhesion and low-adhesion road surface conditions, as shown in embodiments of the present invention. Figure 5 In the middle, (a), (b), and (c) correspond to high-adhesion pavement conditions, and (d), (e), and (f) correspond to low-adhesion pavement conditions. Figure 5 (a) and (d) represent the local error surfaces of the Wavelet-KAN data-driven model under high and low adhesion road surface conditions, where... To determine the local mean square error of the longitudinal force of the Wavelet-KAN data-driven model relative to the CarSim reference, a continuous error function is fitted based on the discrete mean square error of each local region; this is known as the data-driven continuous local error function. and physical-driven continuous local error function They are represented as follows:

[0154]

[0155]

[0156] in, For tire slip ratio, , For vertical loads, the normalized vertical load is calculated using the maximum-minimum normalization method. Mapping vertical loads to a uniform scale ; , These are the minimum and maximum vertical loads in the calibration set, respectively. The fitting coefficients are the data-driven error function. These are the fitting coefficients for the physics-driven error function. For example... Figure 5 As shown, under high-adhesion road surface conditions, the prediction error of the Wavelet-KAN data-driven model generally increases with the increase of absolute slip ratio, and the error is more obvious in the high slip ratio and high vertical load regions; the LuGre dynamic friction physics-driven model has a larger error in the medium slip ratio region, but can provide better dynamic trend constraints in some low slip ratio and high slip ratio regions.

[0157] Under low-adhesion road surface conditions, the error functions of the two models exhibit similar trends, but the error amplitudes change. Therefore, the error functions can reflect the relative reliability of the two models in different local working condition regions. To avoid non-positive values ​​in the continuous error function at boundary regions, a lower error limit is set:

[0158]

[0159]

[0160] For data-driven estimation error, To estimate the error of the physics-driven model, To avoid the fitted function having extremely small positive numbers that are not positive in the boundary region;

[0161] Specifically, the data-driven estimation error corresponds to the sample. and the corresponding physical driving estimation error under the sample They are respectively:

[0162]

[0163]

[0164] in, To avoid the fitted function having extremely small positive numbers that are not positive in the boundary region, For the first Data-driven model estimation error for each sample For the first The estimation error of the physics-driven model under a sample.

[0165] During the testing phase, such as Figure 5 As shown in (c) and (f), the current slip ratio and vertical load are substituted into the continuous error function, and the fusion weights of the Wavelet-KAN data-driven model and the LuGre dynamic friction physics-driven model are calculated according to the inverse error principle. The data-driven fusion weights are... Physics-driven fusion weights They are respectively:

[0166]

[0167]

[0168] in, To fuse weights for data-driven models, Fuse weights for the physics-driven model, satisfying: When the estimation error of the Wavelet-KAN data-driven model under the current operating conditions is small, Increase; when the estimation error of the LuGre dynamic friction physics driving model under the current working condition is small. This increases the contribution ratio of the two models, thereby dynamically adjusting them according to the current operating conditions. Specifically, the data-driven fusion weight and the physics-driven fusion weight for the corresponding sample are as follows:

[0169]

[0170]

[0171] in, For the first Wavelet-KAN data from each sample drives the fusion weights. For the first LuGre dynamic friction physics-driven fusion weights for each sample For the first Wavelet-KAN data-driven model estimation error for each sample For the first Estimation error of the LuGre dynamic friction physical driving model for a sample.

[0172] The longitudinal force predictions from the Wavelet-KAN data-driven model and the LuGre dynamic friction physics-driven model are weighted and summed to output the final tire longitudinal force estimate.

[0173] The final estimated longitudinal force of the tire is:

[0174]

[0175] in, To finally integrate the tire longitudinal force estimation results, The longitudinal force predictions are output by the Wavelet-KAN data-driven model. The longitudinal force prediction is generated by the LuGre dynamic friction physics-driven model.

[0176] Specifically, the estimated final tire longitudinal force value for the corresponding sample is:

[0177]

[0178] in, For the first The final fused tire longitudinal force estimation results for each sample. For the first The longitudinal force prediction value output by the data-driven model for each sample. For the first The longitudinal force prediction values ​​of each sample, driven by the LuGre dynamic friction physics model.

[0179] Figure 6 This is a schematic diagram of the final fused longitudinal force estimation result and the working condition generalization result provided in the embodiments of the present invention. Figure 6 It can include prediction results for high-adhesion pavement, prediction results for low-adhesion pavement, and generalization results for intermediate adhesion conditions that were not involved in training and weight calibration.

[0180] Vertical loads of 7 kN, 9 kN, and 11 kN were tested under high-adhesion and low-adhesion road conditions, respectively. The test results show that the LuGre dynamic friction physics-driven model can describe the overall trend of tire longitudinal force variation with slip ratio, but it exhibits certain systematic errors in the region after the peak. The Wavelet-KAN data-driven model can track local nonlinear changes, but it shows some prediction fluctuations in the high slip ratio region. The fusion model in this embodiment combines the prediction results of both models, making the prediction curve closer to the CarSim reference longitudinal force.

[0181] In the Wavelet-KAN side function comparison experiment, the Wavelet-KAN data-driven model using the second-order Gaussian derivative wavelet side function had a root mean square error of 6.85 N and a mean absolute error of 2.84 N under the conditions of high adhesion road surface and 9 kN vertical load. The root mean square error in the high slip ratio region was 6.81 N.

[0182] Compared with the fixed-weight fusion method, this embodiment dynamically adjusts the fusion weights of the two models according to the error differences of the current local working conditions, and obtains lower prediction errors under different attachment conditions and vertical loads. The root mean square error is reduced by an average of about 12.4%, and the mean absolute error is reduced by an average of about 12.8%.

[0183] Compared with the Magic Formula and the Multilayer Perceptron model, the physical data dual-drive adaptive fusion method in this embodiment reduces the root mean square error by an average of about 69.2% to 70.3% under both high-adhesion and low-adhesion road surface conditions. This indicates that this embodiment can simultaneously utilize the nonlinear fitting capability of the Wavelet-KAN data-driven model and the dynamic trend constraint capability of the LuGre dynamic friction physical-driven model.

[0184] In some embodiments, for intermediate road surface adhesion conditions that are not involved in the training of the improved artificial neural network (i.e., the Wavelet-KAN data-driven model) and the calibration of the local error function, the adhesion coefficient of the low-adhesion road is determined based on the calibrated adhesion coefficient. and high adhesion road adhesion coefficient The corresponding continuous local error function is linearly interpolated to obtain the error function under the current attachment condition.

[0185] linear interpolation coefficients The calculation formula is as follows:

[0186]

[0187] Data-driven interpolation error function under current attachment conditions Interpolation error function with physical drive They are respectively:

[0188]

[0189]

[0190] in, For high-adhesion road surfaces, the adhesion coefficient, For low-adhesion road surfaces, the adhesion coefficient, The current road surface adhesion coefficient, For low-adhesion roads, the data-driven continuous local error function is... For physical driving continuous local error functions, and These are the data-driven and physics-driven continuous local error functions corresponding to high-adhesion roads, respectively. This implementation scheme exhibits strong cross-condition adaptability: for road adhesion conditions not involved in training and error function calibration, linear interpolation of the continuous local error functions under different adhesion conditions yields the error estimate and fusion weights for the current condition, enabling the model to adapt to unseen load and slip combinations and intermediate road adhesion conditions. In the generalization test under a working condition with an adhesion coefficient of 0.50, the root mean square error of the linear interpolation adaptive fusion model is 64.55 N, the mean absolute error is 56.93 N, the coefficient of determination is 0.9928, the root mean square error in the high slip ratio region is 64.07 N, and the peak longitudinal force error is 0.06%.

[0191] Through the above implementation methods, this invention enhances the expressive power of local nonlinear characteristics of tire longitudinal force by using the Wavelet-KAN data-driven model, describes the dynamic friction trend during the tire-road contact process by using the LuGre dynamic friction physics-driven model, and adaptively adjusts the fusion weights according to the local prediction errors of the two models under the current working conditions, thereby improving the accuracy, stability and physical rationality of tire longitudinal force estimation under emergency braking conditions.

[0192] In the above embodiments, the descriptions of each embodiment have different focuses. For parts not described in detail in a certain embodiment, please refer to the relevant descriptions in other embodiments.

[0193] The embodiments, implementation methods, and related technical features of this application can be combined and substituted for each other without conflict.

[0194] The above are merely preferred embodiments of this application and are not intended to limit this application in any way. Any simple modifications, equivalent changes, and alterations made to the above embodiments based on the technical essence of this application without departing from the scope of the technical solution of this application shall still fall within the scope of the technical solution of this application.

Claims

1. A method for estimating tire longitudinal force using dual-drive adaptive fusion of physical data, characterized in that, The method includes the following steps: S100. Obtain tire status data, construct a straight-line emergency braking dataset, and divide the straight-line emergency braking dataset into a training and validation dataset, a weight calibration dataset, a test dataset, and a working condition generalization dataset. S200. Using the tire slip ratio and vertical load from the tire condition data as input, train the improved artificial neural network using the training and validation dataset, and fix the network parameters of the improved artificial data network. S300: Using the relative slip velocity and vertical load in the tire condition data as input, the dynamic friction physical driving model with internal bristle deformation state is used to obtain the prediction of the physical driving longitudinal force. S400. Input the independent calibration sets into the improved artificial neural network and the dynamic friction physics driving model with fixed parameters respectively, and calculate the local prediction error relative to the reference longitudinal force respectively, and establish the data-driven continuous local error function and the physics-driven continuous local error function. S500. Substitute the current slip ratio and current vertical load of the test sample into the data-driven continuous local error function and the physical-driven continuous local error function to obtain the data-driven estimation error and the physical-driven estimation error. Calculate the data-driven fusion weight and the physical-driven fusion weight according to the inverse error principle, and perform a weighted summation of the data-driven longitudinal force prediction and the physical-driven longitudinal force prediction to obtain the tire longitudinal force estimation result.

2. The tire longitudinal force estimation method based on dual-drive adaptive fusion of physical data according to claim 1, characterized in that, The output function of the improved artificial neural network is: ； in, For tire slip ratio, For vertical loads, To improve the network parameters of artificial neural networks; The output function of the dynamic tribological driving model is: ； in, The relative slip velocity, For vertical loads, These are the parameters of the dynamic friction physics driving model.

3. The tire longitudinal force estimation method based on dual-drive adaptive fusion of physical data according to claim 2, characterized in that, The improved artificial neural network includes an input layer, two hidden layers, and an output layer. The input layer includes two nodes corresponding to the slip ratio and vertical load. Each hidden layer includes five nodes. The output layer includes one node corresponding to the prediction of the tire's longitudinal force. A univariate wavelet side function is configured between the layers. Each node in the two hidden layers and the output layer performs an addition operation. The univariate wavelet side function is: ； in, The coefficients of the linear residual term, For input variables, This represents the number of wavelet basis functions in a single-sided function. For the first The magnitude parameters of the wavelet basis functions, For the mother wavelet function, For the first Translation parameters of wavelet basis functions For the first The scaling parameters of the wavelet basis functions; the mother wavelet function is the second-order Gaussian derivative: ； in, This represents an exponential function with the natural constant e as its base.

4. The tire longitudinal force estimation method based on dual-drive adaptive fusion of physical data according to claim 3, characterized in that, The dynamic friction physical driving model is based on internal state variables. and relative slip velocity and the description of the Stribek friction function To update the internal bristle deformation state, the internal state equation is: ； The Stribek friction function is: ； in, For bristle stiffness, The coefficient of friction is Coulomb. The static friction coefficient is The critical velocity, The static friction coefficient is the velocity exponent. According to road adhesion coefficient set up.

5. The tire longitudinal force estimation method based on dual-drive adaptive fusion of physical data according to claim 4, characterized in that, The dynamic friction physical driving model updates its internal state in a discrete-time manner, and the discrete state update formula is as follows: ； The derivative of the internal bristle deformation state is: ； The predicted longitudinal force driven by physics is: ； in, This is the bristle damping coefficient. The coefficient of viscous friction is... For the first The internal bristle deformation state at each sampling time This represents the internal bristle deformation state at the previous sampling time. For time step, It is a positive constant.

6. The tire longitudinal force estimation method based on dual-drive adaptive fusion of physical data according to claim 4, characterized in that, Establishing the continuous local error function includes: A two-dimensional working space is constructed based on the absolute value of the slip ratio and the normalized vertical load; The two-dimensional working space is segmented along the slip ratio direction and then uniformly divided along the vertical load direction to obtain multiple local regions. ; Calculate the mean square error of the data-driven longitudinal force prediction and the physical-driven longitudinal force prediction relative to the reference longitudinal force in each local region; The data-driven local mean square error and the physics-driven local mean square error are respectively: ； ； in, For local areas The number of samples in The sample number. For data-driven models in the first Predicted longitudinal force values ​​for each sample. For the dynamic friction physical driving model in the first Predicted longitudinal force values ​​for each sample. For the first The true value of the reference longitudinal force for each sample; Set a sample size threshold to include local areas. Number of samples When the number of samples in a local region is insufficient, it is merged with the adjacent local regions by comparing it with the sample size threshold.

7. The tire longitudinal force estimation method based on dual-drive adaptive fusion of physical data according to claim 4, characterized in that, The data-driven continuous local error function and the physical drive continuous local error function They are represented as follows: ； ； in, For tire slip ratio, , For vertical loads, the normalized vertical load is calculated using the maximum-minimum normalization method. Mapping vertical loads to a uniform scale ; , These are the minimum and maximum vertical loads in the calibration set, respectively. The fitting coefficients are the data-driven error function. These are the fitting coefficients for the physics-driven error function.

8. The tire longitudinal force estimation method based on dual-drive adaptive fusion of physical data according to claim 7, characterized in that, Data-driven estimation error in corresponding samples and the corresponding physical driving estimation error under the sample They are respectively: ； ； in, To avoid the fitted function having extremely small positive numbers that are not positive in the boundary region, For the first Data-driven model estimation error for each sample For the first The estimation error of the physics-driven model under a single sample; The data-driven fusion weight and the physical drive fusion weights They are respectively: ； ； The final tire longitudinal force estimation result is as follows: ； in, To finally integrate the tire longitudinal force estimation results, The longitudinal force prediction value is output by the data-driven model. This represents the predicted longitudinal force output by the dynamic friction physics-driven model.

9. The tire longitudinal force estimation method based on dual-drive adaptive fusion of physical data according to claim 8, characterized in that, For road adhesion coefficients not involved in improved artificial neural network training and local error function calibration Based on the calibrated low-adhesion road adhesion coefficient and high adhesion road adhesion coefficient Linear interpolation is performed on the corresponding continuous local error function to obtain the error function under the current attachment condition; linear interpolation coefficients The calculation formula is as follows: ； Data-driven interpolation error function under current attachment conditions Interpolation error function with physical drive They are respectively: ； ； in, For low-adhesion roads, the data-driven continuous local error function is... For physical driving continuous local error functions, and These are the data-driven continuous local error function and the physics-driven continuous local error function corresponding to high-adhesion roads, respectively.

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