CN111311905A - Particle swarm optimization wavelet neural network-based expressway travel time prediction method - Google Patents
Particle swarm optimization wavelet neural network-based expressway travel time prediction method Download PDFInfo
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- G08G1/00—Traffic control systems for road vehicles
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Abstract
The invention relates to a particle swarm optimization-based travel time prediction method for a wavelet neural network. The particle swarm optimization algorithm optimizes parameters of the wavelet neural network through continuous iteration, so that the defects of a wavelet neural network model are overcome, including slow convergence speed, easiness in falling into a local minimum value and easiness in generating an oscillation effect. Through comparison experiment analysis, the particle swarm optimization wavelet neural network model can accurately predict the change trend of the travel time and the fluctuation condition of the travel time, and the advantages of high convergence speed, high prediction precision and strong adaptability are proved.
Description
Technical Field
The invention designs a practical model, belongs to the field of intelligent transportation, and particularly relates to a particle swarm optimization wavelet neural network-based expressway travel time prediction method capable of providing trip information with high real-time performance and reliability for travelers.
Background
The accurate prediction of the travel time provides a basis for traffic managers to make management decisions and travelers to reasonably arrange travel plans. Currently, the method of travel time prediction includes: time series models, multiple regression models, Kalman filter prediction, artificial neural networks, and the like. However, the time series model does not consider other factors that affect travel time, but predicts future travel time by analyzing similar trends in past data. The multiple regression model studies data of a target road section and an adjacent road section, and the prediction result is generally not satisfactory. The Kalman filtering model needs to continuously correct the weight in the prediction process, so that the calculation time consumption is too large, and the prediction real-time performance is poor. The artificial neural network is a common method for predicting the travel time, but has the defects of easy falling into a local optimal solution, easy generation of oscillation effect, slow convergence and the like in the application process.
Therefore, when the invention predicts the travel time, the advantages and the disadvantages of the existing method are comprehensively considered, and a new prediction model of the travel time of the expressway is established.
Disclosure of Invention
In view of the defects and research trends in the prior art, the invention aims to provide a particle swarm optimization wavelet neural network-based expressway journey time prediction method model for accurately predicting journey time, thereby providing good theoretical support and decision basis for traffic management and optimization of relevant departments.
In order to realize the purpose of the invention, the adopted technical scheme is as follows:
the method for predicting the travel time of the expressway is researched, and the research method mainly comprises the following steps:
A. processing the highway toll data, and extracting a receipt field required by research;
B. processing the extracted charging data field;
C. on the basis of data processing, predicting the travel time of the highway by using a wavelet neural network model;
D. on the basis of data processing, predicting the travel time of the expressway by utilizing a particle swarm optimization wavelet neural network model;
E. and carrying out comparative analysis on the precision of the 2 prediction models by using 3 evaluation indexes of Mean Absolute Error (MAE), mean relative error (MAPE) and Mean Square Error (MSE). According to the comparison result, the wavelet neural network model optimized by the particle swarm can more accurately realize the prediction of the travel time of the expressway, and shows better adaptability in the verification of actual data.
The expressway travel time prediction method is researched, wherein the specific analysis process of the step A is as follows:
A1. the highway toll in China adopts an informatization system which comprehensively covers the toll collection process, so that a large amount of toll collection data can be collected. The data fields required for the study include instantionid, time in, update, time out, as shown in table 1.
Table 1 charging data field description table
The expressway journey time prediction method is researched, wherein the specific analysis process in the step B is as follows:
B1. the charging data processing is carried out in two steps, first: eliminating abnormal data including missing data, error data and the like; secondly, the method comprises the following steps: screening effective data according to a quartile method, wherein the effective data refers to a data set which can effectively reflect the whole numerical condition, and the interval of the effective data is [ t ]min,tmax]。
B2. The abnormal data mainly includes the following four types:
lack of entry/exit toll station or entry/exit time information: when the charging system software is abnormal or the line transmission is wrong, the charging system cannot input complete charging data information;
same in-out toll station data: when the driver exchanges the toll card in the service area to avoid the behavior of charging, the vehicle recorded in the toll collection system has the same time at the entrance toll station and the exit toll station;
and recording abnormal time data. Although the charging system is increasingly perfect, the defect that the systems of different charging stations are not synchronous exists, so that the time of different charging stations is deviated, and the phenomenon that the entrance time is later than the exit time is caused. This typically occurs when the charging system updates the date in the morning;
and recording abnormal time data. Due to the particularity of the expressway, a service area and a parking area are generally arranged on the road section, so that the phenomenon that long-distance vehicles stay for a long time occurs.
B3. And screening effective data based on a quartile method on the basis of removing error data. The lower limit and the upper limit of the travel time valid data set are calculated according to the formula:
tmin＝t25％-1.5×(t75％-t25％)
tmax＝t75％+1.5×(t75％-t25％)
t25％-25% quantile
t75％- - -75% quantile
tmin-a time of flight valid data set lower limit value
tmax-a time of flight valid dataset upper limit value.
The expressway travel time prediction method is researched, wherein the specific analysis process in the step C is as follows:
C1. and (5) constructing a network. And constructing a three-layer wavelet neural network comprising an input layer, a hidden layer and an output layer. As shown in FIG. 1, wherein X1，X2,...,Xm(m represents the number of input neurons) represents the input to the wavelet neural network, Y1,Y2,...,Yn(n represents the number of output neurons), J represents the number of hidden layer nodes, ωijAnd ωjkThe weights between the input layer and the hidden layer, the hidden layer and the output layer are respectively referred to, wherein i is 1, 2. J ═ 1,2,. J; k is 1, 2.
C2. And (5) initializing the network. Randomly initializing the scaling factor a of a wavelet functionjTranslation factor bjConnection weight ωij(input layer and hidden layer) and ωjk(hidden layer and output layer) setting learning rate η of wavelet neural network1And η2。
The scaling factor is adjusted as follows:
η2-learning rate of wavelet parameters, preferably η2＝0.01。
The adjustment formula of the translation factor is as follows:
η2-learning rate of wavelet parameters, preferably η2＝0.01。
The input layer and the hidden layer can be modified and adjusted by the following formula:
η1-learning rate of network weight parameters, preferably η1＝0.01。
The relationship between the hidden layer and the output layer can be modified by the following formula:
η1-learning rate of network weight parameters, preferably η1＝0.01。
C3. And (6) outputting the prediction. The training samples are input to the network to calculate the predicted output of the network and to calculate the network output and the expected output error e.
C4. And (4) error calculation. The error e between the predicted output and the expected output of the network is calculated. The specific calculation formula is as follows:
yp,k(k) -an actual output value;
tp,k-ideal output value.
C5. And (6) correcting the weight value. In order to enable the error to meet the requirement, a gradient descent method is adopted to correct the weight and the parameters of the wavelet neural network.
C6. If the training times is more than 1000 or e meets the prediction precision requirement (e is less than 0.0001, the error precision is set to be 0.0001, if the error precision is set to be too high, the network convergence speed is slow, and if the error precision is set to be too low, the accuracy of the prediction result is influenced), the training is finished, the prediction result is returned, and otherwise, the learning and the training are continued.
The process of the travel time prediction experiment based on the wavelet neural network is shown in figure 2.
The expressway travel time prediction method is researched, wherein the specific analysis process in the step D is as follows:
D1. network construction: constructing a three-layer POS-WNN neural network comprising an input layer, a hidden layer and an output layer
D2. Parameter initialization processing: the system randomly generates S particles and uses the position vectors of the particles to represent the scale factor and the translation factor a in the wavelet basis functionj，bj(ii) a And a weight value ωij(weight value between ith input and jth hidden layer) and ωj(weight value between jth hidden layer and output layer), the calculation formula is as follows. And meanwhile, setting the maximum and minimum speed, the learning rate and the maximum iteration times of the particles.
xs＝(xs,1,...,xs,d,...,xs,D)＝(a1,...,aJ,b1,...,bJ,ω11,...,ω1J,ω21,...,ω2J,...,ω291,...,ω29J,ω1,...,ωJ)
D＝m×J+J×(m-n)+(m-1)×J
m- - -number of nodes of input layer
J- - -number of hidden layer nodes
n- - -number of output layer nodes
D3. And (5) network training. And calculating the particle fitness in each iteration process based on the error between the actual output value and the ideal output value, wherein the calculation formula is as follows.
Q- -total number of training samples
n- - -number of network output neurons
yp,k(k) - -actual output value
tp,k-ideal output value.
D4. Taking the particle fitness as an index for judging whether the particle fitness meets the set error requirement, finishing training if the particle fitness can meet the set error requirement, namely the fitness value is basically kept unchanged, and turning to the step F; if the error requirement is still not met, the next step is carried out.
D5. Judging whether the training times reach the set maximum iteration times or not, if so, jumping out of the loop, turning to the step F, and stopping training; otherwise, the speed and the position of the particles are updated according to the following formula, and the training is continued by returning to the step C.
vs,d(i+1)＝ω×vs,d(i)+c1r1[ps,d-xs,d(i)]+c2r2[pg,d-xs,d(i)]
xs,d(i+1)＝xs,d(i)+vs,d(i+1)
s＝1,2,..,S；d＝1,2,...,D
c1,c2-acceleration factor
i- -number of current iterations
Omega-inertia factor
r1,r2-random numbers evenly distributed between 0 and 1.
D6. Network debugging: c, selecting a sample value of a specific time period of the training sample as an input value, taking an actual value of another specific time period in the training sample as an ideal output value, calculating an error according to a fitness calculation formula in the step C, and finishing operation if the set error precision is met; if the set error precision can not be met, the step C is carried out.
The experimental flow of the travel time prediction model based on the particle swarm optimization wavelet neural network is shown in fig. 3.
The expressway journey time prediction method is researched, wherein the specific analysis process of the step E is as follows:
E1. and carrying out comparative analysis on the precision of the 2 prediction models by using 3 evaluation indexes of Mean Absolute Error (MAE), mean relative error (MAPE) and Mean Square Error (MSE).
E2. Let tp,kRepresenting actual values of travel time，yp,k(k) The predicted travel time value is represented, and l represents the number of predicted time periods.
E3. Calculating the average absolute error evaluation index, wherein the specific calculation expression is as follows:
mean Absolute Error (MAE) -an indicator used to assess the difference between the actual and predicted values.
E4. Calculating the average relative error evaluation index, wherein the specific calculation expression is as follows:
mean relative error (MAPE) -an indicator of how accurate the travel time prediction is during the travel time prediction process.
E5. Calculating the mean square error evaluation index, wherein the specific calculation expression is as follows:
mean Square Error (MSE) -the degree of change of the overall evaluation data.
And carrying out comparative analysis on the precision of the 2 prediction models by using 3 evaluation indexes of Mean Absolute Error (MAE), mean relative error (MAPE) and Mean Square Error (MSE). The experimental results show that: the average absolute error, the average relative error and the mean square error of the prediction result of the particle swarm optimized wavelet neural network travel time prediction model are respectively reduced by 83.36%, 82.20% and 98.15% compared with the wavelet neural network model. The particle swarm optimized wavelet neural network travel time prediction model not only has high prediction precision, but also can more accurately predict the trend and fluctuation condition of the travel time, has certain advantages in the aspect of convergence speed, and has better adaptability.
The invention discloses a particle swarm optimization wavelet neural network-based travel time prediction method. The particle swarm optimization algorithm optimizes parameters of the wavelet neural network through continuous iteration, so that the defects of a wavelet neural network model, including slow convergence speed, easiness in falling into a local minimum value and easiness in generating an oscillation effect, are overcome. Through comparative experiment analysis, the particle swarm optimization wavelet neural network model can accurately predict the change trend of the travel time and can also accurately predict the fluctuation condition of the travel time. The expressway travel time prediction experiment based on the particle swarm optimization wavelet neural network model proves that the particle swarm optimization wavelet neural network has the advantages of high convergence speed, high prediction precision and strong adaptability.
It should be understood that the present invention is not limited to the above preferred embodiments, and any other products in various forms can be obtained by the present invention, but any changes in the shape or structure thereof, which are the same or similar to the technical solution of the present invention, fall within the protection scope of the present invention.
Drawings
FIG. 1 is a block diagram of a compact wavelet neural network
FIG. 2 wavelet neural network flow chart
FIG. 3 is a flow chart of a particle swarm optimization wavelet neural network travel time prediction model experiment
The method for predicting the travel time of the expressway is researched, and the research method mainly comprises the following steps:
A. processing the highway toll data, and extracting a receipt field required by research;
B. processing the extracted charging data field;
C. on the basis of data processing, predicting the travel time of the highway by using a wavelet neural network model;
D. on the basis of data processing, predicting the travel time of the expressway by utilizing a particle swarm optimization wavelet neural network model;
E. and carrying out comparative analysis on the precision of the 2 prediction models by using 3 evaluation indexes of Mean Absolute Error (MAE), mean relative error (MAPE) and Mean Square Error (MSE). According to the comparison result, the wavelet neural network model optimized by the particle swarm can more accurately realize the prediction of the travel time of the expressway, and shows better adaptability in the verification of actual data.
The expressway travel time prediction method is researched, wherein the specific analysis process of the step A is as follows:
A1. the highway toll in China adopts an informatization system which comprehensively covers the toll collection process, so that a large amount of toll collection data can be collected. The data fields required for the study include instantionid, time in, update, time out, as shown in table 1.
Table 1 charging data field description table
The expressway journey time prediction method is researched, wherein the specific analysis process in the step B is as follows:
B1. the charging data processing is carried out in two steps, first: eliminating abnormal data including missing data, error data and the like; secondly, the method comprises the following steps: screening effective data according to a quartile method, wherein the effective data refers to a data set which can effectively reflect the whole numerical condition, and the interval of the effective data is [ t ]min,tmax]。
B2. The abnormal data mainly includes the following four types:
lack of entry/exit toll station or entry/exit time information: when the charging system software is abnormal or the line transmission is wrong, the charging system cannot input complete charging data information;
same in-out toll station data: when the driver exchanges the toll card in the service area to avoid the behavior of charging, the vehicle recorded in the toll collection system has the same time at the entrance toll station and the exit toll station;
and recording abnormal time data. Although the charging system is increasingly perfect, the defect that the systems of different charging stations are not synchronous exists, so that the time of different charging stations is deviated, and the phenomenon that the entrance time is later than the exit time is caused. This typically occurs when the charging system updates the date in the morning;
and recording abnormal time data. Due to the particularity of the expressway, a service area and a parking area are generally arranged on the road section, so that the phenomenon that long-distance vehicles stay for a long time occurs.
B3. And screening effective data based on a quartile method on the basis of removing error data. The lower limit and the upper limit of the travel time valid data set are calculated according to the formula:
tmin＝t25％-1.5×(t75％-t25％)
tmax＝t75％+1.5×(t75％-t25％)
t25％-25% quantile
t75％- - -75% quantile
tmin-a time of flight valid data set lower limit value
tmax-a time of flight valid dataset upper limit value.
The expressway travel time prediction method is researched, wherein the specific analysis process in the step C is as follows:
C1. and (5) constructing a network. And constructing a three-layer wavelet neural network comprising an input layer, a hidden layer and an output layer. As shown in FIG. 1, wherein X1，X2,...,Xm(m represents the number of input neurons) represents the input to the wavelet neural network, Y1,Y2,...,Yn(n represents the number of output neurons), J represents the number of hidden layer nodes, ωijAnd ωjkThe weights between the input layer and the hidden layer, the hidden layer and the output layer are respectively referred to, wherein i is 1, 2. J ═ 1,2,. J; k is 1, 2.
C2. And (5) initializing the network. Randomly initializing the scaling factor a of a wavelet functionjTranslation factor bjConnection weight ωij(transfusion)In-layer and hidden layer) and ωjk(hidden layer and output layer) setting learning rate η of wavelet neural network1And η2。
The scaling factor is adjusted as follows:
η2-learning rate of wavelet parameters, preferably η2＝0.01。
The adjustment formula of the translation factor is as follows:
η2-learning rate of wavelet parameters, preferably η2＝0.01。
The input layer and the hidden layer can be modified and adjusted by the following formula:
η1-learning rate of network weight parameters, preferably η1＝0.01。
The relationship between the hidden layer and the output layer can be modified by the following formula:
η1-learning rate of network weight parameters, preferably η1＝0.01。
C3. And (6) outputting the prediction. The training samples are input to the network to calculate the predicted output of the network and to calculate the network output and the expected output error e.
C4. And (4) error calculation. The error e between the predicted output and the expected output of the network is calculated. The specific calculation formula is as follows:
yp,k(k) -an actual output value;
tp,k-ideal output value.
C5. And (6) correcting the weight value. In order to enable the error to meet the requirement, a gradient descent method is adopted to correct the weight and the parameters of the wavelet neural network.
C6. If the training times is more than 1000 or e meets the prediction precision requirement (e is less than 0.0001, the error precision is set to be 0.0001, if the error precision is set to be too high, the network convergence speed is slow, and if the error precision is set to be too low, the accuracy of the prediction result is influenced), the training is finished, the prediction result is returned, and otherwise, the learning and the training are continued.
The process of the travel time prediction experiment based on the wavelet neural network is shown in figure 2.
The expressway travel time prediction method is researched, wherein the specific analysis process in the step D is as follows:
D1. network construction: constructing a three-layer POS-WNN neural network comprising an input layer, a hidden layer and an output layer
D2. Parameter initialization processing: the system randomly generates S particles and uses the position vectors of the particles to represent the scale factor and the translation factor a in the wavelet basis functionj，bj(ii) a And a weight value ωij(weight value between ith input and jth hidden layer) and ωj(weight value between jth hidden layer and output layer), the calculation formula is as follows. And meanwhile, setting the maximum and minimum speed, the learning rate and the maximum iteration times of the particles.
xs＝(xs,1,...,xs,d,...,xs,D)＝(a1,...,aJ,b1,...,bJ,ω11,...,ω1J,ω21,...,ω2J,...,ω291,...,ω29J,ω1,...,ωJ)
D＝m×J+J×(m-n)+(m-1)×J
m- - -number of nodes of input layer
J- - -number of hidden layer nodes
n- - -number of output layer nodes
D3. And (5) network training. And calculating the particle fitness in each iteration process based on the error between the actual output value and the ideal output value, wherein the calculation formula is as follows.
Q- -total number of training samples
n- - -number of network output neurons
yp,k(k) - -actual output value
tp,k-ideal output value.
D4. Taking the particle fitness as an index for judging whether the particle fitness meets the set error requirement, finishing training if the particle fitness can meet the set error requirement, namely the fitness value is basically kept unchanged, and turning to the step F; if the error requirement is still not met, the next step is carried out.
D5. Judging whether the training times reach the set maximum iteration times or not, if so, jumping out of the loop, turning to the step F, and stopping training; otherwise, the speed and the position of the particles are updated according to the following formula, and the training is continued by returning to the step C.
vs,d(i+1)＝ω×vs,d(i)+c1r1[ps,d-xs,d(i)]+c2r2[pg,d-xs,d(i)]
xs,d(i+1)＝xs,d(i)+vs,d(i+1)
s＝1,2,..,S；d＝1,2,...,D
c1,c2-acceleration factor
i- -number of current iterations
Omega-inertia factor
r1,r2-random numbers evenly distributed between 0 and 1.
D6. Network debugging: c, selecting a sample value of a specific time period of the training sample as an input value, taking an actual value of another specific time period in the training sample as an ideal output value, calculating an error according to a fitness calculation formula in the step C, and finishing operation if the set error precision is met; if the set error precision can not be met, the step C is carried out.
The experimental flow of the travel time prediction model based on the particle swarm optimization wavelet neural network is shown in fig. 3.
The expressway journey time prediction method is researched, wherein the specific analysis process of the step E is as follows:
E1. and carrying out comparative analysis on the precision of the 2 prediction models by using 3 evaluation indexes of Mean Absolute Error (MAE), mean relative error (MAPE) and Mean Square Error (MSE).
E2. Let tp,kRepresenting the actual value of travel time, yp,k(k) The predicted travel time value is represented, and l represents the number of predicted time periods.
E3. Calculating the average absolute error evaluation index, wherein the specific calculation expression is as follows:
mean Absolute Error (MAE) -an indicator used to assess the difference between the actual and predicted values.
E4. Calculating the average relative error evaluation index, wherein the specific calculation expression is as follows:
mean relative error (MAPE) -an indicator of how accurate the travel time prediction is during the travel time prediction process.
E5. Calculating the mean square error evaluation index, wherein the specific calculation expression is as follows:
mean Square Error (MSE) -the degree of change of the overall evaluation data.
And carrying out comparative analysis on the precision of the 2 prediction models by using 3 evaluation indexes of Mean Absolute Error (MAE), mean relative error (MAPE) and Mean Square Error (MSE). The experimental results show that: the average absolute error, the average relative error and the mean square error of the prediction result of the particle swarm optimized wavelet neural network travel time prediction model are respectively reduced by 83.36%, 82.20% and 98.15% compared with the wavelet neural network model. The particle swarm optimized wavelet neural network travel time prediction model not only has high prediction precision, but also can more accurately predict the trend and fluctuation condition of the travel time, has certain advantages in the aspect of convergence speed, and has better adaptability.
Claims (5)
1. A particle swarm optimization wavelet neural network-based expressway travel time prediction method is characterized by comprising the following steps:
A. processing the highway toll data, and extracting a receipt field required by research;
B. processing the extracted charging data field;
C. on the basis of data processing, predicting the travel time of the highway by using a wavelet neural network model;
D. on the basis of data processing, a particle swarm optimization wavelet neural network model is utilized to predict the travel time of the expressway.
2. The method for predicting the travel time of the highway based on the particle swarm optimization wavelet neural network according to claim 1, wherein the specific analysis process of the step A is as follows:
A1. the highway toll in China adopts an informatization system which comprehensively covers the toll collection process, so that a large amount of toll collection data can be collected; the data fields required for the study include instantionid, time in, EXITSTATION, time out.
3. The method for predicting the travel time of the highway based on the particle swarm optimization wavelet neural network according to claim 1, wherein the specific analysis process of the step B is as follows:
B1. the charging data processing is carried out in two steps, first: eliminating abnormal data including missing data, error data and the like; secondly, the method comprises the following steps: screening effective data according to a quartile method, wherein the effective data refers to a data set reflecting the overall numerical condition, and the interval of the effective data is [ t ]min,tmax]；
B2. The anomaly data contains the following four types:
lack of entry/exit toll station or entry/exit time information: when the charging system software is abnormal or the line transmission is wrong, the charging system cannot input complete charging data information;
same in-out toll station data: when the driver exchanges the toll card in the service area to avoid the behavior of charging, the vehicle recorded in the toll collection system has the same time at the entrance toll station and the exit toll station;
recording abnormal time data; although the charging system is increasingly perfect, the defect that the systems of different charging stations are not synchronous exists, so that the time of different charging stations is deviated, and the phenomenon that the entrance time is later than the exit time is caused;
recording abnormal time data; due to the particularity of the expressway, a service area and a parking area are arranged on a road section, so that the phenomenon that long-distance vehicles stay for a long time occurs;
B3. screening effective data based on a quartile method on the basis of removing error data; the lower limit and the upper limit of the travel time valid data set are calculated according to the formula:
tmin＝t25％-1.5×(t75％-t25％)
tmax＝t75％+1.5×(t75％-t25％)
t25％-25% quantile
t75％- - -75% quantile
tmin-a time of flight valid data set lower limit value
tmax-a time of flight valid dataset upper limit value.
4. The particle swarm optimization wavelet neural network-based expressway travel time prediction method according to claim 1, wherein the specific analysis process of the step C is as follows:
C1. constructing a network; constructing a three-layer wavelet neural network comprising an input layer, a hidden layer and an output layer; as shown in FIG. 1, wherein X1，X2,...,XmRepresenting the input of the wavelet neural network, wherein m represents the number of input neurons; y is1,Y2,...,YnWhere n represents the number of output neurons, J represents the number of hidden layer nodes, ωijAnd ωjkThe weights between the input layer and the hidden layer, the hidden layer and the output layer are respectively referred to, wherein i is 1, 2. J ═ 1,2,. J; k is 1,2,. n;
C2. initializing a network; randomly initializing the scaling factor a of a wavelet functionjTranslation factor bjConnection weight ω between input layer and hidden layerijAnd the connection weight ω between the hidden layer and the output layerjkSetting learning rate η of wavelet neural network1And η2；
The scaling factor is adjusted as follows:
η2-learning rate of wavelet parameters, preferably η2＝0.01；
The adjustment formula of the translation factor is as follows:
η2-learning rate of wavelet parameters, preferably η2＝0.01；
The input layer and the hidden layer are modified and adjusted by the following formula:
η1-learning rate of network weight parameters, preferably η1＝0.01；
The relationship between the hidden layer and the output layer can be modified by the following formula:
η1-learning rate of network weight parameters, preferably η1＝0.01；
C3. Predicting and outputting; inputting the training samples into the network, thereby calculating the predicted output of the network and calculating the error e between the network output and the expected output;
C4. calculating an error; calculating an error e between the predicted output and the expected output of the network; the specific calculation formula is as follows:
yp,k(k) -an actual output value;
tp,k-an ideal output value;
C5. correcting the weight value; correcting the weight and parameters of the wavelet neural network by adopting a gradient descent method;
C6. if the training times are more than 1000 or e meets the prediction precision requirement; e is less than 0.0001, the error precision is set to be 0.0001, the prediction result is returned after the training is finished, and otherwise, the learning and the training are continued.
5. The expressway travel time prediction method based on the particle swarm optimization wavelet neural network according to claim 1,
the specific analysis process of the step D is as follows:
D1. network construction: constructing a three-layer POS-WNN neural network comprising an input layer, a hidden layer and an output layer
D2. Parameter initialization processing: the system randomly generates S particles and uses the position vectors of the particles to represent the scale factor and the translation factor a in the wavelet basis functionj，bj(ii) a And a weight value omega between the ith input and the jth hidden layerijAnd weight value omega between jth hidden layer and output layerjThe calculation formula is as follows; setting the maximum and minimum speed, learning rate and maximum iteration times of the particles;
xs＝(xs,1,...,xs,d,...,xs,D)＝(a1,...,aJ,b1,...,bJ,ω11,...,ω1J,ω21,...,ω2J,...,ω291,...,ω29J,ω1,...,ωJ)
D＝m×J+J×(m-n)+(m-1)×J
m- - -number of nodes of input layer
J- - -number of hidden layer nodes
n- - -number of output layer nodes
D3. Network training; calculating the particle fitness in each iteration process based on the error between the actual output value and the ideal output value, wherein the calculation formula is as follows;
q- -total number of training samples
n- - -number of network output neurons
yp,k(k) - -actual output value
tp,k-an ideal output value;
D4. taking the particle fitness as an index for judging whether the particle fitness meets the set error requirement, finishing training if the particle fitness can meet the set error requirement, namely the fitness value is basically kept unchanged, and turning to the step F; if the error requirement is still not met, the next step is carried out;
D5. judging whether the training times reach the set maximum iteration times or not, if so, jumping out of the loop, turning to the step F, and stopping training; otherwise, updating the speed and the position of the particles according to the following formula, and returning to the step C to continue training;
vs,d(i+1)＝ω×vs,d(i)+c1r1[ps,d-xs,d(i)]+c2r2[pg,d-xs,d(i)]
xs,d(i+1)＝xs,d(i)+vs,d(i+1)
s＝1,2,..,S；d＝1,2,...,D
c1,c2-acceleration factor
i- -number of current iterations
Omega-inertia factor
r1,r2-random numbers uniformly distributed between 0 and 1;
D6. network debugging: c, selecting a sample value of a specific time period of the training sample as an input value, taking an actual value of another specific time period in the training sample as an ideal output value, calculating an error according to a fitness calculation formula in the step C, and finishing operation if the set error precision is met; if the set error precision can not be met, the step C is carried out.
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