Tire longitudinal force and lateral force prediction method based on vehicle state parameter estimation

Abstract

The invention discloses a tire longitudinal force and lateral force prediction method based on vehicle state parameter estimation, which adopts a seven-order spherical radius criterion to replace the original three-order spherical radial volume criterion on the basis of the traditional volume Kalman filter (CKF), and improves the estimation precision by optimizing sampling point distribution and weight configuration. And the stability of numerical calculation is ensured in combination with QR decomposition. A vehicle-mounted sensor is used for collecting real-time data such as a front wheel turning angle and longitudinal / lateral acceleration under a complex working condition, a time sequence feature set is built by combining longitudinal speed, lateral speed, a side slip angle and yaw velocity estimated by an algorithm, and meanwhile tire force calculated by a Dugoff tire model serves as target output. The TCN-GRU-based tire force prediction method is designed, the calculation complexity can be reduced while key time sequence information is kept, and the real-time prediction performance of the tire force is improved.

Description

Technical Field

[0001] The present invention belongs to the field of vehicle dynamics control, and in particular relates to a tire longitudinal force and lateral force prediction method based on vehicle state parameter estimation. Background Art

[0002] In the field of vehicle dynamics control, high-precision state parameter estimation and tire force prediction are core technologies for achieving intelligent chassis active safety control. Existing methods are primarily divided into two categories: physical model-based estimation algorithms and data-driven prediction methods. In the field of state estimation, the extended Kalman filter (EKF), unscented Kalman filter (UKF), cubic Kalman filter (CKF), and their improved algorithms are widely used for real-time estimation of key parameters such as vehicle center of mass slip angle and yaw rate. These methods improve estimation accuracy through nonlinear system modeling and multi-source sensor data fusion. In the field of tire force prediction, traditional methods rely on tire magic formulas or brushes to construct nonlinear mappings, combined with state observers to indirectly calculate longitudinal and lateral forces. Data-driven methods, however, such as deep learning models like long short-term memory networks (LSTMs) and convolutional neural networks (CNNs), use end-to-end training to directly learn tire force dynamic characteristics from historical driving data. Therefore, the combination of multi-sensor information fusion technology and time series neural networks further improves prediction robustness under complex driving conditions. Summary of the Invention

[0003] To solve the above technical problems, the present invention provides a tire longitudinal force and lateral force prediction method based on vehicle state parameter estimation, which improves the vehicle state parameter estimation accuracy and tire prediction accuracy.

[0004] The specific plan is as follows:

[0005] A tire longitudinal force and lateral force prediction method based on vehicle state parameter estimation includes the following steps:

[0006] S1: Using a permanent magnet synchronous motor (PMSM) as the hub motor of the vehicle, a distributed drive electric vehicle (DDEV) vehicle model is constructed based on the three-degree-of-freedom vehicle dynamics model. The distributed drive electric vehicle (DDEV) vehicle model collects the front wheel angle δ and wheel speed ω based on the on-board sensors. ij , longitudinal acceleration a x , lateral acceleration a y , driving torque T dij And the braking torque T bij ;

[0007] S2: The three-degree-of-freedom vehicle dynamics model is discretized using the forward Euler discretization method, and the system state is determined to be the longitudinal velocity, the sideslip angle of the center of mass, and the yaw rate; the system input is the front wheel angle δ, the longitudinal acceleration a x, the system observation is the lateral acceleration a y ;

[0008] S3: Based on the seventh-order spherical radius criterion, a nonlinear filtering strategy is designed to optimize the sampling points and weights of the cubature Kalman filter (CKF) algorithm. By integrating the square root filter architecture of QR decomposition, a square root seventh-order cubature Kalman filter (SR7thCKF) algorithm is constructed. Based on the discrete three-degree-of-freedom vehicle dynamics model, the front wheel angle δ, longitudinal acceleration a x , lateral acceleration a y As the input of the square root seventh-order cubic Kalman filter (SR7thCKF) algorithm, the longitudinal velocity v of the distributed drive electric vehicle (DDEV) vehicle model in complex working conditions such as double lane change, serpentine and step is estimated in real time. x , lateral speed v y , sideslip angle β and yaw rate r;

[0009] S4: The estimated value of the vehicle state parameters is compared with the front wheel angle δ and longitudinal acceleration a measured by the onboard sensor. x , lateral acceleration a y The information is used as the time series feature of the predicted tire force, which includes the tire longitudinal force F xij and tire lateral force F yij Due to the lack of tire force sensors, the Dugoff model is used to calculate tire forces based on estimated vehicle state parameters and sensor information, thereby constructing a tire force prediction dataset covering multiple working conditions.

[0010] S5: The dataset was divided into training and test sets at a ratio of 70% and 30%, respectively. The vehicle state parameter estimates and the time series obtained by on-board sensors were used as input, and tire force was used as output. A tire force prediction method based on the TCN-GRU model was designed. The temporal convolutional network (TCN) expanded the time series receptive field through layered and stacked dilated convolutional layers to capture the short-term fluctuations and long-term trend characteristics of tire force. The gated recurrent unit (GRU) used update gates and reset gates to dynamically adjust the weights of historical information to model the temporal dependencies of tire force under multiple working conditions. By combining the temporal feature extraction capability of TCN and the sequence modeling capability of GRU, the prediction accuracy of tire force was improved.

[0011] In S1, the method for constructing the distributed drive electric vehicle (DDEV) vehicle model is as follows:

[0012] Considering the three-degree-of-freedom vehicle dynamics model with tire cornering stiffness,

[0013]

[0014] Where: m is the total mass of the vehicle, vx is the longitudinal velocity; v y is the lateral velocity; β is the sideslip angle of the center of mass; a x is the longitudinal acceleration; a y is the lateral acceleration; r is the yaw angular velocity; I z is the moment of inertia around the z axis; δ is the front wheel angle; L f and L r Represents the distance from the center of mass to the front axle and rear axle respectively; C yf is the front wheel cornering stiffness; C yr is the rear wheel cornering stiffness;

[0015] The permanent magnet synchronous motor (PMSM) is integrated with the vehicle system. In this configuration, the PMSM model is directly connected to the wheels through the electronic control system. The wheel speed output by the vehicle dynamics model serves as the target speed of the wheel hub motor. The mathematical model of the PMSM is:

[0016]

[0017] Where: i α and i β is the current component of the stator winding in the stationary coordinate system; u α and u β is the voltage component of the stator winding in the stationary coordinate system; R s and L s are resistance and inductance respectively; ψ f is the magnetic linkage; ω m is the mechanical angular velocity of the rotor; θ e is the rotor position; p n is the number of pole pairs; J is the moment of inertia; B is the damping coefficient; T e is the electromagnetic torque; T L is the load torque.

[0018] The discrete three-degree-of-freedom vehicle dynamics model in S2 is as follows

[0019] The state equation is:

[0020]

[0021] The observation equation is:

[0022]

[0023] Among them, the system state is x t =[r t β t v x,t ] T ; System input is u t =[δt a x,t ] T ; System observation is z t =[a y,t ] T

[0024] r t is the yaw angular velocity at time t, r t-1 is the yaw angular velocity value at time t-1,

[0025] β t is the sideslip angle of the center of mass at time t, β t-1 is the sideslip angle value of the center of mass at time t-1,

[0026] v x,t is the longitudinal velocity value at time t, v x,t-1 is the longitudinal velocity value at time t-1,

[0027] δ t is the front wheel turning angle at time t, δ t-1 is the front wheel steering angle at time t-1,

[0028] a x.t is the longitudinal acceleration value at time t, a x,t-1 is the longitudinal acceleration value at time t-1,

[0029] a y,t is the lateral acceleration value at time t, T s is the sampling time;

[0030] x t is the system state matrix, u t System input matrix, z t System observation matrix.

[0031] The square root seventh-order cubic Kalman filter (SR7thCKF) algorithm used in S3 to estimate vehicle state parameters is:

[0032] For the discrete three-degree-of-freedom vehicle dynamics model, it can be written as an n-order system with additive noise:

[0033]

[0034] Where: u t is the input value of the system at time t; x t is the state value at time t; z t is the observed value at time t;

[0035] f is the state equation; h is the measurement function; w t is the process noise, describing the uncertainty in the state equation; v tis the measurement noise, which describes the uncertainty of sensor measurement; w t With v t are independent Gaussian white noises with zero mean, that is, w t ~N(0,Q t ), v t ~N(0,R t );

[0036] Approximate the standard Gaussian weighted integral as:

[0037]

[0038] Where x is the independent variable; f(x) is the function of the independent variable x; I(f) is the integral functional result of the function f(x); ω i is the weight coefficient in numerical integration; ξ i is the sampling point;

[0039] Based on the seventh-order spherical radius criterion, the sampling points and weights corresponding to the SR7thCKF algorithm are:

[0040]

[0041] Among them: the sampling methods are H1, H2, and H3 sampling; A, B, C, D, E, F, and G represent the weight coefficients of the corresponding sampling points respectively;

[0042] The above is the result of allocating sampling points and weights according to the seventh-order spherical radius criterion. The subsequent steps are as follows:

[0043] Determine the number of volume points γ:

[0044] γ=(8 / 3)n(n-1)(n-2)+8n 2 -4n+1 (9)

[0045] Calculate volume points

[0046]

[0047] in: and S t-1|t-1 are the state estimate and square root error covariance matrix of the previous moment respectively.

[0048] Calculate volume points propagated through the equation of state

[0049]

[0050] Calculate state prediction value

[0051]

[0052] Calculate the square root error covariance matrix predicted value S t|t-1 :

[0053] S t|t-1 =qr([X t|t-1 ,chol(Q t-1 )]) (13)

[0054]

[0055] Where: qr represents QR decomposition operation; Q t-1 is the state noise covariance matrix;

[0056] Calculate the updated volume point X i,t|t-1 :

[0057]

[0058] Calculate the volume point Z propagated through the measurement equation i,t|t-1 :

[0059] Z i,t|t-1 =h(X i,t|t-1 ,u t )(16)

[0060] Calculate measurement prediction value

[0061]

[0062] Calculate the cross-covariance matrix P xz,t|t-1 :

[0063]

[0064] Calculate the square root measurement error covariance matrix S zz,t|t-1 :

[0065] S zz,t|t-1 =qr([Z t|t-1 ,chol(R t )]) (19)

[0066] in:

[0067]

[0068] Where: R t is the measurement noise covariance matrix;

[0069] Calculate the Kalman filter gain K t :

[0070]

[0071] Calculate state estimates

[0072]

[0073] Calculate the square root error covariance matrix S t|t :

[0074] S t|t =qr([X t|t-1 -K t Z t|t-1 ,K t chol(R t )]) (twenty three)

[0075] The tire force calculation formula of the Dugoff model in S4 is:

[0076]

[0077] in:

[0078]

[0079] Where: C xij and C yij are the longitudinal slip stiffness and lateral stiffness of the four tires respectively; μ ij is the road adhesion coefficient; α ij is the tire slip angle; ij is the slip rate; v ij is the wheel center speed; F zij is the tire vertical force; ε is the speed influence factor; L is the intermediate calculation variable; F xij is the longitudinal force on the tire, F yij is the lateral force on the tire;

[0080] The formula for calculating tire slip angle is:

[0081]

[0082] Where: t f is the front axle track; t r is the rear axle track; α fl,fr is the sideslip angle of the left and right front wheels; α rl,rr is the sideslip angle of the left and right rear wheels;

[0083] The formula for calculating the vertical force of the tire is:

[0084]

[0085] h gis the height of the vehicle's center of mass, F zfl,zfr is the vertical force on the left and right front wheels; F zrl,zrr is the vertical force on the left and right rear wheels;

[0086] The slip rate calculation formula is:

[0087]

[0088] R ω is the wheel rotation radius, ω ij is the wheel rotation angular velocity;

[0089] The time series features of the input to the TCN-GRU model used to predict tire force in S5 are {δ,a x ,a y ,v x ,v y ,β,r}, the output is {F xij ,F yij}; Among them, the TCN model includes the following modules:

[0090] (1) Causal convolution: ensures that the current output of the time series depends only on the current and past inputs without utilizing future information, thus adhering to causal relationships;

[0091] (2) Dilated convolution: A dilation factor (d = 1, 2, 4, 8) is introduced into the convolution kernel, which gradually increases between layers. Without increasing the network depth or kernel size, the receptive field is expanded to capture long-term dependencies. The calculation formula is:

[0092]

[0093] Where: F(t) is the convolution output at the current time t; x is the input time series; f is the convolution kernel; k is the size of the convolution kernel; d is the dilation factor;

[0094] (3) Residual connection: Each residual block contains two dilated causal convolutions, with weight normalization, ReLU activation, and Dropout added in between. The output of the residual connection is the result of the convolution plus the input. When the result of the convolution is inconsistent with the input dimension, the input dimension can be adjusted through 1*1 convolution.

[0095] The output features of TCN are used as the input of GRU. For each time step, GRU updates the hidden state h t The calculation formula is:

[0096] r t =σ(W r ·x t +U r ·h t-1 ) (31)

[0097] z t =σ(W z ·x t +U z ·h t-1 ) (32)

[0098]

[0099] Among them, x t represents the input at time step t; r t Represents the reset gate; z t represents the update gate; W h Represents the weight matrix associated with the candidate hidden state; W z Represents the weight matrix associated with the update gate; W r Represents the weight matrix associated with the reset gate; U h 、U z 、U r represents the corresponding weight matrix; represents the candidate hidden state; h t-1 represents the hidden state at time step t-1; σ represents the sigmoid function;

[0100] In the constructed TCN-GRU model, TCN is used to extract the temporal features of the input data, followed by sequence modeling through GRU, and finally the fully connected layer integrates the information extracted by the previous layers to map the intermediate features of the model to the final output dimension.

[0101] The tire longitudinal force and lateral force prediction method based on vehicle state parameter estimation has the following advantages compared with the prior art:

[0102] This method enables real-time prediction of tire longitudinal and lateral forces while improving the accuracy of vehicle state parameter estimation. First, to improve the estimation accuracy of vehicle state parameters, a vehicle state parameter estimation method based on the SR7thCKF algorithm is designed. This method replaces the third-order spherical radial volume criterion with a seventh-order spherical radius criterion based on the CKF algorithm. This method improves filtering accuracy by redistributing sampling points and weights, and integrates QR decomposition to enhance the numerical stability of the filtering process. Then, a dataset is constructed using the front wheel angle, longitudinal acceleration, and lateral acceleration measured by on-board sensors under complex driving conditions, including double lane changes, serpentines, and steps, as well as the estimated longitudinal velocity, lateral velocity, center of mass slip angle, and yaw rate. The tire forces calculated using the Dugoff model serve as the prediction output. Finally, the dataset is partitioned into training and test sets with a 70% / 30% split. A tire force prediction method based on the TCN-GRU model is designed. This method first uses a TCN to extract local features from the time series and then expands the receptive field through dilated convolution to effectively extract long-term dependencies. The temporal features extracted by TCN are used as the input of GRU to model the global temporal dependency, which reduces the computational complexity while retaining the key time series information, thereby significantly improving the real-time performance of the model. BRIEF DESCRIPTION OF THE DRAWINGS

[0103] Figure 1 2 is a structural diagram of a tire longitudinal force and lateral force prediction method based on vehicle state parameter estimation in an embodiment of the present invention.

[0104] Figure 2 2 is a structural diagram of a three-degree-of-freedom vehicle dynamics model in an embodiment of the present invention.

[0105] Figure 3 This is a structural diagram of a PMSM-based distributed drive electric vehicle model in an embodiment of the present invention.

[0106] Figure 4 The vehicle state parameter v is based on the experimental serpentine working condition in the embodiment of the present invention. x and v y Estimate the contrast curve.

[0107] Figure 5 3 is an estimation comparison curve of the vehicle state parameters β and r under the serpentine working condition based on experiments in an embodiment of the present invention.

[0108] Figure 6 This is a comparison curve of the left front wheel tire force prediction under serpentine working conditions based on experiments in an embodiment of the present invention. DETAILED DESCRIPTION

[0109] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the implementation of the present invention, not the entire implementation. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making any creative efforts are within the scope of protection of the present invention.

[0110] The present invention aims to design a tire longitudinal force and lateral force prediction method based on vehicle state parameter estimation, so as to improve the accuracy of vehicle state parameter estimation while reducing the cost of on-board sensors, and to design a data-driven model that can predict tire forces based on the combination of sensor data and vehicle state parameter estimates.

[0111] Figure 1 This is a flowchart of a tire longitudinal force and lateral force prediction method based on vehicle state parameter estimation, including the construction of a DDEV vehicle model, a vehicle state parameter estimation method based on SR7thCKF, and a tire force prediction method based on the TCN-GRU model. The specific steps are as follows:

[0112] S1: Using a permanent magnet synchronous motor (PMSM) as the hub motor of the vehicle, a distributed drive electric vehicle (DDEV) vehicle model is constructed based on the three-degree-of-freedom vehicle dynamics model. The distributed drive electric vehicle (DDEV) vehicle model collects the front wheel angle δ and wheel speed ω based on the on-board sensors. ij , longitudinal acceleration a x , lateral acceleration a y , driving torque T dij And the braking torque T bij ;

[0113] The DDEV vehicle model is constructed as follows:

[0114] Figure 2 It is the structural diagram of the three-degree-of-freedom vehicle dynamics model, and its dynamic model is:

[0115] Vertical:

[0116]

[0117] Lateral:

[0118]

[0119] Yaw:

[0120]

[0121] The longitudinal and lateral accelerations are:

[0122]

[0123] The wheel dynamics equation is:

[0124]

[0125] Where: m is the total mass of the vehicle, v x is the longitudinal velocity; v y is the lateral velocity; a x is the longitudinal acceleration; a y is the lateral acceleration; r is the yaw angular velocity; I z is the moment of inertia around the z axis; I ω is the moment of inertia of the tire; δ is the front wheel angle; t f is the front axle track; t r is the rear axle track; R ω is the wheel rotation radius; L f and L r Represents the distance from the center of mass to the front axle and rear axle respectively; T dij and T bij Represents tire driving torque and braking torque respectively; F xij and F yij Respectively represent the longitudinal force and lateral force on the tire; ω ij Wheel rotation angular velocity; fl, fr, rl, rr represent the left front wheel, right front wheel, left rear wheel, and right rear wheel respectively.

[0126] The three-degree-of-freedom vehicle dynamics model with tire cornering stiffness is:

[0127]

[0128] Where: β is the sideslip angle of the center of mass; C yf is the front wheel cornering stiffness; C yr is the rear wheel cornering stiffness; is the derivative value of the yaw rate; is the derivative value of the sideslip angle of the center of mass; is the derivative value of the longitudinal velocity;

[0129] The permanent magnet synchronous motor (PMSM) is integrated with the vehicle system. In this configuration, the PMSM model is directly connected to the wheels through the electronic control system. The wheel speed output by the vehicle dynamics model serves as the target speed of the wheel hub motor. The mathematical model of the PMSM is:

[0130]

[0131] Where: i α and i β is the current component of the stator winding in the stationary coordinate system; u αand u β is the voltage component of the stator winding in the stationary coordinate system; R s and L s are resistance and inductance respectively; ψ f is the magnetic linkage; ω m is the mechanical angular velocity of the rotor; θ e is the rotor position; p n is the number of pole pairs; J is the moment of inertia; B is the damping coefficient; T e is the electromagnetic torque; T L is the load torque.

[0132] Figure 3 This is a structural diagram of a PMSM-based distributed drive electric vehicle model. This model builds a heterogeneous simulation platform based on the Matlab / Simulink PMSM model and the CarSim vehicle dynamics model, enabling powertrain system reconstruction through a co-simulation interface. First, the CarSim native powertrain chain is decoupled, and an external permanent magnet synchronous electric drive unit replaces the traditional internal combustion engine drive module. An electromechanical coupling interface between the in-wheel motor and the suspension system is established. A real-time data exchange protocol is then deployed, enabling autonomous operation of the in-wheel electric drive system within a hardware-in-the-loop (HIL) architecture. In this configuration, the PMSM forms a direct torque transfer path with the wheels via a vector control unit. The wheel angular velocity output by the vehicle dynamics model serves as the target value and is fed into the motor controller. A PID control strategy tuned based on frequency-domain analysis is then employed to achieve dynamic compensation of the drive torque, ultimately completing speed tracking and load disturbance suppression for the electric drive system.

[0133] S2: The three-degree-of-freedom vehicle dynamics model is discretized using the forward Euler discretization method, and the system state is determined to be the longitudinal velocity, the sideslip angle of the center of mass, and the yaw rate; the system input is the front wheel angle δ, the longitudinal acceleration a x , the system observation is the lateral acceleration a y ;

[0134] The forward Euler discretization method is used to discretize the three-degree-of-freedom vehicle dynamics model:

[0135] The state equation is:

[0136]

[0137] The observation equation is:

[0138]

[0139] Where: the system state is x t =[r t β t v x,t ] T ; System input is ut =[δ t a x,t ] T ; System observation is z t =[a y,t ] T .

[0140] r t is the yaw angular velocity at time t, r t-1 is the yaw angular velocity value at time t-1,

[0141] β t is the sideslip angle of the center of mass at time t, β t-1 is the sideslip angle value of the center of mass at time t-1,

[0142] v x,t is the longitudinal velocity value at time t, v x,t-1 is the longitudinal velocity value at time t-1,

[0143] δ t is the front wheel turning angle at time t, δ t-1 is the front wheel steering angle at time t-1,

[0144] a x.t is the longitudinal acceleration value at time t, a x,t-1 is the longitudinal acceleration value at time t-1,

[0145] a y,t is the lateral acceleration value at time t, T s is the sampling time;

[0146] x t is the system state matrix, u t System input matrix, z t System observation matrix.

[0147] S3: Based on the seventh-order spherical radius criterion, a nonlinear filtering strategy is designed to optimize the sampling points and weights of the cubature Kalman filter (CKF) algorithm. By integrating the square root filter architecture of QR decomposition, a square root seventh-order cubature Kalman filter (SR7thCKF) algorithm is constructed. Based on the discrete three-degree-of-freedom vehicle dynamics model, the front wheel angle δ, longitudinal acceleration a x , lateral acceleration a y As the input of the square root seventh-order cubic Kalman filter (SR7thCKF) algorithm, the longitudinal velocity v of the distributed drive electric vehicle (DDEV) vehicle model in complex working conditions such as double lane change, serpentine and step is estimated in real time. x , lateral speed v y , sideslip angle β and yaw rate r;

[0148] The vehicle state parameter estimation method based on SR7thCKF is as follows:

[0149] For the discrete three-degree-of-freedom vehicle dynamics model, it can be written as an n-order system with additive noise:

[0150]

[0151] Where: u t is the input value of the system at time t; x t is the state value at time t; z t is the observed value at time t; f is the state equation; h is the measurement function; w t is the process noise, describing the uncertainty in the state equation; v t is the measurement noise, which describes the uncertainty of sensor measurement; w t With v t are independent Gaussian white noises with zero mean, that is, w t ~N(0,Q t ), v t ~N(0,R t ).

[0152] Approximate the standard Gaussian weighted integral as:

[0153]

[0154] Where: x is the independent variable; f(x) is the function of the independent variable x; I(f) is the integral functional result of the function f(x); ω i is the weight coefficient in numerical integration; ξ i is the sampling point;

[0155] Based on the seventh-order spherical radius criterion, the sampling points and weights corresponding to the SR7thCKF algorithm are:

[0156]

[0157]

[0158] Among them: the sampling methods are H1, H2, and H3 sampling, and A, B, C, D, E, F, and G represent the weight coefficients of the corresponding sampling points respectively;

[0159] The point set in H1 sampling is {m0}, which contains 2n sampling points:

[0160]

[0161] The point set in H2 sampling is {m1}, {m2}, {m3} and {m4}, which contains 4n(n-1) sampling points:

[0162]

[0163] The point set in H3 sampling is {m5}, {m6}, {m7} and {m8}, which contains 4n(n-1)(n-2) / 3 sampling points:

[0164] {m5}={e k +e g +e t ,k <g<l,k,g,l=1,2,…,n}

[0165] {m6}={e k +e g -e t ,k<g<l,k,g,l=1,2,…,n}

[0166] {m7}={e k -e g +e t ,k<g<l,k,g,l=1,2,…,n}

[0167] {m8}={e k -e g -e t ,k<g<l,k,g,l=1,2,…,n}

[0168] The above is the result of allocating sampling points and weights according to the seventh-order spherical radius criterion. The subsequent steps are as follows:

[0169] Determine the number of volume points γ:

[0170] γ=(8 / 3)n(n-1)(n-2)+8n 2 -4n+1 (9)

[0171] Calculate volume points

[0172]

[0173] in: and S t-1|t-1 are the state estimation value and square root error covariance matrix of the previous moment respectively;

[0174] Calculate volume points propagated through the equation of state

[0175]

[0176] Calculate state prediction value

[0177]

[0178] Calculate the square root error covariance matrix predicted value S t|t-1 :

[0179] S t|t-1 =qr([X t|t-1 ,chol(Q t-1 )]) (13)

[0180]

[0181] Where: qr represents QR decomposition operation; Q t-1 is the state noise covariance matrix;

[0182] Calculate the updated volume point X i,t|t-1 :

[0183]

[0184] Calculate the volume point Z propagated through the measurement equation i,t|t-1 :

[0185] Z i,t|t-1 =h(X i,t|t-1 ,u t ) (16)

[0186] Calculate measurement prediction value

[0187]

[0188] Calculate the cross-covariance matrix P xz,t|t-1 :

[0189]

[0190] Calculate the square root measurement error covariance matrix prediction value S zz,t|t-1 :

[0191] S zz,t|t-1 =qr([Z t|t-1 ,chol(R t )]) (19)

[0192] in:

[0193]

[0194] Calculate the Kalman filter gain K t :

[0195]

[0196] Calculate state estimates

[0197]

[0198] Calculate the square root error covariance matrix S t|t :

[0199] S t|t =qr([X t|t-1 -K t Z t|t-1 ,K t chol(R t )]) (twenty three)

[0200] S4: The estimated value of the vehicle state parameters is compared with the front wheel angle δ and longitudinal acceleration a measured by the onboard sensor. x , lateral acceleration a y The information is used as the time series feature of the predicted tire force, which includes the tire longitudinal force F xij and tire lateral force F yij Due to the lack of tire force sensors, the Dugoff model is used to calculate tire forces based on estimated vehicle state parameters and sensor information, thereby constructing a tire force prediction dataset covering multiple working conditions.

[0201] The tire force calculation formula of the Dugoff model is:

[0202]

[0203] in:

[0204]

[0205] Where: C xij and C yij are the longitudinal slip stiffness and lateral stiffness of the four tires respectively; μ ij is the road adhesion coefficient; α ij is the tire slip angle; ij is the slip rate; v ij is the wheel center speed; F zij is the tire vertical force; ε is the speed influence factor, L is the intermediate calculation variable; F xij is the tire longitudinal force; F yij is the tire lateral force;

[0206] The formula for calculating tire slip angle is:

[0207]

[0208] Where: t f is the front axle track; t r is the rear axle track; α fl,fris the sideslip angle of the left and right front wheels; α rl,rr is the sideslip angle of the left and right rear wheels;

[0209] The formula for calculating the vertical force of the tire is:

[0210]

[0211] Where: h g F is the height of the vehicle's center of mass; zfl,zfr is the vertical force on the left and right front wheels; F zrl,zrr is the vertical force on the left and right rear wheels;

[0212] The slip rate calculation formula is:

[0213]

[0214] S5: The dataset was divided into training and test sets at a ratio of 70% and 30%, respectively. The vehicle state parameter estimates and the time series obtained by on-board sensors were used as input, and tire force was used as output. A tire force prediction method based on the TCN-GRU model was designed. The temporal convolutional network (TCN) expanded the time series receptive field through layered and stacked dilated convolutional layers to capture the short-term fluctuations and long-term trend characteristics of tire force. The gated recurrent unit (GRU) used update gates and reset gates to dynamically adjust the weights of historical information to model the temporal dependencies of tire force under multiple working conditions. By combining the temporal feature extraction capability of TCN and the sequence modeling capability of GRU, the prediction accuracy of tire force was improved.

[0215] The tire force prediction method based on the TCN-GRU model is as follows:

[0216] The time series features of the input in the TCN-GRU model are {δ,a x ,a y ,v x ,v y ,β,r}, the output is {F xij ,F yij The TCN model includes the following modules:

[0217] (1) Causal convolution: ensures that the current output of the time series depends only on the current and past inputs without utilizing future information, thus adhering to causal relationships;

[0218] (2) Dilated convolution: A dilation factor (d = 1, 2, 4, 8) is introduced into the convolution kernel, which gradually increases between layers. Without increasing the network depth or kernel size, the receptive field is expanded to capture long-term dependencies. The calculation formula is:

[0219]

[0220] Where: F(t) is the convolution output at the current time t; x is the input time series; f is the convolution kernel; k is the size of the convolution kernel; d is the dilation factor;

[0221] (3) Residual connection: Each residual block contains two dilated causal convolutions, with weight normalization, ReLU activation, and Dropout added in between. The output of the residual connection is the result of the convolution plus the input. If the result of the convolution is inconsistent with the input dimension, the input dimension can be adjusted through 1*1 convolution;

[0222] The output features of TCN are used as the input of GRU. For each time step, GRU updates the hidden state h t The calculation formula is:

[0223] r t =σ(W r ·x t +U r ·h t-1 ) (31)

[0224] z t =σ(W z ·x t +U z ·h t-1 ) (32)

[0225]

[0226] Among them, x t represents the input at time step t; r t Represents the reset gate; z t represents the update gate; W h Represents the weight matrix associated with the candidate hidden state; W z Represents the weight matrix associated with the update gate; W r Represents the weight matrix associated with the reset gate; U h 、U z 、U r represents the corresponding weight matrix; represents the candidate hidden state; h t-1 represents the hidden state at time step t-1; σ represents the sigmoid function.

[0227] The TCN extracts temporal features from the input data, which are then modeled using the GRU. Finally, a fully connected layer integrates the information extracted by previous layers, mapping the model's intermediate features to the final output dimension. This architecture effectively combines the TCN's temporal feature extraction capabilities with the GRU's sequence modeling capabilities, improving tire force prediction accuracy.

[0228] In summary, the present invention designs a method for predicting tire longitudinal and lateral forces based on vehicle state parameter estimation. In order to obtain longitudinal velocity, lateral velocity (which can be calculated through geometric relationships at small turning angles), sideslip angle, and yaw rate, which can be used for tire force prediction, a vehicle state parameter estimation method based on SR7thCKF is designed. Figures 4 and 5 The figure shows the comparison curve of vehicle state parameter estimation under serpentine conditions based on experiments. Compared with CKF, SRCKF, and SR5thCKF, the SR7thCKF algorithm can significantly improve the estimation accuracy of vehicle state parameters. The front wheel angle, longitudinal acceleration, lateral acceleration and vehicle state parameter estimation values ​​measured by the sensor are used as time series features. A tire force prediction method based on TCN-GRU is designed. Figure 6 The figure shows the comparison curve of the left front wheel tire force prediction under the serpentine working condition based on the experiment. Compared with MLP and TCN, the TCN-GRU model has improved the prediction accuracy of tire longitudinal force and lateral force.

[0229] The above is only a preferred embodiment of the present invention. It should be pointed out that for those skilled in the art, several changes and improvements can be made without departing from the overall concept of the present invention, and these should also be regarded as the scope of protection of the present invention.

[0230] The technical means disclosed in the solutions of the present invention are not limited to those disclosed in the above-mentioned embodiments, but also include technical solutions composed of any combination of the above-mentioned technical features. It should be noted that those skilled in the art may make various improvements and modifications without departing from the principles of the present invention, and such improvements and modifications are also considered to be within the scope of protection of the present invention.

Claims

1. A tire longitudinal force and lateral force prediction method based on vehicle state parameter estimation, characterized by: The method comprises the following steps: S1: Using a permanent magnet synchronous motor (PMSM) as the hub motor of the vehicle, a distributed drive electric vehicle (DDEV) vehicle model is constructed based on the three-degree-of-freedom vehicle dynamics model. The distributed drive electric vehicle (DDEV) vehicle model collects the front wheel angle δ and wheel speed ω based on the on-board sensors. ij , longitudinal acceleration a x , lateral acceleration a y , driving torque T dij And the braking torque T bij ; S2: The three-degree-of-freedom vehicle dynamics model is discretized using the forward Euler discretization method, and the system state is determined to be the longitudinal velocity, the sideslip angle of the center of mass, and the yaw rate; the system input is the front wheel angle δ, the longitudinal acceleration a x , the system observation is the lateral acceleration a y ; S3: Based on the seventh-order spherical radius criterion, a nonlinear filtering strategy is designed to optimize the sampling points and weights of the cubature Kalman filter (CKF) algorithm. By integrating the square root filter architecture of QR decomposition, a square root seventh-order cubature Kalman filter (SR7thCKF) algorithm is constructed. Based on the discrete three-degree-of-freedom vehicle dynamics model, the front wheel angle δ, longitudinal acceleration a x , lateral acceleration a y As the input of the square root seventh-order cubic Kalman filter (SR7thCKF) algorithm, the longitudinal velocity v of the distributed drive electric vehicle (DDEV) vehicle model in complex working conditions such as double lane change, serpentine and step is estimated in real time. x , lateral speed v y , sideslip angle β and yaw rate r; S4: The estimated value of the vehicle state parameters is compared with the front wheel angle δ and longitudinal acceleration a measured by the onboard sensor. x , lateral acceleration a y The information is used as the time series feature of the predicted tire force, which includes the tire longitudinal force F xij and tire lateral force F yij Due to the lack of tire force sensors, the Dugoff model is used to calculate tire forces based on estimated vehicle state parameters and sensor information, thereby constructing a tire force prediction dataset covering multiple working conditions. S5: The dataset was divided into training and test sets at a ratio of 70% and 30%, respectively. The vehicle state parameter estimates and the time series obtained by on-board sensors were used as input, and tire force was used as output. A tire force prediction method based on the TCN-GRU model was designed. The temporal convolutional network (TCN) expanded the time series receptive field through layered and stacked dilated convolutional layers to capture the short-term fluctuations and long-term trend characteristics of tire force. The gated recurrent unit (GRU) used update gates and reset gates to dynamically adjust the weights of historical information to model the temporal dependencies of tire force under multiple working conditions. By combining the temporal feature extraction capability of TCN and the sequence modeling capability of GRU, the prediction accuracy of tire force was improved.

2. The tire longitudinal force and lateral force prediction method based on vehicle state parameter estimation according to claim 1, characterized in that: In S1, the method for constructing the distributed drive electric vehicle (DDEV) vehicle model is as follows: The three-degree-of-freedom vehicle dynamics model with tire cornering stiffness is: Where: m is the total mass of the vehicle, v x is the longitudinal velocity; v y is the lateral velocity; β is the sideslip angle of the center of mass; a x is the longitudinal acceleration; a y is the lateral acceleration; r is the yaw angular velocity; I z is the moment of inertia around the z axis; δ is the front wheel angle; L f and L r Represents the distance from the center of mass to the front axle and rear axle respectively; C yf is the front wheel cornering stiffness; C yr is the rear wheel cornering stiffness; is the derivative value of the yaw rate; is the derivative value of the sideslip angle of the center of mass; is the derivative value of the longitudinal velocity; The permanent magnet synchronous motor (PMSM) is integrated with the vehicle system. In this configuration, the PMSM model is directly connected to the wheels through the electronic control system. The wheel speed output by the vehicle dynamics model serves as the target speed of the wheel hub motor. The mathematical model of the PMSM is: Where: i α and i β is the current component of the stator winding in the stationary coordinate system; u α and u β is the voltage component of the stator winding in the stationary coordinate system; R s and L s are resistance and inductance respectively; ψ f is the magnetic linkage; ω m is the mechanical angular velocity of the rotor; θ e is the rotor position; p n is the number of pole pairs; J is the moment of inertia; B is the damping coefficient; T e is the electromagnetic torque; T L is the load torque.

3. The tire longitudinal force and lateral force prediction method based on vehicle state parameter estimation according to claim 2, characterized in that: The discrete three-degree-of-freedom vehicle dynamics model in S2 is as follows The state equation is: The observation equation is: Among them, the system state is x t =[r t β t v x,t ] T ; System input is u t =[δ t a x,t ] T ; System observation is z t =[a y,t ] T ; r t is the yaw angular velocity at time t, r t-1 is the yaw angular velocity value at time t-1, β t is the sideslip angle of the center of mass at time t, β t-1 is the sideslip angle value of the center of mass at time t-1, v x,t is the longitudinal velocity value at time t, v x,t-1 is the longitudinal velocity value at time t-1, δ t is the front wheel turning angle at time t, δ t-1 is the front wheel steering angle at time t-1, a x.t is the longitudinal acceleration value at time t, a x,t-1 is the longitudinal acceleration value at time t-1, a y,t is the lateral acceleration value at time t, T s is the sampling time, x t is the system state matrix, u t System input matrix, z t System observation matrix.

4. The tire longitudinal force and lateral force prediction method based on vehicle state parameter estimation according to claim 1, characterized in that: The square root seventh-order cubic Kalman filter (SR7thCKF) algorithm used in S3 to estimate vehicle state parameters is: For a discrete three-degree-of-freedom vehicle dynamics model, it can be written as an n-order system with additive noise: Where: u t is the input value of the system at time t; x t is the state value at time t; z t is the observed value at time t; f is the state equation; h is the measurement function; w t is the process noise, describing the uncertainty in the state equation; v t is the measurement noise, which describes the uncertainty of sensor measurement; w t With v t are independent Gaussian white noises with zero mean, that is, w t ~N(0,Q t ), v t ~N(0,R t ); Approximate the standard Gaussian weighted integral as: Where: x is the independent variable; f(x) is the function of the independent variable x; I(f) is the integral functional result of the function f(x); ω i is the weight coefficient in numerical integration; ξ i is the sampling point; Based on the seventh-order spherical radius criterion, the sampling points and weights corresponding to the SR7thCKF algorithm are: Among them: the sampling methods are H1, H2, and H3 sampling; A, B, C, D, E, F, and G represent the weight coefficients of the corresponding sampling points respectively; The above is the result of allocating sampling points and weights according to the seventh-order spherical radius criterion. The subsequent steps are as follows: Determine the number of volume points γ: γ=(8 / 3)n(n-1)(n-2)+8n 2 -4n+1 (7) Calculate volume points in: and S t-1|t-1 are the state estimation value and square root error covariance matrix of the previous moment respectively; Calculate volume points propagated through the equation of state Calculate state prediction value Calculate the square root error covariance matrix predicted value S t|t-1 : S t|t-1 =qr([X t|t-1 ,chol(Q t-1 )]) (11) Where: qr represents QR decomposition operation; Q t-1 is the state noise covariance matrix; Calculate the updated volume point X i,t|t-1 : Calculate the volume point Z propagated through the measurement equation i,t|t-1 : Z i,t|t-1 =h(X i,t|t-1 ,u t )(14) Calculate the measured predicted value Calculate the cross-covariance matrix P xz,t|t-1 : Calculate the square root measurement error covariance matrix S zz,t|t-1 : S zz,t|t-1 =qr([Z t|t-1 ,chol(R t )]) (17) in: Where: R t is the measurement noise covariance matrix; Calculate the Kalman filter gain K t : Calculate state estimates Calculate the square root error covariance matrix S t|t : S t|t =qr([X t|t-1 -K t Z t|t-1 ,K t chol(R t )]) (21)。 5. The tire longitudinal force and lateral force prediction method based on vehicle state parameter estimation according to claim 1, characterized in that: The tire force calculation formula of the Dugoff model in S4 is: in: Where: C xij and C yij are the longitudinal slip stiffness and lateral stiffness of the four tires respectively; μ ij is the road adhesion coefficient; α ij is the tire slip angle; ij is the slip rate; v ij is the wheel center speed; F zij is the tire vertical force; ε is the speed influence factor; L is the intermediate calculation variable; F xij is the tire longitudinal force; F yij is the tire lateral force; The formula for calculating tire slip angle is: Where: t f is the front axle track; t r is the rear axle track; α fl,fr is the sideslip angle of the left and right front wheels; α rl,rr is the sideslip angle of the left and right rear wheels; The formula for calculating the vertical force of the tire is: Where: h g F is the height of the vehicle's center of mass; zfl,zfr is the vertical force on the left and right front wheels; F zrl,zrr is the vertical force on the left and right rear wheels; The slip rate calculation formula is: Where: R ω is the wheel rotation radius, ω ij is the angular velocity of the wheel.

6. The tire longitudinal force and lateral force prediction method based on vehicle state parameter estimation according to claim 1, characterized in that: The time series features of the input to the TCN-GRU model used to predict tire force in S5 are {δ,a x ,a y ,v x ,v y ,β,r}, the output is {F xij ,F yij }; Among them, the TCN model includes the following modules (1) Causal convolution: ensures that the current output of the time series depends only on the current and past inputs without utilizing future information, thus adhering to causal relationships; (2) Dilated convolution: A dilation factor (d = 1, 2, 4, 8) is introduced into the convolution kernel, which gradually increases between layers. Without increasing the network depth or kernel size, the receptive field is expanded to capture long-term dependencies. The calculation formula is: Where: F(t) is the convolution output at the current time t; x is the input time series; f is the convolution kernel; k is the size of the convolution kernel; d is the dilation factor; (3) Residual connection: Each residual block contains two dilated causal convolutions, with weight normalization, ReLU activation, and Dropout added in between. The output of the residual connection is the result of the convolution plus the input. When the result of the convolution is inconsistent with the input dimension, the input dimension can be adjusted through 1*1 convolution. The output features of TCN are used as the input of GRU. For each time step, GRU updates the hidden state h t The calculation formula is: r t =σ(W r ·x t +U r ·h t-1 ) (29) z t =σ(W z ·x t +U z ·h t-1 ) (30) Among them, x t represents the input at time step t; r t Represents the reset gate; z t represents the update gate; W h Represents the weight matrix associated with the candidate hidden state; W z Represents the weight matrix associated with the update gate; W r Represents the weight matrix associated with the reset gate; U h 、U z 、U r represents the corresponding weight matrix; represents the candidate hidden state; h t-1 represents the hidden state at time step t-1; σ represents the sigmoid function; In the constructed TCN-GRU model, TCN is used to extract the temporal features of the input data, followed by sequence modeling through GRU, and finally the fully connected layer integrates the information extracted by the previous layers to map the intermediate features of the model to the final output dimension.

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