CN103729688A - Section traffic neural network prediction method based on EMD - Google Patents

Abstract

The invention discloses a section traffic neural network prediction method based on the EMD, and belongs to the technical field of rail transportation. The method comprises the first step of obtaining components of an intrinsic mode function, wherein summary traffic between OD every 30 minutes every day is distributed into section traffic information to form a section traffic original sequence, the EMD processing is carried out on the original sequence, IMF components are obtained, and an IMF matrix is formed; the second step of identifying the components, wherein a Pearson correlation coefficient between each IMF component and the original traffic sequence is calculated, and the relevance between the coefficients and original data is analyzed; the third step of predicting a neural network, wherein a three-layer BP network model is built, test data serving as the input data of an input layer are substituted into the BP neural network to carry out prediction, and corresponding section traffic output can be obtained. According to the method, the EMD and the neural network are mixed, the characteristics of the traffic data are analyzed, and input variables are provided for the neural network prediction method. By means of the method, the prediction precision of the section traffic can be greater than 95%.

Description

A kind of section passenger flow neural net prediction method based on EMD

Invention field

The present invention relates to a kind of section passenger flow neural net prediction method based on EMD, belong to track transport technical field.

Background technology

In recent years, rapidly, the track traffic road network volume of passenger traffic continues soaring in urban rail transit in China development.The huge volume of the flow of passengers and on road network complicated spatial and temporal distributions be that Chinese city track traffic for passenger flow organization security has been brought huge challenge, in real time, short-time traffic flow forecast has become the safe and efficient operation management of Chinese city track traffic road network problem in the urgent need to address accurately.The result of traffic volume forecast will provide reference for Transportation System Management, for example, and operation management planning, the crowded control plan of website passenger flow etc.

For many years, the research that domestic and international researchist is devoted to forecasting traffic flow model and Forecasting Methodology is continuous, but along with the shortening of predicted time span, that traffic flow shows is non-linear, time variation, uncertainty are more and more stronger, causes the prediction effect of traffic flow and precision of prediction not satisfactory.For the section magnitude of traffic flow in short-term, moment Short-Term Traffic Flow comprise following 3 parts: one, remove the telecommunication flow information of the reflection traffic flow basic change rule of all uncertain factors, i.e. the basic trend that traffic flow changes; Two, essential uncertain factor causes traffic flow sudden change trend; Three, the traffic flow sudden change trend that non-intrinsically safe uncertain factor causes.Rear two parts have affected the real-time traffic of traffic flow randomly, traffic flow are centered around occur near basic trend disturbance, even some time, due to the strong interference of uncertain factor, make this disturbance very fierce.Therefore,, for short-term Passenger flow forecast model, it is necessary catching short-term volume of the flow of passengers feature.

Aspect feature extraction, empirical mode decomposition (Empirical Mode Decomposition, EMD) be a kind of newer signal processing method, there is the feature of self-adaptation and high s/n ratio, extremely be suitable for the analyzing and processing of non-stationary, nonlinear properties, and the intrinsic mode functions decompositing by EMD (Intrinsic Mode Function, IMF) component can be used for characteristic information extraction.At present, existing scholar adopts and calculates energy square, Energy-Entropy, Renyi entropy, the Shannon entropy of each IMF and calculate the methods such as IMF singular values of a matrix and carried out the research that fault signature extracts.

Pearson related coefficient-ρ _xythe statistical indicator of correlationship level of intimate between reflection variable, value is between-1 to 1.ρ _xy, claim that X, Y are uncorrelated at=0 o'clock; | ρ _xy|=1 o'clock, claim X, Y complete dependence, now, between X, Y, there is linear functional relation; | ρ _xy| during <1, the variation of X causes the part variation of Y, | ρ _xy| larger, the variation of X causes that the variation of Y is just larger, | ρ _xy| during >0.8, be called height correlation, when | ρ _xy| during <0.3, be called lower correlation, other for moderate relevant.Analyze the correlativity of each IMF component and raw data, reject original series is affected to little component, can reduce computing time, improve the forecasting efficiency of the short-term section volume of the flow of passengers.

${\mathrm{\&rho;}}_{\mathrm{xy}}=\frac{1}{n-1}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\left(\frac{X_i-\stackrel{\&OverBar;}{X}}{S_X}\right)\left(\frac{Y_i-\stackrel{\&OverBar;}{Y}}{S_Y}\right),---12)$

In formula: n-sample size,

the mean value of-sample, S _x, S _y-sample standard deviation;

BP neural network General Requirements is selected neuronic transport function.BP neural network requires the neuronic transport function must can be micro-everywhere, and conventional transport function comprises linear Purelin type and Sigmoid type.Their each self-representation and characteristic are as follows:

Tan-Sigmoid type transport function, this function is that temperature parameter is the improvement of 1/2 Log-Sigmoid type function, and its output area is (1,1), is bipolarity function, and derivative is Ψ ' (x)=4 (e ^2x(1/e ^2x+ 1) ²), derivative codomain scope (0,1].The Log-Sigmoid type function that Tan-Sigmoid type function corrected signal span is 1 than temperature parameter is large, and speed of convergence faster can be provided, and has stronger advantage.Therefore in the present invention, hidden layer transport function adopts Tan-Sigmoid type function; Output layer transport function adopts linear purelin function, thereby makes the output of network can get arbitrary value.

LM (Levenberg-Marquardt) algorithm is a kind of fast algorithm of the numerical optimization technique of utilizing standard, it is the combination of gradient descent method and Gauss-Newton method, the local convergence of existing Gauss-Newton method, has again the global property of gradient method.Described LM algorithm is:

If error criterion function is

$E\left(w\right)=\frac{1}{2}\underset{i=1}{\overset{p}{\mathrm{\&Sigma;}}}{\left|\right|Y_i-{Y_i}^{\&prime;}\left|\right|}^2=\frac{1}{2}\underset{i=1}{\overset{p}{\mathrm{\&Sigma;}}}{e}_i^2\left(w\right),---18)$

In formula: Y _ithe network output vector of-expectation; Y _i'-actual network output vector; P-number of samples; The vector that w-network weight and threshold value form; e _i(w)-error.

If w ^krepresent the weights of the k time iteration and the vector that threshold value forms, the vectorial w that new weights and threshold value form ^k+1for w ^k+1=w ^k+ Δ w.In LM method, weights increment Delta w computing formula is as follows:

Δw＝[J ^T(w)J(w)+μI] ^-1J ^T(w)e(w)，19）

In formula: I-unit matrix; μ-user-defined learning rate; J (w)-Jacobian matrix, that is:

From 19) formula can be found out, if scale-up factor μ=0 is Gauss-Newton method; If μ value is very large, LM algorithm approaches gradient descent method, every iteration success one step, and μ reduces, when approaching error target, similar to Gauss-Newton method gradually like this.Gauss-Newton method is when approaching the minimum value of error, and computing velocity is faster, and precision is also higher.Because LM algorithm has utilized approximate second derivative information, it is more faster than gradient descent method.In addition due to [J ^t(w) J (w)+μ I] be positive definite, so 19) solution of formula always exists, and in this sense, LM algorithm is also better than Gauss-Newton method, because for Gauss-Newton method, and J ^twhether full rank is also a potential problem to J.In actual operation, μ is a tentative parameter, and for given μ, if the Δ w trying to achieve can make error criterion function E (w) reduce, μ reduces; Otherwise μ increases.With 19) formula need to ask the algebraic equation (n is weights number in network) on n rank while revising weights and threshold value.The computation complexity of LM algorithm is O (n ³/ 6),, if n is very large, calculated amount and memory space are all very large.But significantly improving of each iteration efficiency, can improve its overall performance, greatly particularly when accuracy requirement is high.

Summary of the invention

For above-described problem, the present invention is directed to non-linear that current Short-term Traffic Flow shows, time variation, uncertain, in order to catch short-term volume of the flow of passengers feature, use EMD that original passenger flow data is resolved into master data that Changing Pattern is stronger and probabilistic interfering data of a lot of individual different frequencies, and then the component to different frequencies and original series carry out correlation analysis, rejecting affects little component to original series, for artificial neural network provides high-quality, multi-level input variable (artificial neural network is predicted), reduce the difficulty of prediction, improve precision of prediction.

Invention technical scheme be,

A section passenger flow neural net prediction method based on EMD, the method step is:

(1) obtain intrinsic mode functions component

Every segment data is carried out respectively to EMD processing, obtain the IMF component of every segment data, composition IMF matrix;

(2) component recognition

Calculate Pearson's related coefficient of each IMF component and raw data, analyze the correlativity with raw data; Rejecting affects little component to original series, can reduce computing time, improve the forecasting efficiency of the short-term section volume of the flow of passengers;

Described Pearson's related coefficient is:

${\mathrm{\&rho;}}_{\mathrm{xy}}=\frac{1}{n-1}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\left(\frac{X_i-\stackrel{\&OverBar;}{X}}{S_X}\right)\left(\frac{Y_i-\stackrel{\&OverBar;}{Y}}{S_Y}\right),---12)$

Wherein: n-sample size,

the mean value of-sample, S _x, S _y-sample standard deviation;

(3) neural network prediction

Choose sample, sample is normalized, build BP neural network, the input data using test data as input layer, are updated in BP neural network and predict, obtain output and legitimate reading comparative analysis and relative error.

Using remaining component in the component recognition stage as the input of neural network prediction, adopt three layers of BP network model, in the forward transmittance process of signal, input message is successively by input layer, hidden layer, output layer.In transmittance process, information will be processed through each hidden layer processing.When actual output and the desired output of output layer are not inconsistent, proceed to the backpropagation of error.In the back-propagation process of error, reality output and the error of desired output are taked to certain mode, successively by output layer, hidden layer, input layer.In the process of successively anti-pass, error is shared each layer of all neuron equally, and neuron, when receiving error signal, by revising weights, threshold value, thereby reduces error.Each layer of neuronic weights, threshold value constantly change, adjust, until reach error requirements.

In the present invention, RMD is applied in forecast model and removes to improve predictablity rate, try hard to set up a method that adopts EMD and neural network to mix, carry out short-term passenger flow estimation.

In addition, the present invention considers how when setting up forecast model, to determine suitable EMD assembly.The present invention adopts the mode of statistical study to determine suitable EMD assembly, proposes the definition of system and the input variable as forecast model in conjunction with the EMD assembly proposing; Meanwhile, time-related factor is also considered into, because these factors can represent Passenger flow feature.Therefore the EMD assembly that, the present invention has comprised extraction and the hybrid forecasting method passenger flow forecast amount more accurately of time factor.

Finally, adopt LM algorithm during BP neural metwork training of the present invention.LM (Levenberg-Marquardt) algorithm is a kind of fast algorithm of the numerical optimization technique of utilizing standard, it is the combination of gradient descent method and Gauss-Newton method, the local convergence of existing Gauss-Newton method, have again the global property of gradient method, and precision of prediction is high.

Effect of the present invention is: the invention provides the method for mixing EMD and neural network, analyze passenger flow data feature, produce a series of IMF components that comprise original signal different time yardstick local feature information, this makes to decompose the each IMF component obtaining and has obvious physical background; The function of component recognition has been rejected the IMF component little with original series correlativity simultaneously, for neural network prediction is afterwards saved time.Mix the method for EMD and neural network, combine the advantage of the two, can obtain section passenger flow estimation precision and all be greater than 95%.

Accompanying drawing explanation

Fig. 1 is process flow diagram of the present invention.

Fig. 2 is three-layer neural network model schematic diagram of the present invention.

Fig. 3 is neural network prediction process flow diagram of the present invention.

Fig. 4 is the every 30min section guest flow statistics figure of (embodiment) 2012.3.5-3.9 line of Beijing Metro (descending) Xidan-recovery door.

Fig. 5 is (embodiment) EMD experience decomposition model schematic diagram.

Fig. 6 is (embodiment) BP Neural Network Prediction schematic diagram.

Fig. 7 is (embodiment) BP neural network prediction relative error analysis schematic diagram.

Embodiment

The present invention uses EMD methods analyst passenger flow feature, proposes a scheme and determines the input variable of suitable EMD assembly as forecast model; Meanwhile, time-related factor is also considered into, because these factors can represent Passenger flow feature.Fig. 1 is process flow diagram of the present invention.As shown in Figure 1, a kind of section passenger flow neural net prediction method based on EMD, the method step is as follows:

The first step: obtain data intrinsic mode functions component

To in every every day 30 minutes interval periods, between OD (ORIGIN-DESTINATION, traffic terminal), gather passenger flow allocation in section passenger flow information, form section volume of the flow of passengers original series.

According to the characteristic time scale of data, empirically identify built-in oscillation mode, then accordingly a non-stationary signal is decomposed into a series of intrinsic mode functions (Intrinsic Mode Function, be called for short IMF, also referred to as solid-state function) and a redundancy component sum; Each IMF component need meet two conditions:

1. the quantity of zero crossing and the quantity of extreme point equates or differ at the most one;

2. a time point in office, the average of the definite lower envelope line of the coenvelope line that local maximum is definite and local minimum is zero, signal is about time shaft Local Symmetric;

The step that empirical mode decomposition processing obtains intrinsic mode functions IMF component is as follows:

(1) establishing original signal is x (t), finds out its all Local Extremum, and all Local modulus maximas and local minizing point are coupled together with cubic spline curve respectively, obtains the upper and lower envelope of x (t);

For the data at the non-end points of a signal place, can judge whether it is extreme point by the magnitude relationship of it and adjacent data: if it is greater than the data adjacent with its left and right simultaneously, be maximum point; If it is less than the data adjacent with its left and right simultaneously, be minimum point.For the data at end points place, for example left end point, if it is greater than and its right adjacent those data, it is maximum point.But minimum point sequence can be complied with without value at left end point place in this case. form the cubic spline curve of lower envelope and there will be Divergent Phenomenon at the left end of data sequence, and this result of dispersing can make acquired results serious distortion along with constantly the carrying out gradually inside " pollution " whole data sequence of " sieve " process.For a longer data sequence, the data that can constantly abandon two ends according to the situation of extreme point guarantee that the degree of distortion of gained envelope reaches minimum.For a short data sequence, it is completely infeasible that such operation just becomes.

In view of the situation, when due to end points non-greatly (or little) value point, when upper (or under) envelope cannot be determined its end point values at end points place, if can draw the approximate value of this sequence at end points place with the rule of interior data according to end points in extreme point sequence, can prevent from extreme point to carry out the larger swing of envelope appearance that spline interpolation obtains.Take out three extreme points (if the number of maximum point sequence is less than three, getting all elements in sequence) of former extreme point sequence high order end, to got extreme point, utilize fitting of a polynomial algorithm to obtain polynomial fitting, calculate the functional value at polynomial expression corresponding data sequence left end point place, using this functional value as extreme point sequence, in the approximate value at this end points place, in like manner obtain the approximate value of extreme point sequence at right endpoint place.Finally utilize cubic spline function to carry out interpolation to new extreme point sequence and obtain upper and lower envelope.Cubic spline function has value to comply with at end points place, has avoided the swing of upper and lower envelope.Although fitting of a polynomial can only obtain extreme point sequence at end points place the approximate value of (left and right end points).Extreme point sequence has been carried out to approximate continuation, but the object of continuation is not in order to provide former sequence data in addition accurately, and be to provide a kind of condition, envelope is determined with interior data by end points completely, so the processing of the method to former data sequence, not only suppressed end effect, and main information wherein has also intactly been extracted.

The algorithm of fitting of a polynomial described in above-mentioned is:

A. according to particular problem, determine the frequency n of polynomial fitting;

B. calculate Sr and Tr;

C. write out normal equations

$\left\{\begin{array}{cccccc}{S}_0& S_1& \&CenterDot;& \&CenterDot;& \&CenterDot;& S_n\\ S_1& S_2& \&CenterDot;& \&CenterDot;& \&CenterDot;& S_{n+1}\\ \&CenterDot;& \&CenterDot;& & & & \&CenterDot;\\ \&CenterDot;& \&CenterDot;& & & & \&CenterDot;\\ \&CenterDot;& \&CenterDot;& & & & \&CenterDot;\\ S_n& S_{n+1}& \&CenterDot;& \&CenterDot;& \&CenterDot;& S_{2n}\end{array}\right\}\left\{\begin{array}{c}{a}_0\\ a_1\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ a_n\end{array}\right\}=\left\{\begin{array}{c}{t}_0\\ t_1\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ t_n\end{array}\right\},---3)$

D. separate normal equations group and obtain a ₀, a ₁..., a _n; Write out polynomial fitting

$P_n\left(x\right)=\underset{k=1}{\overset{n}{\mathrm{\&Sigma;}}}{a}_k{x}_k,---4)$

(2) remember that the sequence that upper and lower envelope local mean value forms is m ₁, order

h ₁(t)＝x(t)-m ₁，5）

(3) judge h ₁(t) whether meet two required conditions of above-mentioned IMF component, if do not meet, set it as pending signal, repeat (1), (2) two steps,

h ₂(t)＝h ₁(t)-m ₂，6）

So repeat k time,

h _k(t)＝h _k-1(t)-m _k， 7）

Until h _k(t) meet two conditions of IMF component; Note h _k(t) for obtaining first IMF component c ₁(t);

c ₁(t)＝h _k(t)， 8)

(4) IMF component is separated from original signal,

r ₁(t)＝x(t)-c ₁(t)， 9)

(5) by r ₁(t), as new original signal, repeating step (1)～(4), can obtain

$\left\{\begin{array}{c}{r}_2\left(t\right)=r_1\left(t\right)-c_2\left(t\right)\\ r_3\left(t\right)=r_2\left(t\right)-c_3\left(t\right)\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ r_n\left(t\right)=r_{n-1}\left(t\right)-c_n\left(t\right)\end{array}\right.,---10)$

As IMF component c _n(t) be less than a certain threshold value or r _n(t) while becoming monotonic quantity, stop decomposable process, the present invention adopts the latter as end condition;

(6) by formula 9), 10) be added,

$x\left(t\right)=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{c}_i\left(t\right)+r_n\left(t\right),---11)$

In formula: r _n(t) residual volume for decomposing, the average tendency of expression signal; X (t) is original signal; c _i(t) be i IMF component.

By above " screening " process, original signal x (t) finally can be decomposed into n IMF component c stably _i(t), i=1,2 ... n and a residual volume r _n(t) linearity and, and the frequency content of each IMF component arranges from big to small, c ₁(t) frequency is the highest, c _n(t) frequency is minimum, shows that each IMF component is broken down into different frequency ranges, and this is conducive to the extraction of signal characteristic;

Second step, component recognition

EMD method is decomposed fluctuation or the trend of different scale in original section passenger flow data to come step by step, produces a series of data sequences with different characteristic yardstick; The IMF component of low-limit frequency represents secular trend or the average of original series under normal circumstances, and the IMF component of highest frequency represents the Short-term characteristic of original series conventionally; Analyze the correlativity of each IMF component and raw data, reject original series is affected to little component, can reduce computing time, improve the forecasting efficiency of the short-term section volume of the flow of passengers; Related coefficient is the statistical indicator that reflects correlationship level of intimate between variable; Correlation coefficient ρ _xyvalue between-1 to 1, ρ _xy, claim that X, Y are uncorrelated at=0 o'clock; | ρ _xy|=1 o'clock, claim X, Y complete dependence, now, between X, Y, there is linear functional relation; | ρ _xy| during <1, the variation of X causes the part variation of Y, | ρ _xy| larger, the variation of X causes that the variation of Y is just larger, | ρ _xy| during >0.8, be called height correlation, when | ρ _xy| during <0.3, be called lower correlation, other for moderate relevant; Comparatively conventional is Pearson's related coefficient at present;

${\mathrm{\&rho;}}_{\mathrm{xy}}=\frac{1}{n-1}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\left(\frac{X_i-\stackrel{\&OverBar;}{X}}{S_X}\right)\left(\frac{Y_i-\stackrel{\&OverBar;}{Y}}{S_Y}\right),---12)$

In formula: n-sample size, the mean value of-sample, S _x, S _y-sample standard deviation;

The 3rd step, Matlab realize BP neural network prediction

Fig. 2 is three-layer neural network model schematic diagram of the present invention.BP neural network is a kind of MLFFANN, and it is most widely used neural network up to now, generally comprises input layer, hidden layer and output layer.

Its ultimate principle is that study, the training of network is to consist of two rightabout processes, and signal forward transmits and error back propagation.In the forward transmittance process of signal, input message is successively by input layer, hidden layer, output layer, and in transmittance process, information will be processed through each hidden layer processing.When actual output and the desired output of output layer are not inconsistent, proceed to next process, i.e. the backpropagation of error.In the back-propagation process of error, reality output and the error of desired output are taked to certain mode, successively by output layer, hidden layer, input layer, in the process of successively anti-pass, error is shared each layer of all neuron equally, neuron, when receiving error signal, by revising weights, threshold value, thereby reduces error.Fig. 3 is neural network prediction process flow diagram of the present invention.As shown in Figure 3, concrete steps are:

(1) sample chooses

According to remaining ordered sequence in component recognition link, it is carried out to random division, 80% is training set, 20% is test set.

(2) normalized of sample

Because the each data unit gathering is inconsistent, thereby must carry out [1,1] normalized to data, method for normalizing is mainly as follows:

X ₀＝(X-X _min)(X _max-X _min)， 13）

In formula: X, X ₀be respectively the forward and backward value of conversion, X _max, X _minbe respectively maximal value and the minimum value of sample.

(3) BP neural network builds

A. input, output layer node determination

In the present invention, input layer has M input node, represents respectively the IMF component that section passenger flow sequence is different; Output layer has N output node, represents respectively the corresponding following section volume of the flow of passengers.

B. the hidden layer number of plies and hidden layer node number are determined:

Hidden layer can be divided into single hidden layer and many hidden layers according to the number of plies, and many hidden layers are used for representing complicated mapping relations, and generalization ability is strong, but the training time is longer.The hidden layer number of plies will consider from network precision and training time, for better simply mapping relations, in network precision, meets the requirements of in situation, can select single hidden layer in the hope of pick up speed.The track traffic section volume of the flow of passengers presents the gradual change of certain regularity on space-time, and single hidden layer neural network can satisfy the demands.The nodes of hidden layer, in general, node is more, and numerical value and the desired value of output are more approaching, but the training time spending is also longer; Otherwise node is fewer, output valve and desired value differ larger, but the training time can correspondingly reduce, this,, due to more complicated the causing of more its algorithms of node, so need to slowly attempt, finds a suitable intermediate point.Under normal circumstances can be with reference to following formula:

$n=\sqrt{M+N}+a,---14)$

In formula: n is hidden layer node number, M is input number of nodes, and N is output node number, and a is the constant between 0-10.

C. transport function is selected

BP neural network requires the neuronic transport function must can be micro-everywhere, and conventional transport function comprises linear Purelin type and Sigmoid type.

Tan-Sigmoid type transport function, this function is that temperature parameter is the improvement of 1/2 Log-Sigmoid type function, and its output area is (1,1), is bipolarity function, and derivative is Ψ ' (x)=4 (e ^2x(1/e ^2x+ 1) ²), derivative codomain scope (0,1].The Log-Sigmoid type function that Tan-Sigmoid type function corrected signal span is 1 than temperature parameter is large, and speed of convergence faster can be provided, and has stronger advantage.Therefore in the present invention, hidden layer transport function adopts Tan-Sigmoid type function; Output layer transport function adopts linear purelin function, thereby makes the output of network can get arbitrary value.

1. hidden layer output is calculated:

${\mathrm{net}}_i=\underset{j=1}{\overset{M}{\mathrm{\&Sigma;}}}{w}_{\mathrm{ji}}{x}_j+{\mathrm{\&theta;}}_i,---15)$

$y_i=\mathrm{\&phi;}\left({\mathrm{net}}_i\right)=\mathrm{\&phi;}(\underset{j=1}{\overset{M}{\mathrm{\&Sigma;}}}{w}_{\mathrm{ij}}{x}_j+{\mathrm{\&theta;}}_i),---16)$

In formula: net _irepresent the input of i node of hidden layer; y _irepresent the output y of i node of hidden layer _i; x _jrepresent the input of j node of input layer, j=1 ..., M; Wi _jrepresent that i node of hidden layer is to the weights between j node of input layer; θ _irepresent the threshold value of i node of hidden layer;

represent the transport function of hidden layer;

2. output layer output is calculated.

$o_k=\mathrm{\&psi;}\left({\mathrm{net}}_k\right)=\mathrm{\&psi;}(\underset{i=1}{\overset{q}{\mathrm{\&Sigma;}}}{w}_{\mathrm{ki}}{y}_i+a_k)=\mathrm{\&psi;}(\underset{i=1}{\overset{q}{\mathrm{\&Sigma;}}}{w}_{\mathrm{ki}}\mathrm{\&phi;}(\underset{j=1}{\overset{M}{\mathrm{\&Sigma;}}}{w}_{\mathrm{ij}}{x}_j+{\mathrm{\&theta;}}_i)+a_k),---17)$

In formula: net _krepresent the input of k node of output layer; o _krepresent the output of k node of output layer; w _kirepresent that k node of output layer is to the weights between i node of hidden layer, i=1 ..., q; a _krepresent the threshold value of k node of output layer, k=1 ..., L; Ψ (x) represents the transport function of output layer.

MATLAB realizes the initialized weight of BP neural network model and threshold parameter is random generation.

D. learning parameter is selected

1. determining of learning rate: the overall principle is: can not prevent too greatly that adjustment amount is excessive, vibration appears in training; Can not too littlely prevent training time increase, speed of convergence slows down.Therefore generally, the selection range of learning rate, generally at 0.01-0.8, tends to choose less learning rate sometimes, to guarantee the stable of system.The learning rate of BP neural network of the present invention is intended electing 0.01 as, and network training result is more stable.

2. determining of factor of momentum: the span of factor of momentum is between 0-1, at learning rate, it is 0.01 o'clock, the data construct BP neural network providing in the technical information providing according to MATLAB is trained, and analyzes the impact of different factor of momentum for training error.To all situations, error is along with the increase of frequency of training all can decline, but it is the fastest when factor of momentum 0.9, to decline.Factor of momentum is less, and error declines slowlyer, therefore determines that factor of momentum is 0.9 herein.

E.BP neural metwork training

LM (Levenberg-Marquardt) algorithm is a kind of fast algorithm of the numerical optimization technique of utilizing standard, it is the combination of gradient descent method and Gauss-Newton method, the local convergence of existing Gauss-Newton method, has again the global property of gradient method.Described LM algorithm is:

If error criterion function is

$E\left(w\right)=\frac{1}{2}\underset{i=1}{\overset{p}{\mathrm{\&Sigma;}}}{\left|\right|Y_i-{Y_i}^{\&prime;}\left|\right|}^2=\frac{1}{2}\underset{i=1}{\overset{p}{\mathrm{\&Sigma;}}}{e}_i^2\left(w\right),---18)$

In formula: Y _ithe network output vector of-expectation; Y _i'-actual network output vector; P-number of samples; The vector that w-network weight and threshold value form; e _i(w)-error.

If w ^krepresent the weights of the k time iteration and the vector that threshold value forms, the vectorial w that new weights and threshold value form ^k+1for w ^k+1=w ^k+ Δ w.In LM method, weights increment Delta w computing formula is as follows:

Δw＝[J ^T(w)J(w)+μI] ^-1J ^T(w)e(w)， 19）

In formula: I-unit matrix; μ-user-defined learning rate; J (w)-Jacobian matrix, that is:

From 19) formula can find out: if scale-up factor μ=0 is Gauss-Newton method; If μ value is very large, LM algorithm approaches gradient descent method, every iteration success one step, and μ reduces, when approaching error target, similar to Gauss-Newton method gradually like this.Gauss-Newton method is when approaching the minimum value of error, and computing velocity is faster, and precision is also higher.Because LM algorithm has utilized approximate second derivative information, it is more faster than gradient descent method.In addition due to [J ^t(w) J (w)+μ I] be positive definite, so 19) solution of formula always exists, and in this sense, LM algorithm is also better than Gauss-Newton method, because for Gauss-Newton method, and J ^twhether full rank is also a potential problem to J.In actual operation, μ is a tentative parameter, and for given μ, if the Δ w trying to achieve can make error criterion function E (w) reduce, μ reduces; Otherwise μ increases.With 19) formula need to ask the algebraic equation (n is weights number in network) on n rank while revising weights and threshold value.The computation complexity of LM algorithm is O (n ³/ 6),, if n is very large, calculated amount and memory space are all very large.But significantly improving of each iteration efficiency, can improve its overall performance, greatly particularly when accuracy requirement is high.

The calculation procedure of LM algorithm is described below:

1. provide training error permissible value ε, constant μ ₀and β (0< β <1), and initialization weights and threshold vector, make k=0, μ=μ ₀;

2. computational grid output and error criterion function E (w ^k);

3. calculate Jacobian matrix J (w ^k);

4. calculate Δ w;

If 5. E (w ^k) < ε, forward to 7.;

6. with w ^k+1=w ^k+ Δ w is weights and threshold vector, error of calculation target function E (w ^k+1), if E is (w ^k+1) <E (w ^k), making k=k+1,2. μ=μ β, forward to, otherwise 4. μ=μ/β forwards to.

7. algorithm finishes.

(4) BP neural network prediction

Input data using test data as input layer, are brought in BP neural network and predict, obtain output and legitimate reading comparative analysis and relative error.

The invention provides the method for mixing EMD and neural network, analyze passenger flow data feature, for neural net prediction method provides input variable; Can obtain section passenger flow estimation precision and all be greater than 95%.

[embodiment]

Analyze herein and select a line of Beijing Metro (descending) Xidan to actual measurement section on the working day volume of the flow of passengers data that revive gate segment.As shown in Figure 4, Fig. 4 is the every 30min section guest flow statistics figure of (embodiment) 2012.3.5-3.9 line of Beijing Metro (descending) Xidan-recovery door.The present invention is according to the Xidan of 2012.3.5-2012.3.8-recovery door section passenger flow data prediction 2012.3.9 day Xidan-recovery door section volume of the flow of passengers.

A section passenger flow neural net prediction method based on EMD, the method step is as follows:

The first step: obtain data intrinsic mode functions component

Above data are carried out to EMD empirical mode decomposition, be illustrated in fig. 5 shown below, Fig. 5 is (embodiment) EMD experience decomposition model schematic diagram.As can be seen from Figure 5, original section volume of the flow of passengers sequence can be broken down into 5 IMF characteristic components and 1 remaining component, and the frequency content of IMF component is arranged from big to small, and the IMF component of low-limit frequency represents trend or the average of original signal under normal circumstances.

Second step: component recognition;

Analyze the correlativity of each IMF component and raw data, related coefficient is the statistical indicator that reflects correlationship level of intimate between variable; Correlation coefficient ρ _xyvalue between-1 to 1, ρ _xy, claim that X, Y are uncorrelated at=0 o'clock; | ρ _xy|=1 o'clock, claim X, Y complete dependence, now, between X, Y, there is linear functional relation; | ρ _xy| during <1, the variation of X causes the part variation of Y, | ρ _xy| larger, the variation of X causes that the variation of Y is just larger, | ρ _xy| during >0.8, be called height correlation, when | ρ _xy| during <0.3, be called lower correlation, other for moderate relevant; Here adopt Pearson's related coefficient;

${\mathrm{\&rho;}}_{\mathrm{xy}}=\frac{1}{n-1}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\left(\frac{X_i-\stackrel{\&OverBar;}{X}}{S_X}\right)\left(\frac{Y_i-\stackrel{\&OverBar;}{Y}}{S_Y}\right),---12)$

In formula: n-sample size,

the mean value of-sample, S _x, S _y-sample standard deviation;

According to formula 12), ask the Pearson correlation coefficient of each component and original series:

ρ ₁=0.034；ρ ₂=0.585；ρ ₃=0.609；ρ ₄=0.434；ρ ₅=-0.023；ρ _res=0.072；

Wherein, ρ _irepresent the related coefficient of i IMF component and original series; ρ _resrepresent the related coefficient of remaining component and original series.Correlativity by IMF2, IMF3, IMF4 and the original series of Pearson correlation coefficient is larger.

The input of BP neural network	Program runtime (second)	Average relative error value
			IMF1, IMF2, IMF3, IMF4, IMF5, remaining component	1.4440	0.0089
IMF1, IMF2, IMF3, IMF4, remaining component	0.9910	0.0147
			IMF2, IMF3, IMF4, remaining component	0.7720	0.2368

When IMF component is many, reduce input and only select the large component of Pearson correlation coefficient screening correlativity, can save the training time of BP neural network, but also can reduce the accuracy of prediction.Because IMF number of components is fewer in example, consider, in this example using 5 IMF characteristic components and 1 remaining component all as the input of BP neural network.

The 3rd step: Matlab realizes BP neural network prediction

(1) sample chooses

Fig. 4 is that 2012.3.5-02:00 is to 2012.3.9-24:00(embodiment) line Xidan of Beijing Metro-recovery door (descending) every 30min section guest flow statistics figure, totally 236 groups of data.Wherein 200 groups for BP neural metwork training, and 36 groups as test data, and the data in 2012 on March 9, (Friday) are as test data.

(2) normalized of sample

According to formula 13) data are normalized.

(3) BP neural network builds

A. input, output layer node determination

As from the foregoing, BP neural network contains 6 input nodes (5 IMF components and 1 remaining component), 1 output node (the prediction section volume of the flow of passengers).

B. hidden layer number of plies number and hidden layer node number are determined

Many hidden layers are used for representing complicated mapping relations, and generalization ability is strong, but the training time is longer.The track traffic section volume of the flow of passengers presents the gradual change of certain regularity on space-time, from network precision and training time, considers, and in network precision, meets the requirements of in situation, can select single hidden layer in the hope of pick up speed.According to formula 14) hidden layer node number gets 2,3 successively ..., 8, the mean value of gained relative error respectively:

Hidden layer node number	Average relative error value
		3	0.0016
4	0.0175
		5	0.0089
6	0.0031
		7	0.0033
8	0.0520

BP neural network is along with the increase of hidden layer node number, and error first reduces rear increase, so when error arrives minimum point, hidden layer node number is 6.

C. transport function is selected:

Hidden layer transport function adopts Tan-Sigmoid type function.

Output layer transport function adopts linear purelin function.

D. learning parameter is selected determining of learning rate:

Learning rate of the present invention is intended electing 0.01 as.

Determining of factor of momentum: the present invention determines that factor of momentum is 0.9.

E.BP neural metwork training: use LM (Levenberg-Marquardt) algorithm.

(4) BP neural network prediction

According to the 6-6-1 type BP neural network of above structure, 200 groups of data after decomposing are carried out network training as input.The BP neural network that use trains to March 9 (Friday) in 2012 Xidan to revive door section sample predict, partial results is as shown in the table.Obtain output and legitimate reading comparative analysis schematic diagram and relative error schematic diagram, as shown in Figure 6,7, Fig. 6 is (embodiment) BP Neural Network Prediction schematic diagram, and Fig. 7 is (embodiment) BP neural network prediction relative error analysis schematic diagram.According to Fig. 6, Fig. 7, can obtain relative error all within 5%, prediction exact value can reach 95%.

Embodiment: to March 9 (Friday) in 2012 Xidan to revive door section sample carry out predicted portions result table

The present invention proposes the method for mixing EMD and neural network, analyze passenger flow data feature, for neural net prediction method provides input variable.Section passenger flow estimation precision of the present invention is all greater than 95%.

Claims (5)

1. the section passenger flow neural net prediction method based on EMD, is characterized in that, the method step is as follows:

The first step: obtain data intrinsic mode functions component;

To in every every day 30 minutes interval periods, between OD, gather passenger flow allocation in section passenger flow information, form section volume of the flow of passengers original series;

According to the characteristic time scale of data, empirically identify built-in oscillation mode, then accordingly a non-stationary signal is decomposed into a series of intrinsic mode functions and a redundancy component sum, i.e. empirical mode decomposition processing obtains intrinsic mode functions IMF component;

Each IMF component need meet two conditions:

1. the quantity of zero crossing and the quantity of extreme point equates or differ at the most one;

2. a time point in office, the average of the definite lower envelope line of the coenvelope line that local maximum is definite and local minimum is zero, signal is about time shaft Local Symmetric;

Second step: component recognition;

Fluctuation or the trend of different scale in original section passenger flow data are decomposed and come step by step, produce a series of data sequences with different characteristic yardstick; The IMF component of low-limit frequency represents secular trend or the average of original series, and the IMF component of highest frequency represents the Short-term characteristic of original series; Correlation coefficient ρ _xythe statistical indicator that reflects correlationship level of intimate between variable, correlation coefficient ρ _xyvalue between-1 to 1, ρ _xy, claim that X, Y are uncorrelated at=0 o'clock; | ρ _xy|=1 o'clock, claim X, Y complete dependence, now, between X, Y, there is linear functional relation; | ρ _xy| during <1, the variation of X causes the part variation of Y, | ρ _xy| larger, the variation of X causes that the variation of Y is just larger, | ρ _xy| during >0.8, be called height correlation, when | ρ _xy| during <0.3, be called lower correlation, other for moderate relevant; Here, adopt Pearson's related coefficient;

${\mathrm{\&rho;}}_{\mathrm{xy}}=\frac{1}{n-1}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\left(\frac{X_i-\stackrel{\&OverBar;}{X}}{S_X}\right)\left(\frac{Y_i-\stackrel{\&OverBar;}{Y}}{S_Y}\right),---12)$

In formula: n-sample size,

the mean value of-sample, S _x, S _y-sample standard deviation;

The 3rd step: BP neural network prediction;

(1) sample chooses

According to remaining ordered sequence in component recognition link, it is carried out to random division, 80% is training set, 20% test set;

(2) normalized of sample

Because the each data unit gathering is inconsistent, thereby must carry out [1,1] normalized to data, method for normalizing is:

X ₀＝(X-X _min)(X _max-X _min)， 13）

In formula: X, X ₀be respectively the forward and backward value of conversion, X _max, X _minbe respectively maximal value and the minimum value of sample;

(3) BP neural network builds;

(3.1) input, output layer node determination;

Input layer has M input node, represents respectively the IMF component that section passenger flow sequence is different; Output layer has N output node, represents respectively the corresponding following section volume of the flow of passengers;

(3.2) the hidden layer number of plies and hidden layer node number are determined;

The described hidden layer number of plies is single hidden layer;

Hidden layer node is counted formula:

$n=\sqrt{M+N}+a,---14)$

In formula: n is hidden layer node number, M is input number of nodes, and N is output node number, and a is the constant between 0-10;

(3.3) transport function is selected

In the present invention, hidden layer transport function adopts Tan-Sigmoid type function; Output layer transport function adopts linear purelin function;

(3.4) learning parameter is selected

1. determining of learning rate:

The selection range of described learning rate is at 0.01-0.8;

2. determining of factor of momentum: the span of factor of momentum is between 0-1;

(3.5) BP neural metwork training

Use LM (Levenberg-Marquardt) algorithm to carry out BP neural metwork training;

(4) BP neural network prediction

Input data using test data as input layer, are updated in BP neural network and predict, obtain output and legitimate reading comparative analysis and relative error.

2. a kind of section passenger flow neural net prediction method based on EMD according to claim 1, is characterized in that, it is as follows that described empirical mode decomposition processing obtains intrinsic mode functions IMF component method step:

(1) establishing original signal is x (t), finds out its all Local Extremum, and all Local modulus maximas and local minizing point are coupled together with cubic spline curve respectively, obtains the upper and lower envelope of x (t);

For the data at the non-end points of a signal place, by the magnitude relationship of it and adjacent data, judge whether it is extreme point: if it is greater than the data adjacent with its left and right simultaneously, be maximum point; If it is less than the data adjacent with its left and right simultaneously, be minimum point; For the data at end points place, if it is greater than that data adjacent with it, it is maximum point;

When due to end points non-greatly (or little) value point, when upper (or under) envelope cannot be determined its end point values at end points place, if can draw the approximate value of this sequence at end points place with the rule of interior data according to end points in extreme point sequence, can prevent from extreme point to carry out the larger swing of envelope appearance that spline interpolation obtains; Take out three extreme points of former extreme point sequence high order end, if the number of maximum point sequence is less than three, get all elements in sequence, to got extreme point, utilize fitting of a polynomial algorithm to obtain polynomial fitting, calculate the functional value at polynomial expression corresponding data sequence left end point place, using this functional value as extreme point sequence, in the approximate value at this end points place, in like manner obtain the approximate value of extreme point sequence at right endpoint place; Finally utilize cubic spline function to carry out interpolation to new extreme point sequence and obtain upper and lower envelope; Although fitting of a polynomial can only obtain extreme point sequence at end points place the approximate value of (left and right end points); Extreme point sequence has been carried out to approximate continuation, but the object of continuation is not in order to provide former sequence data in addition accurately, and be to provide a kind of condition, envelope is determined with interior data by end points completely, so the processing of above method to former data sequence, not only suppressed end effect, and main information wherein has also intactly been extracted;

Among described fitting of a polynomial algorithm steps be:

A. determine the frequency n of polynomial fitting;

B. calculate S _rand T _r;

C. write out normal equations:

$\left\{\begin{array}{cccccc}{S}_0& S_1& \&CenterDot;& \&CenterDot;& \&CenterDot;& S_n\\ S_1& S_2& \&CenterDot;& \&CenterDot;& \&CenterDot;& S_{n+1}\\ \&CenterDot;& \&CenterDot;& & & & \&CenterDot;\\ \&CenterDot;& \&CenterDot;& & & & \&CenterDot;\\ \&CenterDot;& \&CenterDot;& & & & \&CenterDot;\\ S_n& S_{n+1}& \&CenterDot;& \&CenterDot;& \&CenterDot;& S_{2n}\end{array}\right\}\left\{\begin{array}{c}{a}_0\\ a_1\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ a_n\end{array}\right\}=\left\{\begin{array}{c}{t}_0\\ t_1\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ t_n\end{array}\right\},---3)$

D. separate normal equations group and obtain a ₀, a ₁..., a _n; Write out polynomial fitting:

$P_n\left(x\right)=\underset{k=1}{\overset{n}{\mathrm{\&Sigma;}}}{a}_k{x}_k,---4)$

(2) remember that the sequence that upper and lower envelope local mean value forms is m ₁, order

h ₁(t)＝x(t)-m ₁， 5）

(3) judge h ₁(t) whether meet two required conditions of above-mentioned IMF component, if do not meet, set it as pending signal, repeat (1), (2) two steps, that is,

h ₂(t)＝h ₁(t)-m ₂， 6）

So repeat k time,

h _k(t)＝h _k-1(t)-m _k， 7）

Until h _k(t) meet two conditions of IMF component; Note h _k(t) for obtaining first IMF component c ₁(t);

c ₁(t)＝h _k(t)， 8)

(4) IMF component is separated from original signal:

r ₁(t)＝x(t)-c ₁(t)， 9)

(5) by r ₁(t), as new original signal, repeating step (1)～(4), obtain:

$\left\{\begin{array}{c}{r}_2\left(t\right)=r_1\left(t\right)-c_2\left(t\right)\\ r_3\left(t\right)=r_2\left(t\right)-c_3\left(t\right)\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ r_n\left(t\right)=r_{n-1}\left(t\right)-c_n\left(t\right)\end{array}\right.,---10)$

Work as r _n(t), while becoming monotonic quantity, stop decomposable process;

(6) by formula 9), 10) be added:

$x\left(t\right)=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{c}_i\left(t\right)+r_n\left(t\right),---11)$

In formula: r _n(t) residual volume for decomposing, the average tendency of expression signal; X (t) is original signal, c _i(t) be i IMF component;

By above " screening " process, original signal x (t) finally can be decomposed into n IMF component c stably _i(t), i=1,2 ... n and a residual volume r _n(t) linearity and, and the frequency content of each IMF component arranges from big to small, c ₁(t) frequency is the highest, c _n(t) frequency is minimum, shows that each IMF component is broken down into different frequency ranges, and this is conducive to the extraction of signal characteristic.

3. a kind of section passenger flow neural net prediction method based on EMD according to claim 1, is characterized in that, analyzes the correlativity of each IMF component and raw data, rejects original series is affected to little component.

4. a kind of section passenger flow neural net prediction method based on EMD according to claim 1, is characterized in that, described learning rate elects 0.01 as.

5. a kind of section passenger flow neural net prediction method based on EMD according to claim 1, is characterized in that, described definite factor of momentum is 0.9.

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