CN110533796B - Vehicle rollover prediction algorithm based on truncation importance sampling failure probability method - Google Patents

Abstract

The invention provides a sampling failure probability based on truncation importanceThe vehicle rollover prediction algorithm of the rate method comprises the following steps: s1, regarding each vehicle state quantity as a random variable subject to normal distribution, and randomly generating z sample points; s2, calculating the total failure probability of z sample points by using an importance sampling method; s3, acquiring vehicle state quantity when the vehicle actually runs to obtain m vehicle actual state points in a certain time period; s4, substituting the m actual state points of the vehicle into the calculation formula of the total failure probability to obtain the real-time failure probability of the vehicle in the period of time, and according to the real-time failure probability p_fPredicting the possibility of the rollover of the automobile. The invention selects an importance sampling method to replace the traditional method for calculating the lateral load transfer rate and judging the vehicle rollover, reduces the strong nonlinearity of a complex system and the external interference of uncertainty, and greatly reduces the complexity of calculation, thereby ensuring the real-time performance of a vehicle rollover risk prediction algorithm.

Description

Vehicle rollover prediction algorithm based on truncation importance sampling failure probability method

Technical Field

The invention relates to the technical field of automobile safety, in particular to a vehicle rollover prediction algorithm based on a truncation importance sampling failure probability method.

Background

In the prior art, because a human-vehicle-road interaction system has strong nonlinearity and complexity and uncertainty of vehicle state modeling, a driver of a heavy vehicle or a vehicle active rollover prevention control device must correct actions of the heavy vehicle such as speed, steering and the like in time according to dynamic response of the heavy vehicle and road environment information, so that the deterioration of the vehicle running stability can be effectively avoided.

However, as the driver, the vehicle state and parameters and the environmental road information are changed frequently, the human-vehicle-road interaction algorithm has strong nonlinearity, so that the accurate modeling of the vehicle state also has strong uncertainty. Traditional deterministic schemes have difficulty achieving accurate modeling.

Tsourapas, V. proposes a method of treating diabetes byThe algorithm for judging the rollover risk according to the actual lateral load transfer rate of the vehicle is shown in fig. 4, and the finally obtained failure probability calculation formula is as follows:

two integrals exist in the formula, the calculation is complex, and an accurate numerical solution is difficult to obtain.

Disclosure of Invention

Aiming at the technical problems, the invention aims to provide a vehicle rollover prediction algorithm based on a truncation importance sampling failure probability method, which applies a probability method considering system uncertainty to an automobile dynamic rollover prediction algorithm, reduces strong nonlinearity of a complex system and external interference of uncertainty, and accurately realizes prediction and evaluation of the dynamic rollover danger of a vehicle.

In order to solve the technical problem, the embodiment of the invention adopts the following technical scheme to realize:

1. the vehicle rollover prediction algorithm based on the truncation importance sampling failure probability method comprises the following steps:

s1, generating sample points: selecting n vehicle state quantities, regarding each vehicle state quantity as a random variable obeying normal distribution, and randomly generating z sample points x_k＝(x_k1,x_k2,…x_kn) K is 1,2,3 … z, wherein x_k1,x_k2,…x_knRepresenting different vehicle state quantities in the kth sample point;

s2, calculating the total failure probability of the sample points: sample points are placed in an n-dimensional space, and the total failure probability P of the z sample points is calculated by using an importance sampling method_f；

S3, generating a vehicle actual state point: when the vehicle actually runs, the vehicle state quantity is collected at a certain frequency in a time period, and m vehicle actual state points x in the time period are obtained_j ^*＝(x_j1 ^*,x_j2 ^*,…x_jn ^*) Where j is 1,2, … m, x_j1 ^*,x_j2 ^*,…x_jn ^*Indicating the jth vehicle actual state pointDifferent vehicle state quantities;

s4, calculating the real-time failure probability of the vehicle: m vehicle actual state points x_j ^*＝(x_j1 ^*,x_j2 ^*,…x_jn ^*) Placing in the n-dimensional space and substituting into the total failure probability P_fThe calculation formula of (2) to obtain the real-time failure probability p of the vehicle in the period_fBased on the real-time failure probability p_f' predicting the possibility of the vehicle rollover.

Beneficially or exemplarily, the vehicle state quantities include a vehicle center of mass height, a lateral acceleration at the vehicle center of mass, a yaw rate at the vehicle center of mass, and a roll angle at the vehicle center of mass.

Beneficially or exemplarily, wherein the step S2 includes:

s21, establishing a limit state equation g (x) in the n-dimensional space, substituting the sample point into g (x), if g (x) < 0, indicating that the sample point is invalid, and if g (x) > 0, indicating that the sample point is not invalid;

s22, drawing a limit state surface, and enabling all sample points which enable g (x) to be less than 0 to fall on the limit state surface;

s23, setting design checking points which are the points with the shortest distance to the origin of the n-dimensional space coordinate on the extreme state surface, and setting β₀Calculating a design check point sum β for the distance from the design check point to the origin of coordinates₀A value;

s24, β center of the circle with the origin of coordinates in the n-dimensional space₀Drawing a hypersphere as a radius, and dividing an n-dimensional space into an inner sphere area and an outer sphere area;

s25, calculating the total failure probability P of z sample points by using the Monte Carlo method and the radius importance sampling method_f。

Advantageously or exemplarily, wherein the design verification point x is obtained as described in S23_t＝(x_t1,x_t2,…x_tn) And β₀The procedure of the values is as follows:

calculating the design checking point as x by using the optimization model_t＝(x_t1,x_t2,…x_tn) Will beThe design check point is converted into a design point value of a standard normal space, and u is the value_t＝(u_t1,u_t2,…u_tn) Wherein, in the step (A),

i is 1,2,3 … n, n is the dimension of the sample random variable, μ_iDenotes x_iIs a normal distribution of_iDenotes x_iThe standard deviation of the normal distribution of (a);

according to β₀Definition of (D β)₀Expressed as:

list β₀The constrained optimization model of (2):

and solving the solution of the optimization model by using an optimization tool.

Beneficially or exemplarily, the process of S25 is as follows:

design of the square β of the distance of the proof point to the origin₀ ²Obeying x with degree of freedom n²Distribution, therefore, the total probability of failure P is calculated using the total probability formula_fWritten as follows:

in the formula (I), the compound is shown in the specification,

represents the probability that a sample point falls in the off-sphere region, P { g (x)<0|||x||≥β₀Denotes the probability of failure of the sample points in the out-of-sphere region, | x | |, is the norm of x.

For P { g (x)<0|||x||≥β₀The calculation of } is as follows:

introducing a truncated joint probability density function h_t(x) In h, with_t(x) When x | | ≧ β₀Truncation probability density function of time-random variable, h_t(x) Is expressed as:

in the formula, h_X(x) Is an original important sampling function generated by a screening method and obeying probability density distribution, and represents that a random sample point x is equal to (x)₁,x₂,…x_n) A joint probability density distribution function of (a);

is at the original important sampling function h_X(x) The probability that the sample point falls in the region outside the β sphere,

R^*represents that x | | | | ≧ β in n-dimensional variable space₀A space in (1);

thus, P { g (X)<0|||x||≥β₀Rewrite to:

in the formula (I), the compound is shown in the specification,

is represented by h_t(x) To truncate the mathematical expectation of the sampling density function, I (x) is an indication function when | x | ≧ β₀When i (x) is 1; when | | | x | | non-conducting phosphor<β₀When i (x) is 0;

overall, the total probability of failure P_fThe calculation formula of (a) is as follows:

advantageously or exemplarily, further comprising step S5: determining a real-time failure probability p_f' the evaluation index, the rollover probability model is established, and the real-time failure probability p is judged_f' trusted or not.

Advantageously or exemplarily, the evaluation index is a lateral load transfer rate, which is a ratio of a difference between vertical loads on wheels on both sides of the vehicle to a sum of the vertical loads;

judging the real-time failure probability p_fThe process of' plausibility is as follows:

fitting the real-time failure probability p by using a least square method_fObtaining a least square method fitting curve with the transverse load transfer rate, establishing a rollover probability model, and judging failure probability;

selecting t periods of time, and calculating the real-time failure probability p in the ith period of time_fiAnd transverse load transfer rate y_iTo obtain t data points (p)_fi′,y_i) And i is 1,2, …, t, and a fitting curve is obtained by using a least square method, and is expressed as a polynomial of degree m-1:

y(p_f′)＝a₀+a₁p_f′+a₂p_f′²+…+a_m-1p_f′^m-1，

wherein, a₀,a₁,……,a_m-1Fitting polynomial coefficients of the curve for a least squares method;

setting a threshold when y (p)_fi′)-y_iWhen | is larger than the threshold value, the real-time failure probability p in the ith period is represented_fi' trusted; when y_m-1(p_fi′)-y_iWhen | is less than the threshold value, the real-time failure probability p in the ith period is represented_fi' untrusted.

The vehicle active rollover prevention control device changes the running state of a vehicle to prevent rollover when judging that the vehicle has rollover based on the vehicle rollover prediction algorithm.

The various embodiments of the invention have the following beneficial effects:

the invention selects an importance sampling method to calculate the numerical estimation value of the system failure probability, replaces the traditional method of calculating the transverse load transfer rate and judging the vehicle rollover, reduces the strong nonlinearity of a complex system and the external interference of uncertainty, greatly reduces the complexity of calculation, and ensures the real-time performance of the vehicle rollover risk prediction algorithm.

Drawings

The invention is further illustrated by means of the attached drawings, but the embodiments in the drawings do not constitute any limitation to the invention, and for a person skilled in the art, other drawings can be obtained on the basis of the following drawings without inventive effort.

FIG. 1 is a flow chart of a vehicle rollover prediction algorithm according to embodiments 1 and 2 of the present invention;

FIG. 2 is a graph of the overall probability of failure versus lateral load transfer rate for the vehicle rollover prediction algorithm of embodiment 1 of the present invention;

FIG. 3 is a graph of the overall probability of failure versus lateral load transfer rate for the vehicle rollover prediction algorithm of embodiment 2 of the present invention;

FIG. 4 is a flowchart of a calculation of rollover failure probability and reliability index for a heavy vehicle.

Detailed Description

The invention is further described below with reference to the following examples in conjunction with the accompanying drawings.

The vehicle rollover prediction algorithm based on the truncation importance sampling failure probability method comprises the following steps:

s1, generating sample points: selecting n vehicle state quantities, regarding each vehicle state quantity as a random variable obeying normal distribution, and randomly generating z sample points x_k＝(x_k1,x_k2,…x_kn) K is 1,2,3 … z, wherein x_k1,x_k2,…x_knRepresenting different vehicle state quantities in the kth sample point;

s2, calculating the total failure probability of the sample points: sample points are placed in an n-dimensional space, and the total failure probability P of the z sample points is calculated by using an importance sampling method_f；

S3, generating a vehicle actual state point: when the vehicle actually runs, the vehicle state quantity is collected at a certain frequency in a time period, and m vehicle actual state points x in the time period are obtained_j ^*＝(x_j1 ^*,x_j2 ^*,…x_jn ^*) Where j is 1,2, … m, x_j1 ^*,x_j2 ^*,…x_jn ^*Representing different vehicle state quantities in the jth vehicle actual state point;

s4, calculating the real-time failure probability of the vehicle: m vehicle actual state points x_j ^*＝(x_j1 ^*,x_j2 ^*,…x_jn ^*) Placing in the n-dimensional space and substituting into the total failure probability P_fThe calculation formula of (2) to obtain the real-time failure probability p of the vehicle in the period_fBased on the real-time failure probability p_f' predicting the possibility of the vehicle rollover.

In one embodiment, the vehicle state quantities include a vehicle center of mass height, a lateral acceleration at the vehicle center of mass, a yaw rate at the vehicle center of mass, and a roll angle at the vehicle center of mass. In another embodiment, other vehicle parameters and state quantities that reflect the driving state of the vehicle are also possible.

In one embodiment, the method further comprises step S5 of determining the real-time failure probability p_f' the evaluation index, the rollover probability model is established, and the real-time failure probability p is judged_f' trusted or not.

There is currently no relatively effective criterion for an acceptable level of probability of vehicle rollover failure. The rollover failure probability is used for predicting the probability of rollover of the automobile, and the basis of the widely accepted rollover state judgment at present is the transverse load transfer rate. The two must have a certain internal relation, but are difficult to be expressed by an accurate analytical expression. In the fields of science and technology, for engineering problems that functional expressions among variables are difficult to directly derive, a curve fitting method is commonly used to obtain functional relationships among the variables, and known experimental data are combined with a mathematical method to obtain approximate functional expressions among the variables.

In one embodiment, the evaluation index is a lateral load transfer rate, which is a ratio of a difference between vertical loads on wheels on both sides of the vehicle to a sum of the vertical loads;

judging the real-time failure probability p_fThe process of' plausibility is as follows:

fitting the real-time failure probability p by using a least square method_fObtaining a least square method fitting curve with the transverse load transfer rate, establishing a rollover probability model, and judging failure probability;

selecting t periods of time, and calculating the real-time failure probability p in the ith period of time_fiAnd transverse load transfer rate y_iTo obtain t data points (p)_fi′,y_i) And i is 1,2, …, t, and a fitting curve is obtained by using a least square method, and is expressed as a polynomial of degree m-1:

y(p_f′)＝a₀+a₁p_f′+a₂p_f′²+...+a_m-1p_f′^m-1，

wherein, a₀,a₁,……,a_m-1Fitting polynomial coefficients of the curve for a least squares method;

setting a threshold when y (p)_fi′)-y_iWhen | is larger than the threshold value, the real-time failure probability p in the ith period is represented_fi' trusted; when y_m-1(p_fi′)-y_iWhen | is less than the threshold value, the real-time failure probability p in the ith period is represented_fi' untrusted.

In the embodiment, the least square fitting is adopted, so that the relation between the real-time failure probability and the transverse load transfer rate can be expressed simply, conveniently and accurately, and the reliability of the real-time failure probability can be judged well by the established rollover probability model. The least square method is a strict method based on an error theory, so the method is widely applied to astronomy, physics, chemistry and engineering. It solves the problem of how to find a trustworthy value from a set of measured values. For a plurality of measured data (x) with equal precision_i,y_i) The best fitting curve is sought to minimize the sum of the squares of its errors. The least squares method is considered one of the most reliable methods to find a set of unknowns from a set of measurements.

In another embodiment, other curve fitting methods may be used, such as moving least squares, BP neural networks, and the like.

In one embodiment, the lateral load transfer rate may be calculated by:

wherein FL_iAnd FR_lAnd vertical loads on the left and right wheels of the vehicle, respectively; i and n are the position of the axle and the total axle number, respectively. LTR value is [ -1,1 [)]LTR is 0 when the vehicle is running on a good road surface. When the LTR absolute value is larger than the stable threshold LTR_thWhen the vehicle is about to turn over, the vehicle is in danger of rolling over.

In one embodiment, step S2 includes:

s21, establishing a limit state equation g (x) in the n-dimensional space, substituting the sample point into g (x), if g (x) < 0, indicating that the sample point is invalid, and if g (x) > 0, indicating that the sample point is not invalid;

s22, drawing a limit state surface, and enabling all sample points which enable g (x) to be less than 0 to fall on the limit state surface;

s23, setting design checking points which are the points with the shortest distance to the origin of the n-dimensional space coordinate on the extreme state surface, and setting β₀Calculating a design check point sum β for the distance from the design check point to the origin of coordinates₀A value;

s24, β center of the circle with the origin of coordinates in the n-dimensional space₀Drawing a hypersphere as a radius, and dividing an n-dimensional space into an inner sphere area and an outer sphere area;

s25, calculating the total failure probability P of z sample points by utilizing a truncation importance sampling method_f。

In one embodiment, the design verification point x is determined as described in S23_t＝(x_t1,x_t2,…x_tn) And β₀The procedure of the values is as follows:

calculating the design checking point as x by using the optimization model_t＝(x_t1,x_t2,…x_tn) If the design checking point is converted into the design point value of the standard normal space, u is present_t＝(u_t1,u_t2,…u_tn) Wherein, in the step (A),

i is 1,2,3 … n, n is the dimension of the sample random variable, μ_iDenotes x_iIs a normal distribution of_iDenotes x_iThe standard deviation of the normal distribution of (a);

according to β₀Definition of (D β)₀Expressed as:

since the design checking point is the point on the extreme state plane with the shortest distance to the origin of the n-dimensional space coordinates, β₀Calculating the distance of the design check point to the origin of coordinates and the design check point is on the extreme state surface, thus listing β₀The constrained optimization model of (2):

and solving the solution of the optimization model by using an optimization tool, wherein large-scale mathematical calculation software such as matlab optimization tool can be selected to calculate the optimization model.

In the preferred embodiment, the optimization tool is used to find the design checking point and calculate the distance β from the design checking point to the origin in the normal space₀The size of (2).

The first embodiment is as follows:

wherein the step S25 specifically includes: s25, calculating the total failure probability P of z sample points by utilizing a truncation importance sampling method_f。

Similar to the radius importance sampling, the truncated importance sampling method is also to establish a beta sphere with a design check point as a center and sample the area outside the sphere, but the truncated importance sampling method is to construct a truncated important sampling function outside the beta sphere based on the traditional importance sampling. The method can reduce the sampling in the security domain on the basis of the traditional important sampling method, and further improve the sampling efficiency.

The principle is that in a standard normal space, the distance β from an origin point to the origin point is designed by taking the origin point as a sphere center₀The method comprises the steps of establishing a hypersphere called β sphere for the radius of the sphere, knowing that a failure domain is completely outside β sphere based on the properties of design check points, utilizing a truncation importance sampling method, directly taking a sampling function as an independent normal distribution function, arranging a sampling center at the design check points, taking 1-2 times of a corresponding original random variable variation coefficient according to the distribution of the original random variable, and establishing a β sphere structure truncation importance sampling function sitting outside the sphere.

Specifically, step S25 is as follows:

design of the square β of the distance of the proof point to the origin₀ ²Obeying x with degree of freedom n²Distribution, therefore, the total probability of failure P is calculated using the total probability formula_fWritten as follows:

in the formula (I), the compound is shown in the specification,

represents the probability that a sample point falls in the off-sphere region, P { g (x)<0|||x||≥β₀Denotes the failure probability of the sample point in the area outside the sphere, | | x | | is the norm of x, and the physical meaning thereof denotes that the sample point x ═ x (x)₁,x₂,…x_n) Distance from the origin.

For P { g (x)<0|||x||≥β₀The calculation of } is as follows:

introducing a truncated joint probability density function h_t(x) In h, with_t(x) When x | | ≧ β₀Truncation probability density function of time-random variable, h_t(x) Is expressed as：

In the formula, h_X(x) Is an original important sampling function generated by a screening method and obeying probability density distribution, and represents that a random sample point x is equal to (x)₁,x₂,…x_n) A joint probability density distribution function of (a);

is at the original important sampling function h_X(x) Probability that a sample point falls in the β out-of-sphere region, P_ht＝∫_R*h_X(x)dx；R^*Represents that x | | | | ≧ β in n-dimensional variable space₀A space in (1);

thus, P { g (x)<0|||x||≥β₀Rewrite to:

in the formula (I), the compound is shown in the specification,

is represented by h_t(x) To truncate the mathematical expectation of the sampling density function, I (x) is an indication function when | x | ≧ β₀When i (x) is 1; when | | | x | | non-conducting phosphor<β₀When i (x) is 0;

overall, the total probability of failure P_fThe calculation formula of (a) is as follows:

in the embodiment, the total failure probability is calculated by adopting a truncation importance sampling method and is used as the rollover risk criterion, and compared with the existing algorithm for performing the rollover risk criterion according to the actual traffic flow transverse load transfer rate, the method has the advantages that the strong nonlinearity and uncertainty external interference of a complex system are reduced, the calculation complexity is greatly reduced, and the real-time performance of the vehicle rollover risk prediction algorithm is ensured.

As can be seen from fig. 3, the rollover probability curve is very similar to the lateral load transfer rate in both magnitude and trend. In practical application, the lateral load transfer rate of the vehicle is difficult to obtain accurately in real time and is easy to be interfered by the outside, so that the rollover probability calculated in real time can be completely utilized to predict the rollover risk degree of the heavy vehicle on line in the follow-up rollover warning research of the heavy vehicle.

Example two:

wherein the step S25 specifically includes: s25, calculating the total failure probability P of z sample points by using the Monte Carlo method and the radius importance sampling method_f。

The principle is that in a standard normal space, an original point is taken as a sphere center, and the distance β from a checking point to the original point is designed₀A hypersphere, called β sphere, is established for the radius of the sphere, the failure domain is completely out of β sphere based on the nature of the design check point, and the sampling of the importance of the radius only samples the area outside the β sphere, thereby reducing the sampling of safe areas which are not interested.

The process of S25 is as follows:

according to the drawing process of the hypersphere, the sample points of g (x) less than 0 all fall into the area outside the sphere, and a total probability formula is applied, so that the total failure probability P_fThe calculation formula of (a) is:

P_f＝P{g(x)<0|||x||≥β₀}P{||x||≥β₀}，

wherein P { | | | x | | ≧ β₀Denotes the probability that a sample point falls in the off-sphere region, P { g (x)<0|||x||≥β₀Denotes the failure probability of the sample point in the area outside the sphere, | | x | | is the norm of x, and the physical meaning thereof denotes that the sample point x ═ x (x)₁,x₂,…x_n) Distance from origin;

for P { g (x)<0|||x||≥β₀And performing sampling calculation by adopting a Monte Carlo sampling method, and estimating as follows:

wherein, N represents the total sampling times of the area outside the sphere, namely the total number z of the sample points; nf represents the sampling number of out-of-sphere region failures, i.e. the total number of sample points falling into the out-of-sphere region;

for P { | | | x | | > β₀The calculation of } is as follows:

the probability that the sample point falls into the inner area of the ball is P_s，P_sVolume V equal to a hyper-sphere with radius β 0_{Super sphere}Volume V of a hyper-cube formed by spatial intervals in which random variables are located_{Super cube}The ratio of (A) to (B) is as follows:

that is, P { | | | x | | ≧ β₀}＝1-P_s，

Where n denotes the dimension of the random variable, d denotes the side length of the hyper-cube, and r denotes the radius of the hyper-sphere, i.e. r is β₀The function (·) is a function that calculates the volume of an n-dimensional sphere;

when t is a natural number, (t) ═ t-1! .

P{||x||≥β₀The probability that the sample point falls into the area outside the sphere is represented, the practical meaning is the probability that the vehicle can turn over, and P { | | | x | | ≧ β₀Estimating as a small probability event, and calculating the probability P { | | | | x | ≧ β of the β sphere-outside region in the formula₀And mapping independent normal random variables into one-dimensional random variables which obey standard normal distribution. The standard normal distribution table shows that P (X | ≦ 3) ═ 2 (phi (3) -0.5) ═ 0.9974, that is, the values of the variables are almost all concentrated in [ -3,3]Within the interval, the random variable is set to the interval of [ -3,3 [ ]]For small probability events, the truncation limit of the value area is determined by random variables.

Probability (1-P) of sampling region_s) Mapping toObtaining a specific value range of the one-dimensional variable by using a one-dimensional random variable space, and then obtaining by using a density function of standard normal distribution:

thus, the overall failure probability is given by:

in the embodiment, the radius importance sampling method is adopted to calculate the total failure probability and take the total failure probability as the rollover risk criterion, and compared with the existing algorithm for performing the rollover risk criterion according to the actual traffic flow lateral load transfer rate, the method reduces the strong nonlinearity and uncertainty external interference of a complex system, greatly reduces the calculation complexity, and ensures the real-time performance of the vehicle rollover risk prediction algorithm.

As can be seen from fig. 2, the rollover probability curve is very similar to the lateral load transfer rate in both magnitude and trend. In practical application, the lateral load transfer rate of the vehicle is difficult to obtain accurately in real time and is easy to be interfered by the outside, so that the rollover probability calculated in real time can be completely utilized to predict the rollover risk degree of the heavy vehicle on line in the follow-up rollover warning research of the heavy vehicle.

Finally, it should be noted that the above embodiments are only used for illustrating the technical solutions of the present invention, and not for limiting the protection scope of the present invention, although the present invention is described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications or equivalent substitutions can be made on the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention.

Claims (5)

1. The vehicle rollover prediction algorithm based on the truncation importance sampling failure probability method is characterized by comprising the following steps of:

s1, generating sample points: selecting n vehicle state quantities, and regarding each vehicle state quantity asRandomly generating z sample points x according to random variables of normal distribution_k＝(x_k1，x_k2，...x_kn) Z, wherein x is 1,2,3_k1，x_k2，...x_knRepresenting different vehicle state quantities in the kth sample point;

s2, calculating the total failure probability of the sample points: sample points are placed in an n-dimensional space, and the total failure probability P of the z sample points is calculated by using an importance sampling method_f；

S3, generating a vehicle actual state point: when the vehicle actually runs, the vehicle state quantity is collected at a certain frequency in a time period, and m vehicle actual state points x in the time period are obtained_j ^*＝(x_j1 ^*，x_j2 ^*，...x_jn ^*) Wherein j is 1, 2.. m, x_j1 ^*，x_j2 ^*，...x_jn ^*Representing different vehicle state quantities in the jth vehicle actual state point;

s4, calculating the real-time failure probability of the vehicle: m vehicle actual state points x_j ^*＝(x_j1 ^*，x_j2 ^*，...x_jn ^*) Placing in the n-dimensional space and substituting into the total failure probability P_fThe real-time failure probability p of the vehicle in the time period is obtained_f′；

Wherein step S2 includes:

s21, establishing a limit state equation g (x) in the n-dimensional space, substituting the sample point into g (x), if g (x) < 0, indicating that the sample point is invalid, and if g (x) > 0, indicating that the sample point is not invalid;

s22, drawing a limit state surface, and enabling all sample points which enable g (x) to be less than 0 to fall on the limit state surface;

s23, setting design checking points which are the points with the shortest distance to the origin of the n-dimensional space coordinate on the extreme state surface, and setting β₀Calculating a design check point sum β for the distance from the design check point to the origin of coordinates₀A value;

s24, in the n-dimensional space, with the origin of coordinates as the center of a circle,β₀drawing a hypersphere as a radius, and dividing an n-dimensional space into an inner sphere area and an outer sphere area;

s25, calculating the total failure probability P of z sample points by utilizing a truncation importance sampling method_f；

Wherein the design check point x is obtained as described in S23_t＝(x_t1，x_t2，...x_tn) And β₀The procedure of the values is as follows:

calculating the design checking point as x by using the optimization model_t＝(x_t1，x_t2，...x_tn) If the design checking point is converted into the design point value of the standard normal space, u is present_t＝(u_t1，u_t2，...u_tn) Wherein, in the step (A),

n, n is the dimension of the random variable of the sample, μ_iDenotes x_iIs a normal distribution of_iDenotes x_iStandard deviation of normal distribution;

according to β₀Definition of (D β)₀Expressed as:

list β₀The constrained optimization model of (2):

solving the solution of the optimization model by using an optimization tool;

the process of S25 is as follows:

design of the square β of the distance of the proof point to the origin₀ ²Obeying x with degree of freedom n²Distribution, therefore, the total probability of failure P is calculated using the total probability formula_fWritten as follows:

in the formula (I), the compound is shown in the specification,

representing the probability that the sample point falls into the area outside the sphere, P { g (x) < 0| | | x | | ≧ β₀Denotes the probability of failure of the out-of-sphere region sample points, | x | | | is the norm of x,

for P { g (x) < 0| | | | x | | ≧ β₀The calculation of } is as follows:

introducing a truncated joint probability density function h_t(x) In h, with_t(x) When x | | ≧ β₀Truncation probability density function of time-random variable, h_t(x) Is expressed as:

in the formula, h_X(x) Is an original important sampling function generated by a screening method and obeying probability density distribution, and represents that a random sample point x is equal to (x)₁，x₂，...x_n) A joint probability density distribution function of (a);

is at the original important sampling function h_X(x) The probability that the sample point falls in the region outside the β sphere,

R^*represents that x | | | | ≧ β in n-dimensional variable space₀A space in (1);

therefore, P { g (X) < 0| | | x | | ≧ β₀Rewrite to:

in the formula (I), the compound is shown in the specification,

is represented by h_t(x) To truncate the mathematical expectation of the sampling density function, I (x) is an indication function when | x | ≧ β₀When I (x) is 1, when x < β₀When i (x) is 0;

overall, the total probability of failure P_fThe calculation formula of (a) is as follows:

2. the vehicle rollover prediction algorithm according to claim 1, wherein the vehicle state variables include vehicle center of mass height, lateral acceleration at the vehicle center of mass, yaw rate at the vehicle center of mass, and roll angle at the vehicle center of mass.

3. The vehicle rollover prediction algorithm based on the truncated importance sampling failure probability method according to claim 1, further comprising the step of S5: determining a real-time failure probability p_f' the evaluation index, the rollover probability model is established, and the real-time failure probability p is judged_f' trusted or not.

4. The vehicle rollover prediction algorithm based on the truncated importance sampling failure probability method according to claim 3, wherein the evaluation index is a lateral load transfer rate, which is a ratio of a difference between vertical loads on wheels on both sides of the vehicle and a sum of the vertical loads;

judging the real-time failure probability p_fThe process of' plausibility is as follows:

fitting the real-time failure probability p by using a least square method_fObtaining a least square method fitting curve with the transverse load transfer rate, establishing a rollover probability model, and judging failure probability;

selecting t periods of time, and calculating the real-time failure probability p in the ith period of time_fiAnd transverse load transfer rate y_iTo obtain t data points (p)_fi′，y_i) Where i is 1,2, …, t,and obtaining a fitting curve by using a least square method, wherein the fitting curve is expressed as a polynomial of m-1 degree:

y(p_f′)＝a₀+a₁p_f′+a₂p_f′²+…+a_m-1p_f′^m-1，

setting a threshold when y (p)_fi′)-y_iWhen | is larger than the threshold value, the real-time failure probability p in the ith period is represented_fi' trusted; when y_m-1(p_fi′)-y_iWhen | is less than the threshold value, the real-time failure probability p in the ith period is represented_fi' untrusted.

5. An active rollover prevention control device for a vehicle, characterized in that, when it is judged that the vehicle is rollover, the driving state of the vehicle is changed to prevent the vehicle from rollover, based on the vehicle rollover prediction algorithm according to any one of claims 1 to 4.

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