CN108491958B - Short-time bus passenger flow chord invariant prediction method - Google Patents

Short-time bus passenger flow chord invariant prediction method Download PDF

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CN108491958B
CN108491958B CN201810139745.4A CN201810139745A CN108491958B CN 108491958 B CN108491958 B CN 108491958B CN 201810139745 A CN201810139745 A CN 201810139745A CN 108491958 B CN108491958 B CN 108491958B
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董红召
刘倩
许慧鹏
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Abstract

A chord invariant prediction method for short-time bus passenger flow comprises the following steps: firstly, converting the short-time bus time sequence simulation chord invariants, deducing a chord invariants passenger flow prediction model SI-PFPM through the short-time invariants of a bus passenger flow time sequence chord simulation object, then performing optimized assignment on each parameter in the SI-PFPM by adopting a genetic algorithm, and finally predicting the future bus passenger flow sequence by using a prediction model. The method does not need a large number of data samples, does not need large-scale training, has small calculated amount and is simple and easy to implement. The method can effectively process actual data, realize calculation, training, prediction and evaluation by using the data, and provide a short-time bus passenger flow prediction model with high accuracy and strong generalization capability.

Description

Short-time bus passenger flow chord invariant prediction method
Technical Field
The invention belongs to the technical field of intelligent transportation, computers and physics intersection, and relates to a chord invariant prediction method for short-time bus passenger flow.
Background
With the rapid development of artificial intelligence, an intelligent algorithm plays an increasingly important role in the research of a passenger flow prediction model, and various intelligent prediction methods can predict the bus passenger flow. Liu Lijuan et al propose a method for predicting the short-time passenger flow of a bus rapid transit station based on a deep neural network (DDN for short), wherein input characteristics comprise time characteristics such as a day of the week, an hour of the day, whether a holiday is saved, scene characteristics such as an exit and an entrance, a payment mode and the like, and passenger flow characteristics such as historical average passenger flow and real-time passenger flow, different stacked autoencoders (SAE for short) are trained by combining the characteristics to further initialize DNN, and finally, a mixed model (SAE-DNN) is subjected to example analysis. Li Wenqun et al have established a short-term bus passenger flow prediction model by using a least square support vector machine for a certain route in Changchun, and consider the influence of passenger flow at upstream and downstream stations, historical synchronous passenger flow and historical passenger flow on the prediction performance of the model. The Tien Qingfei and the like adopt a fractal theory to predict the short-time bus passenger flow, establish a time sequence prediction model through an association dimension, analyze the time distribution rule of the station passenger flow by utilizing a phase space reconstruction theory, and finally adopt the time sequence prediction model to predict the station passenger flow by taking the Changchun No. 255 line station as an example. The model has small error, considers the trend of the passenger flow time sequence data, but slightly rough measures the external factors influencing the passenger flow, and only deduces from the dimension change.
Disclosure of Invention
The invention aims to solve the problems in the prior art, and provides a more accurate method for realizing the short-time bus getting-on/off passenger flow prediction under the background that the prediction precision of a plurality of methods is to be improved, the getting-on passenger flow and the getting-off passenger flow are not distinguished and researched, and the actual training data information is incomplete.
The string invariant prediction method is a nonlinear time sequence prediction method for simulating a string structure, and a large number of free parameters do not need to be trained like an artificial neural network, so that the training time is short, the required data volume is small, and the realization is convenient and simple. The prediction of the short-time bus passenger flow is the basis of the real-time dispatching of public transport, and the operation planning and the allocation of people and vehicle resources can be scientifically and reasonably formulated under the condition of accurately mastering the passenger flow change rule. The randomness and the time variability of the short-term passenger flow prediction enable the short-term passenger flow prediction to be significantly different from the medium-term passenger flow prediction. The observation scale of the latter is large, randomness is weakened at the cost of losing information integrity, and related influence factors of short-time prediction are more difficult to capture and analyze, so that the public transport short-time passenger flow prediction research is more difficult. And the number of people getting on or off the bus at the bus line station is macroscopically related to factors such as social and economic development level, bus trip proportion, the property of the land used at the bus station, population distribution, climate and the like, the factors are not easy to quantify and difficult to update, and the original passenger flow training data are difficult to meet the requirements of prediction methods such as a neural network and a support vector machine. However, microscopically, the short-time bus passenger flow data has obvious change rule with time and relatively stable change in a short time, and a chord invariant passenger flow prediction model (SI-PFPM for short) is adopted to predict that the short-time bus passenger flow accords with the time sequence data characteristics of the short-time bus passenger flow.
The invention discloses a short-time bus passenger flow prediction method, which comprises the following steps:
(1) according to the bus passenger flow data characteristics and the prediction principle of a chord invariant model, the SI-PFPM is designed to predict the short-time bus passenger flow, the bus passenger flow time sequence is set as T (k), k is 1, 2, 3 and …, wherein k is the index of the time sequence, T (k) is the passenger flow value corresponding to the index k, the passenger flow unit is the number of people, and the time sequence is converted as follows:
Figure BDA0001577272820000031
in the formula: t (T) represents a traffic volume value corresponding to the current index value T when k is T, T (T + h) represents a traffic volume value corresponding to the current index value T with a delay of h sequences from the current index value T, and expression (1) represents a rate of change of traffic volume between two sequences.
(2) Based on the chord theory, defining a single-end point chord opening model:
Figure BDA0001577272820000032
in the formula: the superscript (1) means that the number of the endpoints is 1, lsLength of the strings, variable h being represented by length of string lsAnd (3) limiting the additional dimension extension, wherein the model meets the boundary condition of the triarrhena:
T(1)(t,h)＝0 (3)
(3) in order to reflect the influence of rare events on the bus passenger flow, a power rate Q model is introduced to carry out deformation processing on an original model:
Figure BDA0001577272820000033
in the formula: q is a power-law parameter, and the definition of a single-end chord reflects that the T sequence is in lsThe linear trend of the above, introducing the double-end point opening chord T(2)(T, h) represents the nonlinear trend of the T sequence:
Figure BDA0001577272820000034
the model should satisfy the boundary conditions of the triarrhena sacchariflora:
T(2)(t,0)＝T(2)(t,ls)＝0 (6)
(4) in SI-PFPM, the chord invariant is defined as a property that does not change in the chord transform, and the set of invariants is defined as a form of correlation function in statistics:
Figure BDA0001577272820000035
in the formula: k is ls-lpr，lprTo predict the step size,/s>lpr，η1∈(-1,1)，η2Epsilon (-1,1) is homotopy parameter, ls，lpr，Q，η1，η2The five parameters are optimally assigned according to different needs of the prediction object, and the weight W (h) is a piecewise function:
Figure BDA0001577272820000041
wherein:
Figure BDA0001577272820000042
(5) simulating chord objects in the passenger flow time series data to find invariants, predicting the later stage passenger flow time series value by using the invariants, and deducing the following invariants by using a prediction function through an equation (7):
R(t0，k)＝R(t0+lpr,k)k＝ls-lpr (10)
in order to express the derivation result in a concise and clear manner, an auxiliary variable A is introduced1(k,t)，A2(k,t)，A3(k,t)，A4(k,t)，A5(k,t)：
Figure BDA0001577272820000043
Deriving a predicted value:
Figure BDA0001577272820000044
in the formula: lprDenotes the prediction step size, t', t0+lpr-lsFrom this formula, it follows: t' < t0According to equation (12), the passenger flow data sequence before T (T') and l after optimized setting can be passeds，lpr，Q，η1，η2These five parameters predict t0+lprIndexing the corresponding passenger flow value; the prediction effect of the SI-PFPM is better in the time with short time sequence intervals, so that the parameter setting is carried out on the prediction step length, and the single-step cycle iterative prediction is carried out on the passenger flow, namely, the I-PFPM is orderedpr1 is ═ 1; finally, l in the SI-PFPM needs to be treateds,Q,η1,η24 parameters are trained, and an optimal parameter combination is searched;
(6) SI-PFPM parameter optimization:
the method comprises the following specific implementation steps of determining the encoding mode, the initial population number, the crossing rate and the variation rate of parameters in the parameter optimization process of the genetic algorithm, constructing a fitness function according to the SI-PFPM parameter optimization problem, and setting termination conditions, wherein the specific implementation steps of using the genetic algorithm in the SI-PFPM parameter optimization are as follows:
1) setting a set of SI-PFPM parameters and a parameter range, randomly generating a group of SI-PFPM parameters, coding the SI-PFPM parameters by adopting a binary coding mode, and determining the initial population size, the variation rate and the cross rate;
2) determining the fitness function as an average relative error function:
Figure BDA0001577272820000051
in the formula: n is the number of training set passenger flow time sequences; a. thetActual passenger flow volume; ftSetting an expected value for the objective function for predicting the passenger flow;
3) calculating a fitness function value, and setting a termination condition: the fitness function value reaches a desired value or the iteration frequency reaches a maximum value; if the terminal condition is reached, outputting the current SI-PFPM parameter value as the optimal parameter combination; if the termination condition is not met, processing the current generation group by using genetic operations such as a wheel disc algorithm elimination mechanism, intersection, mutation and the like to generate a next generation group;
4) and (5) circularly operating the step (3) until a desired value is reached or the iteration number reaches a maximum value.
The invention has the advantages that: the method can predict the nonlinear time sequence, does not need to train a large number of free parameters, only needs to set 4 parameters, has small calculation amount, is simple and easy to implement, can effectively process data aiming at actual data, and has higher prediction precision and higher generalization capability of the SI-PFPM optimized by a genetic algorithm.
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FIG. 1 is a flow chart of parameter optimization of a short-term bus passenger chord invariant prediction model, which begins to directly write and set genetic algorithm parameter values.
Detailed Description
The following further describes the embodiments of the present invention with reference to the drawings and actual data.
The embodiment is applied to the example of passenger flow investigation and operation data of a certain bus line in a super-large city in China. The following is a typical business day statistical table of the number of passengers on the bus.
Figure BDA0001577272820000052
Figure BDA0001577272820000061
(1) The first 16 data in the table are extracted as training sets, and a genetic algorithm is adopted to trains,Q,η1,η2The flow chart of the genetic algorithm is shown in figure 1. The following steps are carried out by combining the flow chart:
1) setting a set of SI-PFPM parameters and a parameter range, randomly generating a group of SI-PFPM parameters, coding the SI-PFPM parameters by adopting a binary coding mode, and determining the initial population size, the variation rate and the crossing rate.
2) Determining the fitness function as an average relative error function:
Figure BDA0001577272820000062
in the formula: n is the number of training set passenger flow time sequences; a. thetActual passenger flow volume; ftTo predict the passenger flow volume, an expected value is set for the objective function.
3) Calculating a fitness function value, and setting a termination condition: the fitness function value reaches a desired value or the iteration number reaches a maximum value. If the terminal condition is reached, outputting the current SI-PFPM parameter value as the optimal parameter combination; if the termination condition is not met, the current generation population is processed by using genetic operations such as a roulette algorithm elimination mechanism, intersection, mutation and the like to generate a next generation population.
4) And (5) circularly operating the step (3) until a desired value is reached or the iteration number reaches a maximum value.
Parameter l trained by genetic algorithms＝4，Q＝1,η1＝0.6986,η2＝-0.1841。
(2) Parameter l to be traineds＝4，Q＝1,η1＝0.6986,η2-0.1841 and substituting the data in the table into the following formula:
Figure BDA0001577272820000071
in the formula: lprDenotes the prediction step size, t', t0+lpr-lsAuxiliary variable A1(k,t)，A2(k,t)，A3(k,t)，A4(k,t)，A5(k,t)：
Figure BDA0001577272820000072
T (17) ═ 16.3092 was calculated, and this value was close to the actual value 17.
The embodiments described in this specification are merely illustrative of implementations of the inventive concept and the scope of the present invention should not be considered limited to the specific forms set forth in the embodiments but rather by the equivalents thereof as may occur to those skilled in the art upon consideration of the present inventive concept.

Claims (1)

1. A chord invariant prediction method for short-time bus passenger flow comprises the following steps:
(1) according to the characteristics of bus passenger flow data and the prediction principle of a chord invariant model, the chord invariant passenger flow prediction model is designed, called SI-PFPM for short time, the short time bus passenger flow is predicted, the bus passenger flow time sequence is set as T (k), k is 1, 2, 3 and …, wherein k is the index of the time sequence, T (k) is the passenger flow value corresponding to the index k, the passenger flow unit is the number of people, and the time sequence is converted as follows:
Figure FDA0002963391030000011
in the formula: t (T) represents a passenger flow volume value corresponding to when k is T, that is, a passenger flow volume value corresponding to the current index value T, T (T + h) represents a passenger flow volume value corresponding to when k is T + h, that is, a passenger flow volume value that lags behind the current index value T by h sequences, and expression (1) represents a change rate of the passenger flow volume between two sequences;
(2) based on the chord theory, defining a single-end point chord opening model:
Figure FDA0002963391030000012
in the formula: the superscript (1) means that the number of the endpoints is 1, lsLength of the strings, variable h being represented by length of string lsAnd (3) limiting the additional dimension extension, wherein the model meets the boundary condition of the triarrhena:
T(1)(t,h)＝0 (3)
(3) in order to reflect the influence of rare events on the bus passenger flow, a power law Q model is introduced to carry out deformation processing on an original model:
Figure FDA0002963391030000013
in the formula: q is a power law parameter, and the definition of a single-end chord reflects that the T sequence is in lsThe linear trend of the above, introducing the double-end point opening chord T(2)(T, h) represents the nonlinear trend of the T sequence:
Figure FDA0002963391030000014
the model should satisfy the boundary conditions of the triarrhena sacchariflora:
T(2)(t,0)＝T(2)(t,ls)＝0 (6)
(4) in SI-PFPM, the chord invariant is defined as a property that does not change in the chord transform, and the set of invariants is defined as a form of correlation function in statistics:
Figure FDA0002963391030000021
in the formula: k is ls-lpr，lprTo predict the step size,/s>lpr，η1∈(-1,1)，η2Epsilon (-1,1) is homotopy parameter, ls，lpr，Q，η1，η2The five parameters are optimally assigned according to different needs of the prediction object, and the weight W (h) is a piecewise function:
Figure FDA0002963391030000022
wherein:
Figure FDA0002963391030000023
(5) simulating chord objects in the passenger flow time series data to find invariants, predicting the later stage passenger flow time series value by using the invariants, and deducing the following invariants by using a prediction function through an equation (7):
R(t0，k)＝R(t0+lpr,k)，k＝ls-lpr (10)
in order to express the derivation result in a concise and clear manner, an auxiliary variable A is introduced1(k,t)，A2(k,t)，A3(k,t)，A4(k,t)，A5(k,t)：
Figure FDA0002963391030000024
Deriving a predicted value:
Figure FDA0002963391030000025
in the formula: lprDenotes the prediction step size, t ═ t0+lpr-lsFrom this equation, we derive: t'<t0According to equation (12), the passenger flow data sequence before T (T') and l after optimized setting can be passeds，lpr，Q，η1，η2These five parameters predict t0+lprIndexing the corresponding passenger flow value; the prediction effect of the SI-PFPM is better in the time with short time sequence intervals, so that the parameter setting is carried out on the prediction step length, and the single-step cycle iterative prediction is carried out on the passenger flow, namely, the I-PFPM is orderedpr1 is ═ 1; finally, l in the SI-PFPM needs to be treateds,Q,η1,η24 parameters are trained, and an optimal parameter combination is searched;
(6) optimizing SI-PFPM parameters:
the method comprises the following specific implementation steps of determining the encoding mode, the initial population number, the crossing rate and the variation rate of parameters in the parameter optimization process of the genetic algorithm, constructing a fitness function according to the SI-PFPM parameter optimization problem, and setting termination conditions, wherein the specific implementation steps of using the genetic algorithm in the SI-PFPM parameter optimization are as follows:
1) setting a set of SI-PFPM parameters and a parameter range, randomly generating a group of SI-PFPM parameters, coding the SI-PFPM parameters by adopting a binary coding mode, and determining the initial population size, the variation rate and the cross rate;
2) determining the fitness function as a mean absolute error function:
Figure FDA0002963391030000031
in the formula: n is the number of training set passenger flow time sequences; a. thetActual passenger flow volume; ftSetting an expected value for the objective function for predicting the passenger flow;
3) calculating a fitness function value, and setting a termination condition: the fitness function value reaches a desired value or the iteration frequency reaches a maximum value; if the terminal condition is reached, outputting the current SI-PFPM parameter value as the optimal parameter combination; if the termination condition is not met, processing the current generation group by using genetic operations such as a wheel disc algorithm elimination mechanism, intersection, mutation and the like to generate a next generation group;
4) and (5) circularly operating the step (3) until a desired value is reached or the iteration number reaches a maximum value.
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