CN104992244A - Airport freight traffic prediction analysis method based on SARIMA and RBF neural network integration combination model - Google Patents

Abstract

The invention relates to an airport freight traffic prediction analysis method based on an autoregressive integrating moving average (SARIMA) and RBF neural network integration combination model. According to the method, an airport freight traffic linear part is predicted by using seasonal SARIMA; a non-linear airport freight traffic part is predicted by using an RBF neural network; and then the non-linear prediction result is used as compensation of the linear prediction result, thereby obtaining a final prediction result.

Description

A kind of airport freight forecast analytical approach based on SARIMA and RBF neural integrated combination model

Technical field

The present invention relates to a kind of transportation planning program design and convert technical field, particularly relate to a kind of airport freight forecast analytical approach based on SARIMA and RBF neural integrated combination model.

Background technology

Along with the high speed development of Commercial Air Service, Civil Aviation Airport transportation scale increases rapidly, and the reasonable prediction of the airport volume of goods transported can provide guide effect for airport development, also can provide decision support for airport administrator.Airport volume of goods transported data are as a kind of time series data, its Forecasting Methodology is along with the continuous breakthrough of technology, two classes can be divided into: a class is traditional prediction method, as: economic measurement method, regression analysis, grey method, autoregression difference moving average (Autoregressive Integrating Moving Average, ARIMA) etc., autoregression difference moving average quite flexible wherein in time series analysis, merge the advantage of time series and regretional analysis, the most extensive in predicted application.Another kind of is artificial intelligent forecast model, as BP neural network model, RBF neural model etc.Wherein RBF neural has overall approximation capability, fundamentally solve the local optimum problem of BP neural network, and topological structure is compact, and structural parameters can realize being separated study, and fast convergence rate is the first-selection of neural network prediction.

Application number is a kind of method that patent document discloses prediction bus passenger flow based on ARIMA model of 201410764609.6, this application mainly sets up the volume of the flow of passengers in optimum ARIMA model prediction a period of time, but the linear segment of passenger flow data sequence mainly portrayed by this model, matching is carried out to the general trend of passenger flow data sequence, but the non-linear factor affecting the change of volume of the flow of passengers data sequence can not be portrayed well.

Application number be 201510019088.6 patent document discloses a kind of based on Grey entropy with improve the traffic flow forecasting method of Bayesian Fusion, this application first sets up linear least-squares regression model respectively according to historical traffic flows and radial basis function neural network model carries out traffic flow forecasting, secondly the degree of association between the magnitude of traffic flow is considered, according to the Grey entropy computational prediction magnitude of traffic flow and historical traffic flows relevance level, and the historical traffic flows choosing relevance level higher inputs data as forecast model, according to the predicted value of each forecast model of input data acquisition, then the method improving Bayesian Fusion and relevant historical traffic flows is combined, calculate the weight of each forecast model when predicting this moment magnitude of traffic flow, the prognosis traffic volume in final this moment of acquisition, realize the prediction of short-term traffic flow.But this model is mainly by weight computing prognosis traffic volume, optimum predicting the outcome can't be reached, this invention simultaneously also just carries out the superposition after weights distribution to two models, certain help is had to raising precision, but inherently do not portray the linear processes factor affecting the magnitude of traffic flow, precision of prediction also has certain room for promotion.

In order to effectively utilize the advantage of various model, Bates etc. proposed the thought of combined prediction in 1969, were combined by several model exactly by appropriate ways, to obtaining optimum prediction result.Economic measurement method and regression analysis are carried out entropy assessment and are combined airport freight forecast by Nan Juan, and this prediction algorithm of display that predicts the outcome has higher precision of prediction; Fu Peihua etc. use Shapley value method BP neural network and Grey Theory Forecast model to be combined, and predict air freight volume, and what obtain predicts the outcome more close to actual result.But predicting the outcome of built-up pattern can't meet the precision of airport actual motion demand at present.

In sum, be badly in need of a kind of scientific and reasonable airport Forecasting Method of Fright Volume in this area, the precision of airport actual motion demand can be reached, for airdrome control decision-making provides foundation.

Summary of the invention

The present invention proposes a kind of airport Forecasting Method of Fright Volume linear SARIMA and linear R BF Artificial neural network ensemble being combined (being designated as: SARIMA-RBF), the method science combine SARIMA and RBF neural advantage separately, final simulation result shows, precision of prediction is improved, and reaches the precision of airport actual motion demand.

The object of the invention is to be achieved by the following technical programs.As shown in Figure 1, the present invention is divided into following operation steps:

Step 1, with SARIMA model to the former sequence Y of the airport volume of goods transported _tcarry out modeling, doping airport volume of goods transported linear segment is a _t, then airport volume of goods transported linear segment prediction residual is E _t: E _t=Y _t-a _t.

Step 2, according to the sample set of the RBF neural determined, the airport volume of goods transported sequence Y after the reconstruct of rank is opened up in input, exports airport volume of goods transported residual error time E, and structure RBF neural forecast model, prediction is compensated SARIMA model residual result e _t.

Step 3, is combined into final predicting the outcome by predicting the outcome of two kinds of models: y _t=a _t+ e _t.

Described step 1 comprises following operation:

(11) airport database system is utilized to obtain the airport volume of goods transported time series data of airport about the time;

(12) according to airport volume of goods transported seasonal effect in time series scatter diagram, its stationarity of autocorrelation function graph identification;

(13) tranquilization (difference) process is carried out to the airport volume of goods transported time series data of non-stationary; And obtain the value of d and D; Wherein d, D represent Out of season and seasonal difference number of times respectively;

(14) determine p, q, possible the value of P, D according to the time series autocorrelogram after steadily and partial autocorrelation figure, then adopt Bayesian Information method (BIC) to determine best model order, check whether there is statistical significance;

(15) linear segment carrying out predicting the airport volume of goods transported by the model of inspection is utilized;

Described step 2 comprises following operation:

(21) one dimension airport volume of goods transported time series is carried out open up rank reconstruct, convert multidimensional time-series to;

Cycle due to SARIMA model is s, and for without loss of generality, if optimum exponent number is m=s+1, the time series obtained is input as: $Y=\left[\begin{array}{cccc}{y}_1& y_2& ...& y_m\\ y_2& y_3& ...& y_{m+1}\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ y_{n-m}& y_{n-m-1}& ...& y_{n-1}\end{array}\right],$ Output is: $E=\left[\begin{array}{c}{e}_1\\ e_2\\ .\\ .\\ .\\ e_{n-m}\end{array}\right].$

Then airport volume of goods transported one dimension residual error time series exports and can be expressed as:

(22) carry out network structure design, determine radial basis function; Radial basis function is exactly certain radially symmetrical scalar function, is normally defined space any point Y to a certain center c _ibetween the monotonic quantity of Euclidean distance.The present invention adopts Gaussian radial basis function, namely and r ∈ R (2)

(23) network training: choose clustering algorithm, utilize that clustering algorithm determines RBF hidden layer center, least-squares algorithm determines to connect weights, training network, matching study section time series, until network convergence is in certain standard.Otherwise, again can change the initial weight even topology of networks of network, until training result is satisfied; Described clustering algorithm adopts the center of K-means clustering algorithm determination basis function, and step is as follows:

Initialization cluster centre { c _i∈ R ⁿ| i=1,2 ..., N}, normally by c _ibe set to initial N training sample, then the sample set of input pressed Nearest Neighbor Method grouping, distribute to center for { c by Y _i∈ R ⁿ| i=1,2 ..., N} input amendment cluster set { θ _i| i=1,2 ..., N}, i.e. Y ∈ θ _iand meet c _i=min||Y-c _i||, wherein, i=1,2 ... N.

Readjust cluster centre, calculate θ _ithe mean value of middle sample, i.e. cluster centre c _i: wherein n _ifor c _iin sail sample number into.Until the distribution of cluster centre no longer changes, { the c obtained _i∈ R ⁿ| i=1,2 ..., N} is the final Basis Function Center of RBF network.

Weight selected least square method directly calculates: $w_i=\exp \left(\frac{N}{{c^2}_{max}}\right||Y-c_i|{|}^2)---\left(3\right)$

(24) inspection segment data is utilized to check the network model trained to predict the non-linear partial of the airport volume of goods transported.

Preferably, data normalization process can be carried out before described airport volume of goods transported time series data is analyzed.Because volume of goods transported historical data is a kind of Non-stationary Data, some data difference are comparatively large, and data difference is excessive can have a negative impact to model training speed.For eliminating this adverse effect, be normalized airport volume of goods transported raw data, concrete formula is as follows:

$y^{*}=\frac{y-y_{\min }}{y_{\max }-y_{\min }}---\left(4\right)$

In formula, y represents airport volume of goods transported original time series, and y* represents pretreated airport volume of goods transported time series, y _minand y _maxrepresent airport volume of goods transported maximal value and minimum value respectively.

Finally the net result of prediction is carried out renormalization, its renormalization formula is:

y＝y ^*(y _max-y _min)+y _min(5)

Accompanying drawing explanation

Fig. 1 is structural representation of the present invention.

Fig. 2 is airport volume of goods transported time series chart

Fig. 3 is airport volume of goods transported time series autocorrelogram

Fig. 4 is 1 differentiated airport volume of goods transported time series chart

Fig. 5 is 1 differentiated airport volume of goods transported time series autocorrelogram

Fig. 6 is 1 difference and 1 seasonality differentiated airport volume of goods transported time series autocorrelogram

Fig. 7 is 1 difference and 1 seasonality differentiated airport volume of goods transported time series partial autocorrelation figure

Fig. 8 is ARIMA (0,1,1) (1,1,1) ¹²the freight forecast of model airport

Fig. 9 is RBF network training result figure

Figure 10 is RBF network airport volume of goods transported residual prediction figure

Figure 11 is three kinds of model prediction result figure

Below in conjunction with drawings and Examples, the present invention is further explained.

Embodiment

Airport is after operation for many years, the impact of the linear factor such as the existing fixing customer group of the airport volume of goods transported, course line quantity, also the impact of economic dispatch non-linear factor is had, the SARIMA-RBF model method that the present invention provides, take into full account the linear processes factor affecting the airport volume of goods transported, to improve the precision of prediction of the airport volume of goods transported.

Experimental data of the present invention selects the true operation data in certain hub domestic in January, 2010-2014 year July, as shown in table 1

Certain hub of table 1 in January, 2010-2014 volume of goods transported in year July

In another embodiment of the present invention, can also be normalized airport volume of goods transported time series data in advance.

Can obviously be found out by Fig. 2, the airport volume of goods transported had obvious ascendant trend from 2010-2014.Airport volume of goods transported autocorrelation figure does not have obvious white noise characteristics as can be seen from Figure 3.Can judge thus, this time series is nonstationary time series.

For the difference number of times of economic time series, the parameter d namely in model ARIMA (p, d, q) only gets 0,1 or 2 usually, simultaneously by judging the exponent number of parameter d to time series sequence chart and autocorrelogram inspection.So, first 1 difference is carried out to airport volume of goods transported time series in the present embodiment, obtain Fig. 4 and Fig. 5, to time series Fig. 2 after first difference, can see that the trend of sequence is eliminated substantially.As can be seen from its autocorrelogram as shown in Figure 5, as k=12, coefficient of autocorrelation still has larger peak, illustrates that sequence contains seasonality, needs to make seasonal difference further.Again time series is made to the seasonal difference of cycle S=12, after difference, seasonal effect in time series autocorrelogram as shown in Figure 6, the related coefficient of the sample of sequence falls into random areas very soon, Sequence Trend is eliminated substantially, but value is still very large as k=12, seasonality still clearly, makes second time seasonal difference to it, find that seasonality is not still improved completely, therefore only do single order seasonal difference.Our known d=1, D=1 thus.

By analyzing, we are known ARIMA (p, d, q) (P, D, Q) ^sd and the D value of model, that is: d=2, D=1.Judged from Fig. 6 and Fig. 7, its partial autocorrelation function is hangover, and autocorrelation function is truncation, so draw p=0, and q=1,2,3.From Fig. 6 and Fig. 7 also, after its seasonal difference, as k=12, its coefficient of autocorrelation still has larger value, shows to there is autoregression in season and moving average in season, selects P=1, Q=1 in the present embodiment.By analysis, tentatively determine ARIMA (0,1,1) (1,1,1) ¹²model is more excellent model.We application model ARIMA (0,1,1) (1,1,1) ¹²to in August, 2014-certain hub volume of goods transported in October predicts, result is as shown in Figure 8.

Utilize that K-means clustering algorithm determines RBF hidden layer center, least-squares algorithm determines to connect weights, training network, matching study section time series, until network convergence is in certain standard.Otherwise, again can change the initial weight even topology of networks of network, until training result is satisfied; Network training result as shown in Figure 9.

Utilize inspection segment data to check the network model trained to predict the non-linear partial of the airport volume of goods transported, obtain volume of goods transported residual prediction figure as shown in Figure 10.

To sum up, in order to the precision of prediction of comparative analysis SARIMA and RBF integrated combination forecast model and other model, in the present embodiment, first optimum SARIMA airport freight forecast model SARIMA (0 is obtained by the SARIMA module in SPSS19.0,1,1) (1,1,1) ¹²realize RBF neural program with MATLAB2014a again and obtain optimum RBF neural airport freight forecast model, the RBF neural program that SARIMA module finally in comprehensive utilization SPSS19.0 and MATLAB2014a realize, obtains SARIMA-RBF airport freight forecast model.Then adopt respectively three kinds of models to certain hub in August, 2014-the airport volume of goods transported in October predicts, finally predicts the outcome as shown in figure 11.As can be seen from Figure 11, when using single model to predict non-linear airport volume of goods transported time series, the precision of prediction of RBF neural model is higher, therefore, the SARIMA-RBF model method that the present invention proposes, on the basis of SARIMA model prediction residual error, RBF neural high-precisionly can portray the non-linear factor affecting the airport volume of goods transported, and then obtains the prediction residual that result compensates SARIMA model.

Table 2 three kinds of model airport freight forecast errors

The mean absolute error number percent of table 3 three kinds of models

From the comparing result of table 2, SARIMA-RBF model mean absolute error and root-mean-square error in the freight forecast of airport are obtained for the lifting of magnitude, and the airport volume of goods transported mean absolute error number percent of SARIMA-RBF model prediction as known from Table 3 improves 6.30% and 3.32% respectively relative to single SARIMA model and single RBF neural model.

Comparing result shows that SARIMA-RBF model prediction has fully utilized SARIMA and RBF neural advantage separately, feature the Changing Pattern of the airport volume of goods transported more all sidedly, improve the precision of prediction of the airport volume of goods transported, reach airport actual motion accuracy requirement.

Although be below described embodiment of the present invention by reference to the accompanying drawings, the present invention is not limited to above-mentioned specific embodiments and applications field, and above-mentioned specific embodiments is only schematic, guiding, instead of restrictive.Those of ordinary skill in the art, under the enlightenment of this instructions and when not departing from the scope that the claims in the present invention are protected, can also make a variety of forms, and these all belong to the row of the present invention's protection.

Claims (4)

1., based on an airport freight forecast analytical approach for SARIMA and RBF neural integrated combination model, it is characterized in that comprising the steps:

Step 1, with SARIMA model to the former sequence Y of the airport volume of goods transported _tcarry out modeling, doping airport volume of goods transported linear segment is a _t, then airport volume of goods transported linear segment prediction residual is E _t: E _t=Y _t-a _t.

Step 2, according to the sample set of the RBF neural determined, the airport volume of goods transported sequence Y after the reconstruct of rank is opened up in input, exports airport volume of goods transported residual error time E, and structure RBF neural forecast model, prediction is compensated SARIMA model residual result e _t.

Step 3, is combined into final predicting the outcome by predicting the outcome of two kinds of models: y _t=a _t+ e _t.

2., as claimed in claim 1 based on the airport freight forecast analytical approach of SARIMA and RBF neural integrated combination model, it is characterized in that described step 1 comprises following content of operation:

(11) airport database system is utilized to obtain the airport volume of goods transported time series data of airport about the time;

(12) according to airport volume of goods transported seasonal effect in time series scatter diagram, its stationarity of autocorrelation function graph identification;

(13) tranquilization (difference) process is carried out to the airport volume of goods transported time series data of non-stationary; And obtain the value of d and D; Wherein d, D represent Out of season and seasonal difference number of times respectively.

(14) determine p, q, possible the value of P, D according to the time series autocorrelogram after steadily and partial autocorrelation figure, then adopt Bayesian Information method (BIC) to determine best model order, check whether there is statistical significance;

(15) linear segment carrying out predicting the airport volume of goods transported by the model of inspection is utilized.

3., as claimed in claim 1 based on the airport freight forecast analytical approach of SARIMA and RBF neural integrated combination model, it is characterized in that described step 2 comprises following content of operation:

(21) one dimension airport volume of goods transported time series is carried out open up rank reconstruct, convert multidimensional time-series to;

(22) carry out network structure design, determine radial basis function;

(23) network training: utilize that clustering algorithm determines RBF hidden layer center, least-squares algorithm determines to connect weights, training network, matching study section time series, until network convergence is in certain standard.Otherwise, again can change the initial weight even topology of networks of network, until training result is satisfied;

(24) inspection segment data is utilized to check the network model trained to predict the non-linear partial of the airport volume of goods transported.

4., as claimed in claim 1 based on the airport freight forecast analytical approach of SARIMA and RBF neural integrated combination model, before it is characterized in that described operation (12), airport volume of goods transported time series data is normalized.