CN114863681B - Vehicle track optimization method for conflict elimination of main line entrance ramp confluence area - Google Patents

Vehicle track optimization method for conflict elimination of main line entrance ramp confluence area Download PDF

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CN114863681B
CN114863681B CN202210472432.7A CN202210472432A CN114863681B CN 114863681 B CN114863681 B CN 114863681B CN 202210472432 A CN202210472432 A CN 202210472432A CN 114863681 B CN114863681 B CN 114863681B
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CN114863681A (en
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赵靖
戚钧杰
章程
王嘉文
马晓旦
江洪
尹富秋
侯剑锋
张范磊
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University of Shanghai for Science and Technology
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    • G—PHYSICS
    • G08—SIGNALLING
    • G08G—TRAFFIC CONTROL SYSTEMS
    • G08G1/00—Traffic control systems for road vehicles
    • G08G1/01—Detecting movement of traffic to be counted or controlled
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    • G—PHYSICS
    • G08—SIGNALLING
    • G08G—TRAFFIC CONTROL SYSTEMS
    • G08G1/00—Traffic control systems for road vehicles
    • G08G1/01—Detecting movement of traffic to be counted or controlled
    • G08G1/0104—Measuring and analyzing of parameters relative to traffic conditions
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    • G—PHYSICS
    • G08—SIGNALLING
    • G08G—TRAFFIC CONTROL SYSTEMS
    • G08G1/00—Traffic control systems for road vehicles
    • G08G1/01—Detecting movement of traffic to be counted or controlled
    • G08G1/0104—Measuring and analyzing of parameters relative to traffic conditions
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Abstract

The invention provides a vehicle track optimization method for conflict elimination of a merging area of a main line entrance ramp, which aims at the merging conflict of an entrance ramp of an express way, establishes a vehicle merging optimization control model and improves the passing efficiency of the express way merging area on the basis of ensuring the merging conflict elimination; the optimization control method adopts linear programming model description, the maximum average running speed of the whole vehicle is the optimization target, and the main line and the ramp traffic flow are constructed in a unified optimization frame, so that the total traffic efficiency of a confluence area is improved; and (4) completely separating the ramp vehicle from the main line vehicle in space-time by considering vehicle constraint, safety constraint and confluence constraint conditions, so as to eliminate the conflict.

Description

Vehicle track optimization method for collision elimination of main line entrance ramp confluence area
Technical Field
The invention belongs to the technical field of vehicle track optimization methods, and particularly relates to a vehicle track optimization method for conflict elimination of a confluence area of a main line entrance ramp.
Background
The urban expressway entrance ramp confluence area is an important conflict point and a bottleneck area of urban road traffic, and in order to relieve the conflict and improve the expressway traffic operation level, a vehicle control method based on a networking vehicle information transmission technology is provided. The existing method is mainly based on the principle of the passable gap to carry out optimization control, however, as the passable gap is a probability value and different drivers understand the passable gap differently, the confluence safety can only be achieved at a high probability, and the conflict cannot be completely eliminated. For the conflict elimination of the merging area of the expressway entrance ramps, no targeted optimization control method is found, and no invention patent of the type is searched.
The literature search of the prior art finds that the optimization control method related to the expressway entrance ramp mainly comprises the following steps:
1. method based on signal lamp control. And installing a signal lamp on the entrance ramp, and controlling the flow and time of the ramp traffic entering the main line by optimizing parameters such as the period duration of the signal lamp, the green light duration and the like, so as to improve the traffic operation efficiency of the confluence area of the entrance ramp. The invention discloses a ramp signal feedforward control method and system based on real-time simulation (CN 201910387724.9), and an express way ramp signal system and an operation method thereof (CN 201010010108.0).
2. Method based on induction and signal light coordination. On the basis of signal control, through setting up the induction information and marking line induction means, coordinate control to the expressway section that contains a plurality of ramps and ground road to promote the whole traffic efficiency in section. Road control facilities and induction facilities are specified in the requirements for setting ramp control systems GB34599-2017 and the design specifications for urban road traffic facilities GB 50688-2011 in China.
3. A vehicle control method based on networked vehicle information. The signal transmission and intelligent interaction technology is applied to a vehicle layer, the current vehicle environment data information is processed, and the next driving decision is given, so that the driving track of the vehicle is controlled, confliction and other conflicts are avoided, and the road traffic capacity is improved. The information interaction principle method of the vehicle and the road side equipment is introduced in the invention patent 'a method and a system for guiding the flow of the expressway ramp based on the road side equipment' (patent number ZL 201810840849.8); in the invention patent application of 'a system and a method for coordinated control of a main line and an entrance ramp of a confluence area of an urban expressway' (application number CN 202110493320.5), detailed program introduction and working principles are provided from the aspects of intelligent information transmission and system judgment decision; the invention discloses a ramp confluence control method facing an urban expressway (patent number ZL 202010736981.1), which introduces a method for information interaction and feedback among vehicles and solves the problem related to an entrance ramp from the energy-saving aspect.
The method 1 and the method 2 optimize the urban expressway entrance ramp confluence area from the perspective of traditional signal control and path induction, and have mature technical achievements at present.
And 3, by utilizing the networking vehicle information interaction and processing technology and controlling the running track of the vehicle, the entrance ramp confluence conflict is relieved, and the traffic capacity of the whole system is improved. However, the existing method is based on the principle of inserting gaps for optimal control, and the principle belongs to a probability value problem, and the actual application effect of the method can be greatly changed along with the difference of road layout and driving environment, so that the method only belongs to the problem of confluence safety under a large probability rate, and cannot completely eliminate confluence conflicts. In addition, the conventional design method allows the vehicle to perform the merging operation in the whole section of the acceleration lane, which requires more huge and complicated calculation capability in the case of a larger number of vehicles and more complicated traffic layout, and is also disadvantageous in the elimination of the merging conflict.
The existing control method can not completely eliminate the problem of confluence conflict of vehicles on the urban expressway entrance ramp, and a scientific and reasonable control method for improving the traffic efficiency of the urban expressway entrance ramp confluence area on the premise of ensuring intrinsic safety is lacked.
Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to provide a vehicle speed guiding optimization method for avoiding avoidance signals to control an intersection dilemma area.
Aiming at the defects of the prior art, the method aims to provide a vehicle track optimization method for conflict elimination of a main line inlet ramp confluence area.
The technical scheme of the invention is as follows:
a vehicle track optimization method for eliminating conflict of a merging area of an expressway entrance ramp is characterized in that the speed of each vehicle at each moment is controlled by solving the following optimization model, and the track of a controlled vehicle is obtained. The model is expressed by a linear programming algorithm, the maximum average running speed of the whole vehicle is an optimization target, and vehicle constraint, safety constraint and confluence constraint conditions are considered, wherein:
the input parameters of the optimization model include: Δ t, unit time interval of system operation, s; t is mer Total system run time, s; x is the number of mer The longitudinal length of the ramp confluence functional zone, m;
Figure BDA0003623370210000031
the initial coordinate position of a vehicle with the number p of the main line of the express way;
Figure BDA0003623370210000032
initial coordinate positions of ramp vehicles; n, number of vehicles on a main line of the expressway, veh; m, the number of vehicles on the ramp, veh; v. of max The maximum speed of the road section is m/s; v. of min The minimum speed of the road section, m/s; a is max Maximum acceleration of the road section, m/s 2 ；a min Minimum acceleration of road section, m/s 2 ；j max Speed of change of road section limitation, m/s 3 ；d min Minimum locomotive spacing constraint, m; g is a radical of formula min Minimum headway constraint, s; w, lane width, m;
Figure BDA0003623370210000033
unified initial speed of the main line vehicles of the expressway, m/s;
Figure BDA0003623370210000034
initial speed of the ramp vehicle, m/s; the main parameter schematic diagram is shown in FIG. 1;
the output parameters of the optimization model include:
Figure BDA0003623370210000035
numbering a main line of the express way as the speed of a vehicle p at a time node t;
Figure BDA0003623370210000036
the speed of the ramp vehicle at a time node t;
additional auxiliary variables related to decision (output) variables include:
Figure BDA0003623370210000037
acceleration of the express way vehicle at time node t with number p,
Figure BDA0003623370210000038
m/s 2 ；
Figure BDA0003623370210000039
the acceleration of the ramp vehicle at time node t,
Figure BDA00036233702100000310
m/s 2 ；
Figure BDA00036233702100000311
the cumulative distance traveled by the expressway vehicle numbered p at the time node t,
Figure BDA00036233702100000312
m；
Figure BDA00036233702100000313
the accumulated travel distance of the ramp vehicle at the time node t,
Figure BDA00036233702100000314
m；
Figure BDA00036233702100000315
the coordinate position of the express way vehicle numbered p at time node t,
Figure BDA00036233702100000316
Figure BDA00036233702100000317
the coordinate position of the ramp vehicle at time node t,
Figure BDA00036233702100000318
Figure BDA0003623370210000041
the objective function is to maximize the average traveling speed of all vehicles, as shown in formula (1);
Figure BDA0003623370210000042
the control range of the model is determined according to the vehicle position farthest from the negative direction of the confluence functional zone under the initial condition and the vehicle position farthest from the positive direction of the confluence functional zone after the running time is finished, namely the requirement of the formula (2) is met;
Figure BDA0003623370210000043
the vehicle constraint requirement satisfies the following three constraint conditions:
firstly, the vehicle speed is limited, vehicles running on a normal road must comply with a speed threshold set by the road, and the speed of the vehicles at every moment should not exceed a range, which is expressed as formulas (3) - (4);
Figure BDA0003623370210000044
Figure BDA0003623370210000045
secondly, the acceleration of the vehicle is limited, the acceleration and the deceleration of the vehicle are limited in a range according to the real performance of the vehicle, and the acceleration of the vehicle at every moment should not exceed a range, and is expressed as formulas (5) - (6);
Figure BDA0003623370210000046
Figure BDA0003623370210000047
thirdly, limiting the change rate of the acceleration degree of the vehicle, wherein the change rate of the acceleration degree of the vehicle at every moment should not exceed a range according to the driving habits, the comfort degree, the vehicle performance and the like of a real road driver, and is expressed as formulas (7) - (8);
Figure BDA0003623370210000051
Figure BDA0003623370210000052
the safety constraint requirement satisfies the following six constraint conditions:
one is that the distance between the heads of the main line vehicles should be kept within a safe range to avoid collisions, given by equation (9):
Figure BDA0003623370210000053
secondly, the distance between the vehicle heads of the ramp vehicles should be kept within a safe range, and is given by the formula (10):
Figure BDA0003623370210000054
thirdly, the distance between the ramp vehicle and the main line vehicle should be kept within a safe range, which is given by the equations (11) - (12):
Figure BDA0003623370210000055
Figure BDA0003623370210000056
Figure BDA0003623370210000057
fourthly, the requirement that the safe time interval between the heads of the main line vehicles is required to be kept is given by an equation (13):
Figure BDA0003623370210000058
fifthly, the requirement that the safety time interval between the front ends of the ramp vehicles should be kept is given by the formula (14):
Figure BDA0003623370210000059
sixthly, the time interval between the ramp vehicle and the main line vehicle is required to maintain a safe time interval, and the time interval is given by the following equations (15) to (16):
Figure BDA0003623370210000061
Figure BDA0003623370210000062
Figure BDA0003623370210000063
the vehicle confluence constraint requirement meets the following two constraint conditions:
one is that when the ramp vehicle is in the merge area, the main line vehicle should satisfy equation (17):
Figure BDA0003623370210000064
Figure BDA0003623370210000065
secondly, when the main line vehicle is in the confluence area, the ramp vehicle should satisfy the formula (18):
Figure BDA0003623370210000066
Figure BDA0003623370210000067
the optimization process considers vehicle constraint, safety constraint and confluence constraint, completely separates ramp vehicles from main line vehicles in space-time, simultaneously constructs the main line and ramp traffic in a unified optimization model, and takes the maximization of the average speed of all vehicles as an optimization target, thereby improving the overall traffic efficiency of the main line and the ramp of the expressway on the basis of ensuring that confluence conflict is completely eliminated.
Compared with the prior art, the invention has the following beneficial effects:
1. the invention provides a vehicle track optimization method for conflict elimination of an expressway entrance ramp confluence area, which ensures complete isolation of ramp vehicles from main line vehicles when the ramp vehicles are confluent through constraint arrangement of the confluence area, and realizes conflict elimination.
2. The method simultaneously takes traffic safety and efficiency as guidance, and can improve the traffic efficiency of the merging area of the ramp at the entrance of the expressway on the basis of eliminating merging conflict.
Drawings
FIG. 1 is a schematic diagram of the main parameters of the present invention;
FIG. 2 is a schematic view of a scene condition in embodiment 1 of the present invention;
fig. 3 is a vehicle speed trajectory diagram obtained in embodiment 1 of the invention;
fig. 4 is a vehicle position track diagram obtained in embodiment 1 of the present invention.
Detailed Description
A more detailed description of the vehicle trajectory optimization method for mainline on-ramp merge zone conflict resolution of the present invention will now be described in conjunction with a schematic drawing, wherein there is shown a preferred embodiment of the present invention, it being understood that a person skilled in the art may modify the invention described herein while still achieving the advantageous effects of the present invention, and therefore the following description should be construed as being widely known to a person skilled in the art, and not as limiting the present invention.
Example 1:
the scene geometry in embodiment 1 of the present invention is shown in fig. 2, where an outermost lane is set on the expressway main line, ramp vehicles are normally connected and set as 1 vehicle, and the method of the present invention is used to control the speed trajectory of the vehicle with the maximum average speed of all vehicles as the optimization target, and compare the speed trajectory with the general vehicle merging method. The design input parameters are as follows: delta t, unit time interval of system operation, 0.5s; t is mer Taking 30s as the total running time of the system; x is a radical of a fluorine atom mer Taking 50m as the longitudinal length of the ramp confluence functional zone;
Figure BDA0003623370210000071
taking-40, -80, -120, -160, -200 initial coordinate positions of the vehicle in the main line of the expressway;
Figure BDA0003623370210000072
taking-100 as the initial coordinate position of the ramp vehicle; n, taking 5veh as the number of the main line vehicles of the expressway; v. of max Taking 25m/s as the maximum speed of the road section; v. of min Taking 0m/s as the minimum speed of the road section; a is max Maximum acceleration of road section, 2m/s 2 ；a min Minimum acceleration of road section, take-4 m/s 2 ；j max The acceleration rate of the road section limit is 1m/s 3 ；d min The minimum distance between the car heads is restricted, and 20m is taken;g min taking 2s as the minimum headway time constraint; w, lane width, taking 4m;
Figure BDA0003623370210000073
unified initial speed of the main line vehicles of the expressway is taken as 16m/s;
Figure BDA0003623370210000074
the initial speed of the ramp vehicle is 8m/s, and the specific results are shown in Table 1:
Figure BDA0003623370210000075
table 1 representation of the parameters of example 1
The specific process is briefly described as follows:
step 1: and substituting the input parameters into the linear programming optimization model established by the invention. In order to solve the representation of the model involved in the inventive method, a classical large M linear method is used, where M represents an infinite number, e represents an infinitesimal number, and n, M, u, o, a, b, c, f, d, g all represent a binary variable, specifically n + M =1, u + o =1, a + b =1, c + f =1, d + g =1.
Figure BDA0003623370210000081
s.t.
Figure BDA0003623370210000082
Figure BDA0003623370210000083
Figure BDA0003623370210000084
Figure BDA0003623370210000085
Figure BDA0003623370210000086
Figure BDA0003623370210000087
Figure BDA0003623370210000088
Figure BDA0003623370210000089
Figure BDA00036233702100000810
Figure BDA00036233702100000811
Figure BDA00036233702100000812
Figure BDA00036233702100000813
Figure BDA00036233702100000814
Figure BDA00036233702100000815
Figure BDA00036233702100000816
Step 2: the model is a linear programming model, and an optimization problem solver (such as CPLEX) can be used for solving, and the obtained vehicle speed track and the vehicle position track are respectively shown in fig. 3 and 4.
And step 3: and (5) evaluating a design scheme. Average velocity and Time To Collision (TTC) safe time ratios are used as evaluation indices and compared to conventional control schemes. The TTC time 1.5s is used as a safety threshold in the safety time ratio index. In the traditional control scheme, the ramp vehicle starts to converge into a main line after entering an accelerating lane formally according to the principle of a penetration gap, and is not limited by the fact that convergence (convergence restriction) must be carried out in a tail-end convergence functional area. The evaluation results are shown in table 2, the safety time proportion of the scheme of the invention reaches 100%, compared with the traditional control scheme, the safety of the vehicle is improved by 10.9%, and the traffic efficiency is improved by 16.3%, which shows that the method of the invention can improve the traffic efficiency of the confluence area of the express way on the basis of ensuring the elimination of confluence conflict.
Group of The method of the invention Traditional method based on principle of gap capable of being crossed
Average velocity (m/s) 23.27 22.24
TTC safe time ratio (%) 100％ 90.2％
TABLE 2 optimization results and comparison of the methods of the invention
The above description is only a preferred embodiment of the present invention, and does not limit the present invention in any way. It will be understood by those skilled in the art that various changes, substitutions and alterations can be made herein without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (4)

1. A vehicle track optimization method for eliminating confliction at a main line entrance ramp confluence area is characterized in that vehicle constraint, safety constraint and confluence constraint are considered by taking the maximum average running speed of all vehicles as an optimization target, ramp vehicles and main line vehicles are completely separated in space-time, and meanwhile, the main line vehicles and ramp traffic flow are constructed in a unified optimization model, the average speed of all vehicles is maximized as the optimization target, so that the overall traffic efficiency of the main line and the ramp is improved on the basis of ensuring complete elimination of confluent confliction;
the optimization model is expressed by a linear programming algorithm, an objective function of the optimization model is a formula I, and the formula I is expressed as follows:
Figure FDA0003966798260000011
in the formula I, delta t is a unit time interval of system operation; t is mer The total running time of the system; n1 and N2 respectively represent the number of vehicles on a main line of the expressway and the number of vehicles on a ramp; p is the index number of the vehicle on the main line of the express way, and the value range is [1, N1 ]]Taking the value as an integer; t is the index number of the ramp vehicle, and the value range is [1, N2 ]]Taking the value as an integer;
Figure FDA0003966798260000012
to be fastThe cumulative total trip distance for the vehicle with speed P,
Figure FDA0003966798260000013
Figure FDA0003966798260000014
wherein
Figure FDA0003966798260000015
Indicating the main line vehicle initial speed numbered P,
Figure FDA0003966798260000016
representing the acceleration of the main-line vehicle numbered P at time node t,
Figure FDA0003966798260000017
representing the total number of time nodes;
Figure FDA0003966798260000018
the accumulated total travel distance for the vehicle numbered T on the ramp,
Figure FDA0003966798260000019
wherein
Figure FDA00039667982600000110
Indicating the initial speed of the ramp vehicle numbered T,
Figure FDA00039667982600000111
the acceleration of the ramp vehicle with the number T at a time node T is represented, and the rest parameters are the same as the above;
the control range of the optimization model is determined according to the vehicle position farthest from the negative direction of the confluence functional zone under the initial condition and the vehicle position farthest from the positive direction of the confluence functional zone after the running time is finished, namely the requirement of a formula II is met, wherein the formula II is expressed as follows:
Figure FDA0003966798260000021
in the second formula, the first formula is shown in the specification,
Figure FDA0003966798260000022
numbering an initial coordinate position of a vehicle with a number P for a main line of the expressway;
Figure FDA0003966798260000023
the initial coordinate position of the vehicle with the number T on the ramp is obtained;
Figure FDA0003966798260000024
for the last coordinate position of the vehicle numbered expressway,
Figure FDA0003966798260000025
Figure FDA0003966798260000026
for the last coordinate position of the vehicle numbered ramp,
Figure FDA0003966798260000027
Figure FDA0003966798260000028
the parameter meanings are the same as above;
the vehicle constraints include a vehicle speed limit, a vehicle acceleration limit, and a vehicle acceleration rate change limit;
the vehicle speed limit, which is expressed by formula three and formula four, specifically limits that the main line vehicles must comply with the speed threshold set by the road, and the vehicle speed at each moment should not exceed a range:
Figure FDA0003966798260000029
in the third formula, v max The maximum speed of the road section is taken; v. of min The minimum speed of the road section;
Figure FDA00039667982600000210
numbering the speed of the vehicle P at a time node t for the main line of the expressway;
the fourth formula is:
Figure FDA00039667982600000211
in the fourth formula, the first step is,
Figure FDA00039667982600000212
the speed of a ramp vehicle with the number of T at a time node T;
the acceleration limit of the vehicle is defined by the acceleration and the deceleration of the vehicle according to the real performance of the vehicle, the acceleration of the vehicle at every moment should not exceed a range, and the acceleration limit is represented by a fifth formula and a sixth formula, wherein the fifth formula is as follows:
Figure FDA00039667982600000213
in the fifth formula, a max Is the maximum acceleration of the road section; a is a min Is the minimum acceleration of the road section;
Figure FDA00039667982600000214
the acceleration of the express way vehicle with the number P at the time node t is shown;
the sixth formula is:
Figure FDA0003966798260000031
in the formula six, the first step is that,
Figure FDA0003966798260000032
the acceleration of the ramp vehicle with the serial number T at a time node T is obtained;
the vehicle acceleration rate limitation is that the acceleration rate of the vehicle at every moment should not exceed a range according to the driving habits, comfort degree and vehicle performance of a real road driver, and is expressed by a seventh formula and an eighth formula, wherein the seventh formula is:
Figure FDA0003966798260000033
in the seventh formula, j max A rate of change of acceleration for a road segment limit;
Figure FDA0003966798260000034
taking the value of the acceleration change rate of the main line vehicle with the vehicle number P at the time node t, wherein the parameters are in the same way as the above;
the formula eight is:
Figure FDA0003966798260000035
in the above-mentioned formula eight, the first step,
Figure FDA0003966798260000036
taking the value of the acceleration change rate of the ramp vehicle with the vehicle number T at a time node T, wherein the parameters are in the same way as the above;
2. the method for optimizing the vehicle track facing the collision elimination at the main line entrance ramp confluence region according to claim 1, wherein the safety constraints include that the distance between the heads of the main line vehicles should be kept within a safety range to avoid collision, the distance between the heads of the ramp vehicles should be kept within a safety range, the distance between the ramp vehicles and the main line vehicles should be kept within a safety range, the time interval between the heads of the main line vehicles should be kept at a safety time interval requirement, the time interval between the heads of the ramp vehicles should be kept at a safety time interval requirement, and the time interval between the ramp vehicles and the main line vehicles should be kept at a safety time interval requirement.
3. The method for optimizing vehicle trajectories for eliminating collision at a confluence area of a main line on-ramp road according to claim 2, wherein the distance between the heads of the main line vehicles is kept within a safe range to avoid collision, and the formula is nine:
Figure FDA0003966798260000041
in the formula nine, d min Is a minimum locomotive head spacing constraint;
Figure FDA0003966798260000042
the coordinate position of the express way vehicle with the number P at the time node t is shown;
the distance between the vehicle heads of the ramp vehicle is kept in a safe range and is expressed by a formula ten, wherein the formula ten is as follows:
Figure FDA0003966798260000043
in the above-mentioned formula ten, the first,
Figure FDA0003966798260000044
the coordinate position of the ramp vehicle with the number T at the time node T is shown;
the distance between the ramp vehicle and the main line vehicle is kept within a safe range and is expressed by a formula eleven and a formula twelve, wherein the formula eleven is as follows:
Figure FDA0003966798260000045
Figure FDA0003966798260000046
the formula twelve is:
Figure FDA0003966798260000047
Figure FDA0003966798260000048
the requirement that the time interval between the heads of the main line vehicles should be kept safe is expressed by a formula thirteen, wherein the formula thirteen is as follows:
Figure FDA0003966798260000049
in the formula thirteen, g min Is the minimum headway constraint;
the requirement that the time interval between the vehicle heads of the ramp is required to keep a safe time interval is expressed by a formula fourteen:
Figure FDA00039667982600000410
the same parameters in the formula fourteen are the same as the above;
the time interval between the ramp vehicle and the main line vehicle, which is required to keep a safe time interval, is expressed by a formula fifteen and a formula sixteen, wherein the formula fifteen is as follows:
Figure FDA0003966798260000051
Figure FDA0003966798260000052
the formula sixteen is:
Figure FDA0003966798260000053
Figure FDA0003966798260000054
4. the method for optimizing vehicle trajectories for collision mitigation in a main line entry ramp junction according to claim 1, wherein the junction constraint requires that when a ramp vehicle is in the junction, the main line vehicle should satisfy formula seventeen; the confluence constraint requires that when a main line vehicle is in a confluence area, ramp vehicles meet a formula eighteen, wherein the formula seventeen is expressed as:
Figure FDA0003966798260000055
Figure FDA0003966798260000056
the formula eighteen is expressed as:
Figure FDA0003966798260000057
Figure FDA0003966798260000058
seventeenth formula and eighteen formula, x mer The longitudinal length of the merging functional zone of the ramp, and the meanings of the other parameters are as aboveThe same applies.
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