A Steering Wheel Angle Estimation Method Based on Least Squares and Support Vector Regression

Abstract

The present invention is a steering wheel angle estimation method based on least squares and support vector regression. It includes: step one, establishing a nonlinear expression function of vehicle driving according to the lateral mechanical characteristics of the vehicle; step two, designing a mechanism-based estimation strategy for the steering wheel angle of the car based on recursive least squares, to achieve accurate estimation of the steering wheel angle when the lateral acceleration of the car is small; step three, correcting the steering wheel angle estimation value when the lateral acceleration of the car is large through a car data-driven steering wheel angle estimation strategy based on support vector regression. The present invention accurately estimates the steering wheel angle of the car under different lateral accelerations, provides a reference scheme for the estimation of the steering wheel angle of the car driven by a hybrid of mechanism and data, and effectively provides a signal reference for the reverse wheel angle fault diagnosis and fault-tolerant control of the future intelligent car wire control steering system, overcoming the parameter uncertainty and vehicle state measurement noise problems faced by vehicle system dynamics.

Description

Technical Field

[0001] This invention belongs to the field of automotive technology, specifically a steering wheel angle estimation method based on least squares and support vector regression. Background Technology

[0002] With the continuous advancement of automotive electrification and intelligentization technologies, the automotive steering system, as the most important actuator for lateral movement, is gradually evolving from traditional power steering to steer-by-wire. Steer-by-wire systems break the mechanical connection between the steering wheel and steering wheels in traditional power steering systems. By adding a driver-simulated road feel feedback motor and recognizing the driver's steering intention based on the steering wheel angle, a complete decoupling between the driver and the steering wheels can be easily achieved. This offers numerous advantages, including flexible system layout, isolation from road bumps, and variable transmission ratios. The effectiveness of the steering wheel angle sensor is particularly crucial for steer-by-wire systems, directly determining whether the driver's steering intention can be accurately recognized. To improve the reliability and safety of steer-by-wire systems, accurate estimation of the steering wheel angle is essential during the system architecture design to determine in real-time whether the steering wheel angle sensor has malfunctioned. Currently used mechanism-based steering wheel angle estimation methods are susceptible to degradation due to uncertainties in vehicle system parameters when the vehicle's lateral acceleration is high, affecting subsequent steering wheel angle fault diagnosis and fault-tolerant control. Summary of the Invention

[0003] This invention provides a steering wheel angle estimation method based on least squares and support vector regression, which accurately estimates the steering wheel angle of a car under different lateral accelerations. It provides a reference scheme for steering wheel angle estimation driven by a combination of mechanism and data, and effectively provides a signal reference for fault diagnosis and fault-tolerant control of steering wheel angle in future intelligent vehicle steer-by-wire systems. It overcomes the parameter uncertainty and vehicle state measurement noise problems faced by vehicle system dynamics.

[0004] The technical solution of this invention is described below in conjunction with the accompanying drawings:

[0005] A method for estimating steering wheel angle based on least squares and support vector regression includes the following steps:

[0006] Step 1: Establish a nonlinear expression function for vehicle driving based on the lateral mechanical characteristics of the vehicle;

[0007] Step 2: Design a mechanism-based estimation strategy for car steering wheel angle based on recursive least squares;

[0008] Step 3: Correct the estimated steering wheel angle when the lateral acceleration of the vehicle is large by using a data-driven steering wheel angle estimation strategy based on support vector regression.

[0009] Furthermore, the specific method for step one is as follows:

[0010] 11) Establish a two-degree-of-freedom vehicle dynamics model, as shown below:

[0011]

[0012]

[0013] In the formula, m represents the total vehicle mass; v x Indicates the vehicle's longitudinal speed; This indicates the sideslip angular velocity of the vehicle's center of gravity. Indicates the vehicle's yaw rate; F represents the yaw acceleration of the vehicle. yf F represents the equivalent lateral force of the front tire; yr δ represents the equivalent lateral force of the rear tire. f Indicates the steering angle of the vehicle's front wheels; I z yaw moment of inertia of the vehicle; a represents the distance from the vehicle's center of gravity to the front axle; b represents the distance from the vehicle's center of gravity to the rear axle.

[0014] 12) A linear tire model is used to describe the equivalent lateral forces of the front and rear tires, as shown below:

[0015] F yf =C f α f (3)

[0016] F yr =C r α r (4)

[0017] In the formula, F yf F represents the equivalent lateral force of the front tire; yr C represents the equivalent lateral force of the rear tire; f Indicates the front wheel lateral stiffness; C r Indicates the rear wheel lateral stiffness; α f Indicates the front wheel slip angle; α r Indicates the rear wheel slip angle;

[0018] 13) The front and rear wheel slip angles are approximately expressed as:

[0019]

[0020]

[0021] In the formula, β represents the vehicle's sideslip angle;

[0022] 14) By rearranging formulas (1)-(6) and incorporating the small-angle assumption, the linear two-degree-of-freedom vehicle dynamics model is obtained as follows:

[0023]

[0024]

[0025] In the formula, This indicates the sideslip angular velocity of the vehicle's center of gravity.

[0026] 15) The vehicle's center of gravity sideslip angular velocity is equivalently replaced by lateral acceleration, that is:

[0027]

[0028] In the formula, a y Indicates the lateral acceleration of the vehicle;

[0029] 16) For an automotive electronic power steering system, the vehicle steering wheel angle θ to be estimated. c With the vehicle's front wheel steering angle δ f If a definite transmission ratio exists, then:

[0030] θ c =δ f ·G c (10)

[0031] In the formula, θ c Indicates the steering wheel angle of the vehicle; G c Indicates the gear ratio of the electronically controlled power steering system;

[0032] 17) When the car is driving under steady-state conditions, the vehicle's sideslip angle β and yaw rate are... All are constant values, including the vehicle's yaw acceleration. and vehicle center of gravity sideslip angular velocity Since all values ​​are 0, after combining formulas (7)-(10) and rearranging, we obtain the nonlinear expression function of vehicle driving:

[0033]

[0034]

[0035] In the formula, k represents the steady-state yaw rate gain.

[0036] Furthermore, the specific method for step two is as follows:

[0037] 21) Rewrite formula (11) in discrete function form, that is:

[0038] ξ(k)=f(k,θ c(k)) (13)

[0039] ξ(k)=[v x (k),a y (k)] T (14)

[0040] In the formula, ξ(k) represents the measurable state vector of the vehicle at time k; v x (k) represents the longitudinal speed of the vehicle at time k; a y (k) represents the lateral acceleration of the vehicle at time k; f(k,θ) c (k) represents the nonlinear expression function of vehicle movement at time k;

[0041] 22) Taylor expansion is used to locally linearize the measurable state vector ξ(k) of the vehicle at time k:

[0042] ξ(k)≈H(k)(θ c (k)-θ c (k-1))+f(k-1,θ c (k-1)) (15)

[0043]

[0044] In the formula, ξ(k) represents the measurable state vector of the vehicle at time k; ξ(k-1) represents the measurable state vector of the vehicle at time k-1; H(k) represents the value of f(k-1,θ) at time k. c (k-1)) for θ c The Jacobian matrix of (k-1) digits; θ c (k) represents the steering wheel angle of the vehicle at time k; θ c (k-1) represents the steering wheel angle of the vehicle at time k-1; f(k-1,θ) c (k-1)) represents the nonlinear expression function of vehicle movement at time k-1;

[0045] 23) Let Δξ(k)=ξ(k)-f(k-1,θ c (k-1))+H(k)θ c (k-1), combined with formula (15), we get:

[0046] Δξ(k)≈H(k)θ c (k) (17)

[0047] In the formula, Δξ(k) represents the measurable state vector increment of the vehicle at time k;

[0048] 24) The recursive least squares cost function to be used is set as follows:

[0049]

[0050] In the formula, Represents the recursive least squares cost function based on the nonlinear expression function of vehicle driving; This represents the estimated steering wheel angle of the vehicle. Let f(i, θ) represent the estimated vehicle steering angle obtained at time i based on least squares; η represents the forgetting coefficient of the recursive least squares cost function; Δξ(i) represents the measurable state vector increment of the vehicle at time i; H(i) represents f(i-1, θ) at time i. c (i-1)) for θ c The Jacobian matrix of (i-1); θ c (i-1) represents the steering wheel angle of the vehicle at time i; f(i-1,θ) c (i-1)) represents the nonlinear expression function of vehicle movement at time i-1;

[0051] 25) The estimated vehicle steering wheel angle obtained based on least squares is expressed as:

[0052]

[0053] Q(k)=G(k-1)H T (k)[I+H(k)G(k-1)H T (k)] -1 (20)

[0054] G(k)=η -1 [IQ(k)H(k)]G(k-1)η -1 (twenty one)

[0055] In the formula, This represents the estimated vehicle steering wheel angle obtained at time k based on least squares. Let f(k-1,θ) represent the estimated steering wheel angle of the vehicle at time k-1; Δξ(k) represent the measurable state vector increment of the vehicle at time k; Q(k) represent the recursive least squares quantization matrix based on the nonlinear expression function of vehicle driving at time k; c (k-1)) represents the nonlinear expression function of vehicle movement at time k-1; H(k-1) represents the nonlinear expression function of vehicle movement at time k-1. c (k-2)) with respect to θ c The Jacobian matrix of (k-2) digits; θ c (k-2) represents the steering wheel angle of the vehicle at time k-2; f(k-2,θ) c(k-2)) represents the nonlinear expression function of vehicle driving at time k-2; I represents the identity matrix; G(k) represents the recursive least squares iteration matrix based on the nonlinear expression function of vehicle driving at time k; G(k-1) represents the recursive least squares iteration matrix based on the nonlinear expression function of vehicle driving at time k-1.

[0056] Furthermore, the specific method for step three is as follows:

[0057] 31) The steering wheel angle of a car is estimated using a data-driven method based on support vector regression;

[0058] Let the input variable x for support vector regression be:

[0059]

[0060] In the formula, x represents the input variable for support vector regression; a x Indicates the longitudinal acceleration of the vehicle; a y Indicates the lateral acceleration of the vehicle;

[0061] 32) Establish a support vector regression sample dataset X:

[0062] X={(x i ,θ ci )|i=1,2,…N,x i ∈R d θ ci ∈R} (23)

[0063] In the formula, X represents the support vector regression sample dataset; N represents the number of sample data; R represents a real number; d represents the input dimension of support vector regression, and d = 5; x i θ represents the support vector regression input variable for the i-th sample data; ci This represents the actual value of the vehicle steering wheel angle for the i-th sample data;

[0064] 33) Design the support vector regression curve function f(x):

[0065]

[0066] In the formula, f(x) represents the support vector regression curve function; w represents the support vector regression curve function weight; κ represents the support vector regression curve function bias; and x represents the support vector regression input variable. This represents the estimated vehicle steering wheel angle obtained based on support vector regression.

[0067] 34) The process of estimating the steering wheel angle through support vector regression is transformed into a quadratic convex optimization problem to be solved, and the support vector regression solution formula is established:

[0068]

[0069] In the formula, θ c Indicates the steering wheel angle of the vehicle; ε represents the support vector regression error threshold.

[0070] 35) Introducing a relaxation factor into formula (25) yields the optimized support vector regression solution:

[0071]

[0072] In the formula, w represents the weight of the support vector regression curve function; Λ represents the penalty coefficient of the support vector regression curve function; ξ i ξ represents the relaxation factor of the upper boundary of the regression curve function for the i-th support vector; i * κ represents the lower boundary relaxation factor of the support vector regression curve function for the i-th support vector; x represents the input variable of support vector regression; κ represents the bias of the support vector regression curve function.

[0073] 36) Introducing Lagrange multipliers into formula (26), and obtaining the result through dual transformation:

[0074]

[0075] In the formula, α i Denotes the i-th upper boundary Lagrange multiplier; α i * Denotes the i-th lower boundary Lagrange multiplier; α j Denotes the j-th upper boundary Lagrange multiplier; α j * Denotes the j-th lower boundary Lagrange multiplier; x i x represents the support vector regression input variable for the i-th sample data; j This represents the support vector regression input variable for the j-th sample data;

[0076] 37) Solve equation (27) to obtain the values ​​of the upper and lower boundary Lagrange multipliers. Use the Carlow-Kun-Tucker condition to quickly obtain the bias κ of the support vector regression curve function. Finally, the estimated value of the vehicle steering wheel angle obtained based on support vector regression is expressed as:

[0077]

[0078] In the formula, α represents the estimated vehicle steering wheel angle obtained based on support vector regression. i * κ represents the i-th lower boundary Lagrange multiplier; i This represents the function bias of the regression curve for the i-th support vector;

[0079] 38) The estimated value of the vehicle steering wheel angle correction obtained by combining least squares and support vector regression is:

[0080]

[0081] In the formula, This represents the estimated steering wheel angle of the vehicle. This represents the estimated vehicle steering wheel angle obtained based on least squares. This represents the estimated vehicle steering wheel angle obtained through support vector regression; a y Indicates the lateral acceleration of a vehicle; a t This indicates the threshold value for switching lateral acceleration of the vehicle.

[0082] The beneficial effects of this invention are as follows:

[0083] 1. The nonlinear expression function for vehicle driving established in this invention can better express the steady-state motion characteristics of a car under steering wheel angle input;

[0084] 2) The recursive least squares-based vehicle steering wheel angle estimation strategy of this invention can effectively overcome vehicle state measurement noise and achieve accurate estimation of steering wheel angle when the lateral acceleration of the vehicle is small.

[0085] 3) The vehicle data-driven steering angle estimation strategy based on support vector regression in this invention can overcome the problem of vehicle system parameter uncertainty disturbance in steering angle estimation when the vehicle's lateral acceleration is large;

[0086] 4) The vehicle steering wheel angle estimation method based on least squares and support vector regression in this invention can accurately estimate the steering wheel angle under different lateral accelerations of the vehicle, providing a reference scheme for vehicle steering wheel angle estimation driven by a combination of mechanism and data. Attached Figure Description

[0087] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments. It should be understood that the following drawings only illustrate certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other relevant drawings can be obtained based on these drawings without paying any creative work.

[0088] Figure 1 This is a diagram illustrating the overall structural architecture of the present invention;

[0089] Figure 2 This is a schematic diagram of a two-degree-of-freedom vehicle dynamics model;

[0090] Figure 3A diagram showing the comparison between the estimated and actual steering wheel angle at a vehicle speed of 20 km / h;

[0091] Figure 4 A schematic diagram illustrating the error between the estimated and actual steering wheel angle at a vehicle speed of 20 km / h.

[0092] Figure 5 A diagram showing the comparison between the estimated and actual steering wheel angle at a vehicle speed of 60 km / h.

[0093] Figure 6 This diagram illustrates the error between the estimated and actual steering wheel angle values ​​when the car is traveling at 60 km / h. Detailed Implementation

[0094] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0095] See Figure 1 A method for estimating steering wheel angle based on least squares and support vector regression includes the following steps:

[0096] Step 1: Establish a nonlinear expression function for vehicle driving based on the lateral mechanical characteristics of the vehicle;

[0097] The specific method is as follows:

[0098] 11) This invention focuses on the lateral motion of the vehicle related to the steering wheel angle, therefore ignoring vehicle roll, pitch, and vertical motion, and establishing a... Figure 2 The two-degree-of-freedom vehicle dynamics model shown below is as follows:

[0099]

[0100]

[0101] In the formula, m represents the total vehicle mass; v x Indicates the vehicle's longitudinal speed; This indicates the sideslip angular velocity of the vehicle's center of gravity. Indicates the vehicle's yaw rate; F represents the yaw acceleration of the vehicle. yf F represents the equivalent lateral force of the front tire; yr δ represents the equivalent lateral force of the rear tire. f Indicates the steering angle of the vehicle's front wheels; I zyaw moment of inertia of the vehicle; a represents the distance from the vehicle's center of gravity to the front axle; b represents the distance from the vehicle's center of gravity to the rear axle.

[0102] 12) A linear tire model is used to describe the equivalent lateral forces of the front and rear tires, as shown below:

[0103] F yf =C f α f (32)

[0104] F yr =C r α r (33)

[0105] In the formula, F yf F represents the equivalent lateral force of the front tire; yr C represents the equivalent lateral force of the rear tire; f Indicates the front wheel lateral stiffness; C r Indicates the rear wheel lateral stiffness; α f Indicates the front wheel slip angle; α r Indicates the rear wheel slip angle;

[0106] 13) The front and rear wheel slip angles are approximately expressed as:

[0107]

[0108]

[0109] In the formula, α f Indicates the front wheel slip angle; α r Indicates the rear wheel slip angle; δ f β represents the front wheel steering angle; β represents the vehicle's sideslip angle; a represents the distance from the vehicle's center of gravity to the front axle; b represents the distance from the vehicle's center of gravity to the rear axle; v x Indicates the vehicle's longitudinal speed; Indicates the vehicle's yaw rate;

[0110] 14) By rearranging formulas (1)-(6) and incorporating the small-angle assumption, the linear two-degree-of-freedom vehicle dynamics model is obtained as follows:

[0111]

[0112]

[0113] In the formula, a represents the distance from the vehicle's center of gravity to the front axle; b represents the distance from the vehicle's center of gravity to the rear axle; C f Indicates the front wheel lateral stiffness; C r Indicates the rear wheel lateral stiffness; δ f Indicates the steering angle of the vehicle's front wheels; I zβ represents the vehicle's yaw moment of inertia; β represents the vehicle's sideslip angle. This represents the sideslip angular velocity of the vehicle's center of gravity; v x Indicates the vehicle's longitudinal speed; Indicates the vehicle's yaw rate; The value represents the vehicle's yaw rate; m represents the vehicle's mass.

[0114] 15) The vehicle's center of gravity sideslip angular velocity is equivalently replaced by lateral acceleration, that is:

[0115]

[0116] In the formula, This represents the sideslip angular velocity of the vehicle's center of gravity; v x Indicates the longitudinal speed of the vehicle; a y Indicates the lateral acceleration of the vehicle; Indicates the vehicle's yaw rate;

[0117] 16) For an automotive electronic power steering system, the vehicle steering wheel angle θ to be estimated. c With the vehicle's front wheel steering angle δ f If a definite transmission ratio exists, then:

[0118] θ c =δ f ·G c (39)

[0119] In the formula, θ c Indicates the steering wheel angle of the vehicle; δ f Indicates the steering angle of the vehicle's front wheels; G c Indicates the gear ratio of the electronically controlled power steering system;

[0120] 17) When the car is driving under steady-state conditions, the vehicle's sideslip angle β and yaw rate are... All are constant values, including the vehicle's yaw acceleration. and vehicle center of gravity sideslip angular velocity Since all values ​​are 0, after combining formulas (7)-(10) and rearranging, we obtain the nonlinear expression function of vehicle driving:

[0121]

[0122]

[0123] In the formula, θ c This indicates the steering wheel angle; a represents the distance from the vehicle's center of gravity to the front axle; b represents the distance from the vehicle's center of gravity to the rear axle; v x G represents the longitudinal speed of the vehicle. c Indicates the gear ratio of the electronically controlled power steering system; ay Represents the vehicle's lateral acceleration; k represents the steady-state yaw rate gain; C f Indicates the front wheel lateral stiffness; C r Indicates the rear wheel lateral stiffness; m represents the vehicle mass; This indicates the vehicle's yaw rate.

[0124] Step 2: Design a mechanism-based estimation strategy for car steering wheel angle based on recursive least squares to achieve accurate estimation of steering wheel angle when the lateral acceleration of the car is small;

[0125] The specific method is as follows:

[0126] By collecting the vehicle's longitudinal speed v x and vehicle lateral acceleration a y Combining the nonlinear expression function of vehicle driving in formula (11), the steering wheel angle θ of the vehicle can be approximately estimated. c Considering the actual longitudinal vehicle speed v collected... x and vehicle lateral acceleration a y There is some noise, which can affect the performance of vehicle steering wheel angle estimation. Therefore, this invention uses recursive least squares to estimate the mechanism of vehicle steering wheel angle.

[0127] 21) Rewrite formula (11) in discrete function form, that is:

[0128] ξ(k)=f(k,θ c (k)) (42)

[0129] ξ(k)=[v x (k),a y (k)] T (43)

[0130] In the formula, ξ(k) represents the measurable state vector of the vehicle at time k; v x (k) represents the longitudinal speed of the vehicle at time k; a y (k) represents the lateral acceleration of the vehicle at time k; f(k,θ) c (k) represents the nonlinear expression function of vehicle movement at time k;

[0131] 22) Taylor expansion is used to locally linearize the measurable state vector ξ(k) of the vehicle at time k:

[0132] ξ(k)≈H(k)(θ c (k)-θ c (k-1))+f(k-1,θ c (k-1))(44)

[0133]

[0134] In the formula, ξ(k) represents the measurable state vector of the vehicle at time k; ξ(k-1) represents the measurable state vector of the vehicle at time k-1; H(k) represents the value of f(k-1,θ) at time k. c (k-1)) for θ c The Jacobian matrix of (k-1) , θ c (k) represents the steering wheel angle of the vehicle at time k; θ c (k-1) represents the steering wheel angle of the vehicle at time k-1; f(k-1,θ) c (k-1)) represents the nonlinear expression function of vehicle movement at time k-1.

[0135] 23) To facilitate the estimation of the vehicle steering wheel angle using recursive least squares, let Δξ(k)=ξ(k)-f(k-1,θ) c (k-1))+H(k)θ c (k-1), combined with formula (15), we get:

[0136] Δξ(k)≈H(k)θ c (k) (46)

[0137] In the formula, Δξ(k) represents the measurable state vector increment of the vehicle at time k; H(k) represents f(k-1,θ) at time k. c (k-1)) for θ c The Jacobian matrix of (k-1) , θ c (k-1) represents the steering wheel angle of the vehicle at time k-1; f(k-1,θ) c (k-1)) represents the nonlinear expression function of vehicle movement at time k-1;

[0138] 24) The recursive least squares cost function to be used is set as follows:

[0139]

[0140] In the formula, Represents the recursive least squares cost function based on the nonlinear expression function of vehicle driving; This represents the estimated steering wheel angle of the vehicle. Let f(i, θ) represent the estimated vehicle steering angle obtained at time i based on least squares; η represents the forgetting coefficient of the recursive least squares cost function; Δξ(i) represents the measurable state vector increment of the vehicle at time i; H(i) represents f(i-1, θ) at time i. c (i-1)) for θ c The Jacobian matrix of (i-1), θ c (i-1) represents the steering wheel angle of the vehicle at time i; f(i-1,θ)c (i-1)) represents the nonlinear expression function of vehicle movement at time i-1;

[0141] 25) The estimated vehicle steering wheel angle obtained based on least squares is expressed as:

[0142]

[0143] Q(k)=G(k-1)H T (k)[I+H(k)G(k-1)H T (k)] -1 (49)

[0144] G(k)=η -1 [IQ(k)H(k)]G(k-1)η -1 (50)

[0145] In the formula, This represents the estimated vehicle steering wheel angle obtained at time k based on least squares. Let f(k, θ) represent the estimated steering wheel angle at time k-1; Δξ(k) represent the measurable state vector increment of the vehicle at time k; Q(k) represent the recursive least squares quantization matrix based on the nonlinear expression function of vehicle driving at time k; and H(k) represent f(k-1, θ) at time k. c (k-1)) for θ c The Jacobian matrix of (k-1) , θ c (k-1) represents the steering wheel angle of the vehicle at time k-1; f(k-1,θ) c (k-1)) represents the nonlinear expression function of vehicle movement at time k-1; H(k-1) represents the nonlinear expression function of vehicle movement at time k-1. c (k-2)) with respect to θ c The Jacobian matrix of (k-2) , θ c (k-2) represents the steering wheel angle of the vehicle at time k-2; f(k-2,θ) c (k-2)) represents the nonlinear expression function of vehicle driving at time k-2; I represents the identity matrix; G(k) represents the recursive least squares iteration matrix based on the nonlinear expression function of vehicle driving at time k; G(k-1) represents the recursive least squares iteration matrix based on the nonlinear expression function of vehicle driving at time k-1.

[0146] Step 3: Correct the estimated steering wheel angle when the lateral acceleration of the vehicle is large by using a data-driven steering wheel angle estimation strategy based on support vector regression.

[0147] The specific method is as follows:

[0148] 31) The estimated value of the vehicle steering wheel angle can be obtained by recursive least squares through formulas (18)-(21). lateral acceleration a of the vehicle y Smaller, i.e., the vehicle's lateral acceleration a y Less than 3m / s 2 At that time, this method has high estimation accuracy; as the vehicle's lateral acceleration a... y The front wheel lateral stiffness C gradually increases. f Rear wheel lateral stiffness C r The inherent uncertainties in vehicle system parameters affect the accuracy of the vehicle steering wheel angle estimate obtained through recursive least squares. Therefore, in the case of vehicle lateral acceleration a... y Larger, i.e., the lateral acceleration a of the vehicle y Greater than or equal to 3m / s 2 At that time, a data-driven method based on support vector regression was used to estimate the steering wheel angle of the car.

[0149] Let the input variable x for support vector regression be:

[0150]

[0151] In the formula, x represents the input variable for support vector regression; This represents the yaw rate of the vehicle; v x Indicates the longitudinal speed of the vehicle; a x Indicates the longitudinal acceleration of the vehicle; a y Indicates the lateral acceleration of the vehicle;

[0152] 32) Establish a support vector regression sample dataset X:

[0153] X={(x i ,θ ci )|i=1,2,…N,x i ∈R d θ ci ∈R} (52)

[0154] In the formula, X represents the support vector regression sample dataset; N represents the number of sample data; R represents a real number; d represents the input dimension of support vector regression, and in this invention, d = 5; x i θ represents the support vector regression input variable for the i-th sample data; ci This represents the actual value of the vehicle steering wheel angle for the i-th sample data;

[0155] 33) Design the support vector regression curve function f(x):

[0156]

[0157] In the formula, f(x) represents the support vector regression curve function; w represents the support vector regression curve function weight; κ represents the support vector regression curve function bias; and x represents the support vector regression input variable. This represents the estimated vehicle steering wheel angle obtained based on support vector regression.

[0158] 34) The process of estimating the steering wheel angle through support vector regression is transformed into a quadratic convex optimization problem to be solved, and the support vector regression solution formula is established:

[0159]

[0160] In the formula, w represents the weight of the support vector regression curve function; θ c κ represents the steering wheel angle of the vehicle; x represents the input variable for support vector regression; κ represents the function bias of the support vector regression curve; ε represents the error threshold for support vector regression; N represents the number of sample data.

[0161] 35) To improve the accuracy of the vehicle steering wheel angle estimate obtained based on support vector regression, a relaxation factor is introduced into formula (25) to address the noise disturbance problem in the sample data. The optimized support vector regression solution is then obtained as follows:

[0162]

[0163] In the formula, w represents the weight of the support vector regression curve function; Λ represents the penalty coefficient of the support vector regression curve function; ξ i ξ represents the relaxation factor of the upper boundary of the regression curve function for the i-th support vector; i * θ represents the lower boundary relaxation factor of the regression curve function for the i-th support vector; N represents the number of sample data; c ε represents the steering wheel angle; w represents the support vector regression error threshold; x represents the support vector regression curve function weights; and κ represents the support vector regression input variables.

[0164] 36) Introducing Lagrange multipliers into formula (26), and obtaining the result through dual transformation:

[0165]

[0166] In the formula, N represents the number of sample data; α i Denotes the i-th upper boundary Lagrange multiplier; α i * Denotes the i-th lower boundary Lagrange multiplier; α j Denotes the j-th upper boundary Lagrange multiplier; α j * Denotes the j-th lower boundary Lagrange multiplier; xi x represents the support vector regression input variable for the i-th sample data; j θ represents the support vector regression input variable for the j-th sample data; ci ε represents the actual value of the vehicle steering wheel angle for the i-th sample data; ε represents the support vector regression error threshold.

[0167] 37) Solve equation (27) to obtain the values ​​of the upper and lower boundary Lagrange multipliers. Use the Carlow-Kun-Tucker condition to quickly obtain the bias κ of the support vector regression curve function. Finally, the estimated value of the vehicle steering wheel angle obtained based on support vector regression is expressed as:

[0168]

[0169] In the formula, The expression represents the estimated vehicle steering wheel angle obtained based on support vector regression; w represents the weight of the support vector regression curve function; κ represents the bias of the support vector regression curve function; x represents the input variable of support vector regression; N represents the number of sample data; α i Denotes the i-th upper boundary Lagrange multiplier; α i * Denotes the i-th lower boundary Lagrange multiplier; x i κ represents the support vector regression input variable for the i-th sample data; i This represents the function bias of the regression curve for the i-th support vector;

[0170] 38) The estimated value of the vehicle steering wheel angle correction obtained by combining least squares and support vector regression is:

[0171]

[0172] In the formula, This represents the estimated steering wheel angle of the vehicle. This represents the estimated vehicle steering wheel angle obtained based on least squares. This represents the estimated vehicle steering wheel angle obtained through support vector regression; a y Indicates the lateral acceleration of a vehicle; a t This indicates the threshold value for switching lateral acceleration of the vehicle.

[0173] A co-simulation platform based on MATLAB / Simulink and the vehicle dynamics software CarSim was built to test the steering wheel angle estimation method designed in this invention. In the co-simulation platform, the steering wheel angle was controlled to rotate from 0° with an amplitude of 100° and a frequency of 0.165Hz, and the target car was set to move at a constant speed of 20km / h and 60km / h. The final experimental results are as follows. Figure 3 , Figure 4, Figure 5 , Figure 6 As shown in the figure, the steering wheel angle estimation method outputs an estimated steering wheel angle that closely follows the actual steering wheel angle. Under different operating conditions, the error in the angle estimation can be maintained within 2°, thus maintaining high accuracy.

[0174] In summary, this invention accurately estimates the steering wheel angle of a car under different lateral accelerations, overcomes the parameter uncertainties and vehicle state measurement noise problems faced by vehicle system dynamics, provides a reference scheme for the estimation of car steering wheel angle driven by a hybrid mechanism and data approach, and effectively provides a signal reference for the fault diagnosis and fault-tolerant control of the steering wheel angle of future intelligent vehicle steer-by-wire systems.

[0175] The preferred embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the scope of protection of the present invention is not limited to the specific details in the above embodiments. Within the scope of the technical concept of the present invention, any person skilled in the art can make equivalent substitutions or changes based on the technical solution and inventive concept of the present invention within the scope of the technology disclosed in the present invention. These simple modifications are all within the scope of protection of the present invention.

[0176] It should also be noted that the various specific technical features described in the above specific embodiments can be combined in any suitable manner without contradiction. In order to avoid unnecessary repetition, the present invention will not describe the various possible combinations separately.

[0177] Furthermore, various different embodiments of the present invention can be combined in any way, as long as they do not violate the spirit of the present invention, they should also be regarded as the content disclosed by the present invention.

Claims

1. A method for estimating steering wheel angle based on least squares and support vector regression, characterized in that, Includes the following steps: Step 1: Establish a nonlinear expression function for vehicle driving based on the vehicle's lateral mechanical characteristics, as follows: 11) Establish a two-degree-of-freedom vehicle dynamics model, as shown below: In the formula, m represents the total vehicle mass; v x Indicates the vehicle's longitudinal speed; This indicates the sideslip angular velocity of the vehicle's center of gravity. Indicates the vehicle's yaw rate; F represents the yaw acceleration of the vehicle. yf F represents the equivalent lateral force of the front tire; yr δ represents the equivalent lateral force of the rear tire. f Indicates the steering angle of the vehicle's front wheels; I z yaw moment of inertia of the vehicle; a represents the distance from the vehicle's center of gravity to the front axle; b represents the distance from the vehicle's center of gravity to the rear axle. 12) A linear tire model is used to describe the equivalent lateral forces of the front and rear tires, as shown below: F yf =C f a f (3) F yr =C r a r (4) In the formula, F yf F represents the equivalent lateral force of the front tire; yr C represents the equivalent lateral force of the rear tire; f Indicates the front wheel lateral stiffness; C r Indicates the rear wheel lateral stiffness; α f Indicates the front wheel slip angle; α r Indicates the rear wheel slip angle; 13) The front and rear wheel slip angles are approximately expressed as: In the formula, β represents the vehicle's sideslip angle; 14) By rearranging formulas (1)-(6) and incorporating the small-angle assumption, the linear two-degree-of-freedom vehicle dynamics model is obtained as follows: In the formula, This indicates the sideslip angular velocity of the vehicle's center of gravity. 15) The vehicle's center of gravity sideslip angular velocity is equivalently replaced by lateral acceleration, that is: In the formula, a y Indicates the lateral acceleration of the vehicle; 16) For an automotive electronic power steering system, the vehicle steering wheel angle θ to be estimated. c With the vehicle's front wheel steering angle δ f If a definite transmission ratio exists, then: i c =d f ·G c (10) In the formula, θ c Indicates the steering wheel angle of the vehicle; G c Indicates the gear ratio of the electronically controlled power steering system; 17) When the car is driving under steady-state conditions, the vehicle's sideslip angle β and yaw rate are... All are constant values, including the vehicle's yaw acceleration. and vehicle center of gravity sideslip angular velocity Since all values ​​are 0, after combining formulas (7)-(10) and rearranging, we obtain the nonlinear expression function of vehicle driving: In the formula, k represents the steady-state yaw rate gain; Step 2: Based on the established nonlinear expression function of vehicle driving, design a mechanism-based estimation strategy for the car steering wheel angle using recursive least squares, as follows: 21) Rewrite formula (11) in discrete function form, that is: ξ(k)=f(k,θ c (k)) (13) ξ(k)=[v x (k),a y (k)] T (14) In the formula, ξ(k) represents the measurable state vector of the vehicle at time k; v x (k) represents the longitudinal speed of the vehicle at time k; a y (k) represents the lateral acceleration of the vehicle at time k; f(k,θ) c (k) represents the nonlinear expression function of vehicle movement at time k; 22) Taylor expansion is used to locally linearize the measurable state vector ξ(k) of the vehicle at time k: ξ(k)≈H(k)(θ c (k)-θ c (k-1))+f(k-1,θ c (k-1)) (15) In the formula, ξ(k) represents the measurable state vector of the vehicle at time k; ξ(k-1) represents the measurable state vector of the vehicle at time k-1; H(k) represents the value of f(k-1,θ) at time k. c (k-1)) for θ c The Jacobian matrix of (k-1) digits; θ c (k) represents the steering wheel angle of the vehicle at time k; θ c (k-1) represents the steering wheel angle of the vehicle at time k-1; f(k-1,θ) c (k-1)) represents the nonlinear expression function of vehicle movement at time k-1; 23) Let △ξ(k)=ξ(k)-f(k-1,θ c (k-1))+H(k)θ c (k-1), combined with formula (15), we get: △ξ(k)≈H(k)θ c (k) (17) In the formula, △ξ(k) represents the measurable state vector increment of the vehicle at time k; 24) The recursive least squares cost function to be used is set as follows: In the formula, Represents the recursive least squares cost function based on the nonlinear expression function of vehicle driving; This represents the estimated steering wheel angle of the vehicle. Let f(i, θ) represent the estimated vehicle steering angle obtained at time i based on least squares; η represents the forgetting coefficient of the recursive least squares cost function; Δξ(i) represents the measurable state vector increment of the vehicle at time i; H(i) represents f(i-1, θ) at time i. c (i-1)) for θ c The Jacobian matrix of (i-1); θ c (i-1) represents the steering wheel angle of the vehicle at time i; f(i-1,θ) c (i-1)) represents the nonlinear expression function of vehicle movement at time i-1; 25) The estimated vehicle steering wheel angle obtained based on least squares is expressed as: In the formula, This represents the estimated vehicle steering wheel angle obtained at time k based on least squares. Let f(k-1,θ) represent the estimated steering wheel angle of the vehicle at time k-1; Δξ(k) represent the measurable state vector increment of the vehicle at time k; Q(k) represent the recursive least squares quantization matrix based on the nonlinear expression function of vehicle driving at time k; c (k-1)) represents the nonlinear expression function of vehicle movement at time k-1; H(k-1) represents the nonlinear expression function of vehicle movement at time k-1. c (k-2)) with respect to θ c The Jacobian matrix of (k-2) digits; θ c (k-2) represents the steering wheel angle of the vehicle at time k-2; f(k-2,θ) c (k-2)) represents the nonlinear expression function of vehicle driving at time k-2; I represents the identity matrix; G(k) represents the recursive least squares iteration matrix based on the nonlinear expression function of vehicle driving at time k; G(k-1) represents the recursive least squares iteration matrix based on the nonlinear expression function of vehicle driving at time k-1; Step 3: The estimated steering wheel angles under different lateral accelerations are corrected using a recursive least squares-based mechanism-based estimation strategy and a support vector regression-based data-driven estimation strategy. Details are as follows: 31) The steering wheel angle of a car is estimated using a data-driven method based on support vector regression; Let the input variable x for support vector regression be: In the formula, x represents the input variable for support vector regression; a x Indicates the longitudinal acceleration of the vehicle; a y Indicates the lateral acceleration of the vehicle; 32) Establish a support vector regression sample dataset X: In the formula, X represents the support vector regression sample dataset; N represents the number of sample data; R represents a real number; d represents the input dimension of support vector regression, and d = 5; x i This represents the support vector regression input variable for the i-th sample data; θ ci This represents the actual value of the vehicle steering wheel angle for the i-th sample data; 33) Design the support vector regression curve function f(x): In the formula, f(x) represents the support vector regression curve function; w represents the support vector regression curve function weight; κ represents the support vector regression curve function bias; and x represents the support vector regression input variable. This represents the estimated vehicle steering wheel angle obtained based on support vector regression. 34) The process of estimating the steering wheel angle through support vector regression is transformed into a quadratic convex optimization problem to be solved, and the support vector regression solution formula is established: In the formula, θ c Indicates the steering wheel angle of the vehicle; ε represents the support vector regression error threshold. 35) Introducing a relaxation factor into formula (25) yields the optimized support vector regression solution: In the formula, w represents the weight of the support vector regression curve function; Λ represents the penalty coefficient of the support vector regression curve function; ξ i This represents the upper boundary relaxation factor of the regression curve function for the i-th support vector; κ represents the lower boundary relaxation factor of the support vector regression curve function for the i-th support vector; x represents the input variable of support vector regression; κ represents the bias of the support vector regression curve function. 36) Introducing Lagrange multipliers into formula (26), and obtaining the result through dual transformation: In the formula, α i Denotes the i-th upper boundary Lagrange multiplier; α i * Denotes the i-th lower boundary Lagrange multiplier; α j Denotes the j-th upper boundary Lagrange multiplier; α j * Denotes the j-th lower boundary Lagrange multiplier; x i x represents the support vector regression input variable for the i-th sample data; j This represents the support vector regression input variable for the j-th sample data; 37) Solve equation (27) to obtain the values ​​of the upper and lower boundary Lagrange multipliers. Use the Carlow-Kun-Tucker condition to quickly obtain the bias κ of the support vector regression curve function. Finally, the estimated value of the vehicle steering wheel angle obtained based on support vector regression is expressed as: In the formula, α represents the estimated vehicle steering wheel angle obtained based on support vector regression. i * κ represents the i-th lower boundary Lagrange multiplier; i This represents the function bias of the regression curve for the i-th support vector; 38) The estimated value of the vehicle steering wheel angle correction obtained by combining least squares and support vector regression is: In the formula, This represents the estimated steering wheel angle of the vehicle. This represents the estimated vehicle steering wheel angle obtained based on least squares. This represents the estimated vehicle steering wheel angle obtained through support vector regression; a y Indicates the lateral acceleration of a vehicle; a t This indicates the threshold value for switching lateral acceleration of the vehicle.

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