CN106845768B - Bus travel time model construction method based on survival analysis parameter distribution - Google Patents

Abstract

The invention discloses a method for constructing a bus travel time model based on survival analysis parameter distribution, which is characterized in that the travel time of each bus in three sections of upstream, platform and downstream of a bus platform adjacent area and corresponding influence variable data are collected, the travel time is compared with the time duration in the survival analysis, the time duration is assumed to be approximately obeyed to the parameter distribution, each independent variable is brought into the model for solving, a probability density function of an optimal model is selected for integration to obtain an expected function of the optimal model, the expected function is used as a bus travel time evaluation model, and the accuracy of the model is verified. The method is simple and easy to process, can calculate the theoretical bus travel time, and compares and evaluates the actual bus travel time, thereby providing a theoretical basis for an operation manager to implement control measures aiming at the influence variables, and further providing bus competitiveness.

Description

Construction Method of Bus Travel Time Model Based on Parameter Distribution of Survival Analysis

technical field

The invention belongs to the technical field of traffic intelligent management and control, and in particular relates to a method for constructing a bus travel time evaluation model in the adjacent area of a bus stop based on the distribution of survival analysis parameters.

Background technique

With the rapid development of economy and the acceleration of urbanization, the increase of people's travel frequency and the expansion of life and employment radius have put forward higher requirements for the service level of public transport and the coverage of bus stops. Therefore, the construction of bus stop facilities has accelerated in recent years. An important guarantee and support for the operating system. However, the low efficiency of bus operation in the area adjacent to the bus station has become one of the main problems restricting the development of urban public transport. These factors have seriously affected the driving time of the bus in the adjacent area of the bus station and the corresponding stop service location and time, thereby increasing the delay time and driving risk of the bus, and also affecting the normal operation of urban public transportation and the convenience of citizens. Travel has an impact and has become a major bottleneck restricting the development of public transportation.

Existing research cannot discriminate the influencing factors of bus operation in the area adjacent to the bus platform, nor can it quantitatively calculate the theoretical travel time of the bus under the interference of the influencing factors. Operations are properly evaluated. At present, the relevant departments of traffic management are only qualitatively making corresponding measures, such as increasing the video monitoring factors affecting the travel time and carrying out corresponding management, but the relevant departments have not made full use of actual data to identify the travel time of buses in real time, let alone The quantitative and qualitative systematic research on the post-operation evaluation of buses has not been well answered from related research. Therefore, the quantitative study of the bus travel time in the adjacent area of the bus platform should be included in the planning and construction of urban public transport, and countermeasures should be taken according to the evaluation of the bus operation status to improve the operating efficiency of the bus. reflect.

Contents of the invention

Purpose of the invention: In view of the deficiencies in the prior art in the post-evaluation research of bus travel time in the adjacent area of the bus stop, the present invention proposes a bus travel time evaluation model based on the distribution of survival analysis parameters based on the existing intelligent traffic control and management technology The construction method, based on the model constructed by the present invention, can quantitatively evaluate the bus travel time, so that effective control measures can be implemented for its significant influencing factors.

Technical scheme: in order to realize the above-mentioned purpose of the invention, the technical scheme of the present invention is:

A method for constructing a bus travel time model based on survival analysis parameter distribution, comprising the following steps:

(1) Divide the adjacent area of the bus platform into upstream, platform and downstream sections, collect the video data of the adjacent area of the bus platform, and obtain the travel time of each vehicle in the three sections and the corresponding influencing variable data;

(2) Comparing the bus travel time in the adjacent area of the bus platform to the time duration in survival analysis, assuming that it approximately obeys the distribution of multiple parameters, different survival analysis models are established, and the correlation coefficient between the influencing variables is calculated through correlation analysis, and the result is obtained Influencing variables with low correlation are brought into the survival analysis model that obeys the parameter distribution to solve, and the optimal model is selected;

(3) Integrate the probability density function of the optimal parameter survival analysis model to obtain the expectation function, which is used as the bus travel time evaluation model.

In the step (1), the influencing variables include car violation time ratio, non-motor vehicle violation time ratio, car flow, non-motor vehicle flow, bus stop time, bus delay, bus stop position and bus stop time. Whether the car changes lanes.

In the step (2), the distribution forms subject to various parameters include exponential, Weibull, lognormal, Gompertz and generalized Gamma distributions.

In described step (2), the correlation between numerical variables is measured with simple Pearson correlation coefficient; The correlation between sequence variable and sequence variable or with numerical variable is measured with Spearman correlation coefficient; Relate to classification The correlation of the variables is reflected by the correlation index of the symmetry measure in the cross contingency table.

In the step (2), AIC and BIC values are calculated for each specific parameter distribution, and the minimum AIC or BIC value, or the minimum AIC and BIC value are selected as the optimal parameter model.

Beneficial effects: the method of the present invention builds a bus travel time evaluation model based on the distribution of survival analysis parameters. The method is simple and easy to implement, and the evaluation model is highly accurate. The theoretical bus travel time can be calculated based on the input data of the influencing variables based on the model constructed by the present invention , so as to provide a theoretical basis for operation managers to implement control measures for influencing variables, and predict the impact of variables on travel time changes, so that operation managers can provide users with better bus operation information services, thereby providing public transport competitiveness. The theoretical model constructed by the method of the invention calculates the bus travel time in the adjacent area of the bus platform and has practical engineering application value.

Description of drawings

Fig. 1 is a flow chart of the method of the embodiment of the present invention.

Fig. 2 is a specific schematic diagram of the detection points and division intervals of the bus stop in the embodiment of the present invention.

Figure 3 is a fitting relationship diagram between the expected value of the bus travel time in the downstream section and the actual observed value.

Detailed ways

Below in conjunction with specific embodiment, further illustrate the present invention, should be understood that these embodiments are only used to illustrate the present invention and are not intended to limit the scope of the present invention, after having read the present invention, those skilled in the art will understand various equivalent forms of the present invention All modifications fall within the scope defined by the appended claims of the present application.

As shown in Figure 1, a kind of bus travel time model construction method based on survival analysis parameter distribution disclosed by the embodiment of the present invention mainly includes the following steps:

(1) Obtain the travel time of each bus in the three intervals of the upstream, platform and downstream of the adjacent area of the platform and the corresponding influencing variable data. The adjacent area of the bus platform is divided into three sections: upstream, platform and downstream, and each bus is taken as the research object, and the video data of the buses in the adjacent area of the bus platform in the three sections are collected through video equipment, and the data of each bus is obtained from the video data. The travel time data of the car in the three intervals, and the data of the influencing variables corresponding to the travel time of each car.

(2) Comparing travel time to the duration of time in survival analysis, construct a survival analysis model in which travel time approximately obeys different parameter distributions, and bring less correlated variables into the model to solve and then select the optimal model. The bus travel time in the adjacent area of the bus platform belongs to the scope of the generalized survival time, which can be compared to the time duration in the survival analysis, so that the survival analysis method can be used for research. The travel time is the continuation of the state of the bus passing through the corresponding section, and there is an obvious duration process start time-duration time-end time.

The bus travel time distribution can be described by the following probability density function, survival function and hazard function. Assuming that the bus travel time in the adjacent area of the bus platform approximately obeys a certain parameter distribution, a parameter model with better mathematical properties can be used for analysis. And in the parametric method, there are many alternative distribution forms of travel time, such as exponential, Weibull, lognormal, Gompertz and generalized Gamma distribution.

Before establishing the evaluation model of bus travel time, it is necessary to conduct a correlation check on the quality of the data. The correlation coefficient between variables can be calculated by correlation analysis to test the correlation between two variables (or samples). The correlation between numerical variables can be directly measured by simple Pearson correlation coefficient; the correlation between ordinal variables and ordinal variables or numerical variables needs to use Spearman correlation coefficient; the correlation involving categorical variables requires Reflected by the correlation index of the symmetry measure in the cross contingency table. Information from other studies also needs to be incorporated when removing any highly correlated variable, and if other studies show that a given variable has a significant effect on the dependent variable, it should still be retained.

It is determined that there is no strong correlation between the covariates, and the selected variables are brought into the survival analysis model that obeys the parameter distribution to solve the problem. The AIC (Akaike information criterion) and BIC (Baysian information criterion) indicators are often used not only to measure the specific parameter model The advantages and disadvantages of the medium variable can be used to select the optimal parameter model. For each specific parameter distribution, the AIC and BIC values can be calculated, and the one with the smallest AIC or BIC value, or both AIC and BIC values, is selected as the optimal parameter model, which indicates that the fitting effect of the model is better.

(3) The optimal parameter model is obtained by combining the selection, and the probability density function is integrated to obtain the expectation function, and the expectation function can be used as a bus travel time evaluation model. Furthermore, the travel time obtained by real-time measurement and the data of significant influencing variables can be combined, and the bus travel time evaluation model can be used to calculate the travel time of the bus in the corresponding interval, and compared with the actual measured travel time, so as to verify the accuracy of the model .

Below this embodiment is used in Nanjing City to select motor vehicle and non-motor vehicle without the road halfway bus platform of physical isolation facility as research object, further illustrates the implementation details of the inventive method and verifies the validity of the inventive method. The characteristics of this type of bus stop are: the motor vehicle lane and the bicycle lane are separated by road markings, and the bus stop is set on the sidewalk, as shown in Figure 1.

Taking this type of bus platform as an example, explain the position of the detection point in the adjacent area of the bus platform, and install video detection equipment at a high-altitude location that can include the traffic conditions around cross-sections 1, 2, 3 and 4 and the service conditions of the stop platform, such as Each detection point is 20 meters apart, and the specific distance can be adjusted appropriately according to the actual situation, as shown in Figure 2.

The following is used to select a bus station in Nanjing City that meets the above-mentioned type of standard, and the data is obtained by placing a camera on a high building under clear weather from May to July 2013. Mark cross-sections 1, 2, 3, and 4 on the video, so as to record the instantaneous travel time of the bus passing through cross-sections 1, 2, 3, and 4 through video, and record the influencing variables corresponding to the travel time, as shown in Table 1 below Show.

A total of 176 bus examples of this type of bus platform were collected in the video database, and the travel time data of 3 sections in the adjacent area of the bus were selected. and influencing variables to form a data sample.

Table 1 Explanation of influencing variables

Survival analysis methods usually use three functions to describe the distribution characteristics of survival time t: (1) the probability survival function reflecting the individual survival time beyond t; (2) the unconditional probability density function reflecting the occurrence of a specific event at time t; (3 ) reflects the probability hazard function that the individual will end in the next instant. And the risk function in the parametric method has a variety of distribution forms to choose from, such as exponential, Weibull, lognormal, Gompertz and generalized Gamma distribution.

First, let the bus travel time in the adjacent area of the bus platform be T, assuming that there is a linear relationship between the time logarithm logT and the variable as follows:

Among them, X _j and β _j are the influencing variables and the influencing variable coefficients to be solved, β ₀ is the constant coefficient to be solved, j=1,2,...,p, p is the number of influencing variables, σ(σ> 0) is an unknown scale function, ε is a random error term and is a random variable, the probability density function is g(ε,d), the survival function is G(ε,d), and d is an unknown parameter, which indicates that the adjacent area of the bus stop The bus travel time T is related to the distribution of the random error term.

Assuming that the risk function of the bus travel time in the adjacent area of the bus platform approximately obeys the exponential distribution, the following parametric model with better mathematical properties can be used for analysis. Let σ=1 in the above formula (1), then the relationship between the travel time T of the i-th bus in the adjacent area of the bus stop and the variable is as follows:

in _n is the number of buses in the sample data collected in the adjacent area of the bus platform, εi is an independent and identically distributed random variable, and obeys the double exponential distribution. The probability density function g(ε) of the double exponential distribution and the survival function G(ε) are respectively:

The probability density function of the bus travel time T in the adjacent area of the bus platform can be obtained by the following derivation:

Where ε=(logt-μ)/σ, since g(ε) obeys the double exponential distribution, if its probability density function is substituted into the above formula (5), then the probability density function of T can be obtained as:

Introduce the influence of variables, so let The probability density function of the i-th bus travel time T _i can be derived as follows:

Assuming that the bus travel time in the adjacent area of the bus platform _obeys the Weibull distribution with parameters λ and γ, a similar process can be derived as follows:

Assuming that the bus travel time in the adjacent area of the bus platform obeys a normal distribution, Among them, Φ is the standard normal distribution function. Similar to the above derivation process, the probability density function of the i-th bus travel time T _i can be obtained as follows:

Assuming that the bus travel time in the adjacent area of the bus platform obeys the normal Gompertz distribution, the probability density function of the bus travel time Ti in the adjacent area of the _i -th bus platform can be obtained as follows:

When the bus travel time T in the adjacent area of the bus platform obeys a generalized gamma distribution with three parameters μ _i , σ ² and κ, its probability density function is: Wherein, γ=1/κ ² , z=sign(κ)[(logt-μ)/σ], s=γe ^|κ|z , and Φ(z) is a standard normal function. I(γ,s) is an incomplete Gamma function, and Γ(γ) is a complete Gamma function. When the parameters σ and κ take different values, the exponential distribution, Weibull distribution and lognormal distribution all belong to the generalized Gamma distribution family.

In the upstream section of the bus platform, according to the data types of the variables given in Table 1, the corresponding correlation coefficient calculation methods are used respectively. If the correlation test value between the variables is less than 0.05, the null hypothesis that the correlation coefficient between the variables is 0 is rejected. , indicating that the correlation coefficient between these variables is significantly different from 0, but the specific degree of correlation is reflected by the value of the correlation coefficient. The absolute value of the correlation coefficient between variables is generally less than 0.40, indicating that there is only a very low or low degree of correlation between them. In the upstream area adjacent to the bus station, only the correlation coefficient between the bus stop time, the bus stop position and the bus delay is greater than 0.40, indicating that there is a certain moderate correlation between the three, and the bus stop time is selected to keep and into the model calculation. In the platform interval adjacent to the bus platform, the correlation coefficients between all variables are less than 0.40, and all variables are selected into the model for calculation. In the downstream area adjacent to the bus stop, the correlation coefficients between all variables are less than 0.40, and all variables are selected into the model for calculation.

Table 2 Influencing variable coefficients of each model in the upstream section of the bus station

Table 3 Influencing variable coefficients of each model in the bus station platform interval

Table 4 Influencing variable coefficients of each model in the downstream section of the bus station

Table 2-4 shows the fitting results of each model under the influence of variables in the upstream section, platform and downstream section of the bus station (in the table, C represents the coefficient of the influencing variable selected into the model, and P represents the value of the test significance, in the table Omit the variable with no significant effect, that is, the variable whose significance p value is less than 0.1), from the data in the last two rows, the BIC and AIC values corresponding to the generalized gamma distribution model are both the smallest, because the generalized gamma distribution model is exponential , Weibull and the generalized distribution cluster of the lognormal model, so the lognormal model with the smallest value is selected as the specific optimal model, and the BIC corresponding to the generalized gamma distribution model of the lognormal model is shown in Table 3 and AIC values are the smallest, in summary, the lognormal model is the best. Table 2-4 also shows the estimated results of the covariate coefficients of each model under the influence of variables. The variables that affect the bus travel time in the upstream section are the bus stop time and non-motorized vehicle flow; The variables that have an impact on time are car flow, bus delay, and bus stop location; the variables that have an impact on bus travel time in the downstream section are car flow.

Figure 3 also shows the comparison and fitting results between the expected value of bus travel time and the actual observed value in the downstream interval. The fitting effect value of the expected value of bus travel time and the actual observed value in the downstream interval is 0.7513. The evaluation results of the model are good.

Therefore, the parameter distribution model based on survival analysis can be used, combined with the variables that significantly affect the operation of the bus, to calculate the theoretical bus travel time, and can be compared with the actual travel time, so as to judge the accuracy of the bus travel time, and then evaluate the bus travel time. The effect of bus operation is convenient for decision makers to make better management and control decisions, thereby improving the quality of bus system operation and service.

Claims (4)

1. The bus travel time model construction method based on survival analysis parameter distribution, it is characterized in that, comprises the steps: (1) Divide the adjacent area of the bus platform into upstream, platform and downstream sections, collect the video data of the adjacent area of the bus platform, and obtain the travel time of each vehicle in the three sections and the corresponding influencing variable data; (2) Comparing the bus travel time in the adjacent area of the bus platform to the time duration in survival analysis, assuming that it approximately obeys the distribution of multiple parameters, different survival analysis models are established, and the correlation coefficient between the influencing variables is calculated through correlation analysis, and the result is obtained Influencing variables with low correlation are brought into the survival analysis model that obeys the parameter distribution to solve, and the optimal model is selected; AIC and BIC values are calculated for each specific parameter distribution, and the AIC or BIC value is selected to be the smallest, or AIC and BIC The one with the smallest value is regarded as the optimal parameter model; (3) Integrate the probability density function of the optimal parameter survival analysis model to obtain the expectation function, which is used as the bus travel time evaluation model. 2. the bus travel time model building method based on survival analysis parameter distribution according to claim 1, is characterized in that, in described step (1), described influence variable comprises car violation time ratio, bicycle violation Time ratio, car flow, non-motorized vehicle flow, bus stop time, bus delay, bus stop position and whether the bus changes lanes. 3. the bus travel time model building method based on survival analysis parameter distribution according to claim 1, it is characterized in that, in described step (2), obey multiple parameter distribution forms and comprise index, Weibull, logarithm positive State, Gompertz, and Generalized Gamma distributions. 4. the bus travel time model building method based on survival analysis parameter distribution according to claim 1, is characterized in that, in described step (2), the correlation between numerical variable is measured with simple Pearson correlation coefficient ; The correlation between ordinal variables and ordinal variables or numerical variables is measured by Spearman correlation coefficient; the correlation involving categorical variables is reflected by the correlation index of symmetric measurement in the cross contingency table.