CN115424436A - Redundancy-based urban road network optimization design method under influence of rainstorm - Google Patents
Redundancy-based urban road network optimization design method under influence of rainstorm Download PDFInfo
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- G—PHYSICS
- G08—SIGNALLING
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- G08G1/00—Traffic control systems for road vehicles
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- G08G1/0104—Measuring and analyzing of parameters relative to traffic conditions
- G08G1/0125—Traffic data processing
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- G06F30/27—Design optimisation, verification or simulation using machine learning, e.g. artificial intelligence, neural networks, support vector machines [SVM] or training a model
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- G06N3/12—Computing arrangements based on biological models using genetic models
- G06N3/126—Evolutionary algorithms, e.g. genetic algorithms or genetic programming
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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
- G08G1/048—Detecting movement of traffic to be counted or controlled with provision for compensation of environmental or other condition, e.g. snow, vehicle stopped at detector
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- G—PHYSICS
- G08—SIGNALLING
- G08G—TRAFFIC CONTROL SYSTEMS
- G08G1/00—Traffic control systems for road vehicles
- G08G1/09—Arrangements for giving variable traffic instructions
- G08G1/0962—Arrangements for giving variable traffic instructions having an indicator mounted inside the vehicle, e.g. giving voice messages
- G08G1/0968—Systems involving transmission of navigation instructions to the vehicle
- G08G1/096805—Systems involving transmission of navigation instructions to the vehicle where the transmitted instructions are used to compute a route
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- G—PHYSICS
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- G08G—TRAFFIC CONTROL SYSTEMS
- G08G1/00—Traffic control systems for road vehicles
- G08G1/09—Arrangements for giving variable traffic instructions
- G08G1/0962—Arrangements for giving variable traffic instructions having an indicator mounted inside the vehicle, e.g. giving voice messages
- G08G1/0968—Systems involving transmission of navigation instructions to the vehicle
- G08G1/096833—Systems involving transmission of navigation instructions to the vehicle where different aspects are considered when computing the route
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- Y02T10/10—Internal combustion engine [ICE] based vehicles
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Abstract
The invention belongs to the technical field of traffic planning, and discloses a redundancy-based urban road network optimization design method under the influence of rainstorm, which comprises the following steps: obtaining normal distribution parameters of reduction coefficients of average running speeds of all attribute road sections under the influence of rainstorm, and obtaining network redundancy of the urban road under the influence of the rainstorm; establishing an urban road network redundancy optimization model facing the influence of rainstorm according to the urban road network redundancy under the influence of rainstorm, the total travel time cost and the total construction cost of travelers; and solving the rainstorm influence-oriented urban road network redundancy optimization model by adopting a genetic algorithm, setting constraint conditions of urban road types, road capacities and construction funds, and calculating the fitness of the genetic algorithm to obtain an urban road network optimization scheme. The design method of the invention increases the redundancy of the road network, so that the urban road network can better bear the traffic problem caused by rainstorm.
Description
Technical Field
The invention belongs to the technical field of traffic planning, and relates to a redundancy-based urban road network optimization design method under the influence of rainstorm.
Background
Urban roads are important components of urban infrastructure, and urban traffic is inseparable from the production and life of residents. Except for the influence of rainstorm weather, cities often lack the corresponding drainage system planning design when developing and constructing rapidly, and continuous rainstorm often causes waterlogging and ponding points in a plurality of urban areas of the cities, even short-term ponding and outage, aggravates urban traffic jam, and seriously influences the normal operation of urban road traffic systems. Therefore, in rainstorm weather, urban road traffic is extremely fragile, and is particularly characterized by reduction of road service functions, reduction of vehicle running speed, increase of road network congestion delay indexes and the like. How to reduce the influence of heavy rain on urban traffic and improve the operation efficiency of urban traffic in heavy rain weather becomes a difficult problem to be solved urgently in many cities.
The evaluation of urban road network systems by using the toughness of the urban road network has received more and more attention of scholars. The toughness of the traffic system reflects the stability and reliability of the traffic system, mainly reflects the replaceability, easy repairability, survivability and the like under major emergencies, adopts the key area multipath and multi-mode connection ratio as a reference characterization index of the toughness of the traffic system, and particularly highlights the importance of redundancy to the toughness of urban traffic.
Redundancy is one of important attributes of toughness, can improve the reliability of a system to a certain extent, and is an important factor for maintaining stable and continuous operation of a complex system, and a schematic diagram of a redundancy path is shown in fig. 1. The redundancy has very important application value in the traffic field, and system redundancy design is carried out no matter on urban roads or public transport, rail traffic and the like so as to solve the traffic problems in emergency such as emergencies. The urban road network with redundancy can provide more path choices for travelers, so that traffic operation under the condition of heavy rain presents diversified characteristics, the influence of heavy rain on the traffic operation efficiency of the urban roads is reduced, and the urban road network can still continuously and stably operate under the heavy rain. At present, in the stage of urban road network design, the research on the redundancy of a traffic network is less. Therefore, in the stage of designing the urban road network, improving the urban road network redundancy under the rainstorm condition has important practical significance for improving the capability of a road network system for coping with the rainstorm.
Disclosure of Invention
The invention aims to provide a redundancy-based urban road network optimization design method under the influence of heavy rain, which increases the redundancy of a road network, so that the urban road network can better bear the traffic problem caused by the heavy rain, and the safety of a road traffic system is improved.
In order to achieve the purpose, the invention adopts the following technical scheme:
the invention provides a redundancy-based urban road network optimization design method under the influence of rainstorm, which comprises the following steps:
acquiring normal distribution parameters of a reduction coefficient of the average running speed of each attribute road section under the influence of rainstorm to obtain the failure probability of the motor vehicle in each attribute road section unit under the influence of the rainstorm;
obtaining the failure probability of all reasonable feasible paths under the influence of the rainstorm according to the failure probability of the motor vehicle in each attribute road section unit under the influence of the rainstorm;
according to the failure probabilities of all reasonable feasible paths under the influence of rainstorm, obtaining the network redundancy of the urban road under the influence of the rainstorm;
establishing an urban road network redundancy optimization model facing the influence of rainstorm according to the urban road network redundancy under the influence of rainstorm, the total travel time cost of travelers in the urban road network and the total construction cost of the urban road network;
and solving the rainstorm influence-oriented urban road network redundancy optimization model by adopting a genetic algorithm, setting constraint conditions of urban road types, road capacities and construction funds, and calculating the fitness of the genetic algorithm to obtain an urban road network optimization scheme.
Preferably, each attribute road section unit comprises a branch road, a secondary trunk road, a non-bridge tunnel trunk road, a underpass tunnel trunk road, an overpass express road, a non-bridge tunnel express road and a underpass tunnel express road.
Preferably, the rainstorm influence-oriented urban road network redundancy optimization model is as follows:
max F(X)＝π N (X)/[C N (X)+C P (X)]，
wherein X is the vector of the number of roads in the road network, and X = [) 1 ,X 2 ,…,X i ]；
X i For the set of road segments on the ith road, X i ＝[X i,1 ,X i,2 ,…,X i,m ]；
X i,m The road section with the attribute corresponding value of m on the ith road is m, and the m belongs to {0,1,2,3,4,5,6};
π N (X) is the network redundancy of the urban road under the influence of rainstorm;
C p the total travel time cost for travelers in the urban road network;
C N the total construction cost of the urban road network.
Preferably, the total travel time cost of travelers in the urban road network is as follows:
C p ＝∑ a∈A x a ·t a ·c·T·n a ，
in the formula, A is a road section set of an effective path;
x a is the traffic flow of the road section a, pcu/h;
t a is the time impedance of the road segment a, h;
c is the per-capita time value of urban residents, yuan/min;
t is the annual road service time h;
n a the design age, year for road segment a.
Preferably, the total construction cost of the urban road network is as follows:
C N ＝∑ m L m ·c m ，m∈{0,1,2,3,4,5,6}，
in the formula, L m The total length of the road section with the attribute corresponding value m is km;
c m the unit length construction cost of the road section with the attribute corresponding value of m is ten thousand yuan/km.
Compared with the prior art, the invention has the beneficial effects that:
the urban road network redundancy optimization model for the influence of rainstorm simultaneously considers the urban road network redundancy under the influence of rainstorm, the total travel time cost of travelers in the urban road network and the total construction cost of the urban road network, and expects that the number of effective redundant paths in the road network is maximized under the lower travel time cost and construction cost of the finally planned road network, so that the redundancy of the road network is increased, the urban road network can better bear the traffic problem caused by the rainstorm, the safety of a road traffic system is improved, and the influence of the rainfall on the traffic system and the recovery cost are reduced.
Drawings
Fig. 1 is a schematic diagram of redundant paths in an urban road network.
FIG. 2 is a graph showing the reduction ratio of standard speed of different types of road section units according to the intensity of rainfall.
FIG. 3 is a flow chart of a genetic algorithm solving a redundancy optimization model.
Fig. 4 is a schematic diagram of a 25-node checkerboard network.
FIG. 5 shows the convergence of the 25-node checkerboard network redundancy optimization model solution.
Fig. 6 is a schematic diagram of an optimized 25-node checkerboard network.
Fig. 7 is a schematic diagram of a 30-node strip trunk network.
Fig. 8 shows the convergence of the solution of the 30-node strip trunk network redundancy optimization model.
Fig. 9 is a schematic diagram of an optimized 30-node strip trunk.
Detailed Description
The following examples are intended to illustrate the invention, but are not intended to limit the scope of the invention. Unless otherwise specified, the technical means used in the examples are conventional means well known to those skilled in the art.
The road grade in the invention is divided into four grades: express way, main road, secondary trunk way and branch road, the road type divide into 3 types: the invention relates to an elevated bridge, a non-bridge tunnel and a underpass, therefore, the invention considers 7 different attribute road sections which are respectively a branch road, a secondary trunk road, a non-bridge tunnel trunk road, a underpass tunnel trunk road, an elevated bridge express way, a non-bridge tunnel express way and an underpass tunnel express way.
Example one
(1) And acquiring normal distribution parameters of the reduction coefficients of the average running speeds of all attribute road sections under the influence of rainstorm to obtain the failure probability of the motor vehicle in all attribute road section units under the influence of the rainstorm.
The rainfall intensity is generally classified by taking the rainfall of 12 hours or the rainfall of 24 hours as a measurement standard, and the rainfall of 12 hours is more than 30.0mm and the rainfall of 24 hours is more than 50.0mm from the rainstorm intensity in the rainfall rating (GB/T28592-2012). The failure of a generic road segment unit is defined as follows: and when the actual running speed of the motor vehicle on each grade road section is less than the speed threshold value of the grade road, the section is considered to be invalid. Probability of failure lambda of section a under the influence of heavy rain a Comprises the following steps:
wherein P (-) is the probability of an event occurring;
v is the average speed of the motor vehicle on the road section a;
v f the speed threshold value corresponding to the road section failure.
The speed limits of motor vehicles on different levels of urban roads are shown in table 1.
TABLE 1 speed limit of motor vehicles on different grades of urban roads
Zou Zhiyun et al (Zou Zhiyun, mao Baohua, gong Quanzhou, et al. Urban road network failure (congestion) correlation analysis [ J ]. Traffic transportation system engineering and information, 2009,9 (02): 110-114.) define the operating speed of failed road segment unit as: the express line is less than 30km/h, the main line is less than 25km/h, the secondary line is less than 20km/h, and the branch line is less than 18km/h. Based on the method, the failure speed threshold values of different levels of urban roads and different types of road section units are set as shown in the table 2.
TABLE 2 speed thresholds corresponding to unit failures of different types of road sections and urban roads with different grades
The road traffic impedance function (road resistance function for short) is a functional relation between the running time of a road section and the traffic flow of the road section, is used for calculating the actual running time of the road section under a specific flow, and can represent the unblocked degree of a road. In the traffic distribution phase in the "four-phase" of the traffic plan, the time impedance of each attribute road segment unit needs to be calculated. For the urban road network, the time impedance of the road section is in positive correlation with the road section flow, the influence of the traffic flow is considered by the most widely applied U.S. Federal road administration function (BPR function), and the time impedance t of the road section a a In particular toThe form is as follows:
in the formula, t 0 The travel time of the road section a in free flow, h;
x a is the traffic flow of the road section a, pcu/h;
c a the actual traffic capacity of the road section a is pcu/h;
α and β are model undetermined parameters, and α =2.5 and β =4.5 in consideration of rainfall situations.
The traffic capacities of urban roads in different levels are different, the influence of rainfall on various aspects of the urban roads is comprehensively considered, and the actual traffic capacities c of road section units in various levels and various types under normal (no rainfall) conditions and rainstorm conditions are set a As shown in table 3, the reduced trafficability is rounded to be trafficability in a heavy rain.
TABLE 3 road segment Unit throughput
Since v = l a /t a Then, then
Can be converted into
The probability of failure λ of the section a under the influence of a heavy rain a Can be further expressed as:
in the formula I a Is the length of the section a.
The traffic conditions are different due to different total mileage and motor vehicle holding amount of each urban road, and the reduction coefficient of the average running speed on the road section a under the influence of rainstorm is assumed
According to normal distribution
The reduction factor of the average running vehicle speed on the section a under the influence of heavy rain
Is expressed as:
thus, the probability of failure λ of the section a under the influence of heavy rain a Can be further expressed as:
reduction factor for average running speed on road section a under influence of heavy rain
The invention is obtained through practical tests. Under different rainfall intensities, 200 cars in a certain city are selected and used as a standard car model, travel track data in three time periods of an early peak 7-9, a midday peak 12-14 and a late peak 17-19 are recorded, GPS longitude and latitude of each track point are converted into Gold longitude and latitude, and the GPS longitude and latitude are matched to an urban road network of a Gold map, so that the daily travel condition of the car in the selected time period is obtained. Based on the instantaneous speed of each vehicle, the average value of the instantaneous speed of the vehicle within 3min is counted as the average speed of the vehicle on each road section, and the results are shown in tables 4 to 6.
TABLE 4 average speed of underpass tunnel under different rainfall intensity
TABLE 5 average speed of overpass under different rainfall intensity
TABLE 6 average speed of non-bridge tunnel road under different rainfall intensity
As can be seen from tables 4 to 6, the average speeds of the three types of roads generally decrease with the increase of the rainfall intensity, but the average speeds of the individual roads increase in the case of medium rain or heavy rain, because the travel demand of people changes when the rainfall intensity is high, the number of trips decreases, and the road saturation decreases. For further comparison, the link standard speeds under different rainfall conditions were calculated for each link based on the above data, and the average of the standard speeds of 4 links for each pattern was determined as the average speed of the link for that pattern, as shown in table 7.
TABLE 7 Standard speeds of different types of road section units
Further analyzing the standard speed proportion of each road section unit relative to the rain-free weather in different time periods and different rainfall intensities, and drawing a graph of the reduction proportion along with the change of the rainfall intensity, as shown in fig. 2. On the whole, under different rainfall intensities, the overhead bridge is minimally influenced by rainfall in the peak time period and the flat peak time period, and the influence on the tunnel and the non-bridge tunnel road is larger; specifically, it can be found that:
(1) As the intensity of rainfall increases, the standard speed reduction coefficient of the vehicle at the underpass tunnel tends to increase along with the increase of the intensity of rainfall. The influence is small in light rain and medium rain, the reduction ratios of the vehicle speed in the early peak are respectively 6.8 percent and 6.7 percent, the vehicle speed in the late peak is 17.9 percent and 25.0 percent, and the vehicle speed in the late peak is 2.1 percent and 18.2 percent; during heavy rain and heavy rain, the reduction ratio is greatly influenced, the early peak reduction ratio is 30.3 percent and 39.8 percent, the noon peak reduction ratio is 34.7 percent and 53.2 percent, and the late peak reduction ratio is 52.3 percent and 57.8 percent, because water is generated in the tunnel, and the road blocking cannot normally pass.
(2) The standard speed folding proportion of the viaduct has no obvious change rule along with the increase of rainfall intensity. The influence of light rain and medium rain is small, the reduction ratio of the early peak is 7.9 percent and 9.5 percent, the noon peak is 4.5 percent and 6.4 percent, and the late peak is 5.4 percent and 12.8 percent; the influence of heavy rain is large, the reduction ratio of the early peak is 20.8 percent, the noon peak is 22.8 percent, and the late peak is 21.2 percent. The speed reduction proportion of the viaduct influenced by heavy rain is larger than that under the condition of heavy rain, because the travel traffic flow can be reduced by heavy rain, and the road section saturation is reduced.
(3) The standard speed reduction proportion of the non-bridge tunnel road in each period of time is in a trend of obviously increasing along with the increase of rainfall intensity. During the early peak period, the reduction ratio is increased from 14.9% in a light rain scene to 50.4% in a heavy rain scene; at the midday peak time, the light rain is increased from 9.8% under the light rain scene to 65.7% under the heavy rain scene; the late peak increases from 3.1% to 39.4%.
Therefore, except for the common factors of wet and slippery road surface, obstructed driver sight and weak visibility to road conditions and traffic signs caused by rainfall, different types of roads are obviously affected by rainfall under different time periods and different rainfall conditions; when the rainfall is large, the tunnel generates water accumulation, and compared with the normal condition, the speed is obviously reduced; although the viaduct is not easy to accumulate water, rainfall influences the path selection of travelers, and drivers may prefer to select the viaduct section, so that the saturation of the viaduct section is higher, and the vehicle speed is still reduced.
Through K-S inspection, the reduction coefficient of the average running speed on the road section a under the influence of rainstorm obtained by the invention
The statistical value of (a) conforms to the normal distribution. Based on the diversity of the urban road attributes, 7 road section attributes such as a branch road, a secondary trunk road, a non-bridge tunnel trunk road, a underpass tunnel trunk road, a viaduct express way, a non-bridge tunnel express way, an underpass tunnel express way and the like are considered, and the reduction coefficient of the average running speed of each attribute road section unit under the influence of heavy rain is obtained
The normal distribution parameters of (2) are shown in Table 8.
TABLE 8 Normal distribution parameters for the reduction factor of the average operating speed of each attribute road segment unit under the influence of heavy rain
| Road segment attributes | Normal distribution parameter |
| Underpass tunnel express way | (0.294,0.063) |
| Non-bridge tunnel express way | (0.219.0.096) |
| Viaduct expressway | (0.146,0.070) |
| Main trunk of underpass tunnel | (0.228,0.218) |
| Non-bridge tunnel trunk road | (0.206,0.118) |
| Secondary trunk road | (0.218,0.135) |
| Branch circuit | (0.175,0.188) |
Further, the failure probability lambda of the motor vehicle under the influence of heavy rain in 7 types of attribute road section units such as a branch road, a secondary trunk road, a non-bridge tunnel trunk road, a underpass tunnel trunk road, an overpass express way, a non-bridge tunnel express way and an underpass tunnel express way is calculated by the formula (5) respectively a 。
(2) And obtaining the failure probability of all reasonable feasible paths under the influence of the rainstorm according to the failure probability of the motor vehicle under the influence of the rainstorm in each attribute road section unit.
In an urban road network, a plurality of reasonable feasible paths exist between any OD pairs, which means that a plurality of routes can be communicated between origin and destination points, so that traffic flow evacuation is realized. For the determined urban road network, a reasonable feasible path set between any OD pairs can be solved, and the failure probability lambda of the kth reasonable feasible path between the OD pairs (r, s) rs,k Can be expressed as:
where K is the kth feasible path between OD pair (r, s), K =1,2, … …, K;
A k the set of link elements for the kth reasonably feasible path.
The probability of failure for all reasonably feasible paths under the influence of a storm can be further calculated from equation (6).
(3) Obtaining the redundancy pi of the urban road network under the influence of the rainstorm according to the failure probabilities of all reasonable feasible paths under the influence of the rainstorm N 。
All road segment units belonging to a reasonably feasible path should meet validity and rationality.
1) Dial (Dial R B.A robust multiple path traffic model in which devices are driven and paths are generated [ J ]. Transportation Research,1971,5 (2): 83-111.) defines an effective path as: a path is a valid path if it consists of only the segments that distance the road network users from the starting point. That is, the road segments on all valid paths should satisfy the formula:
in the formula, c r (a h ) From the starting point r to the starting point a of the road section a h The minimum travel cost of;
c r (a t ) From the starting point r to the starting point a of the road section a h And the end point a of the link a t The minimum travel cost of;
a is the set of segments of the active path.
This formula restricts nodes in the path from being duplicated, i.e., the path contains no loops.
2) When a segment of the primary or secondary route encounters an interruption or closure, travelers are more inclined to select other routes with acceptable travel costs as their alternate routes. To ensure that the travel cost of all reasonable alternative paths remains relative to the shortest pathWithin an acceptable range, introducing a cost tolerance factor
To ensure the reasonability of the road section,
in the formula, c a The travel cost for the road section a;
A m the road section unit set is the mth reasonable feasible path;
According to the legacy of the logical differentiation model [ J M]Transfer Research Part B: methodological,1997,31 (4): 315-326.) in intercity road network Research, cost tolerance factor
Can be set to 1.6; in the urban road network research, the value can be between 1.3 and 1.5.
Based on the above constraints, the total cost c of ensuring the mth reasonable feasible path m The upper limit value:
in the formula, c r (r) is the minimum travel cost from the starting point r to r after each OD traffic allocation;
c r (s) is the minimum travel cost from the origin r to the destination s after each OD traffic allocation;
The meaning of equation (9) is that the travel cost of the path between the origin-destination point pair does not exceed (1 + τ) which is the minimum travel cost between the origin-destination point pair r max ) At times, the road user may accept the path.
The user balance distribution model is a long-term balance process, but when rainfall occurs, the travel demand and the path selection of road users are likely to change, the traffic flow distribution is more complex than that under the normal condition, the long-term balance process does not exist any more, and a balance solution for user balance distribution cannot be found. In addition, the system optimization model reflects an ideal goal, namely, the total travel cost of the system is minimum, and the achievement of the goal requires that all travelers cooperate with each other to jointly make efforts for the optimization of the system, which is not very consistent with the reality. The method selects a capacity limit-increment loading method distribution model in an unbalanced distribution method to distribute the traffic flow of the urban road network under the rainfall condition. The method gradually superposes the traffic flow, can present the process of the traffic flow from less to more, can be used for better simulating the process of passenger flow selection under the rainfall scene because the impedance is continuously corrected due to the continuous change of the traffic flow of the road section, and sets the OD flow distribution times K =5. In the distribution process, the OD trip meter needs to be decomposed into K OD branch meters, but a multi-path distribution model is adopted when the flow distribution is carried out on each OD branch meter. Similarly, each time an OD branch table is assigned, a road weight is corrected by using the road impedance function until all OD values are loaded on the traffic network.
Then the path redundancy between OD pairs (r, s) is π rs ：
Further, urban road network redundancy pi under the influence of rainstorm N Comprises the following steps:
in the formula, N is the number of OD pairs (r, s).
(4) And establishing an urban road network redundancy optimization model facing the influence of the rainstorm according to the urban road network redundancy under the influence of the rainstorm, the total travel time cost of travelers in the urban road network and the total construction cost of the urban road network.
1) Determining total travel time cost C of travelers in urban road network p
The running efficiency of the road network is measured by adopting the total travel time cost of all travelers in the urban road network, and the total travel time cost is determined by the time value of residents. The time value is a monetary manifestation of the amount of lost benefit resulting from the non-productive consumption of time and the amount of added benefit over time. The travel time value refers to the opportunity cost of travel time consumed by travelers in the travel process. For travelers, the saved travel time is valuable in that this portion of the time is available for work, creating even greater value. The travel time value judgment of the residents will influence the selection behaviors such as departure time, travel times, travel paths, travel modes and the like. The study on the travel time value is not only an important representation of the urban traffic service level and a basis of traffic demand management, but also can grasp the travel behavior rules of urban residents, adjust the urban traffic travel structure, improve the running efficiency of urban traffic, and has important strategic significance for promoting urban traffic development.
Total travel time cost C of travelers in urban road network p The specific formula is related to the flow distribution result of each road section, the time value of urban residents per capita and the design service life of the road, and is as follows:
C p ＝∑ a∈A x a ·t a ·c·T·n a in the formula (12),
in the formula, A is a road section set of an effective path;
x a is the traffic flow of the road section a, pcu/h;
t a is the time impedance of the road segment a, h;
c is the per-capita time value of urban residents, yuan/min;
t is the annual road service time h;
n a the design age, year for road segment a.
Referring to the main result and conclusion of the fifth city comprehensive traffic survey in Zhengzhou city (2018), the average value of the monthly income of the residents in Zhengzhou city is 4569 yuan, the average hourly wage of the residents in Zhengzhou city can be calculated and obtained by assuming 22 days of operation in one month and 8 hours of operation in one day, the travel time value of the residents is calculated according to 95.2% of the hourly wage, and the average travel time value c of the residents in Zhengzhou city is calculated to be 25.7 yuan/hour, namely 0.4283 yuan/minute.
According to the City road engineering design Specification (CJJ 37-2012) (2016 edition), the design service life of each grade of road is n a Respectively taking the following components: the expressway has 20 years, the main road has 20 years, the secondary road has 15 years and the branch road has 10 years.
When the travel time cost of urban residents is calculated, the service time of each road is 10h each day. For example, a trunk section unit length l of a particular bidirectional 6 lanes a 2.5km, traffic flow x a 2000pcu/h, single lane throughput 1200pcu/h, then t 0 ＝l a /v f =2.5km/80km/h =0.03125h, and the time impedance t of the link is calculated by the formula (2) a 2.21min, the total travel time cost of urban residents in the designed service life of the road section is 2000 × 2.21 × 0.4283 × 10 × 365 × 20=1.381953 billion yuan.
2) Determining the total construction cost C of an urban road network N
Along with the continuous acceleration of urbanization construction speed, municipal road projects are continuously increased, and cost management in municipal road construction is directly related to the economic benefit of municipal roads and is an important link in municipal road engineering project management. In the construction of municipal roadsIn time, the fund should be reasonably utilized, and the occurrence of unreasonable excess phenomenon is avoided as much as possible, so that the fund waste is caused. The invention considers the construction cost of urban roads with different road grades and different types, and the total construction cost C of the urban road network for a given road network topological structure N Can be expressed as:
C N ＝∑ m L m ·c m m is equal to {0,1,2,3,4,5,6} equation (13),
in the formula, L m The total length of the road section with the attribute corresponding value m is km;
c m the unit length construction cost of the road section with the attribute corresponding value of m is ten thousand yuan/km.
The attribute correspondence values m of the different attribute links are shown in table 9.
TABLE 9 Attribute correspondences for different attribute road segments
The construction cost of the urban road is affected differently by various factors such as design requirements and construction schemes, and 7 roads such as a viaduct expressway, a non-bridge and tunnel expressway, a downward-passing expressway, a non-bridge and tunnel main road, a downward-passing main road, a non-bridge and tunnel secondary main road and a non-bridge and tunnel branch road are considered, wherein the expressway and the main road are considered according to 6 bidirectional lanes, the secondary main road is considered according to 4 bidirectional lanes and the branch road is considered according to 2 bidirectional lanes, and the construction cost of different roads is set as shown in table 10.
TABLE 10 construction costs of different roads
Then, the urban road network redundancy optimization model for the influence of rainstorm is as follows:
max F(X)＝π N (X)/[C N (X)+C P (X)]in the formula (14),
wherein X is the vector of the number of roads in the road network, and X = [) 1 ,X 2 ,…,X i ]；
X i For a set of road segments on the ith road, X i ＝[X i,1 ,X i,2 ,…,X i,m ]；
X i,m The road section with the attribute corresponding value of m on the ith road is m, and the m belongs to {0,1,2,3,4,5,6};
π N (X) is the network redundancy of the urban road under the influence of rainstorm;
C p the total travel time cost for travelers in the urban road network;
C N the total construction cost of the urban road network.
(5) And solving the rainstorm influence-oriented urban road network redundancy optimization model by adopting a genetic algorithm, setting constraint conditions of urban road types, road capacities and construction funds, and calculating the fitness of the genetic algorithm to obtain an urban road network optimization scheme.
The genetic algorithm solving process is shown in fig. 3, urban road network redundancy under the influence of rainstorm obtained by a formula (11) is used as an initialization population of the genetic algorithm, the urban road type, the road capacity and the construction fund constraint conditions are set to calculate the fitness of the genetic algorithm, and finally the optimal scheme is output.
1) In order to meet the requirement that the road types of different road sections on the same road are consistent, the road types are constrained as follows:
x i,a ＝x i,b a, b ∈ {1,2, …, m } equation (15),
in the formula, x i,a The road type of a road section a on the ith road;
x i,b is the road type of the section b on the ith road.
2) To ensure that the traffic flow on a road segment is not greater than the capacity of the road segment, the road capacity constraints are as follows:
0≤x a ≤x a,max in the formula (16),
in the formula, x a Is the traffic flow for road segment a;
x a,max of section aMaximum capacity of traffic.
3) Under normal conditions, the capital used by cities to construct municipal roads is limited, and to ensure that the total construction cost of the planned roads is not greater than the available construction capital, the construction capital constraints are as follows:
∑C N (X) is less than or equal to formula (17) B,
wherein B is a fund that can be used for road construction.
EXAMPLES example 1
In the embodiment, a 25-node checkerboard type road network is selected. The checkerboard type road network comprises 10 roads, 25 nodes and 40 road section units, wherein the length l of each road section unit a 2400m, as shown in fig. 4, there are 25 × 24=600 OD point pairs in the network, and the demand between any OD point pair is 60pcu/h in normal weather. In a heavy rain scenario, it is assumed that traffic demand is reduced by 5%.
Carrying out traffic distribution by adopting a capacity limit-increment loading distribution method (taking K = 5) to obtain the time impedance t of each section unit in the time impedance formula (2) a Then, according to the normal distribution parameters of the speed reduction coefficients of the different-grade and different-type road section units in the table 8, the formula (4) of the probability density function and the formula (5) of the failure probability, the failure probability of each road section unit under the influence of the rainstorm is calculated and obtained, as shown in the table 11. As can be seen from table 11, under the rainstorm scenario, the failure probability of the expressway is close to 0, which indicates that the expressway has higher reliability in rainfall; the failure probability of the main trunk of the underpass tunnel is greater than that of the non-bridge tunnel main trunk.
TABLE 11 time impedance and failure probability of each segment Unit
The present embodiment will have a cost tolerance factor
Setting the OD point pairs as 1.5, calculating to obtain reasonable feasible paths among any OD point pairs, wherein the number of the reasonable feasible paths of 94 OD pairs in the total 600 OD pairs is 6, the proportion is 15.7 percent, namely the failure probability of the reasonable feasible paths is 15.7 percent, and substituting the reasonable feasible paths into the path formula (11) can obtain the redundancy pi of the 25-node checkerboard type trunk network N =5.60. The practical significance of the method is that 5.60 reliable reasonable feasible paths exist between each OD pair in the checkerboard road network on average, and the checkerboard road network is high in redundancy. The construction cost of the 25-node checkerboard road network obtained according to the table 6 is 174.88 billion yuan, and the total travel time cost is 72.62 billion yuan.
When the urban road network redundancy optimization model for rainstorm influence is solved by adopting a genetic algorithm, the population number is measured to be 50 by writing a program through python, the variation probability pm =0.03, the cross probability pc =0.8 and the evolution algebra is 200. And setting a constraint condition, and setting the fund B available for road construction to be 50 hundred million yuan.
Fig. 5 shows the convergence of the 25-node checkerboard road network redundancy optimization model solution. As can be seen from fig. 5, in the iteration process of the first 50 generations, as the iteration process increases, the population individual average fitness rapidly increases, and the iteration starts to stabilize around the 150 th generation.
Finally, the objective function value is 0.0450627 obtained through calculation, and the corresponding obtained control variable is X 1 ＝[2,2,1,1,2,2,1,1,2,2]The corresponding road network structure after optimization design is shown in fig. 6, the road network redundancy at this time is 6.38, the total construction cost is 49.92 million yuan, and the total travel time cost is 86.75 million yuan. The road grade and type in the road network after optimization are non-bridge tunnel main road and non-bridge tunnel secondary main road.
EXAMPLE 2
The strip trunk network selected in this example is shown in fig. 7. The network comprises 13 roads, 30 nodes and 47 link units, and forms OD point pairs of 30 multiplied by 29=870 pairs, and travel demands among the OD pairs are consistent with a 25-node checkerboard road network. In fig. 7, (i) represents the ith road. The length of each road section unit is 2400m, so that the length in the east-west direction is 21.6km, and the width in the north-south direction is 4.8km. According to the urban integrated traffic system planning standard (GB/T51328-2018), when the urban area of the strip-shaped urban center exceeds 30km, I-level expressways are arranged; and when the speed exceeds 20km, a II-level express way is required to be arranged. In addition, the strip city should ensure that the main roads in the long axis direction are through, and not less than two main roads, the road grade should not be lower than that of the II-grade main road, so three roads in the east-west direction should be set as express roads or main roads, the roads in the north-south direction are shorter, the borne traffic function is smaller, and the roads are set as main roads or secondary main roads.
The python programming is adopted, the population quantity solved by the genetic algorithm is 50, the mutation probability pm =0.03, the cross probability pc =0.8, and the evolution algebra is 200 generations.
Fig. 8 shows a convergence process of the solution of the redundant optimization design model of the strip trunk network, and as can be seen from fig. 8, in the first 50 generations of iteration processes, along with the increase of the iteration process, the population individual average fitness rapidly increases, and the iteration starts to tend to be stable around the 130 th generation, the finally obtained objective function value is 0.0249630, and the corresponding control variable is X 4 ＝[4,4,4,2,2,2,1,2,1,2,1,2,2]The optimized strip-shaped trunk network is shown in fig. 9, the redundancy of the trunk network is 5.74, the construction cost is 155.52 million yuan, and the total travel time cost is 74.36 million yuan. In the trunk network, roads in the long axis direction are all set as viaduct expressways, and other roads are non-bridge tunnel main roads and non-bridge tunnel secondary roads in grades and types.
Table 12 shows the calculation of the original redundancy of the checkerboard trunk network and the calculation of the redundancy optimization design of the checkerboard trunk network in example 1, and the calculation of the result of the redundancy optimization design of the strip trunk network in example 2.
TABLE 12 summary of the calculation results
As can be seen from table 12, 1) the chess board network has high redundancy, and the gain of setting the viaduct expressway for improving the redundancy is much smaller than the increase of the construction cost. Therefore, the trunk network after the redundancy optimization design has no express way, so that the construction cost is greatly reduced while the redundancy is slightly improved. However, since the traffic distribution in the model solving process adopts the capacity limit-increment loading method, the method is still the shortest path distribution method in nature, and the Braess paradox exists, that is, in the case of individually selecting a path, an extra road segment is added to a road network, and the overall operation level of the road network is reduced. Therefore, although the redundancy after the optimized design is improved from 5.60 to 6.38, the total travel time cost is increased from 72.62 billion to 86.7 billion. 2) Compared with a checkerboard road network, the redundancy of the strip road network is poor, so that the scheme of setting the viaduct expressway is considered preferentially, the diversity of road section units and paths is increased, and the redundancy is improved rapidly. 3) When the urban road network redundancy optimization design is carried out, the redundancy, the construction cost and the total travel time cost of the scheme are considered, and the constructed model has certain rationality and construction significance.
The method is based on the failure probability of a reasonable feasible path, takes the grade and the type of the road as decision variables, establishes an urban road network redundancy calculation model under the influence of heavy rain, and solves the nonlinear programming problem by adopting a genetic algorithm. Further, example analysis was performed based on the checkerboard road network and the strip road network.
The calculation example shows that the redundancy of the checkerboard type road network is high, the redundancy of an original checkerboard type road trunk network (provided with express ways) is 5.60, the construction cost is 174.88 hundred million yuan, the redundancy of a checkerboard type road trunk network structure (not provided with express ways) which is subjected to redundancy optimization is 6.38, the construction cost is only 49.92 hundred million yuan, the construction cost is greatly reduced while the redundancy is slightly improved, but the Braess paradox exists due to the fact that the capacity limitation-incremental loading method is adopted to distribute flow, and the total travel time cost is increased from 72.62 million yuan to 86.7 yuan.
The example also shows that the redundancy of the optimized strip trunk network structure (provided with the express way) is 5.74, the construction cost reaches 155.52 hundred million, and the strip trunk network can increase the diversity of road section units and paths by arranging the express way so as to improve the redundancy of the road network.
The above-mentioned embodiments are only preferred embodiments of the present invention, and are not intended to limit the scope of the present invention, and it is obvious to those skilled in the art that other embodiments can be easily made by replacing or changing the technical contents disclosed in the present specification, and therefore, all changes and modifications made on the principle of the present invention should be included in the claims of the present invention.
Claims (5)
1. A redundancy-based urban road network optimization design method under the influence of rainstorm is characterized by comprising the following steps:
acquiring normal distribution parameters of a reduction coefficient of the average running speed of each attribute road section under the influence of rainstorm to obtain the failure probability of the motor vehicle in each attribute road section unit under the influence of the rainstorm;
obtaining the failure probability of all reasonable feasible paths under the influence of the rainstorm according to the failure probability of the motor vehicle in each attribute road section unit under the influence of the rainstorm;
according to the failure probabilities of all reasonable feasible paths under the influence of rainstorm, the network redundancy of the urban road under the influence of the rainstorm is obtained;
establishing an urban road network redundancy optimization model facing the influence of rainstorm according to the urban road network redundancy under the influence of rainstorm, the total travel time cost of travelers in the urban road network and the total construction cost of the urban road network;
and solving the rainstorm influence-oriented urban road network redundancy optimization model by adopting a genetic algorithm, setting constraint conditions of urban road types, road capacities and construction funds, and calculating the fitness of the genetic algorithm to obtain an urban road network optimization scheme.
2. The method of claim 1, wherein the attribute section units comprise a branch road, a secondary trunk road, a non-bridge tunnel trunk road, a underpass tunnel trunk road, an overpass express way, a non-bridge tunnel express way and an underpass tunnel express way.
3. The method for optimally designing the urban road network under the influence of the rainstorm according to claim 1, wherein the urban road network redundancy optimization model for the influence of the rainstorm is as follows:
max F(X)＝π N (X)/[C N (X)+C P (X)]，
wherein X is the vector of the number of roads in the road network, and X = [) 1 ,X 2 ,…,X i ]；
X i For a set of road segments on the ith road, X i ＝[X i,1 ,X i,2 ,…,X i,m ]；
X i,m The road section with the attribute corresponding value of m on the ith road is m, and the m belongs to {0,1,2,3,4,5,6};
π N (X) is the network redundancy of the urban road under the influence of rainstorm;
C p the total travel time cost for travelers in the urban road network;
C N the total construction cost of the urban road network.
4. The method for optimally designing the urban road network under the influence of the rainstorm according to claim 1 or 3, wherein the total travel time cost of travelers in the urban road network is as follows:
C p ＝∑ a∈A x a ·t a ·c·T·n a ，
in the formula, A is a road section set of an effective path;
x a is the traffic flow of the road section a, pcu/h;
t a is the time impedance of the road segment a, h;
c is the per-capita time value of urban residents, yuan/min;
t is the annual road service time h;
n a the design age, year for road segment a.
5. The method for optimally designing the urban road network under the influence of the rainstorm according to claim 1 or 3, wherein the total construction cost of the urban road network is as follows:
C N ＝∑ m L m ·c m ，m∈{0，1，2，3，4，5，6}，
in the formula, L m The total length of the road section with the attribute corresponding value m is km;
c m the unit length construction cost of the road section with the attribute corresponding value of m is ten thousand yuan/km.
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