CN101807341B - Speed limit determining method based on safety - Google Patents

Abstract

The speed limit of a vehicle should ensure the efficiency and the safety, but an interactive relationship exists between the efficiency and the safety. Based on the safety constraint conditions, the invention comprises the following five steps: 1. establishing a limit speed model with respect to the safety based on the principle that the speed limit on a highway should ensure that the accident death rate is less than an acceptable tolerance value; 2. determining the limit speed and a 85% speed relation model; 3. establishing a traffic accident prediction model; 4. quantifying the traffic safety service level, wherein the accident rate is used as an index for quantifying the safety service level; and 5. establishing a time-cost function of a high-grade highway based on the 85% speed and the design speed, and establishing an objective function of the operating efficiency by using the minimum time-cost. The invention establishes a limit speed optimization model using the operating efficiency as the objective function, and can calculate the optimum speed limit in the specific benefit orientation by using the limit speed optimization model.

Description

Speed limit based on security is determined method

Technical field

The present invention is based on a speed limit that obtains under the constraint condition of safety factor and determines method, can belong to the traffic safety field in the hope of the best speed limit under the specific benefit orientation.

Background technology

Speed limit is important ladder of management in the highway traffic control control, development along with highway construction in recent years, the improvement of highway communication condition, the raising that driver's driving quality is general and the enhancing of performance of motor vehicle, carry out the demand that the highway speed limit can not satisfy numerous highway users according to design rate or experience, therefore, be necessary this problem is studied, find the highway speed limit method for designing of reasonable science, to adapt to the highway traffic control demand.

Doctor Cheng Guozhu of China Harbin Institute of Technology is based on the Optimum Theory of operational research, with running car broad sense expense minimum is objective function, security, fuel economy, comfortableness with vehicle ' are constraint condition, set up mathematical model, as formula (1):

$f\left(v\right)=\mathrm{<figure-callout\; id="100"\; label="QL\; P\; g"\; filenames="HSA00000084393000011.png"\; state="\{\{state\}\}">QL</figure-callout>}\frac{P_g}{}\frac{{}_{}}{100}0.0013v^2-\mathrm{<figure-callout\; id="100"\; label="QL\; P\; g"\; filenames="HSA00000084393000011.png"\; state="\{\{state\}\}">QL</figure-callout>}\frac{P_g}{}\frac{{}_{}}{100}0.2518v+\frac{\mathrm{QL}\frac{G}{365*8}E}{v}+22.497\frac{P_g}{100}-\frac{\mathrm{QLGE}}{365*8}\frac{1}{v_i}---\left(1\right)$

In the formula: G---per-capita gross domestic product, unit/people/year;

E---average carrying coefficient, people/car;

Q---the volume of traffic, amount/day;

L---highway length, km/h;

V---operating speed, km/h;

v _i---the desirable speed of a motor vehicle of driver, km/h;

P _g---the oil consumption expense.

But this model has only utilized the data of U.S. major accident research institute (NCSS) when considering the security constraint condition, do not have well to consider the characteristics of China's road traffic accident, and the speed limit that utilizes this method to obtain does not conform to the actual conditions.Therefore, necessary actual conditions according to China are formulated a cover and are fit to feasible method for limiting speed China's national situation, reasonable, with raising traffic circulation efficient, and guarantee driving safety, development promotes social harmony.

Summary of the invention

Vehicle-speed limit is answered guaranteed efficiency, safety, and efficient is conflicting with safety, and under the free flow condition, the speed of a motor vehicle is high more, and then operational efficiency is high more, but security can descend.Therefore, how speed limit being set, can raising the efficiency, can guarantee safety again, is the important content that the present invention studies.In view of cart and this body structure of dolly and performance exist certain difference, and consider the vehicle ' characteristics, when carrying out speed limit, be necessary cart, dolly separated so that speed limit is more reasonable.

Step 1: the highroad vehicle speed restriction should guarantee accident death rate less than acceptable tolerance value, based on this principle, formulates maximum speed limit and sees formula (2) about the constraint condition model of security.

C(V _PSL，D _Geometry)≤C _critical (2)

In the formula: D _Geometry---linear variable, such as the gradient, curvature etc.;

C ()---accident rate adopts the prediction accident rate as its index;

C _Critical---the accident rate of highway expectation accident level.

V _Psl---maximum speed limit

Step 2: determine maximum speed limit and 85% speed of a motor vehicle relational model

Cumulative frequency is 85% o'clock a corresponding abscissa value among Fig. 1, promptly in the vehicle fleet that observes, has the place speed of a motor vehicle of 85% vehicle to be less than or equal to this value.

By gathering the highway and the Class I highway speed of a motor vehicle, maximum speed limit, longitudinal gradient, radius of horizontal curve data, utilize Stata9.0 software to carry out statistical study, adopt the regression analysis of rejecting backward: set up full model earlier, judgement according to index of correlation (| Z| value minimum) among the output result, one of each rejecting least meets the variable that enters model, no longer contains till the independent variable that does not meet criterion in regression equation.Therefore, remove incongruent independent variable successively and return again, finally obtain the linear relationship model of 85% speed of a motor vehicle of large and small car and speed limit, see formula (3) and formula (4).

Dolly:

V _{85_car}＝a ₁LnC _sl-a ₂(3)

Cart:

V _{85_truck}＝a ₃LnT _sl-a ₄(4)

In the formula: V _{85_car}---dolly 85% speed, km/h;

C _Sl-dolly maximum speed limit, km/h;

LnC _Sl-Ln (dolly maximum speed limit);

V _{85_truck}---cart 85% speed, km/h;

T _Sl---cart maximum speed limit, km/h;

LnT _Sl---Ln (cart maximum speed limit).

a ₁, a ₂, a ₃, a ₄---undetermined coefficient obtains by data statistic analysis software.

Step 3: utilize 85% speed of a motor vehicle of image data, longitudinal gradient, curvature, adopt progressively probability model homing method, set up two traffic Accident Forecast Model respectively with cart and dolly factor independent variable with statistical analysis software STATA9.0.Model is shown in (5), (6).

Dolly:

E(Crashy)＝Expo*EXP(a ₅+a ₆V85_car+a ₇Inverser)(5)

Cart:

E(Crashy)＝Expo*EXP(a ₈+a ₉V85_truck-a ₁₀Grade)(6)

Parameter is represented meaning:

L---road section length

The absolute volume of traffic sum of mean hours that Hourflow---dolly and cart are unidirectional, veh/h.

EXPO---traffic risk exposure index, the i.e. product of L and Hourflow

Inverser---curvature

Grade---the longitudinal gradient gradient

E (Crashy)---the accident number that takes place every year on average

a ₅, a ₆, a ₇, a ₈, a ₉, a ₁₀---undetermined coefficient obtains by data statistic analysis software

Formula (3) is updated to formula (5), can obtains traffic Accident Forecast Model, see formula (7) based on the dolly maximum speed limit.Formula (4) is updated to formula (6), can obtains traffic Accident Forecast Model, see formula (8) based on the cart maximum speed limit.

Dolly:

Crashy＝Expo*EXP(a ₁₁+a ₁a ₆LnCsl+a ₇Inverser)(7)

Cart:

Crashy＝Expo*EXP(a ₁₂+a ₃a ₉LnTsl+a ₁₀Grade)(8)

Parameter is represented meaning:

a ₁₁, a ₁₂---undetermined coefficient obtains by statistical analysis software

Step 4: the traffic safety service level quantizes

In line with the principle of practical application, choose the quantizating index of accident rate as the security service level, accident rate is the accident number in annual every kilometer of high-grade highway highway section.The height of accident rate is the direct embodiment of road safety level, can reflect road operation security level quantitatively.According to the characteristic that the high-grade highway accident is obeyed Poisson distribution, adopt generalized linear to return the accident mean measures equation that obtains high-grade highway, see formula (9).The predicted value of accident mean measures equation thought the highway safety level expected

C _critical＝L*EXP(a ₁₃+a ₁₄Hourflow+a ₁₅Hourflow ²+a ₁₆Hourflow ³)(9)

In the formula:

a ₁₃, a ₁₄, a ₁₅, a ₁₆---undetermined coefficient obtains by data statistic analysis software.

Wushu (7), formula (8), formula (9) substitution formula (2) obtain the security constraint condition model based on large and small car:

Dolly:

Expo*EXP (a ₁₁+ a ₁a ₆LnCsl+a ₇Inverser)≤L*EXP (a ₁₃+ a ₁₄Hourflow+a ₁₅Hourflow ²+ a ₁₆Hourflow ³) (10) cart:

Expo*EXP (a ₁₂+ a ₃a ₉LnTsl+a ₁₀Grade)≤L*EXP (a ₁₃+ a ₁₄Hourflow+a ₁₅Hourflow ²+ a ₁₆Hourflow ³) (11) parameter represents meaning the same

According to the important technological parameters of domestic automobile as can be known, the average max. speed of dolly is 160km/h, and the average max. speed of cart is 85km/h.In addition, the 67 regulation of People's Republic of China's law on road traffic safety implementing regulations (No. the 405th, State Council Decree), the F-Zero that the Speed Limitation on Freeway sign is indicated must not surpass 120km/h.

Dolly:

$\left\{\begin{array}{c}{V}_{\mathrm{PSL}\_\mathrm{car}}\&le;V_{\mathrm{Design}}\\ V_{\mathrm{PSL}\_\mathrm{car}}\&le;160\\ V_{\mathrm{PSL}\_\mathrm{car}}\&le;120\end{array}\right.---\left(12\right)$

Cart:

$\left\{\begin{array}{c}{V}_{\mathrm{PSL}\_\mathrm{truck}}\&le;V_{\mathrm{Design}}\\ V_{\mathrm{PSL}\_\mathrm{truck}}\&le;85\\ V_{\mathrm{PSL}\_\mathrm{truck}}\&le;120\end{array}\right.---\left(13\right)$

In the formula: V _PSL---maximum speed limit, km/h;

V _Design---highway section design rate, km/h.

Step 5: operational efficiency is to be benchmark with operating speed (85% speed of a motor vehicle) and design rate, makes up the time cost function of high-grade highway, with the objective function of time cost minimum as operational efficiency.

The driver is according to road and transportation condition, and total hope is to exchange high conevying efficiency at a high speed, and the speed of a motor vehicle is high more, and the time that is spent on road is short more, and time cost is also few more.Do not reach design rate by 85% speed of a motor vehicle and cause the time cost of the value of time increase on the way and few creation as operational efficiency, the calculating of the time value is certificate with the per-capita gross domestic product.The time cost function of operational efficiency as the formula (14), time cost is the smaller the better.

$\min \left(C_t\right)=\min [\frac{G}{365\&times;8}E\&CenterDot;Q\&CenterDot;(\frac{L}{V_{85}}-\frac{L}{V_{\mathrm{Design}}})]---\left(14\right)$

In the formula: C _t---high-grade highway passenger time cost in transit, unit;

G---per-capita gross domestic product, unit/people/year;

E---average carrying coefficient, people/car;

The volume of traffic of Q---dolly or cart ,/day;

L---road section length, km;

V ₈₅---85% bit rate, km/h;

V _Design---highway section design rate, km/h.

Formula (3), (4) substitution (14) are got large and small car maximum speed limit model:

Dolly:

$\mathrm{Min}=\frac{G}{365\&times;8}{E}_{\mathrm{car}}{Q}_{\mathrm{car}}(\frac{L}{a_1\mathrm{Ln}\left(V_{\mathrm{PSL}\_\mathrm{car}}\right)-a_2}-\frac{L}{V_{\mathrm{Design}}})$

$\left\{\begin{array}{c}{V}_{\mathrm{PSL}\_\mathrm{car}}\&le;V_{\mathrm{Design}}\\ V_{\mathrm{PSL}\_\mathrm{car}}\&le;120\\ \mathrm{Expo}*\mathrm{EXP}(a_{11}+a_1{a}_6\mathrm{LnCsl}+a_7\mathrm{Inverser})\&le;L*\mathrm{EXP}(a_{13}+a_{14}\mathrm{Hourflow}+a_{15}\mathrm{Hourflo}{w}^2+a_{16}\mathrm{Hourflo}{w}^3)\end{array}\right.---\left(21\right)$

In the formula: V _{Psl_car}---dolly maximum speed limit, km/h;

V _Design---highway section design rate, km/h;

G---per-capita gross domestic product, unit/people/year;

E _Car---the average carrying coefficient of dolly, people/car;

Q _Car---the dolly average daily traffic volume ,/day;

L---road section length, km;

EXPO---traffic risk exposure index, i.e. L and Hourflow product;

Inverser---horizontal curve curvature, 1/m;

C _Critical---the accident rate of highway expectation accident level;

The absolute volume of traffic sum of mean hours that Hourflow---dolly and cart are unidirectional, veh/h.

Cart:

$\mathrm{Min}=\frac{G}{365\&times;8}{E}_{\mathrm{truck}}{Q}_{\mathrm{truck}}(\frac{L}{a_3\mathrm{Ln}\left(V_{\mathrm{PSL}\_\mathrm{truck}}\right)-a_4}-\frac{L}{V_{\mathrm{Design}}})$

$\left\{\begin{array}{c}{V}_{\mathrm{PSL}\_\mathrm{truck}}\&le;V_{\mathrm{Design}}\\ V_{\mathrm{PSL}\_\mathrm{truck}\&le;85}\\ V_{\mathrm{PSL}\_\mathrm{truck}}\&le;120\\ \mathrm{Expo}*\mathrm{EXP}(a_{12}+a_3{a}_9\mathrm{LnTsl}+a_{10}\mathrm{Grade})\&le;L*\mathrm{EXP}(a_{13}+a_{14}\mathrm{Hourflow}+a_{15}{\mathrm{Hourflow}}^2+a_{16}{\mathrm{Hourflow}}^3)\end{array}\right.---\left(22\right)$

In the formula: Vpsl_truck---dolly maximum speed limit, km/h;

V _Design---highway section design rate, km/h;

G---per-capita gross domestic product, unit/people/year;

E _Truck---the average carrying coefficient of cart, people/car;

Q _Truck---the cart average daily traffic volume ,/day;

L---road section length, km;

The absolute volume of traffic sum of mean hours that Hourflow---dolly and cart are unidirectional, veh/h.

EXPO---traffic risk exposure index, i.e. L and Hourflow product;

Grade---the longitudinal gradient gradient;

C _Critical---the accident rate of highway expectation accident level;

Annotate: the large and small inapplicable high speed of car maximum speed limit model and some special road sections such as Class I highway tunnel, Qiao Qu, charge station and accident prone location.The present invention only carries out its maximum speed limit research at the large and small car of high-grade highway (comprising highway and Class I highway).Vehicle is pressed wheelbase and is divided, the wheelbase≤3.8m of dolly wherein, the wheelbase＞3.8m of cart.

The present invention formulates a cover according to the actual conditions of China and is fit to feasible method for limiting speed China's national situation, reasonable, to improve traffic circulation efficient, guarantee driving safety.

Description of drawings

Fig. 1 speed cumulative frequency distribution curve

Embodiment:

Dolly:

The first step: image data

Choosing Guangdong, to connect highway K22230-K2229 section clearly be research object, about 1 kilometer, and toward Lianzhou City's direction.This section design rate is 100km/h, and radius of horizontal curve is 1000 meters, the longitudinal gradient gradient 3%, and 1000/h of the unidirectional mean hours volume of traffic, the dolly annual average daily traffic is 18000/h, the cart annual average daily traffic is 6000/h.

Second step: calculate this highway section expectation highway safety level

E(Crashy)＝EXP(0.332-0.002Hourflow+1.040×10 ^-5Hourflow ²-4.220×10 ^-9Hourflow ³)＝exp(0.332-0.002*1000+1.04*10 ^-5*1000 ²-4.22*10 ^-9*1000 ³)＝54

The 3rd step: calculate traffic risk exposure index

EXPO＝Hourflow*L＝1000

The 4th step: calculate critical speed limit

EXPO*Exp[-18.032+2.735Ln(V _{PSL_car})+280.495Inverse]≤C _critical

Solve critical speed limit Vpsl-car=160km/h

V _{PSL_car}≤V _Design

The 5th step: according to constraint condition V _{PSL_car}≤ 120 to draw this highway section speed limit at last be 100km/h

The 6th step: calculate per-capita gross domestic product G and the average carrying coefficient of dolly E.

1. per-capita gross domestic product index G.Chinese GDP per capita was 3267 dollars in 2008, predicted that GDP per capita in 2010 is 3811 dollars, and getting GDP in this example is 3500 dollars, reserved growth space, the dollar-yuan peg got 1: 6.83, the G=3500 * 6.83=23905 in the time cost function, and unit is unit/people/year.

2. average carrying coefficient E.According to people such as the auspicious rings of phoenix about research to traffic volume of highway and freight volume conversion method, in China's passenger vehicle, the station wagon proportion respectively will reach 84% and 90% by 2010 with the year two thousand twenty with increasing, and its main cause is that car will progressively enter family.The average seat of passenger vehicle will be and reduce trend for this reason, it is predicted, 2010 and the year two thousand twenty will be respectively 10.24 people/car and 8.77 people/car.For the passenger vehicle rate of actual loading, will be the trend of raising, but its increase rate is limited, rate of actual loading the year two thousand twenty will be 80% according to estimates.Here be averaged carrying coefficient E=7.016 people/car.

The 7th step: the time cost that calculates operational efficiency

When this highway section maximum speed limit is 100km/h, operational efficiency time cost minimum be 1653.4 yuan for cart, computing method are the same, when the highway section maximum speed limit was 85km/h, operational efficiency time cost minimum was

Claims (1)

1. determine method based on the speed limit of security, it is characterized in that carrying out according to the following steps:

Step 1: the highroad vehicle speed restriction should guarantee accident death rate less than acceptable tolerance value, based on this principle, formulates maximum speed limit and sees formula (2) about the constraint condition model of security;

C(V _PSL，D _Geometry)≤C _critical (2)

In the formula: D _Geometry---linear variable;

C ()---accident rate adopts the prediction accident rate as its index;

Ccritical---the accident rate of highway expectation accident level;

Vpsl---maximum speed limit

Step 2: determine maximum speed limit and 85% speed of a motor vehicle relational model

85% speed of a motor vehicle has the place speed of a motor vehicle of 85% vehicle to be less than or equal to this value promptly in the vehicle fleet that observes;

By gathering the highway and the Class I highway speed of a motor vehicle, maximum speed limit, longitudinal gradient, radius of horizontal curve data, utilize Stata9.0 software to carry out statistical study, adopt the regression analysis of rejecting backward to obtain the linear relationship model of 85% speed of a motor vehicle of large and small car and speed limit, see formula (3) and formula (4);

Dolly:

V _{85_car}＝a ₁LnC _sl-a ₂(3)

Cart:

V _{85_truck}＝a ₃LnT _sl-a ₄(4)

In the formula: V85_car---dolly 85% speed, km/h;

Csl---dolly maximum speed limit, km/h;

LnCsl---Ln (dolly maximum speed limit);

V85_truck---cart 85% speed, km/h;

Tsl---cart maximum speed limit, km/h;

LnTsl---Ln (cart maximum speed limit);

A1, a2, a3, a4---undetermined coefficient obtains by data statistic analysis software;

Step 3: utilize 85% speed of a motor vehicle of image data, longitudinal gradient, curvature, adopt progressively probability model homing method with statistical analysis software Stata9.0, set up two traffic Accident Forecast Model with cart and dolly factor independent variable respectively, model is shown in (5), (6);

Dolly:

E(Crashy)＝Expo*EXP(a ₅+a ₆V85_car+a ₇Inverser)(5)

Cart:

E(Crashy)＝Expo*EXP(a ₈+a ₉V85_truck-a ₁₀Grade)(6)

Parameter is represented meaning:

L---road section length

The absolute volume of traffic sum of mean hours that Hourflow---dolly and cart are unidirectional, veh/h;

EXPO---traffic risk exposure index, the i.e. product of L and Hourflow

Inverser---curvature

Grade---the longitudinal gradient gradient

E (Crashy)---the accident number that takes place every year on average

A5, a6, a7, a8, a9, a10---undetermined coefficient obtains by data statistic analysis software;

Formula (3) is updated to formula (5), obtains traffic Accident Forecast Model, see formula (7) based on the dolly maximum speed limit; Formula (4) is updated to formula (6), obtains traffic Accident Forecast Model, see formula (8) based on the cart maximum speed limit;

Dolly:

Crashy＝Expo*EXP(a ₁₁+a ₁a ₆LnCsl+a ₇Inverser)(7)

Cart:

Crashy＝Expo*EXP(a ₁₂+a ₃a ₉LnTsl+a ₁₀Grade)(8)

Parameter is represented meaning:

A11, a12---undetermined coefficient obtains by statistical analysis software, and all the other parameter meanings are the same;

Step 4: the traffic safety service level quantizes

In line with the principle of practical application, choose the quantizating index of accident rate as the security service level, accident rate is the accident number in annual every kilometer of high-grade highway highway section; The height of accident rate is the direct embodiment of road safety level, can reflect road operation security level quantitatively; According to the characteristic that the high-grade highway accident is obeyed Poisson distribution, adopt generalized linear to return the accident mean measures equation that obtains high-grade highway, see formula (9); The predicted value of accident mean measures equation thought the highway safety level expected

C _critical＝L*EXP(a ₁₃+a ₁₄Hourflow+a ₁₅Hourflow ²+a ₁₆Hourflow ³)(9)

In the formula:

A13, a14, a15, a16---undetermined coefficient obtains by data statistic analysis software;

Wushu (7), formula (8), formula (9) substitution formula (2) obtain the security constraint condition model based on large and small car:

Dolly:

Expo*EXP(a ₁₁+a ₁a ₆LnCsl+a ₇Inverser)≤L*EXP(a ₁₃+a ₁₄Hourflow+a ₁₅Hourflow ²+a ₁₆Hourflow ³)(10)

Cart: Expo*EXP (a ₁₂+ a ₃a ₉LnTsl+a ₁₀Grade)≤L*EXP (a ₁₃+ a ₁₄Hourflow+a ₁₅Hourflow ²+ a ₁₆Hourflow ³) (11)

Parameter represents meaning the same;

According to the important technological parameters of domestic automobile as can be known, the average max. speed of dolly is 160km/h, and the average max. speed of cart is 85km/h; In addition, the 67 regulation of People's Republic of China's law on road traffic safety implementing regulations, the F-Zero that the Speed Limitation on Freeway sign is indicated must not surpass 120km/h;

Dolly:

Cart:

In the formula: VPSL---maximum speed limit, km/h;

VDesign---highway section design rate, km/h;

Step 5: with 85% speed of a motor vehicle and design rate is benchmark, makes up the time cost function of high-grade highway, minimum as the objective function that makes up operational efficiency with time cost;

Do not reach design rate by 85% speed of a motor vehicle and cause the time cost of the value of time increase on the way and few creation as operational efficiency, the calculating of the time value is certificate with the per-capita gross domestic product; The time cost function of operational efficiency as the formula (14), time cost is the smaller the better;

In the formula: Ct---high-grade highway passenger time cost in transit, unit;

G---per-capita gross domestic product, unit/people/year;

E---average carrying coefficient, people/car;

The volume of traffic of Q---dolly or cart ,/day;

L---road section length, km;

V85---85% bit rate, km/h;

VDesign---highway section design rate, km/h;

Formula (3), (4) substitution (14) are got large and small car maximum speed limit model:

Dolly:

In the formula: Vpsl_car---dolly maximum speed limit, km/h;

VDesign---highway section design rate, km/h;

G---per-capita gross domestic product, unit/people/year;

Ecar---the average carrying coefficient of dolly, people/car;

Qcar---dolly average daily traffic volume ,/day;

L---road section length, km;

EXPO---traffic risk exposure index, i.e. L and Hourflow product;

Inverser---horizontal curve curvature, 1/m;

Ccritical---the accident rate of highway expectation accident level;

The absolute volume of traffic sum of mean hours that Hourflow---dolly and cart are unidirectional, veh/h;

Cart:

In the formula: Vpsl_truck---cart maximum speed limit, km/h;

VDesign---highway section design rate, km/h;

G---per-capita gross domestic product, unit/people/year;

Etruck---the average carrying coefficient of cart, people/car;

Qtruck---cart average daily traffic volume ,/day;

L---road section length, km;

The absolute volume of traffic sum of mean hours that Hourflow---dolly and cart are unidirectional, veh/h;

EXPO---traffic risk exposure index, i.e. L and Hourflow product;

Grade---the longitudinal gradient gradient;

Ccritical---the accident rate of highway expectation accident level.

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