CN113407906B - Method for determining traffic travel distribution impedance function based on mobile phone signaling data - Google Patents
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Abstract
The invention discloses a method for determining a traffic travel distribution impedance function based on mobile phone signaling data, which is characterized in that travel OD data in a specific period is obtained according to the mobile phone signaling data of a large sample, travel probability is obtained by combining travel distance obtained by a Goodyear map API, different forms of impedance functions are selected respectively by utilizing a nonlinear regression tool in an SPSS, the travel distance and the travel probability are regressed in different regions, then comparison analysis is carried out on the R side, different functions in one region and different regions of the same function respectively, sectional fitting is finally carried out on the impedance functions according to comparison results, and sectional impedance functions suitable for a city are regressed and analyzed by taking the city as an example, so that qualitative and quantitative basis is provided for improving travel distribution model prediction. Meanwhile, the characteristics of large sample size, wide coverage, mature and stable obtaining mode, low cost and the like of the big data of the mobile phone are utilized, the accuracy of the result is improved, the cost of the process is reduced, and the research efficiency is improved.
Description
Technical Field
The invention belongs to the field of intelligent traffic, and particularly relates to a method for determining a traffic travel distribution impedance function based on mobile phone signaling data.
Background
The traffic travel distribution is an important step in traffic travel demand prediction, and the existing traffic distribution prediction model mainly comprises a growth coefficient method, a gravity model method, a probability distribution model and the like, and compared with other distribution prediction models, the gravity model method comprehensively considers regional socioeconomic growth influence factors influencing poor travel classification among cells and travel such as time and distance impedance among traffic cells, and is the most widely used traffic distribution prediction method in traffic planning at home and abroad. Before the prediction of the gravity model traffic distribution, the model needs to be calibrated, wherein the selection and calibration of the impedance function are important, and the traditional distribution impedance is basically obtained by taking travel time or travel distance as an impedance value according to the same city or small sample investigation, but the distribution impedance is not limited to a simple value considering the applicability of the model, and the more general rule impedance function form of the impedance factor is considered.
Disclosure of Invention
In view of the lack of a method for determining an impedance function in the prior art, the invention provides a method for determining a traffic trip distribution impedance function based on mobile phone signaling data, and aims to acquire trip OD data in a specific period according to mobile phone signaling data of a large sample, acquire trip probability by combining trip distances acquired by a Goodyear map API, respectively select different forms of impedance functions by utilizing a nonlinear regression tool in an SPSS, respectively select different forms of impedance functions in different regions to carry out regression on the trip distances and the trip probability, respectively carry out comparison analysis on different regions of the same function from an R side, different functions of the region, and finally select to carry out piecewise fitting on the impedance function according to a comparison result, and carry out regression analysis on the piecewise impedance function suitable for a city domain by taking the city domain as an example, thereby providing qualitative and quantitative basis for improving the prediction of the trip distribution model. Meanwhile, the characteristics of large sample size, wide coverage, mature and stable obtaining mode, low cost and the like of the big data of the mobile phone are utilized, the accuracy of the result is improved, the cost of the process is reduced, and the research efficiency is improved.
The technical scheme is as follows:
a method for determining a traffic travel distribution impedance function based on mobile phone signaling data comprises the following steps:
s1, obtaining trip OD data of the whole city domain in the early peak time by using mobile phone signaling data; acquiring the travel OD of the travel starting point in each subarea in the ArcGIS;
s2, calling a Goldmap API, acquiring travel distance and travel person data, and calculating travel probability;
s3, using a non-linear regression tool of the spss, selecting an impedance function sub-region to carry out regression on the travel distance and the travel probability to obtain a parameter and a fitting goodness R side, comparing the R side, selecting a function with a higher R side, and calculating an error square sum;
s4, calculating an error square sum, carrying out comparison analysis on different functions of the same region, and then carrying out comparison analysis on different regions of the same function;
s5, performing piecewise fitting on the function according to the fitting result and the regional travel distance piecewise pair, and obtaining a final fitting function.
The specific steps of step S1 are as follows:
s11, after preprocessing the obtained mobile phone signaling data, identifying a user stop standing point based on the base station residence time and the service radius, and when the residence time of a user in a range of the service radius threshold D with a certain base station as the center exceeds a time threshold T, taking the base station as the user stop standing point, obtaining a travel OD according to the travel stop standing point, and extracting the departure time to obtain the travel OD of an early peak;
and S12, displaying positions in the ArcGIS according to the longitude and latitude coordinates of the travel starting point in the travel OD obtained in the S11, importing the map files of the sub-regions, and sequentially selecting O points in the range of the refined region through a position selection tool to obtain the travel OD of the sub-regions.
The specific steps of step S2 are as follows:
s21, according to the coordinates of the travel starting point O and the travel destination D, the Alde navigation planning path API is crawled to obtain travel distance data of each OD travel, and the units are as follows: km, and matching with corresponding OD travel times in the mobile phone signaling data to obtain travel distance and travel time data corresponding to each OD of the city domain and each partition;
and S22, counting the travel times in each interval at a distance interval of 1km, and calculating the travel probability corresponding to each area, wherein the travel probability=the travel times/the total travel times.
The specific steps of step S3 are as follows:
s31, selecting five functional forms of a power function, an exponential function, a composite function, a Rayleigh function and a general traffic impedance function, and carrying out regression analysis on the travel distance and the travel probability obtained in the step S2, wherein the functional forms are as follows:
power function:
exponential function:
composite function:
rayleigh function:
general traffic impedance function:
the following formulas:
tij: travel distance between mobile phone base stations i, j; α, β and γ are parameters of the traffic impedance function;
s32, SPSS software is opened, the data of the travel distance and the travel probability of the whole city domain obtained in the step S1 are imported, analysis-regression-nonlinear regression is selected, each impedance function is input to fit the data in sequence, and the parameter regression results of the city domain and each partition are obtained;
s33, comparing a distribution curve of the actual travel distance with a regression simulation curve, comparing the goodness of fit R, selecting a function with a higher R, and calculating the error square sum.
The specific steps of step S4 are as follows:
s41, calculating the error square sum of three functions with higher R sides in S3, wherein the formula of the error square sum is as follows:
wherein: tij: travel distance between mobile phone base stations i, j; f (t) ij ) For a value calculated from the corresponding impedance function;the average value of the observation values, namely the average value of the travel probability;
s42, drawing an actual travel distance, a travel probability distribution curve and a regression fit curve of the same region in the same coordinate system, and respectively analyzing the fit effects of different functions of each region;
s43, representing curves of actual travel distances and probabilities of different areas in the same coordinate system, analyzing characteristics of travel distances between the urban area and each area, representing simulation results of three functions of each area according to the higher R direction in the same coordinate system, and analyzing simulation results of the three functions in different distance ranges.
The specific steps of step S5 are as follows:
s51, taking a city domain range as an example, selecting distance segments according to the analysis result of the S4, and fitting the travel distance and travel probability of each segment respectively to finally obtain a corrected impedance function;
s52, checking the actual value of the impedance function and the model, and calculating the mean square error.
The beneficial effects of the invention are that
The main data source of the invention is mobile phone signaling data, which has the characteristics of high sample size, low cost and wide coverage range, and the acquisition mode is stable and mature, and the invention can record the space-time information of the user activity track more completely, thus being a high-quality data source for urban traffic analysis. According to the method, early peak trip OD data is acquired by utilizing mobile phone signaling data, trip probability is acquired by combining trip distance acquired by a Goodyear map API, impedance functions in different forms are selected respectively by utilizing a nonlinear regression tool in an SPSS, trip distance and trip probability are regressed in different areas, then comparison analysis is carried out on R side, different functions in an area and different areas of the same function respectively, sectional fitting is carried out on the impedance functions according to comparison results, and a sectional impedance function is obtained, so that a qualitative and quantitative basis is provided for improving trip distribution model prediction. The method has general applicability to different cities, has higher accuracy and plays an important role in the accuracy of urban traffic travel prediction.
Drawings
FIG. 1 is a flow chart of the method of the present invention
FIG. 2 is a schematic diagram of analysis region division in an embodiment
FIG. 3 is a chart showing travel distance and travel probability in the embodiment
FIG. 4 is a graph of actual probability in an embodiment
FIG. 5 is a graph showing the impedance distribution of the actual values and model values of the market range according to the embodiment
FIG. 6 is a graph showing the distribution of the actual and model impedance values in the central urban area
FIG. 7 is a graph showing the impedance distribution of the actual values and model values of the middle east sub-center range
FIG. 8 is a graph showing the impedance distribution of actual values and model values in the mid-western range
FIG. 9 is a graph showing the impedance distribution of actual values and model values in the range of a commercial city of a bridge in an embodiment
FIG. 10 is a graph showing the actual travel distance distribution in the embodiment
FIG. 11 is a graph showing a simulated travel distance distribution of a composite function in an embodiment
FIG. 12 is a diagram showing a simulated travel distance distribution of Rayleigh function in an embodiment
FIG. 13 is a graph showing a simulated travel distance distribution of a general impedance function in an embodiment
FIG. 14 is a graph of the fitting result of the unsegmented impedance function in the embodiment
FIG. 15 is a graph of fitting a piecewise impedance function in an embodiment
Detailed Description
The invention is further illustrated below with reference to examples, but the scope of the invention is not limited thereto:
as shown in fig. 2, the example takes mobile phone data of a certain day of 5 months in 2019 of kunshan as a sample, and the research unit is partitioned according to the spatial structure of kunshan city, and is specifically divided into: urban core area, eastern auxiliary center, western auxiliary center and flower bridge business city.
The method flow chart of the invention is given in connection with fig. 1, and the specific steps are as follows:
step S1, obtaining travel OD data of the whole city domain in the early peak time by using mobile phone signaling data, and obtaining travel ODs of travel starting points in various subareas in ArcGIS, wherein the method is preferable and specifically comprises the following steps:
s11, after preprocessing the obtained mobile phone signaling data, identifying a user stop standing point based on the base station residence time and the service radius, and when the residence time of the user in the range of the service radius threshold D with a certain base station as the center exceeds a time threshold T, taking the base station as the user stop standing point, obtaining a travel OD according to the travel stop standing point, and extracting the departure time to obtain the travel OD of the early peak. In this case time threshold t=40 min.
S12, displaying positions in the ArcGIS according to the longitude and latitude coordinates of the travel starting point obtained in the S11, importing the map files of the sub-regions, sequentially selecting O points in the range of the thinned region through a position selection tool, and obtaining the travel OD of the sub-regions
Step S2 calls a Goldmap API, obtains travel probability from the obtained travel distance, calculates travel probability, and preferably specifically comprises the following steps:
and S21, climbing the Goodyear navigation planning path API according to the coordinates of the travel starting point O and the travel destination D to obtain travel distance data (unit: m) of each OD travel, and matching the travel distance data with the corresponding OD travel personnel in the mobile phone signaling data to obtain travel distance and travel personnel data corresponding to each OD in the city domain and each partition.
And S22, counting the travel times in each interval at a distance interval of 1km, and calculating the travel probability corresponding to each area, wherein the travel probability=the travel times/the total travel times. Fig. 3 is a travel distance correspondence probability table.
And S3, selecting an impedance function subarea by utilizing a non-linear regression tool of the spss, carrying out regression on the travel distance and the travel probability to obtain parameters and a fitting goodness R party, comparing the R party, selecting a function with a higher R party, and calculating an error square sum.
Preferably, the method specifically comprises the following steps:
s31, selecting five functional forms of a power function, an exponential function, a composite function, a Rayleigh function and a general traffic impedance function, and carrying out regression analysis on the travel distance and the travel probability obtained in the step S1, wherein each regression analysis parameter;
s32, SPSS software is opened, the data of the travel distance and the travel probability of the whole city domain obtained in the step S1 are imported, analysis-regression-nonlinear regression is selected, each impedance function is input to fit the data in sequence, and the parameter regression results of the city domain and each partition are obtained. The results of the parameters are shown in the following table:
TABLE 1 regression summary of traffic impedance function parameters (I)
TABLE 2 regression summary of traffic impedance function parameters (II)
S33, comparing the distribution curve of the actual travel distance with the regression simulation curve, comparing the fitting goodness R,
as can be seen from the regression results of the two most commonly used traffic impedance functions for each region of Kunshan, the fitting degree of the power function and the exponential function to the travel distance of Kunshan is very low, the R-party of the power function and the exponential function is lower than 0.5, and the actual travel situation statistical data of the Kunshan region and each region can be compared, the actual probability curve is shown in figure 4, the travel probability function changing along with the travel distance is not a simple monotonic function, but a complex function which increases before decreases, and the power function and the exponential function are monotonic, so the fitting degree is lower and do not accord with the actual situation. Therefore, it is not reasonable to treat a single power function or an exponential function as a traffic impedance function in normal times, which does not coincide with the actual situation. The R side obtained by the composite function, the Rayleigh function and the general impedance function is relatively high, the fitting degree of the function model is relatively high, and the actual traveling conditions of the Kunshan city domain and each region are basically met. In order to further analyze and compare the accuracy of the three functions, the simulation data of the three functions are compared and analyzed in combination with the actual situation, and the fitting degree and the error situation are further discussed.
Step S4, calculating an error square sum, carrying out comparison analysis on different functions of the same area, and then carrying out comparison analysis on different areas of the same function, wherein the steps are as follows:
step S41, calculating the error square sum of three functions;
s42, drawing an actual travel distance, a travel probability distribution curve and a regression fit curve of the same region in the same coordinate system, and respectively analyzing the fit effects of different functions of each region;
and comparing the distribution curve of the actual travel distance with the regression simulation curve, and calculating the error square sum so as to verify the reliability of the travel distribution model.
Urban area range travel distance distribution check
The impedance distribution curve of the actual value and the model value in the city domain range is shown in fig. 5, and the fitting degree and the error value of each simulation function in the city domain range are shown in table 3.
TABLE 3 fitting degree and error value of each simulation function in the market Domain
| Composite function | Rayleigh Li Hanshu | General impedance function | |
| R square | 0.934 | 0.849 | 0.949 |
| Sum of squares error | 0.023％ | 0.052％ | 0.018％ |
The R-squares of the three types of functions in the SPSS regression result are respectively 0.934, 0.849 and 0.949, and the fitting degree of the general impedance function is highest. The sum of the squares of the error of the average integrated impedance and the average integrated impedance of investigation for various purposes calculated from the calibration parameters is small, wherein the sum of the squares of the error of the general impedance function is minimal, thereby indicating that the parameters of the general impedance function calibration are more accurate.
Checking travel distance distribution of each zone
The impedance distribution curve diagram of the actual value and the model value in the central urban area range is shown in fig. 6, and the fitting degree and the error value of each simulation function in the central urban area are shown in table 4.
TABLE 4 fitting degree and error value of simulation functions for center urban area
| Composite function | Rayleigh Li Hanshu | General impedance function | |
| R square | 0.923 | 0.837 | 0.939 |
| Sum of squares error | 0.027％ | 0.057％ | 0.021％ |
The R-party of the three types of functions in the SPSS regression result is 0.923, 0.837 and 0.939 respectively, and the fitting degree of the general impedance function is highest. Compared with an actual curve, the travel distance distribution simulation curve in the central urban area range has the advantages that the sum of squares of errors of the composite function and the general impedance function is small and has little difference, the sum of squares of errors of the general impedance function is minimum, and the simulation result is the most accurate.
Eastern auxiliary center travel distance distribution check
The impedance distribution curve of the actual value and the model value of the eastern auxiliary center range is shown in fig. 7, and the fitting degree and the error value of each simulation function of the eastern auxiliary center are shown in table 5.
TABLE 5 fitting degree and error value of simulation functions for eastern auxiliary center
| Composite function | Rayleigh Li Hanshu | General impedance function | |
| R square | 0.934 | 0.846 | 0.950 |
| Sum of squares error | 0.025％ | 0.057％ | 0.019％ |
The R-squares of the three types of functions in the SPSS regression result are 0.934, 0.846 and 0.950 respectively, and the fitting degree of the general impedance function is highest. The minimum sum of squares of travel distribution errors in the range of the eastern auxiliary center is a general impedance function, and the simulation result is the most accurate.
Western auxiliary center travel distance distribution check
The impedance distribution curve of the actual value and the model value of the western auxiliary center range is shown in fig. 8, and the fitting degree and the error value of each simulation function of the western auxiliary center are shown in table 6.
TABLE 6 fitting degree and error value of simulation functions for western Paris center
| Composite function | Rayleigh Li Hanshu | General impedance function | |
| R square | 0.827 | 0.795 | 0.913 |
| Sum of squares error | 0.035％ | 0.041％ | 0.017％ |
The R-squares of the three types of functions in the SPSS regression result are 0.827, 0.795 and 0.913 respectively, and the fitting degree of the general impedance function is highest. The minimum sum of squares of travel distribution errors in the western auxiliary center range is a general impedance function, and the simulation result is the most accurate.
Check for travel distance distribution of bridge business city
The impedance distribution curve of the actual value and the model value in the range of the bridge business city is shown in fig. 9, and the fitting degree and the error value of each simulation function in the bridge business city are shown in table 7.
TABLE 7 fitting degree and error value of each simulation function of flower bridge business city
| Composite function | Rayleigh Li Hanshu | General impedance function | |
| R square | 0.932 | 0.864 | 0.950 |
| Sum of squares error | 0.021％ | 0.041％ | 0.015％ |
The R-squares of the three types of functions in the SPSS regression result are respectively 0.932, 0.864 and 0.950, and the fitting degree of the general impedance function is highest. The minimum sum of squares of travel distribution errors in the range of the bridge business city is a general impedance function, and the simulation result is the most accurate.
S43, representing curves of actual travel distances and probabilities of different areas in the same coordinate system, analyzing characteristics of travel distances between a city domain range and each area, representing simulation results of each area according to a composite function, a Rayleigh function and a general impedance function in the same coordinate system, and analyzing simulation results of the three functions in different distance ranges.
Actual travel distance distribution contrast
Referring to fig. 10, the travel distances between the city area range and each region are mostly concentrated in the travel range of 2-3km, but the travel distances between each region are concentrated in the travel range of 2-3km, and the concentration degree of the travel distances is respectively east auxiliary center > city area range > central city area > bridge business city > west auxiliary center; after the travel distance is more than 6km, the travel probability of the western auxiliary center becomes maximum, and the travel probability of the flower bridge business city becomes minimum along with the further increase of the travel distance; because the western auxiliary center is in a strip shape from the perspective of the space shape, the compactness of the base station is not high, and the space shape of the flower bridge business city is relatively round, so that the compactness is high; after 15km, the travel probability of each zone is reduced to be very low and the travel probability is not very different.
Comparison of simulation results of traffic impedance functions
With reference to fig. 11, the composite function can better simulate the travel distance distribution in the travel distance range smaller than 5km, but after the travel distance is larger than 5km, the travel distribution curves in the city domain range and each area almost overlap, so that the difference and variation of the travel distance larger than 5km cannot be well simulated.
In combination with fig. 12, from the view of the city domain range simulated by the rayleigh function and the function form of each region, the travel distance concentration range and the change condition of each region are relatively close to the actual travel distance distribution condition, but the travel probability value simulated as a whole is lower than the value of the actual travel probability, and the error value range is within-0.02, so that the simulation result of the rayleigh function cannot well reflect the travel probability condition.
With reference to fig. 13, the range of the city domain simulated by the general impedance function is close to the travel distance concentration range and the change condition of each area, and the actual condition is close to the actual condition, and the simulated travel probability value and the change condition of the probability value of each area along with the increase of the travel distance are very close to the actual condition, so that the general impedance function can well simulate the travel distance distribution condition of the city domain range and each area.
Firstly, from the comparison of simulation results of the same impedance function in different ranges, the general impedance function is better than the simulation results of the composite function and the Rayleigh function, so that the value of the trip probability can be simulated more accurately, and the situation that the trip probability of each area changes along with the trip distance can be simulated better; secondly, comparing the simulation and actual conditions of different impedance functions in the same area, wherein the R-side of the general impedance function is highest, the sum of squares of errors is also smallest, the simulation result is most accurate, the complex function is the second, and the Rayleigh function is the last; finally, although all three traffic impedance functions meet the calibration allowable error range, the general impedance function is most suitable for the actual situation and the model parameters are more reliable by integrating the comparison analysis results.
However, all impedance functions have a common problem, and when the travel distance is large, the function simulation values are all lower than the actual impedance, so that the problem that the remote travel amount is inconsistent with the actual impedance is caused, and the general impedance function is corrected by adopting a piecewise fitting method based on the calibration of the functions.
Step S5, selecting a proper function by taking a city domain as an example according to an analysis fitting result, and carrying out sectional fitting on the function according to regional travel distance sectional pairs to obtain a final fitting function, wherein the method is preferable and specifically comprises the following steps:
s51, selecting distance segments according to the analysis result of S4 by taking the urban area range as an example, and fitting the travel distance and travel probability of each segment respectively to finally obtain the corrected impedance function.
Fitting is carried out on the whole market domain and each auxiliary center during regression of the impedance function, and the research aims at market domain traffic model research, so that the impedance function regressed in the range of the market domain is finally uniformly adopted for calculation. The partition fitting result can be used as a reference for regional traffic model research.
The analog value of the general gamma function in the city domain is far lower than the actual value after the travel distance is greater than 7km (as shown in fig. 14), so the impedance function after the travel distance is greater than 7km (as shown in fig. 15) is corrected by adopting a piecewise fitting method, namely the general gamma function is kept unchanged when the travel distance is between 0 and 7km, and after the travel distance is greater than 7km, the second half section of function is fitted by adopting the power function, and finally the corrected impedance function is obtained as follows:
wherein d is ij The trip impedance, i.e. the trip distance value.
S52, checking the actual value of the impedance function and the model, and calculating the mean square error.
Checking the actual value and the analog value of the impedance function, the function fitting degree is high, and the average value of the integral error square sum is 0.3%.
The specific embodiments described herein are offered by way of example only to illustrate the spirit of the invention. Those skilled in the art may make various modifications or additions to the described embodiments or substitutions thereof without departing from the spirit of the invention or exceeding the scope of the invention as defined in the accompanying claims.
Claims (1)
1. A method for determining a traffic travel distribution impedance function based on mobile phone signaling data is characterized by comprising the following steps:
s1, obtaining travel OD data of the whole market in the early peak time by using mobile phone signaling data, and obtaining travel ODs of travel starting points in various subareas in an ArcGIS; the specific steps of step S1 are as follows:
s11, after preprocessing the obtained mobile phone signaling data, identifying a user stop standing point based on the base station residence time and the service radius, and when the residence time of a user in a range of the service radius threshold D with a certain base station as the center exceeds a time threshold T, taking the base station as the user stop standing point, obtaining a travel OD according to the travel stop standing point, and extracting the departure time to obtain the travel OD of an early peak;
s12, displaying positions in the ArcGIS according to longitude and latitude coordinates of the travel starting point in the travel OD obtained in the S11, importing the map files of the sub-regions, and sequentially selecting O points in the range of the refinement region through a position selection tool to obtain the travel OD of the sub-regions;
s2, calling a Goldmap API, acquiring travel distance and travel person data, and calculating travel probability; the specific steps of step S2 are as follows:
s21, according to the coordinates of the travel starting point O and the travel destination D, the Alde navigation planning path API is crawled to obtain travel distance data of each OD travel, and the units are as follows: km, and matching with corresponding OD travel times in the mobile phone signaling data to obtain travel distance and travel time data corresponding to each OD of the city domain and each partition;
s22, counting the travel times in each interval at a distance interval of 1km, and calculating the travel probability corresponding to each area, wherein the travel probability=the travel times/the total travel times;
s3, using a non-linear regression tool of the spss, selecting an impedance function sub-region to carry out regression on the travel distance and the travel probability to obtain a parameter and a fitting goodness R side, comparing the R side, selecting a function with a higher R side, and calculating an error square sum; the specific steps of step S3 are as follows:
s31, selecting five functional forms of a power function, an exponential function, a composite function, a Rayleigh function and a general traffic impedance function, and carrying out regression analysis on the travel distance and the travel probability obtained in the step S2, wherein the functional forms are as follows:
power function:
exponential function:
composite function:
rayleigh function:
general traffic impedance function:
the following formulas:
tij: travel distance between mobile phone base stations i, j; α, β and γ are parameters of the traffic impedance function;
s32, SPSS software is opened, the data of the travel distance and the travel probability of the whole city domain obtained in the step S1 are imported, analysis-regression-nonlinear regression is selected, each impedance function is input to fit the data in sequence, and the parameter regression results of the city domain and each partition are obtained;
s33, comparing a distribution curve of the actual travel distance with a regression simulation curve, comparing a fitting goodness R side, selecting a function with a higher R side, and calculating an error square sum;
s4, calculating an error square sum, carrying out comparison analysis on different functions of the same region, and then carrying out comparison analysis on different regions of the same function; the specific steps of step S4 are as follows:
s41, calculating the error square sum of three functions with higher R sides in S3, wherein the formula of the error square sum is as follows:
wherein: tij: travel distance between mobile phone base stations i, j; f (t) ij ) For a value calculated from the corresponding impedance function;the average value of the observation values, namely the average value of the travel probability;
s42, drawing an actual travel distance, a travel probability distribution curve and a regression fit curve of the same region in the same coordinate system, and respectively analyzing the fit effects of different functions of each region;
s43, representing curves of actual travel distances and probabilities of different areas in the same coordinate system, analyzing characteristics of the city areas and travel distances among the areas, representing simulation results of three functions of the areas according to the higher R direction in the same coordinate system, and analyzing simulation results of the three functions in different distance ranges;
s5, performing piecewise fitting on the function according to the regional travel distance piecewise pairs according to the fitting result, and obtaining a final fitting function; the specific steps of step S5 are as follows:
s51, taking a city domain range as an example, selecting distance segments according to the analysis result of the S4, and fitting the travel distance and travel probability of each segment respectively to finally obtain a corrected impedance function;
s52, checking the actual value of the impedance function and the model, and calculating the mean square error.
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