Road adhesion coefficient estimation algorithm considering tire modeling uncertainty

Abstract

The invention provides a road surface peak adhesion coefficient dynamic estimation algorithm considering tire modeling uncertainty so as to estimate a point estimation value and a confidence interval of a road surface adhesion coefficient at the same time. Comprising the following steps: S1, modeling a tire model and analyzing uncertainty; s2, analyzing the uncertainty propagation characteristics of the tire model; and S3, estimating the road adhesion coefficient considering the uncertainty of the tire model. Compared with the prior art, under the complex coupling excitation condition, compared with a traditional dynamic point estimation method, the method has better estimation accuracy and convergence speed, meanwhile, an effective confidence interval is provided, and multi-dimensional information reference is input for vehicle dynamic control.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of electric vehicle control, and particularly relates to a road adhesion coefficient dynamics estimation method considering tire modeling uncertainty. BACKGROUND

[0002] The tire is the only component of a vehicle in contact with the road, and accurate acquisition of the road adhesion coefficient is of great significance for improving vehicle safety and reducing energy consumption. The road adhesion coefficient directly represents the maximum adhesion force that the road can provide to the tire. In the active safety control system, the value directly determines the final control performance of the vehicle in the driving process. In addition, the road adhesion coefficient also plays a key role in the trajectory planning module of the automatic driving system. However, the road adhesion coefficient cannot be directly measured by sensors. Therefore, it is necessary to design an estimation method of the road adhesion coefficient based on easily measured dynamic information.

[0003] Existing road adhesion coefficient estimation methods can be divided into methods based on dynamic models and data-driven methods. However, the method based on the dynamic model is limited by the modeling accuracy, and the data-driven method is limited by the quality and scale of the training data and external environmental conditions. In addition, inaccurate road adhesion coefficient estimation results may cause the vehicle control system to misjudge the friction limit, thereby affecting the vehicle stability control, and therefore, quantifying the uncertainty of the road adhesion coefficient estimation result is crucial for providing multi-dimensional reference information for the control system. However, in the existing road adhesion coefficient estimation methods, the research on evaluating the uncertainty of the road adhesion coefficient estimation result is very limited.

[0004] The parameters appearing in the claims and their meanings are shown in the following table:

[0005]

[0006]

[0007] SUMMARY

[0008] The present application is a road adhesion coefficient estimation framework based on D-S evidence theory uncertainty modeling and propagation, which is proposed to overcome the defects of the prior art. The framework simultaneously outputs the road adhesion coefficient estimation result and the confidence interval to improve the credibility of the estimation system. By establishing the propagation mechanism of tire model uncertainty in the response function, the propagated uncertainty is effectively quantified. Combined with the dynamic road estimator, the effective confidence interval output is realized on the basis of the original "point" estimation, which provides multi-dimensional information reference for the dynamic control input.

[0009] The purpose of the application can be achieved by the following technical solutions: a road surface adhesion coefficient dynamics estimation method considering tire modeling uncertainty, comprising the following steps:

[0010] S1, tire model modeling and uncertainty analysis;

[0011] S2, tire model uncertainty propagation characteristic analysis;

[0012] S3, road surface adhesion coefficient estimation considering tire model uncertainty;

[0013] Further, the tire model modeling and uncertainty analysis in the S1 step is as follows:

[0014] S11: Use the tire to complete the tire test on the six-component test bench, collect the tire test data. And fit to get the MF (Magic Formula, MF) tire model.

[0015] S12: Traverse the tire test data, find the smallest confidence interval length δ ε , and quantitatively obtain the confidence interval of the random error ε1 of the fitted tire model as [-δ ε / 2, δ ε / 2].

[0016] S13: Using the test data obtained by S11, fit the simplified tire model y=f sim (x, τ).

[0017] S14: Quantitative analysis of the uncertainty of the parameter τ of the simplified tire model and compensate the system error.

[0018] Further, the specific process of step S14 is as follows:

[0019] Assume that the parameter τ obeys Gaussian distribution, and its confidence interval [τ min , τ max ] can be obtained by the following formula:

[0020]

[0021] Define ε2 as the error calculation between the MF tire model and the simplified tire model when calculating the road surface adhesion coefficient numerical solution θ * (f, x, y) using the tire model and input and output (x, y).

[0022] ε2(x, y) = θ * (f MF , x, y) - θ * [f sim (x, τ1), x, y]

[0023] The output of the simplified tire model is compensated by a look-up table to improve the accuracy of the road adhesion coefficient estimation.

[0024] Further, the tire model uncertainty propagation characteristics in the S2 step are analyzed as follows:

[0025] S21: Establish a tire model system response function and calculate the basic credibility distribution;

[0026] S22: Calculate the response function output;

[0027] Further, the specific process of step S21 is as follows:

[0028] The system containing the tire model is expressed in the form of the response function as follows:

[0029] y res =f res (x res ,u res )

[0030] Where y res is the system output, x res = τ1, u res = [x, y] T .

[0031] The basic credibility distribution (BPA) of each response function input x res,i on each focus element is calculated

[0032] Further, the specific process of step S22 is as follows:

[0033] Get the global confidence interval y res ∈ [y res,min , y res,max ] of the output response on all response focus elements:

[0034]

[0035] And estimate the probability distribution of the output response as follows:

[0036]

[0037] Take the expectation of the output response as the output value of the response function, as shown in the following formula.

[0038]

[0039] Furthermore, the road adhesion coefficient estimation analysis considering tire model uncertainties in step S3 is as follows:

[0040] S31: Based on the Burckhardt tire model and single-wheel dynamics model, design a longitudinal road adhesion coefficient estimator that considers the interconnected disturbance of tire longitudinal force and road adhesion coefficient, and quantifies and propagates tire model error.

[0041] S32: Design of lateral road adhesion coefficient based on Brush tire model and two-degree-of-freedom vehicle kinematics model, and lateral road adhesion coefficient estimator considering tire model error quantification and propagation;

[0042] S33: Design of a road adhesion coefficient estimator for longitudinal and lateral excitation coupling conditions, considering tire model error quantification and propagation:

[0043] Furthermore, the specific process of designing the longitudinal force and road adhesion coefficient interconnection perturbation based on the Burckhardt tire model and single-wheel dynamics model in step S31, and considering the quantification and propagation of tire model error, is as follows:

[0044] Establish a Burckhardt tire model. Establish a single-wheel dynamics model of the vehicle. Calculate the vertical loads on each wheel.

[0045] Based on the established tire model and single-wheel dynamics model, a disturbance estimator for the interconnected disturbance between tire longitudinal force and road adhesion coefficient is constructed:

[0046]

[0047] in, Here, y is the longitudinal force estimate, y is an intermediate variable within the estimator, K is the longitudinal force estimator gain, and f is the longitudinal force estimator gain. x For the improved Burckhardt tire model, This is an estimate of the road adhesion coefficient based on the longitudinal estimator. The fitting results for the tire model parameters, γ is the gain of the road adhesion coefficient estimator, θ x,* This is the numerical solution of the road adhesion coefficient calculated given the tire longitudinal slip model, slip ratio, and longitudinal tire force.

[0048] Normalizing the longitudinal force of the tire in the above formula using the vertical load, we get:

[0049]

[0050] in, To utilize the estimated adhesion coefficient, the derivative term of the slip ratio... It can be calculated using numerical differentiation algorithms such as Lagrange interpolation polynomials based on the slip ratio.

[0051] Based on the analysis in S21, the confidence interval [y] of the output response is calculated. resmin ,y resmax ], and the output value y of the response function. res,out .

[0052] Based on the estimator established above, a longitudinal road adhesion coefficient estimator considering tire model error quantization and propagation is calculated:

[0053]

[0054] Thus, the estimated value of the road surface adhesion coefficient is obtained. and confidence interval

[0055] Furthermore, the specific process of designing a lateral road adhesion coefficient estimator based on the Brush tire model and a two-degree-of-freedom vehicle kinematics model in step S32, and considering the quantization and propagation of tire model errors, is as follows:

[0056] A Brush model is established as a simplified tire model in the road adhesion coefficient estimator under lateral excitation.

[0057] A two-degree-of-freedom vehicle kinematic model was established, and the slip angle of each wheel was calculated.

[0058] The road adhesion coefficient estimator under lateral excitation is shown in the following formula.

[0059]

[0060] in, f is the estimated total lateral force for each tire. y For Brush tire model, This is an estimate of the road adhesion coefficient based on a lateral estimator. The fitting results for the tire model parameters,

[0061] ρ is the gain of the road adhesion coefficient estimator, θ y,* This is the numerical solution for the road adhesion coefficient calculated given a tire slip model, the slip angle of each wheel, the total lateral tire force, and the estimated total lateral tire force.

[0062] Based on the uncertainty propagation characteristics analysis of the S2 tire model, the response function is taken as follows:

[0063]

[0064] Based on the estimator established above, a lateral road adhesion coefficient estimator considering tire model error quantization and propagation is calculated:

[0065]

[0066] Thus, the estimated value of the road surface adhesion coefficient is obtained. and confidence interval

[0067] Furthermore, the road adhesion coefficient estimator designed in step S33, considering the longitudinal and lateral excitation coupling conditions and taking into account the quantification and propagation of tire model errors, is as follows:

[0068] Assuming the adhesion limits are equal under pure longitudinal and pure lateral conditions, the friction ellipse model is simplified to a friction circle model. Therefore, the relationship shown in the following equation can be established to correct the longitudinal and lateral adhesion limits under longitudinal-lateral coupled excitation conditions.

[0069]

[0070] Where θ is the road surface adhesion coefficient, θ x and θ y C1 and C2 are the longitudinal and lateral adhesion limits under longitudinal-lateral coupling excitation conditions, respectively, and are the longitudinal and lateral adhesion limit correction coefficients.

[0071] The road adhesion coefficient, considering the longitudinal and lateral excitation coupling condition, is estimated as follows:

[0072]

[0073] Where, θ dyn,* The result is a correction to the numerical solution of the road adhesion coefficient obtained from the longitudinal and lateral estimators, given the tire model, tire motion state, and tire force in one direction. Its confidence interval is [θ]. dyn,*,min ,θ dyn,*max ], K dyn For the estimator gain, This is a point estimate of the road adhesion coefficient based on dynamic information. and These represent the lower and upper bounds of the interval estimation of road adhesion coefficient based on dynamic information.

[0074] Compared with the prior art, the present invention has the following advantages:

[0075] I. This invention considers coupled excitation and proposes a pavement adhesion coefficient estimation framework based on uncertainty modeling and propagation using DS evidence theory. This framework simultaneously outputs the pavement adhesion coefficient estimation result and confidence interval to improve the reliability of the estimation system and provide multi-dimensional information reference for dynamic control input.

[0076] Second, this invention systematically analyzes and quantifies the modeling approximation uncertainty of the tire model. Based on DS evidence theory, a propagation mechanism of tire model uncertainty in the response function is established, effectively quantifying the propagation uncertainty. Attached Figure Description

[0077] Figure 1 This is a schematic diagram of the method flow of the present invention.

[0078] Figure 2 This is a technical roadmap of the present invention. Detailed Implementation

[0079] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0080] Examples

[0081] like Figure 1 As shown, a dynamic estimation algorithm for road adhesion coefficient considering tire modeling uncertainties is characterized by the following steps:

[0082] S1: Tire modeling and uncertainty analysis;

[0083] S2: Analysis of uncertainty propagation characteristics in tire models;

[0084] S3: Estimation of road adhesion coefficient considering tire model uncertainties.

[0085] This embodiment applies the above method, and the specific process includes:

[0086] I. Tire Modeling and Uncertainty Analysis

[0087] (1.1) Tire tests were conducted on a six-component force test bench. For the tire motion state x and tire force y, tire experimental data (x...) were collected under the condition of road adhesion coefficient θ0. i ,y i There are N0 groups in total. N0 = 10056. The MF tire model is fitted using the MATLAB Curve Fitting toolbox as y = f MF (x,τ0), where τ0 is the model parameter.

[0088] (1.2) Let the error of the tire experimental data be ε1, and assume that it follows a zero-mean Gaussian distribution. Based on the 3σ criterion, select a confidence level of α. conf =0.9974, and by iterating through the tire test data, the minimum confidence interval length δ is found. ε ,satisfy:

[0089]

[0090] The square brackets are Iverson brackets, indicating that the expression inside takes a value of 1 if it is true, and 0 otherwise. The confidence interval for the tire test data error ε1 is [-δ]. ε / 2,δ ε / 2].

[0091] (1.3) Using a similarity algorithm, tire working points (x) under different road surface adhesion coefficients are generated based on the results of the MF model. MF ,y MF ):

[0092]

[0093] For the tire motion state x in the N0 group tire test data i The tire operating points (x) under N1 different road surface adhesion coefficients were obtained respectively. MF ,y MF There are N = N0N1 groups in total, and N1 = 5 is selected. A simplified tire model y = f is fitted using the MATLAB Curve Fitting toolbox. sim (x,τ).

[0094] (1.4) Assume that the parameter follows a Gaussian distribution, and its confidence interval is [τ]. min ,τ max It can be obtained from the following formula:

[0095]

[0096] Where z represents the distribution of the model parameters τ and the given confidence level α. conf The parameters are determined under the given conditions, and z is a standard Gaussian distribution with (α) conf The +1) / 2 quantile can be obtained from a quantile table. Based on the 3σ criterion, a confidence level of α is selected. conf = 0.9974. The diag operation represents taking all the main diagonal elements of a matrix to form a vector, J f To fit the data (x) MF ,y MF The Jacobian matrix of the tire model parameter τ, ε MSE The mean square error can be obtained from the following formula:

[0097]

[0098] For ease of subsequent analysis, ε1 is treated as a new model parameter and incorporated into a simplified tire model:

[0099] f sim (x,τ1)=f sim (x,τ)+ε1

[0100] (1.5) Define ε2 as the numerical solution θ of the road adhesion coefficient calculated using the tire model and input / output (x,y). * When (f,x,y), the error between using the MF tire model and the simplified tire model is calculated.

[0101] ε2(x,y)=θ * (f MF ,x,y)-θ * [f sim (x,τ1),x,y]

[0102] The data is stored offline in the form of a lookup table. The output of the tire model is simplified by compensating for the lookup table, thereby improving the accuracy of the road adhesion coefficient estimation.

[0103] II. Analysis of Uncertainty Propagation Characteristics of Tire Model

[0104] (2.1) Truncation of probability density distribution of uncertainty parameters in tire model:

[0105] The system containing the tire model can be expressed as a response function in the following form:

[0106] y res =f res (x res ,u res )

[0107] Among them, y res For system output, x res =τ1,u res =[x,y] T Using the Dempster-Shafer Evidence Theory, we first examine the n-dimensional input x. res =[x res,1 ,x res,2 ,...,x res,n The corresponding confidence interval [x] res,min,i ,x res,max,i Constructing a recognition framework Θ(x) res ), and equally divided into N sub,i Each subinterval (i = 1, 2, ..., n) is used as the focal element E(x). i ∈[x min,sub,i (j),x max,sub,i (j)]), where x min,sub,i (j) and x max,sub,i (j) represents the input x of the i-th response function. res,i The lower and upper bounds of the j-th confidence subinterval, j = 1, 2, ..., N sub,i In [x] res,min,i ,xres,max,i The probability density distribution of each input is truncated, and a normalization algorithm is used to eliminate edge loss, as shown in the following formula, where N is taken as N. sub,i =4.

[0108]

[0109] Among them, f p,norm,i Input x to the normalized i-th response function res,i The probability density function, f p,i Input x to the i-th response function before normalization res,i The probability density function, based on the Gaussian distribution assumption mentioned above, is shown in the following equation.

[0110]

[0111] Where, μ i and σ i Let be the mean and variance of the Gaussian distribution, respectively. Based on the 3σ criterion used above, they can be calculated using the following formula:

[0112]

[0113] (2.2) Basic credibility allocation:

[0114] Using the normalized probability density distribution f p,norm,i Calculate the input x of each response function res,i The basic probability assignment (BPA) on each focal element is denoted as m. i (j)(i=1,2,...,n, j=1,2,...,N sub,i ), as shown in the following formula.

[0115]

[0116] For each response function input x res,i The corresponding coaxial elements establish a joint coaxial element E. k :

[0117] E k :=E(x res,1 ∈[x min,sub,1 (j1),x max,sub,1 (j1)]^...^x res,n ∈[x min,sub,k (j n ),x max,sub,k (j n )])

[0118]

[0119] Assuming that the parameters are independent of each other, then the joint focal element E k The BPA is:

[0120]

[0121] (2.3) Calculate the response function output:

[0122] For each joint focal element E k Extremum analysis was performed to obtain the output response y on the joint focal element. res The maximum and minimum values ​​are used to construct the response focal element E. y,k (y res ∈[y res,min (k),y res,max (k)]). To improve computational efficiency, where y res,min (k) and y res,max The value of (k) is approximated by the strategy shown in the following formula:

[0123]

[0124] The global confidence interval y of the output response on all response focal elements can be obtained. res ∈[y res,min ,y res,max ]:

[0125]

[0126] Apply steps s to the global confidence interval of the output response. y Perform a traversal, considering each value y res,l With all response focal elements E y,k The numerical relationship of all response focal elements E y,k Partitioning the set of focal elements that represent the trust function and the likelihood function and As shown in the following formula. Let s y This is 1 / 50 of the global confidence interval length of the output response.

[0127]

[0128] Based on the above division relationship, calculate the value y for each output response. res,l The corresponding cumulative trust function F Bel and cumulative likelihood function F Pl As shown in the following formula, the probability distribution of the output response is estimated.

[0129]

[0130] Estimate the probability distribution of the output response using the following formula.

[0131]

[0132] The expected output response is used as the output value of the response function, as shown in the following equation.

[0133]

[0134] III. Estimation of Road Adhesion Coefficient Considering Tire Model Uncertainties

[0135] (3.1) Design an interconnected disturbance estimator for tire longitudinal force and road adhesion coefficient based on the Burckhardt tire model and single-wheel dynamics model:

[0136] Establish an improved Burckhardt tire model:

[0137]

[0138] Where, μ x To utilize the adhesion coefficient, θ x denoted as the road surface adhesion coefficient, c1, c2, c3, and c4 are fitting parameters that affect the shape of the curve, and sgn is the sign function.

[0139] Establish a single-wheel dynamics model for the vehicle:

[0140] F x =μ x ·F z

[0141]

[0142] Among them, F z For vertical loads, the vertical loads on each wheel can be calculated using the following formula, ω and They are angular velocity and angular acceleration, respectively. ω Let T be the wheel's moment of inertia, T be the driving or braking torque at the wheel end, R be the wheel's effective rolling radius, and v be the moment of inertia. wc This represents the longitudinal velocity of the wheel's center.

[0143] Formulas for calculating the vertical load on each wheel:

[0144]

[0145] Among them, F z,fl ,F z,fr ,F z,rl ,F z,rr These represent the vertical loads on the left front wheel, right front wheel, left rear wheel, and right rear wheel of the vehicle, respectively; m is the total mass of the vehicle; g is the acceleration due to gravity; and l... f and l r These are the distances from the vehicle's center of gravity to the front and rear axles, respectively, where l is the wheelbase and a is the distance from the center of gravity to the front and rear axles, respectively.x and a y These represent the longitudinal and lateral accelerations of the vehicle, h, respectively. g b is the height of the vehicle's center of gravity. f and b r These refer to the front track and rear track of the vehicle, respectively.

[0146] Based on the established tire model and single-wheel dynamics model, a disturbance estimator for the interconnected disturbance between tire longitudinal force and road adhesion coefficient is constructed:

[0147]

[0148] in, Here, y is the longitudinal force estimate, y is an intermediate variable within the estimator, K is the longitudinal force estimator gain, and f is the longitudinal force estimator gain. x For the improved Burckhardt tire model, This is an estimate of the road adhesion coefficient based on the longitudinal estimator. The fitting results for the tire model parameters, γ is the gain of the road adhesion coefficient estimator, θ x,* This is the numerical solution of the road adhesion coefficient calculated given the tire longitudinal slip model, slip ratio, and longitudinal tire force.

[0149] Normalizing the longitudinal force of the tire in the above formula using the vertical load, we get:

[0150]

[0151] in, To utilize the estimated adhesion coefficient, the derivative term of the slip ratio... It can be calculated using numerical differentiation algorithms such as Lagrange interpolation polynomials based on the slip ratio.

[0152] (3.2) Design a longitudinal road adhesion coefficient estimator that considers tire model error quantification and propagation:

[0153] Based on the analysis in S21 and S22, the confidence interval y of the output response is calculated. res,1 ∈[y res,1,min ,y res,1,max ] and y res,2 ∈[y res,2,min ,y res,2，max ], and the output value of the response function. and

[0154] Combined with model simplification error ε 2,x ,get:

[0155]

[0156] Substituting the above equation back into the estimator established in S31, and taking γ = 5 and K = 5, we obtain the longitudinal road adhesion coefficient estimator considering tire model error quantization and propagation:

[0157]

[0158] Thus, the estimated value of the road surface adhesion coefficient is obtained. and confidence interval

[0159] (3.3) Design of a lateral road adhesion coefficient estimator based on the Brush tire model and a two-degree-of-freedom vehicle kinematic model:

[0160] The Brush model is selected as the simplified tire model in the road adhesion coefficient estimator under lateral excitation:

[0161]

[0162] Among them, F y Let sgn be the lateral force of the tire, α be the sign function, and θ be the tire slip angle. y F is the road surface adhesion coefficient. z θ is the vertical load, c is the tire lateral stiffness, and 3θ is the lateral load. y F z / c represents the tire slip angle saturation value α corresponding to the peak lateral force of the tire. sl .

[0163] A two-degree-of-freedom vehicle kinematic model was established, and the slip angles of each wheel were obtained as shown below:

[0164]

[0165]

[0166] In the formula, α fl ,α fr ,α rl ,α rr These are the tire slip angles for the left front wheel, right front wheel, left rear wheel, and right rear wheel of the vehicle, respectively. f and b r These represent the front and rear track widths of the vehicle, respectively, β is the sideslip angle, and l f and l r These are the distances from the vehicle's center of gravity to the front and rear axles, respectively. v is the yaw rate. x Let δ be the longitudinal velocity of the vehicle's center of gravity, and δ be the wheel steering angle.

[0167] The road adhesion coefficient estimator under lateral excitation is shown in the following formula.

[0168]

[0169] in, f is the estimated total lateral force for each tire. y For Brush tire model, This is an estimate of the road adhesion coefficient based on a lateral estimator. The fitting results for the tire model parameters, ρ is the gain of the road adhesion coefficient estimator, θ y,* This is the numerical solution for the road adhesion coefficient calculated given a tire slip model, the slip angle of each wheel, the total lateral tire force, and the estimated total lateral tire force.

[0170] (3.4) Design a lateral road adhesion coefficient estimator that considers the quantification and propagation of tire model errors:

[0171] Based on the uncertainty propagation characteristics analysis of the S2 tire model, the response function is taken as follows:

[0172]

[0173] The confidence interval [y] of the output response is calculated. res,3,min ,y res,3,max ], and the output value of the response function.

[0174] Combined with model simplification error ε 2,y ,get:

[0175]

[0176] Similar to the longitudinal estimator, in practical applications, different lateral estimator gains ρ can be tried from small to large and the estimation effect can be observed. Too small a gain ρ will cause the estimation result to converge too slowly, while too large a gain will cause the estimated value to oscillate. A trade-off should be made according to the actual needs.

[0177] Finally, substituting the above equation back into the estimator model for lateral excitation, and taking ρ = 5, we obtain:

[0178]

[0179] Thus, the estimated value of the road surface adhesion coefficient is obtained. and confidence interval

[0180] (3.5) Design a road adhesion coefficient estimator for longitudinal and lateral excitation coupling conditions:

[0181] Assuming that the adhesion limit is equal under pure longitudinal and pure lateral conditions, the friction ellipse model is simplified to a friction circle model.

[0182] Therefore, the relationship shown in the following equation can be established to correct the longitudinal and lateral adhesion limits under longitudinal-lateral coupling excitation conditions.

[0183]

[0184] Where θ is the road surface adhesion coefficient, θ x and θ y C1 and C2 are the longitudinal and lateral adhesion limits under longitudinal-lateral coupling excitation conditions, respectively, and are the longitudinal and lateral adhesion limit correction coefficients.

[0185] A strategy that uses tire slip ratio and tire slip angle to quantify longitudinal and lateral excitation levels, respectively:

[0186]

[0187] Where, σ x and σ y These are the theoretical sliding levels for the longitudinal and lateral directions, respectively. and These are the estimated values ​​of the adhesion limit correction coefficients for the longitudinal and lateral directions, respectively.

[0188] (3.6) Design a longitudinally coupled road adhesion coefficient estimator that considers tire model error quantization and propagation:

[0189] The pavement adhesion coefficient estimator considering the longitudinal and lateral excitation coupling condition is shown in the following equation:

[0190]

[0191] Where, θ dyn,* The result is a correction to the numerical solution of the road adhesion coefficient obtained from the longitudinal and lateral estimators, given the tire model, tire motion state, and tire force in one direction. Its confidence interval is [θ]. dyn,*,min ,θ dyn,*max ], K dyn For the estimator gain, This is a point estimate of the road adhesion coefficient based on dynamic information. and These represent the lower and upper bounds of the interval estimation of road adhesion coefficient based on dynamic information.

Claims

1. A dynamic estimation algorithm for road adhesion coefficient considering tire modeling uncertainties, characterized in that, Includes the following steps: S1: Tire modeling and uncertainty analysis; S2: Analysis of uncertainty propagation characteristics in tire models; S3: Estimation of road adhesion coefficient considering tire model uncertainties.

2. The dynamic estimation algorithm for road adhesion coefficient considering tire modeling uncertainty according to claim 1, characterized in that, Step S1 specifically includes the following steps: S11: Use tires to complete tire tests on a six-component force test bench, collect tire test data, and fit the MF (Magic Formula, MF) tire model; S12: Iterate through the tire test data to find the minimum confidence interval length δ. ε The confidence interval for the random error ε1 of the fitted tire model obtained by quantization is [-δ]. ε / 2,δ ε / 2]; S13: Using the tire test data obtained in S11, fit a simplified tire model y = f sim (x,τ); S14: Quantitatively analyze the uncertainty of parameter τ in the simplified tire model and compensate for system errors.

3. The dynamic estimation algorithm for road adhesion coefficient considering tire modeling uncertainty according to claim 2, characterized in that, Step S14 specifically includes the following steps: Assuming the parameter τ follows a Gaussian distribution, its confidence interval [τ] can be obtained according to the 3σ criterion. min ,τ max ]; Define ε2 as the numerical solution θ for calculating the road adhesion coefficient using a tire model and its corresponding input / output (x, y). * When (f,x,y), the error between using the MF tire model and the simplified tire model; ε2(x,y)=θ * (f MF ,x,y)-θ * [f sim (x,τ1),x,y] The data is stored offline in the form of a lookup table. The output of the tire model is simplified by compensating for the lookup table, thereby improving the accuracy of road surface adhesion coefficient estimation.

4. The dynamic estimation algorithm for road adhesion coefficient considering tire modeling uncertainty according to claim 1, characterized in that, Step S2 specifically includes the following steps: S21: Establish the response function of the tire model system and calculate the basic confidence level assignment; S22: Calculate the response function output.

5. The dynamic estimation algorithm for road adhesion coefficient considering tire modeling uncertainty according to claim 4, characterized in that, Step S21 specifically includes the following steps: The system containing the tire model can be expressed as a response function in the following form: y res =f res (x res ,u res ) Among them, y res For system output, x res =τ1,u res =[x,y] T ; Calculate each response function input x res,i Basic Probability Assignment (BPA) on each focal element 6. The dynamic estimation algorithm for road adhesion coefficient considering tire modeling uncertainty according to claim 4, characterized in that, Step S22 specifically includes the following steps: Obtain the global confidence interval y of the output response on all response focal elements. res ∈[y res,min ,y res,max ]: Output response value y res,l The corresponding cumulative trust function F Bel and cumulative likelihood function F Pl As shown in the following formula: in, and The set of focal elements representing the trust function and the likelihood function; And estimate the probability distribution of the output response using the following formula: The expected output response is taken as the output value of the response function, as shown in the following equation:

7. The dynamic estimation algorithm for road adhesion coefficient considering tire modeling uncertainty according to claim 1, characterized in that, Step S3 specifically includes the following steps: S31: Design a longitudinal road adhesion coefficient estimator based on the Burckhardt tire model and single-wheel dynamics model, considering tire model error quantification and propagation. S32: A lateral road adhesion coefficient estimator based on the Brush tire model and a two-degree-of-freedom vehicle kinematics model, considering the quantification and propagation of tire model errors; S33: Design of a road adhesion coefficient estimator based on a friction ellipse model, considering the quantification and propagation of tire model errors under longitudinal and lateral excitation coupling conditions.

8. The dynamic estimation algorithm for road adhesion coefficient considering tire modeling uncertainty according to claim 7, characterized in that, Step S31 specifically includes the following steps: Based on the established Burckhardt tire model and single-wheel dynamics model, an interconnected perturbation estimator for tire longitudinal force and road adhesion coefficient is constructed: in, Here, y is the longitudinal force estimate, y is an intermediate variable within the estimator, K is the longitudinal force estimator gain, and f is the longitudinal force estimator gain. x For the improved Burckhardt tire model, This is an estimate of the road adhesion coefficient based on the longitudinal estimator. The fitting results for the tire model parameters, γ is the gain of the road adhesion coefficient estimator. The numerical solution of the road adhesion coefficient is calculated given a tire longitudinal slip model, slip ratio, and longitudinal tire force. Normalizing the longitudinal force of the tire in the above formula using the vertical load, we get: in, To utilize the estimated adhesion coefficient, the derivative term of the slip ratio... It can be calculated using numerical differentiation algorithms such as Lagrange interpolation polynomials based on the slip ratio; Based on the analysis in S21, the confidence interval [y] of the output response is calculated. resmin ,y resmax ], and the output value y of the response function. res,out ; Based on the estimator established above, a longitudinal road adhesion coefficient estimator considering tire model error quantization and propagation is calculated: Thus, the estimated value of the road surface adhesion coefficient is obtained. and confidence interval 9. The dynamic estimation algorithm for road adhesion coefficient considering tire modeling uncertainty according to claim 7, characterized in that, Step S32 specifically includes the following steps: The road adhesion coefficient estimator based on the Brush model and a two-degree-of-freedom kinematic model is designed as follows: in, f is the estimated total lateral force for each tire. y For Brush tire model, This is an estimate of the road adhesion coefficient based on a lateral estimator. The fitting results for the tire model parameters, ρ is the gain of the road adhesion coefficient estimator. The numerical solution for the road adhesion coefficient is calculated given a tire slip model, the slip angle of each wheel, the total lateral tire force, and the estimated total lateral tire force. Based on the uncertainty propagation characteristics analysis of the S2 tire model, the response function is taken as follows: Based on the estimator established above, a lateral road adhesion coefficient estimator considering tire model error quantization and propagation is calculated: Thus, the estimated value of the road surface adhesion coefficient is obtained. and confidence interval 10. The dynamic estimation algorithm for road adhesion coefficient considering tire modeling uncertainty according to claim 7, characterized in that, Step S33 specifically includes the following steps: Assuming the adhesion limits are equal under pure longitudinal and pure lateral conditions, the friction ellipse model is simplified to a friction circle model. Therefore, the following relationship can be established to correct the longitudinal and lateral adhesion limits under longitudinal-lateral coupled excitation conditions: Where θ is the road surface adhesion coefficient, θ x and θ y C1 and C2 are the longitudinal and lateral adhesion limits under the longitudinal-lateral coupling excitation condition, respectively, and are the longitudinal and lateral adhesion limit correction coefficients. The road adhesion coefficient, considering the longitudinal and lateral excitation coupling condition, is estimated as follows: in, The confidence interval for the numerical solution of the road adhesion coefficient obtained from the longitudinal and lateral estimators, given the tire model, tire motion state, and tire force in one direction, is as follows: K dyn For the estimator gain, This is a point estimate of the road adhesion coefficient based on dynamic information. and These represent the lower and upper bounds of the interval estimation of road adhesion coefficient based on dynamic information.

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