CN111674387B - Method for generating novel rollover early warning index based on derivative iterative prediction - Google Patents

Method for generating novel rollover early warning index based on derivative iterative prediction Download PDF

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CN111674387B
CN111674387B CN202010459010.7A CN202010459010A CN111674387B CN 111674387 B CN111674387 B CN 111674387B CN 202010459010 A CN202010459010 A CN 202010459010A CN 111674387 B CN111674387 B CN 111674387B
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vehicle
rollover
warning index
early warning
mass
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CN111674387A (en
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曹铭纯
王春燕
刘利锋
王展
赵万忠
刘晓强
秦亚娟
张自宇
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Nanjing University of Aeronautics and Astronautics
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B60—VEHICLES IN GENERAL
    • B60W—CONJOINT CONTROL OF VEHICLE SUB-UNITS OF DIFFERENT TYPE OR DIFFERENT FUNCTION; CONTROL SYSTEMS SPECIALLY ADAPTED FOR HYBRID VEHICLES; ROAD VEHICLE DRIVE CONTROL SYSTEMS FOR PURPOSES NOT RELATED TO THE CONTROL OF A PARTICULAR SUB-UNIT
    • B60W30/00—Purposes of road vehicle drive control systems not related to the control of a particular sub-unit, e.g. of systems using conjoint control of vehicle sub-units, or advanced driver assistance systems for ensuring comfort, stability and safety or drive control systems for propelling or retarding the vehicle
    • B60W30/02—Control of vehicle driving stability
    • B60W30/04—Control of vehicle driving stability related to roll-over prevention
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B60—VEHICLES IN GENERAL
    • B60W—CONJOINT CONTROL OF VEHICLE SUB-UNITS OF DIFFERENT TYPE OR DIFFERENT FUNCTION; CONTROL SYSTEMS SPECIALLY ADAPTED FOR HYBRID VEHICLES; ROAD VEHICLE DRIVE CONTROL SYSTEMS FOR PURPOSES NOT RELATED TO THE CONTROL OF A PARTICULAR SUB-UNIT
    • B60W40/00—Estimation or calculation of non-directly measurable driving parameters for road vehicle drive control systems not related to the control of a particular sub unit, e.g. by using mathematical models
    • B60W40/10—Estimation or calculation of non-directly measurable driving parameters for road vehicle drive control systems not related to the control of a particular sub unit, e.g. by using mathematical models related to vehicle motion
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B60—VEHICLES IN GENERAL
    • B60W—CONJOINT CONTROL OF VEHICLE SUB-UNITS OF DIFFERENT TYPE OR DIFFERENT FUNCTION; CONTROL SYSTEMS SPECIALLY ADAPTED FOR HYBRID VEHICLES; ROAD VEHICLE DRIVE CONTROL SYSTEMS FOR PURPOSES NOT RELATED TO THE CONTROL OF A PARTICULAR SUB-UNIT
    • B60W30/00—Purposes of road vehicle drive control systems not related to the control of a particular sub-unit, e.g. of systems using conjoint control of vehicle sub-units, or advanced driver assistance systems for ensuring comfort, stability and safety or drive control systems for propelling or retarding the vehicle
    • B60W30/02—Control of vehicle driving stability
    • B60W30/04—Control of vehicle driving stability related to roll-over prevention
    • B60W2030/043—Control of vehicle driving stability related to roll-over prevention about the roll axis
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B60—VEHICLES IN GENERAL
    • B60W—CONJOINT CONTROL OF VEHICLE SUB-UNITS OF DIFFERENT TYPE OR DIFFERENT FUNCTION; CONTROL SYSTEMS SPECIALLY ADAPTED FOR HYBRID VEHICLES; ROAD VEHICLE DRIVE CONTROL SYSTEMS FOR PURPOSES NOT RELATED TO THE CONTROL OF A PARTICULAR SUB-UNIT
    • B60W2520/00—Input parameters relating to overall vehicle dynamics
    • B60W2520/10—Longitudinal speed
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B60—VEHICLES IN GENERAL
    • B60W—CONJOINT CONTROL OF VEHICLE SUB-UNITS OF DIFFERENT TYPE OR DIFFERENT FUNCTION; CONTROL SYSTEMS SPECIALLY ADAPTED FOR HYBRID VEHICLES; ROAD VEHICLE DRIVE CONTROL SYSTEMS FOR PURPOSES NOT RELATED TO THE CONTROL OF A PARTICULAR SUB-UNIT
    • B60W2520/00—Input parameters relating to overall vehicle dynamics
    • B60W2520/10—Longitudinal speed
    • B60W2520/105—Longitudinal acceleration
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B60—VEHICLES IN GENERAL
    • B60W—CONJOINT CONTROL OF VEHICLE SUB-UNITS OF DIFFERENT TYPE OR DIFFERENT FUNCTION; CONTROL SYSTEMS SPECIALLY ADAPTED FOR HYBRID VEHICLES; ROAD VEHICLE DRIVE CONTROL SYSTEMS FOR PURPOSES NOT RELATED TO THE CONTROL OF A PARTICULAR SUB-UNIT
    • B60W2520/00—Input parameters relating to overall vehicle dynamics
    • B60W2520/12—Lateral speed
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B60—VEHICLES IN GENERAL
    • B60W—CONJOINT CONTROL OF VEHICLE SUB-UNITS OF DIFFERENT TYPE OR DIFFERENT FUNCTION; CONTROL SYSTEMS SPECIALLY ADAPTED FOR HYBRID VEHICLES; ROAD VEHICLE DRIVE CONTROL SYSTEMS FOR PURPOSES NOT RELATED TO THE CONTROL OF A PARTICULAR SUB-UNIT
    • B60W2520/00—Input parameters relating to overall vehicle dynamics
    • B60W2520/12—Lateral speed
    • B60W2520/125—Lateral acceleration
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B60—VEHICLES IN GENERAL
    • B60W—CONJOINT CONTROL OF VEHICLE SUB-UNITS OF DIFFERENT TYPE OR DIFFERENT FUNCTION; CONTROL SYSTEMS SPECIALLY ADAPTED FOR HYBRID VEHICLES; ROAD VEHICLE DRIVE CONTROL SYSTEMS FOR PURPOSES NOT RELATED TO THE CONTROL OF A PARTICULAR SUB-UNIT
    • B60W2540/00—Input parameters relating to occupants
    • B60W2540/18—Steering angle

Abstract

The invention discloses a method for generating a novel rollover early warning index based on derivative iterative prediction, which comprises the following steps of: the method for establishing the four-degree-of-freedom dynamic model of the vehicle comprises the following steps: longitudinal movement, lateral movement, yaw movement, and roll movement; combining the established four-degree-of-freedom dynamic model of the vehicle, considering the influence of the unsprung mass and the inertia force on the vehicle rollover, respectively carrying out force and moment balance analysis on the sprung mass and the unsprung mass, and improving the traditional rollover warning index LTR; the rollover early warning index LTR after the improvement is combined * A novel rollover early warning index PTLTR is generated by adopting a derivative iterative prediction method. The invention analyzes the rollover early warning index, considers the influence of the unsprung mass and the inertia force of the whole vehicle on rollover, improves the transverse load transfer rate, and provides a novel rollover early warning index based on a derivative iteration theory.

Description

Method for generating novel rollover early warning index based on derivative iterative prediction
Technical Field
The invention belongs to the technical field of automobile safety, and particularly relates to a method for generating a novel rollover early warning index based on derivative iterative prediction.
Background
The advent of automobiles has brought about a tremendous change in human life. In recent years, with the rapid development of social economy, automobiles have been widely popularized and used as a travel tool, and become a necessity in life of people. However, due to the rapid increase of the number of automobiles, the road traffic flow is increasing, and a series of safety accidents are generated at the same time, which becomes a great important problem in the modern society.
Some vehicles such as SUV, passenger car, truck and the like have high mass center position, large mass and low suspension rigidity, and are easy to have rollover accidents. In the traffic accident of the automobile, although the proportion of the rollover accidents is low, the fatality rate is very high. According to statistics of the U.S. highway traffic safety administration, more than 210 thousands of traffic accidents occur in the U.S. in 2012-2017, and 3 thousands of people have lost in the accidents in 2017, wherein the death rate of the rollover accidents accounts for 11 percent and is the second largest traffic accident which is next to the collision accident. According to the statistics of the national police bureau, the number of people died due to rollover accidents in 2015 in China is 51, and accounts for 39% of the total number of people died. Therefore, the side turning accident has serious consequences, and the research on the side turning safety performance is also necessary.
In the driving process of the automobile, objective time lag exists in the system. When the risk of rollover occurs, the state of the vehicle body is often difficult to correct in a short time, so that the vehicle is overturned. A proper early warning algorithm is provided, and a corresponding system is assembled for the vehicle, so that a driver can know the rollover risk of the vehicle earlier, the time lag danger is compensated, a control action is made in advance, and the occurrence of accidents is avoided.
The rollover early warning index is an index for measuring the rollover risk degree of a vehicle, and the traditional rollover early warning index is generally LTR which is defined as the difference value of vertical load forces borne by tires on the left side and the right side of the vehicle accounting for the total load of the vehicle. However, the conventional rollover early warning index can only represent the rollover risk degree of the vehicle at the current moment, and cannot warn the vehicle at the future moment.
However, researches show that early rollover warning is carried out, a driver or a controller is told to take appropriate control measures in advance, the rollover preventing capability of the vehicle is improved, the expected path can be better tracked in the vehicle running process, and the rollover risk can be effectively reduced. Most of existing control systems use rollover warning indexes as criteria for triggering a controller and a final control target, however, the existing rollover warning indexes are often not accurate enough, cannot give a good rollover warning effect to a driver, and are not beneficial to rollover prevention control of a vehicle. Therefore, an accurate rollover warning index is required to ensure the stability and reliability of the rollover prevention control system.
Disclosure of Invention
In view of the defects of the prior art, the invention aims to provide a method for generating a novel rollover early warning index based on derivative iterative prediction; the invention considers the influence of unsprung mass and inertia force on rollover, improves the traditional LTR rollover early warning index, and generates a novel rollover early warning index by combining a derivative iterative prediction method on the basis. The rollover early warning index can further consider the influence of the prediction of future time on rollover, is more accurate than the traditional rollover early warning index, and solves the problems that the rollover early warning index is not accurate enough and cannot give early warning at future moments to cause poor reliability and stability of a vehicle rollover prevention system.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
the invention discloses a method for generating a novel rollover early warning index based on derivative iterative prediction, which comprises the following steps:
(1) establishing a four-degree-of-freedom dynamic model of the vehicle, which comprises the following steps: longitudinal movement, lateral movement, yaw movement, and roll movement;
(2) combining the established vehicle four-degree-of-freedom dynamic model, considering the influence of the unsprung mass and the inertia force on vehicle rollover, respectively performing force and moment balance analysis on the sprung mass and the unsprung mass, improving the traditional rollover early warning index LTR to obtain the improved rollover early warning index LTR * ；
(3) The rollover early warning index LTR after the improvement is combined * A novel rollover early warning index PTLTR is generated by adopting a derivative iterative prediction method.
Further, the vehicle four-degree-of-freedom dynamic model in the step (1) comprises the following degrees of freedom: roll motion rotating about the roll axis x-axis, longitudinal motion horizontally displaced along the x-axis, yaw motion rotating about the z-axis, and lateral motion horizontally displaced along the y-axis, according to newton's theorem and darnaebel's principle, are specifically modeled as follows:
and (3) longitudinally moving the whole vehicle, and analyzing stress in the x direction:
ma x -mv y r＝∑F x (1)
and (3) carrying out lateral motion of the whole vehicle, and analyzing the stress in the y direction:
Figure GDA0003691089110000021
the whole vehicle performs yaw motion, and performs moment balance on the z axis:
Figure GDA0003691089110000022
the whole vehicle moves laterally, and moment balance is carried out on an x axis:
Figure GDA0003691089110000023
the lateral acceleration at the vehicle centroid is:
Figure GDA0003691089110000024
meanwhile, the force and moment spread of the vehicle on each shaft is as follows:
Figure GDA0003691089110000025
substituting the formulas (1), (2), (3), (4) and (5) into the formula (6) to obtain a four-degree-of-freedom dynamic model of the vehicle as follows:
Figure GDA0003691089110000031
in the formula, m is the vehicle mass; a is x Is the longitudinal acceleration; v. of y Is the lateral velocity; m is a unit of s The sprung mass of the whole vehicle; r is a yaw angular velocity; f xij 、F yij The four longitudinal and lateral forces of the tire are respectively given, and subscripts ij are fl, fr, rl and rr respectively represent left front wheel, right front wheel, left rear wheel and right rear wheel; δ represents a steering wheel angle; a is y Is the lateral acceleration; v. of x Is the longitudinal velocity; i is xz The moment of inertia of the sprung mass of the automobile around the x axis of the vehicle coordinate system; e is the distance from the sprung mass to the centre of roll; i is z The moment of inertia of the whole vehicle mass around the z axis of a vehicle coordinate system;
Figure GDA0003691089110000032
the vehicle body is in a side inclination angle;
Figure GDA0003691089110000033
is the vehicle body roll angle velocity;
Figure GDA0003691089110000034
roll stiffness;
Figure GDA0003691089110000035
roll damping is adopted; a is the distance from the center of mass to the front axle; b is the distance from the center of mass to the rear axle; t is the distance between the tires on two sides; g is the acceleration of gravity.
Further, the calculation formula of the conventional rollover warning index LTR in the step (2) is as follows:
Figure GDA0003691089110000036
in the formula, F R ,F L Respectively the respective vertical counter forces of the right and left wheels of the vehicle.
Further, the rollover warning index LTR improvement step in the step (2) is as follows:
(2.1) performing moment balance analysis on the roll center O point of the vehicle for the sprung mass:
Figure GDA0003691089110000037
(2.2) aiming at unsprung mass, obtaining a moment from a central point of a wheel grounding connecting line:
Figure GDA0003691089110000038
(2.3) lateral acceleration of the sprung mass relative to the overall vehicle acceleration a yCG ：
Figure GDA0003691089110000039
(2.4) deducing an improved rollover warning index LTR according to the result * The following were used:
Figure GDA00036910891100000310
in the formula, a ys Lateral acceleration of the sprung mass; m is d Is an unsprung mass; h is d Is the unsprung mass center-to-ground distance.
Further, the step (3) specifically includes:
(3.1) discretization of vehicle four-degree-of-freedom dynamic model
The vehicle four-degree-of-freedom dynamic model is a continuous linear steady system, and for the continuous linear steady system, the discrete model is expressed as follows:
x n+1 ＝Gx n +Hu k (13)
in the formula, G and H are state matrixes after discretization of the multi-free model of the whole vehicle, u k For driver steering wheel input, x n Is a state variable of the system;
calculating the state quantity of the next moment by using the state variable of the previous moment through the discrete modelSuppose the discretization system is at t 0 The time state variable is x 0 The state variable at the next time is represented as:
x 1 ＝Gx 0 +Hu k1 (14)
due to small discrete time, the input u of the system is in short time k Keeping the same; state variable x 2 By a state variable x 0 And the iterative input calculation of the system yields:
x 2 ＝G 2 x 0 +GHu k1 +Hu k1 (15)
(3.2) assuming that the steering wheel input does not change much in a short time t between 0.1s and 0.2s, nT is obtained by n iterative calculations s Predicted value x of second n ：
Figure GDA0003691089110000041
Substituting the above formula into formula (12) to obtain nT s LTR of time * The value:
Figure GDA0003691089110000042
wherein y is the modified LTR * A value;
Figure GDA0003691089110000043
(3.3) discretizing the steering wheel input correspondingly in Matlab:
u all ＝[u t0 u t1 ...u tk ] T (18)
the state variable x corresponding to each time instant all Expressed by the following formula:
Figure GDA0003691089110000044
k, is calculated by k iterations s The value of the predicted state variable is:
Figure GDA0003691089110000051
substituting the predicted state variable into equation (12) to obtain kT s Later predicted lateral load transfer rate values:
Figure GDA0003691089110000052
according to the Lagrange median theorem and the corresponding limit rule thereof, the derivative prediction principle theory is adopted, and the transverse load transfer rate at the next moment is expressed as follows:
y n+1 ＝y n +y′ n ·Δt′ (21)
substituting the transverse load transfer rate obtained after the discrete prediction into an equation (21) to obtain a transverse load transfer rate predicted value on the basis of the iterative prediction:
Figure GDA0003691089110000053
in the formula, Δ t' is the prediction step size selected for the second time.
The invention has the beneficial effects that:
the invention analyzes the rollover early warning index, considers the influence of the unsprung mass and the inertia force of the whole vehicle on rollover, improves the transverse load transfer rate, and provides a novel rollover early warning index based on a derivative iteration theory. This novel early warning index can carry out the early warning to the future constantly, has real-time and accuracy, can ensure the reliability and the stability of preventing the control system that turns on one's side, is favorable to improving the ability that prevents the vehicle and turn on one's side to help the better anticipated route of tracking at the vehicle course of traveling.
Drawings
Fig. 1 is a flow chart of deriving a novel rollover warning index PTLTR according to the present invention.
FIG. 2a is a model view of the longitudinal, yaw and lateral degrees of freedom of the vehicle of the present invention.
Fig. 2b is a model diagram of the roll degree of freedom of the vehicle according to the present invention.
Detailed Description
In order to facilitate understanding of those skilled in the art, the present invention will be further described with reference to the following examples and drawings, which are not intended to limit the present invention.
Referring to fig. 1, the method for generating a novel rollover warning index based on derivative iterative prediction according to the present invention includes the following steps:
(1) establishing a four-degree-of-freedom dynamic model of the vehicle, which comprises the following steps: longitudinal movement, lateral movement, yaw movement, and roll movement;
referring to fig. 2a and 2b, the four-degree-of-freedom dynamic model of the vehicle includes the following degrees of freedom: roll motion rotating around the roll axis x-axis, longitudinal motion horizontally displaced along the x-axis, yaw motion rotating around the z-axis, and lateral motion horizontally displaced along the y-axis, according to newton's theorem and darlinger's principle, are specifically modeled as follows:
and (3) longitudinally moving the whole vehicle, and analyzing stress in the x direction:
ma x -mv y r＝∑F x (1)
and (3) carrying out lateral motion of the whole vehicle, and analyzing the stress in the y direction:
Figure GDA0003691089110000061
the whole vehicle performs yaw motion, and performs moment balance on the z axis:
Figure GDA0003691089110000062
the whole vehicle moves laterally, and moment balance is carried out on an x axis:
Figure GDA0003691089110000063
the lateral acceleration at the vehicle centroid is:
Figure GDA0003691089110000064
meanwhile, the force and moment spread of the vehicle on each shaft is as follows:
Figure GDA0003691089110000065
substituting the formulas (1), (2), (3), (4) and (5) into the formula (6) to obtain a four-degree-of-freedom dynamic model of the vehicle as follows:
Figure GDA0003691089110000066
in the formula, m is the vehicle mass; a is x Is the longitudinal acceleration; v. of y Is the lateral velocity; m is s The sprung mass of the whole vehicle; r is a yaw angular velocity; f xij 、F yij The four longitudinal and lateral forces of the tire are respectively shown, and subscripts ij are fl, fr, rl and rr which respectively represent left front, right front, left rear and right rear wheels; δ represents a steering wheel angle; a is y Is the lateral acceleration; v. of x Is the longitudinal velocity; i is xz The moment of inertia of the sprung mass of the automobile around the x axis of the vehicle coordinate system; e is the distance from the sprung mass to the centre of roll; i is z The moment of inertia of the whole vehicle mass around the z axis of a vehicle coordinate system;
Figure GDA0003691089110000071
the vehicle body is in a side inclination angle;
Figure GDA0003691089110000072
is the vehicle body roll angle velocity;
Figure GDA0003691089110000073
roll stiffness;
Figure GDA0003691089110000074
roll damping is adopted; a is the distance from the center of mass to the front axle; b is the distance from the center of mass to the rear axle; t is the distance between the tires on two sides; g is the acceleration of gravity.
(2) Combining the established vehicle four-degree-of-freedom dynamic model, considering the influence of the unsprung mass and the inertia force on vehicle rollover, respectively performing force and moment balance analysis on the sprung mass and the unsprung mass, improving the traditional rollover early warning index LTR to obtain the improved rollover early warning index LTR * ；
The traditional formula for calculating the rollover warning index LTR is as follows:
Figure GDA0003691089110000075
in the formula, F R ,F L Respectively the respective vertical counter forces of the right and left wheels of the vehicle.
The rollover warning index LTR is improved as follows:
(2.1) performing moment balance analysis on the roll center O point of the vehicle for the sprung mass:
Figure GDA0003691089110000076
(2.2) aiming at unsprung mass, obtaining a moment from a central point of a wheel grounding connecting line:
Figure GDA0003691089110000077
(2.3) lateral acceleration of sprung Mass relative to vehicle acceleration a yCG ：
Figure GDA0003691089110000078
(2.4) deducing an improved rollover warning index according to the resultLTR * The following were used:
Figure GDA0003691089110000079
in the formula, a ys Lateral acceleration of the sprung mass; m is d Is the unsprung mass; h is d Is the unsprung mass center-to-ground distance.
(3) The rollover early warning index LTR after the improvement is combined * A novel rollover early warning index PTLTR is generated by adopting a derivative iterative prediction method.
(3.1) discretization of vehicle four-degree-of-freedom dynamic model
The vehicle four-degree-of-freedom dynamic model is a continuous linear steady system, and for the continuous linear steady system, the discrete model is expressed as follows:
x n+1 ＝Gx n +Hu k (13)
in the formula, G and H are state matrixes after discretization of the multi-free model of the whole vehicle, u k For driver steering wheel input, x n Is a state variable of the system;
calculating the state quantity of the next moment by using the state variable of the previous moment through the discrete model, and assuming that the discretization system is at t 0 The time state variable is x 0 The state variable at the next time is represented as:
x 1 ＝Gx 0 +Hu k1 (14)
due to small discrete time, the input u of the system is in short time k Keeping the original shape; state variable x 2 By a state variable x 0 And the iterative input calculation of the system yields:
x 2 ＝G 2 x 0 +GHu k1 +Hu k1 (15)
(3.2) assuming that the steering wheel input does not change much in a short time t between 0.1s and 0.2s, nT is obtained by n iterative calculations s Predicted value x in seconds n ：
Figure GDA0003691089110000081
Substituting the above formula into formula (12) to obtain nT s LTR of time * The value:
Figure GDA0003691089110000082
wherein y is the modified LTR * A value;
Figure GDA0003691089110000083
(3.3) discretizing the steering wheel input correspondingly in Matlab:
u all ＝[u t0 u t1 ...u tk ] T (18)
the state variable x corresponding to each time instant all Expressed by the following formula:
Figure GDA0003691089110000084
k, calculated by k iterations s The value of the predicted state variable is:
Figure GDA0003691089110000085
substituting the predicted state variable into equation (12) to obtain kT s Later predicted lateral load transfer rate values:
Figure GDA0003691089110000091
according to the Lagrange median theorem and the corresponding limit rule thereof, the derivative prediction principle theory is adopted, and the transverse load transfer rate at the next moment is expressed as follows:
y n+1 ＝y n +y′ n ·Δt′ (21)
substituting the transverse load transfer rate obtained after the discrete prediction into an equation (21) to obtain a transverse load transfer rate predicted value on the basis of the iterative prediction:
Figure GDA0003691089110000092
in the formula, Δ t' is the prediction step size selected for the second time.
While the invention has been described in terms of its preferred embodiments, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention.

Claims (2)

1. A method for generating a novel rollover early warning index based on derivative iterative prediction is characterized by comprising the following steps:
(1) establishing a four-degree-of-freedom dynamic model of the vehicle, which comprises the following steps: longitudinal movement, lateral movement, yaw movement, and roll movement;
(2) combining the established vehicle four-degree-of-freedom dynamic model, considering the influence of the unsprung mass and the inertia force on vehicle rollover, respectively performing force and moment balance analysis on the sprung mass and the unsprung mass, improving the traditional rollover early warning index LTR to obtain the improved rollover early warning index LTR * ；
(3) The rollover early warning index LTR after the improvement is combined * Generating a novel rollover early warning index PTLTR by adopting a derivative iterative prediction method;
the vehicle four-degree-of-freedom dynamic model in the step (1) comprises the following degrees of freedom: roll motion rotating about the roll axis x-axis, longitudinal motion horizontally displaced along the x-axis, yaw motion rotating about the z-axis, and lateral motion horizontally displaced along the y-axis, according to newton's theorem and darnaebel's principle, are specifically modeled as follows:
and (3) longitudinally moving the whole vehicle, and analyzing stress in the x direction:
ma x -mv y r＝∑F x (1)
and (3) carrying out lateral motion of the whole vehicle, and analyzing the stress in the y direction:
Figure FDA0003691089100000011
the whole vehicle performs yaw motion, and performs moment balance on the z axis:
Figure FDA0003691089100000012
the whole vehicle moves laterally, and moment balance is carried out on an x axis:
Figure FDA0003691089100000013
the lateral acceleration at the vehicle centroid is:
Figure FDA0003691089100000014
meanwhile, the force and moment spread of the vehicle on each shaft is as follows:
Figure FDA0003691089100000015
substituting the formulas (1), (2), (3), (4) and (5) into the formula (6) to obtain a four-degree-of-freedom dynamic model of the vehicle as follows:
Figure FDA0003691089100000021
in the formula, m is the vehicle mass; a is x Is the longitudinal acceleration; v. of y Is the lateral velocity; m is s The sprung mass of the whole vehicle; r is a yaw angular velocity; f xij 、F yij The four longitudinal and lateral forces of the tire are respectively shown, and subscripts ij are fl, fr, rl and rr which respectively represent left front, right front, left rear and right rear wheels; δ represents a steering wheel angle; a is y Is the lateral acceleration; v. of x Is the longitudinal velocity; i is xz The moment of inertia of the sprung mass of the automobile around the x axis of the vehicle coordinate system; e is the distance from the sprung mass to the centre of roll; i is z The moment of inertia of the whole vehicle mass around the z axis of a vehicle coordinate system;
Figure FDA0003691089100000022
the vehicle body is in a side inclination angle;
Figure FDA0003691089100000023
is the vehicle body roll angle velocity;
Figure FDA0003691089100000024
roll stiffness;
Figure FDA0003691089100000025
roll damping is achieved; a is the distance from the center of mass to the front axle; b is the distance from the center of mass to the rear axle; t is the distance between the tires on two sides; g is the acceleration of gravity;
the calculation formula of the traditional rollover warning index LTR in the step (2) is as follows:
Figure FDA0003691089100000026
in the formula, F R ,F L The vertical counter forces of the wheels on the right side and the left side of the vehicle are respectively;
the rollover warning index LTR improvement step in the step (2) is as follows:
(2.1) performing moment balance analysis on the roll center O point of the vehicle for the sprung mass:
Figure FDA0003691089100000027
(2.2) aiming at unsprung mass, obtaining a moment from a central point of a wheel grounding connecting line:
Figure FDA0003691089100000028
(2.3) lateral acceleration of the sprung mass relative to the overall vehicle acceleration a yCG ：
Figure FDA0003691089100000029
(2.4) deducing an improved rollover warning index LTR according to the result * The following were used:
Figure FDA00036910891000000210
in the formula, a ys Lateral acceleration of the sprung mass; m is d Is the unsprung mass; h is d Is the unsprung mass center-to-ground distance.
2. The method for generating a novel rollover warning indicator based on derivative iterative prediction as claimed in claim 1, wherein the step (3) specifically comprises:
(3.1) discretizing a four-degree-of-freedom dynamic model of the vehicle:
the vehicle four-degree-of-freedom dynamic model is a continuous linear steady system, and for the continuous linear steady system, the discrete model is expressed as follows:
x n+1 ＝Gx n +Hu k (13)
in the formula, G and H are state matrixes after discretization of the multi-free model of the whole vehicle, u k For driver steering wheel input, x n Is a state variable of the system;
calculating the state quantity of the next moment by using the state variable of the previous moment through the discrete model, and assuming that the discretization system is at t 0 The time state variable is x 0 The state variable at the next time is represented as:
x 1 ＝Gx 0 +Hu k1 (14)
due to small discrete time, the input u of the system is in short time k Keeping the same; state variable x 2 By a state variable x 0 And the iterative input calculation of the system yields:
x 2 ＝G 2 x 0 +GHu k1 +Hu k1 (15)
(3.2) assuming that the steering wheel input does not change much in a short time t between 0.1s and 0.2s, nT is obtained by n iterative calculations s Predicted value x in seconds n ：
Figure FDA0003691089100000031
Substituting the above formula into formula (12) to obtain nT s LTR of time * The value:
Figure FDA0003691089100000032
wherein y is the modified LTR * A value;
Figure FDA0003691089100000033
D＝0；
(3.3) discretizing the steering wheel input correspondingly in Matlab:
u all ＝[u t0 u t1 ... u tk ] T (18)
the state variable x corresponding to each time instant all Expressed by the following formula:
Figure FDA0003691089100000041
k, calculated by k iterations s The value of the predicted state variable is:
Figure FDA0003691089100000042
substituting the predicted state variable into equation (12) to obtain kT s Later predicted lateral load transfer rate values:
Figure FDA0003691089100000043
according to the Lagrange median theorem and the corresponding limit rule thereof, a derivative prediction principle theory is adopted, and the transverse load transfer rate at the next moment is expressed as follows:
y n+1 ＝y n +y′ n ·Δt′ (21)
substituting the transverse load transfer rate obtained after the discrete prediction into an equation (21) to obtain a transverse load transfer rate predicted value on the basis of the iterative prediction:
Figure FDA0003691089100000044
in the formula, Δ t' is the prediction step size selected for the second time.
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