CN109584563B - Urban expressway section traffic capacity reliability distribution analysis method based on Weibull distribution - Google Patents
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Abstract
The invention provides a city expressway section traffic capacity reliability distribution analysis method based on Weibull distribution, which can explain the random traffic capacity of expressway sections under multiple bottlenecks, and comprises the following steps of setting multiple detection points for the section to be analyzed; acquiring environmental information of each detection point; acquiring shape parameters and scale parameters of each detection point according to the environment information; and acquiring the traffic flow mutation probability of each detection point according to the shape parameters and the scale parameters of each detection point. The method is based on the hypothesis that the mutation probabilities of the bottleneck road sections are mutually independent, the hypothesis is verified by experimental results, the theoretical average traffic capacity and the mutation probabilities of the road sections with different lengths can be given in a short time according to requirements, and the result is in accordance with the actual situation.
Description
Technical Field
The invention relates to the field of traffic, in particular to a reliability distribution analysis method for traffic capacity of urban expressway sections based on Weibull distribution
Background
With the deep knowledge of the randomness of traffic capacity, the corresponding concept thereof is becoming an important class application of road reliability analysis and practical application. Traffic capacity is understood here as a variable before sudden changes in road traffic. Most technicians demonstrate the variability of pre-mutation traffic by observing traffic mutations at different flows. Brilon et al theoretically presented the concept of random traffic capacity analysis, while based on the Minderhoud and van Toorenburg ideas, presented a statistical approach based on statistical methods to screen data and subsequently provide consistent random capacity estimates. Dong and Mahmassani use this concept to improve travel time prediction, thereby optimizing route selection models built from real-time information of travelers. Ningwu et al proposed multi-bottleneck, multi-road section traffic capacity failure probability analysis through highway traffic capacity research in Germany, but it still adopted manual settings for model parameter calibration. Brilon et al applied the concept of random traffic capacity to evaluate large-scale highway network planning systems. Elenteriadou et al then applied the random traffic capacity to traffic sudden changes on the highway and proposed an active control strategy for the ramp. In China, a random traffic capacity measurement model of the expressway is provided based on actual measurement data of the expressway in Shanghai, such as a quarter of university at the same Ji, an shining in the future and the like. Zhangongfei, Liruimin and the like analyze the reliability of travel time under the condition of random variation based on the same-row capacity.
In the prior art, for a long road section without clearly defined bottleneck, the random traffic capacity distribution of the road section is mostly based on the minimum value or minimum value of the monitoring point position, and the result often lacks accuracy. In addition, due to the difference of road conditions, most researches are often random to the calibration of randomly distributed parameters. To overcome these two problems, first, based on the understanding of the traffic capacity distribution function proposed by Brilon et al [13], a probability distribution curve is fitted with corresponding calibration parameters obtained by combining the maximum likelihood estimation of Weibull distribution, and then the quantitative relationship between the parameters and the influencing factors is analyzed by regression analysis. Finally, a model of the sudden change probability based on the Weibull distribution is introduced to explain the random traffic capacity of the express way section under a plurality of bottlenecks.
Disclosure of Invention
In order to solve the problems, the invention provides a Weibull distribution-based urban expressway section traffic capacity reliability distribution analysis method capable of explaining random traffic capacity of expressway sections under multiple bottlenecks
Comprises the following steps of (a) carrying out,
setting a plurality of detection points for a road section to be analyzed;
acquiring environmental information of each detection point;
acquiring a shape parameter alpha and a scale parameter beta of each detection point according to the environment information;
and acquiring the traffic flow mutation probability of each detection point according to the shape parameter alpha and the scale parameter beta of each detection point.
Further, in the above-mentioned case,
the environment information comprises weather information, lane number information and light information.
Further, in the above-mentioned case,
the shape parameter alpha and the scale parameter beta of each detection point are obtained according to the environment information,
the shape parameter alpha is obtained according to the following formula,
α＝9.371+0.115x1+1.512x2-0.331x3 2；
the scale parameter beta is obtained according to the following formula,
β＝1017.24-101.141x1+1673.232x2-471.333x3 2；
wherein x1As a light index, daytime x10, x night1Is 1, x2The number of lanes; x is the number of3Weather conditions, sunny day x3Is 0, cloudy x3Is 1, foggy day x3Is 2.
Further, in the above-mentioned case,
the acquiring of the traffic flow mutation probability of each detection point according to the shape parameter alpha and the scale parameter beta of each detection point comprises acquiring the traffic flow mutation probability of each detection point according to the following formula,
Further, in the above-mentioned case,
for a single road section j, under the condition of the duration of t and the length of l, the mutation probability is
The probability of sudden change occurring in the continuous section of the total length L within the time of the duration T is obtained by the following formula,
in the formula: alpha is alphac,iThe scale parameter of the measured point i; beta is ac,iAs the shape parameter of the measured i point, k is the road section density, kcIs the critical density.
The invention has the beneficial effects that:
by collecting and analyzing express way data, the invention provides a real-time evaluation method for explaining the reliability of an express way section formed by combining a plurality of detection points through random traffic capacity and mutation probability. The method is based on the hypothesis that the mutation probabilities of the bottleneck road sections are mutually independent, the hypothesis is verified by experimental results, the theoretical average traffic capacity and the mutation probabilities of the road sections with different lengths can be given in a short time according to requirements, and the result is in accordance with the actual situation.
Drawings
Fig. 1 is a schematic illustration of a road section according to an embodiment of the present invention.
Fig. 2 is a schematic diagram of probability distribution of a partial road segment according to an embodiment of the present invention.
FIG. 3 is a schematic diagram of comparison of Weibull distribution parameters according to an embodiment of the present invention.
Fig. 4 is a schematic view of a part of continuous road section traffic flow mutation probability distribution according to an embodiment of the invention.
Detailed Description
The idea of the invention for solving the background technical problem is that firstly, based on the understanding of the traffic capacity distribution function, the maximum likelihood estimation of the Weibull distribution is combined to obtain the corresponding calibration parameters to fit a probability distribution curve, and then the quantitative relation between the parameters and the influence factors is analyzed through regression analysis. Finally, a model of the sudden change probability based on the Weibull distribution is introduced to explain the random traffic capacity of the express way section under a plurality of bottlenecks.
The following describes the random traffic capacity and calculation method of the expressway of the invention.
The research on continuous traffic flow shows that the traffic flow sudden change phenomenon exists. Therefore, a new definition of the random traffic capacity of the road sections based on the sudden change of the traffic flow is generated. Subsequently, the industry proposed a traffic capacity distribution function. The function establishes the following formula by improving the service life of the system and taking the sudden change condition of the traffic flow as the system failure state by applying a PLM (product limit method) method:
Fc(q)＝1-Sc(q) (1)
in the formula: sc(q) is a traffic flow non-abrupt change probability distribution function; fc(q) is a traffic flow mutation probability distribution function; q is traffic volume (veh/h); q. q.siIs the traffic flow rate (veh/h) during the ith period; n isiFor the presence of q ≧ qiThe number of time periods of; diIs at qiThe number of mutations in time; { B } is a period where there is a sudden change, i.e., the speed of the vehicle is higher than the set speed threshold value during the i-th period, but is lower than the set speed threshold value (in the free-flow state) during the i + 1-th period.
In order to distinguish time periods in the set { B }, determining a speed threshold is a key point of calculation, considering that the speed in a certain time period is higher than a critical speed by adopting a three-parameter relation of a traffic flow theory, the speed is considered to be in a non-congestion state, otherwise, the speed is considered to be in a congestion state, determining the actual speed threshold based on a relation curve between the speed and the flow of an express way in the Zhejiang plain area in a certain time period, and considering the speed corresponding to the top end of the curve as the speed threshold. In total, 16 segments of Zhejiang Shaoxing Shengzhou and Xinchang were measured in an embodiment of the present invention. The data acquisition time is 3 months and 1-21 days in 2017, the data acquisition is carried out through radar gun data acquisition, the critical speed of the road section is shown in the table 1 through calculation, and a schematic diagram of a part of the road section is shown in the figure 1.
TABLE 1 spatial average speed threshold for measured road section
Calculating the speed threshold value of the road section, finding out the interval meeting the conditions according to the definition in the set { B }, counting the speed value measured by the coil, counting the traffic flow rate (veh/h), the traffic volume (veh/h) in 5 minutes and the speed value 5 minutes before the traffic flow sudden change by taking 5 minutes as a break, and obtaining a random traffic capacity probability distribution scatter diagram according to a formula 1.1. The parameters alpha and beta of Weibull distribution are estimated by the obtained scattered point data through maximum likelihood estimation, then a Weibull distribution curve is obtained, the Weibull distribution is used as a distribution function of random traffic capacity, and the formula is as follows:
wherein q is the traffic volume (veh/h); alpha is a scale parameter (veh/h); beta is a shape parameter; fcAnd (q) is the traffic flow mutation probability.
The probability distribution of the partial road sections (SXSZ07 and SXXC03 detection points) is shown in FIG. 2; further, the values of the weibull distribution parameters obtained by the maximum likelihood estimation at each link are shown in table 2:
TABLE 2 calibration parameters of the measured section of road under different conditions
Note: in the measured days, fog does not appear at night, so statistics is not carried out.
According to the road conditions corresponding to different parameter results, three factors of weather (rain, fog and fine), light (day/night) and lane number (the road surface material of the measured road section is asphalt) which have great influence on the parameters are discovered through actual observation. Therefore, the three factors are taken as mutually independent parameter variables, each influencing factor is quantified, and then regression analysis is carried out on parameter results, wherein the regression equation is as follows:
α＝9.371+0.115x1+1.512x2-0.331x3 2 (3)
β＝1017.24-101.141x1+1673.232x2-471.333x3 2 (4)
in the formula x1As a light indicator (0 at day and 1 at night); x is the number of2The number of lanes; x is the number of3Weather conditions (0 on sunny days, 1 on cloudy days, 2 on foggy days).
The result calculated by the above formula is compared with the result of actual measurement, and the comparison result is shown in fig. 3. According to the analysis result, the correlation is higher by comparing the calculated value of the parameter with the actual measured value; in addition, through hypothesis test (t test), the P-Value of the shape parameter beta is 0.465, the P-Value of the scale parameter alpha is 0.284, and the absolute hypothesis shows that the two have obvious correlation, so that the two can be approximately considered to be in accordance with a linear relationship.
The following describes the analysis of the reliability of the expressway detection points and road sections according to the present invention.
For bottlenecks between longer segments or longer segments, abrupt changes in the flow of the segment traffic may be considered independent if the distance is far enough. Thus, for express ways without defined bottlenecks, the probabilities of abrupt changes occurring are also independent of each other when the distance between detection points is sufficiently far. So that the following reasonable assumptions can be made for the abrupt probability distribution in a series of express road segments:
1. all mutational conditions occur in the free flow regime;
2. the distances between the bottlenecks to be studied are far enough, and the mutation possibilities are independent of each other;
3. the distribution of mutation probabilities is time-independent.
However, considering that the positions of some sudden change occurrence points are too close to each other, in this case, the position can be approximately regarded as a sudden change point, and the function distribution function of the single sudden change point without sudden change is as follows:
according to the assumption that the mutation probability distributions are independent of each other for successive mutation points along the expressway, the unmutated distribution function of this mutated position sequence is:
in the formula: alpha is alphac,iIs the scale parameter (veh/h) of the measured point i; beta is ac,iIs the shape parameter of the measured i point.
Considering that the road conditions in each measurement position are different (the parameter calibration is influenced by three factors, namely light, weather and lane number), in the measurement process, the light and weather parameters can be considered to be the same, but the variable of the lane number cannot be ignored, so that the probability distribution has a form of Weibull distribution but is not the Weibull distribution. More importantly, the joint distribution of the mutation probability of each measurement position cannot explain the situation of the road section near the measurement position, namely, the reliability analysis of the road section cannot be described in detail. In order to solve the problem, a method for calculating the probability distribution of the sudden change of the road section is introduced.
The following describes the reliability analysis method for continuous road sections in the expressway detection sequence
The method for evaluating the trafficability of the single detection position is described in terms of probability distribution, and the trafficability function before sudden change of the single detection position can be determined. In order to describe the link abrupt probability distribution, the density k in the link needs to be introduced, but in actual observation, the traffic density is not easy to detect. Before the sudden change of the traffic capacity of a certain road section in the express way, the critical density k of the road sectioncCorresponds to the distribution function of the capacity c before sudden change. The basic relationship q ═ k × v, q ═ c according to the traffic flow is also true; so that c is kc×vcWherein k iscAnd vcRespectively corresponding to the critical density and the critical speed of the traffic capacity before sudden change. So that the capacity F is passed before sudden changec(q) distribution function and critical velocity
Given by the probability distribution function of (2), the critical density
May also be derived. So that the express way section density probability distribution function
The probability distribution function P (c ≦ q) ═ F of traffic volume mutation of single detection positionc(q) is converted.
Since the traffic flow near the inspection site is regarded as a continuous flow, the traffic flow-related sudden traffic capacity distribution Fc(q) is approximately considered to fit a Weibull (Weibull) distribution. According to the characteristics of Weibull distribution, the critical speed v is assumedcThe distribution is also Weibull distribution, so that the distribution function can be obtained as formula (7):
when the velocity at the detection position is approximately constant, equation (8) can be obtained in this case:
for the traffic capacity before sudden change, the trial range of the formula is that the quick road section with the length delta L is effective within the time interval delta t of corresponding analysis. It may be assumed that the detection position is located in the middle of Δ L, for example, if a certain critical speed v of the highway section is measured within a time interval of 5 minutesc60km/h, the pre-mutation traffic capacity scale parameter β obtained by maximum likelihood estimationcAnd a shape parameter alphacIs only right for probability distribution function
Is valid, and for the shape parameter, it does not change with the length of the road section as long as the road condition is the same. For the convenience of calculation, the shape parameters of all points in the effective road section of the measured position are assumed to be consistent, and the shape parameters are calculated by the pair ScAnd (q) popularizing, namely, when the shape parameters in the effective road section of the detected position are consistent, according to a popularization idea of the joint mutation probability of a plurality of detected positions. The traffic flow mutation probability of a single road section is as follows:
equations (9), (10) are derived from the above equations:
the larger the distance in the measured range, the smaller the scale parameter, which is consistent with the observation of the actual condition. Also, considering the mutual independence of the mutation probabilities between the links, it can be generalized as follows:
the above equation is a joint probability distribution function of abrupt change of the road traffic flow in m effective road sections L within a set time interval Δ t. The function can be used to evaluate the stability of any continuous finite segment group within a finite period of time. According to the popularization idea from the stability of the detection points to the stability of the road sections around the detection points, for a large traffic network, the long-time reliability of the road network can also be obtained, the reliability of the express road sections can be defined as the probability that the sudden change of the traffic flow does not occur in any road section sequence group at any time. By this definition, reliability can be expressed as a probability distribution function that no sudden traffic change occurs over time and space. For a single road section j, under the condition of duration t and length l, the mutation probability is as follows:
the same principle is that:
in the continuous section, the traffic capacity scale parameter alpha, the density k and the length l of the express section jjIn the off period tjDifferent values may be taken.
This equation describes the probability of a sudden change occurring within a continuous section of the total length L over time for a duration T. According to the formula, the reliability of the road network formed by long continuous road sections can be quantitatively described according to the time length.
In an embodiment of the present invention, with the previous obtained data (survey time is 3 months 1-21 days 2017), the results of the partial road segments are shown in fig. 4, and the error analysis and the correlation analysis are respectively performed on the probability distributions, and are quantified by the average error percentage and the pearson correlation coefficient, and the error percentage analysis results of the four graphs are: 13.71% (9:00-9:30), 9.84% (8:00-8:15), 29.33% (16:00-17:30), 21.41% (8:30-9: 15); the analytical result of the Pearson correlation coefficient is as follows: 0.87(9:00-9:30),0.91(8:00-8:15),0.79(16:00-17:30),0.83(8:30-9:15). From the above quantitative error and correlation analysis, the following conclusions can be drawn:
(1) for the evaluation in the same time period, the longer the statistical time span is, the worse the accuracy is;
(2) for the evaluation in the same time period, the longer the time interval is, the worse the accuracy is;
(3) the sensitivity of the change in the time span to the accuracy of the prediction is greater than the effect of the time interval.
For this reason, both describe the probability distribution of the whole traffic volume from some certain amount of time interval, and the variation of the time span is larger than that of the time interval. From field observation, the larger the time interval is, the more various the change conditions of parameters such as vehicle speed, traffic volume, density and the like in the interval are, so that the determination of scale parameters and the size of mutation probability are influenced, and the conclusion is met with logic and actual observation. Therefore, the reliability description of the road section of the prediction model in a short time interval and a short time span can be obtained, and the prediction model is more suitable for the actual situation. In addition, through statistical results, most data are concentrated in a certain interval, which is consistent with actual observation, and the stability of the data also conforms to the quantitative description of a prediction model.
By collecting and analyzing express way data, the invention provides a real-time evaluation method for explaining the reliability of an express way section formed by combining a plurality of detection points through random traffic capacity and mutation probability. The method is based on the assumption that the mutation probabilities of the bottleneck road sections are independent from each other, and the assumption is established to a certain extent. In addition, experimental results also show that the distribution function can give theoretical average traffic capacity and mutation probability of road sections with different lengths as required in a short time, and the results are in accordance with the actual conditions. The invention provides a better solution for analyzing the traffic flow mutation risk in the express road section or the road network, in particular for analyzing the mutation probability of each bottleneck between the express road sections.
Finally, it should be noted that: the above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments are still modified, or some or all of the technical features are equivalently replaced; such modifications and substitutions do not depart from the spirit and scope of the present invention, and they should be construed as being included in the following claims and description.
Claims (2)
1. A reliability distribution analysis method for traffic capacity of urban expressway sections based on Weibull distribution is characterized by comprising the following steps,
setting a plurality of detection points for a road section to be analyzed;
acquiring environmental information of each detection point;
acquiring a shape parameter alpha and a scale parameter beta of each detection point according to the environment information;
acquiring the traffic flow mutation probability of each detection point according to the shape parameter alpha and the scale parameter beta of each detection point;
the shape parameter alpha and the scale parameter beta of each detection point are obtained according to the environment information,
the shape parameter alpha is obtained according to the following formula,
α＝9.371+0.115x1+1.512x2-0.331x3 2；
the scale parameter beta is obtained according to the following formula,
β＝1017.24-101.141x1+1673.232x2-471.333x3 2；
wherein x1As a light index, daytime x10, x night1Is 1, x2The number of lanes; x is the number of3Weather conditions, sunny day x3Is 0, cloudy x3Is 1, foggy day x3Is 2;
the acquiring of the traffic flow mutation probability of each detection point according to the shape parameter alpha and the scale parameter beta of each detection point comprises acquiring the traffic flow mutation probability of each detection point according to the following formula,
wherein q is traffic, β is a scale parameter, α is a shape parameter, and Fc(q) is the traffic flow mutation probability;
critical speed v for a time interval Δ t, effective for a highway section of length Δ Lc＝60km/h，
Pre-mutation traffic capacity scale parameter beta obtained by maximum likelihood estimationcAnd a shape parameter alphacIs only right for probability distribution function
Is effective;
the shape parameters of all points in the effective road section of the measured position are consistent, and the passing pair Sc(q) generalizing, when the shape parameters in the effective road section of the detected position are consistent, adopting the following formula to jointly mutate probability according to a plurality of detected positions;
in the m effective road sections L, evaluating the stability of any continuous limited road section group in a limited time period by using a combined probability distribution function of sudden change of road traffic flow;
the reliability of the express way section is defined as the probability that the sudden change of the traffic flow does not occur in any section sequence group at any time;
the reliability is expressed as a probability distribution function of no traffic capacity sudden change in the whole time and space, and the sudden change probability of a single road section j under the conditions of the duration of t and the length of l is as follows:
in the continuous section, the traffic capacity scale parameter alpha, the density k and the length l of the express section jjIn the off period tjTaking the value of the difference between the values,
in order to obtain the probability of sudden change in the continuous road sections with the total length L within the time of the duration T, the reliability of the road network consisting of longer continuous road sections is quantitatively described according to the time length;
in the formula, alphac,iThe shape parameter of the measured i point; beta is ac,iAs a scale parameter of the measured i point, k is the road section density, kcFor critical density, T is the total length L duration, L is the total length, j is the individual link, T is the individual link duration, and L is the individual link length.
2. The reliability distribution analysis method for the traffic capacity of the urban expressway sections based on the Weibull distribution as claimed in claim 1,
the environment information comprises weather information, lane number information and light information.
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