LU502895B1

LU502895B1 - A collaborative forecasting method for the air traffic state in the context of long-range operation

Info

Publication number: LU502895B1
Application number: LU502895A
Authority: LU
Inventors: Junqiang Wan; Hao Liu; Honghai Zhang; Wenying Lv; Lei Yang
Original assignee: Univ Nanjing Aeronautics & Astronautics
Priority date: 2022-10-12
Filing date: 2022-10-12
Publication date: 2024-04-12

Abstract

The invention presents a collaborative forecasting method for the air traffic state. According to the spatial heterogeneity and nonlinear correlation properties between sectors in the long- range operating environment, exploring the internal mapping relationship of the sector by analyzing the spatial heterogeneity and nonlinear correlation properties through time-lagged cross-correlation analysis. With the input of traffic state in selected sectors which are highly correlated, establishing the model which takes the targeted sector’s traffic state as output. According to the result of provided example, the prediction method could directly improve the traffic state prediction performance, which could provide technical support for safer, more efficient and intelligent air traffic operation.

Description

DESCRIPTION

A collaborative forecasting method for the air traffic state in the LU502895 context of long-range operation

FIELD OF THE INVENTION

The invention refers to a collaborative forecasting method for the air traffic state in the context of long-range operation, belonging to the field of air traffic management.

BACKGROUND OF THE RELATED ART

Traffic prediction plays an important role in developing advanced air traffic management, which provides the capability for risk identification and response in the dynamic air traffic environment, working as the foundation for air traffic management activities such as airspace optimization, slot allocation, and so on. However, compared with general flights, long-range flights have the characteristic of a wider flight span and longer flight hours As a result, they tend to be exposed to a more complex air traffic operating environment, which increases the difficulty of characterizing, measuring, and predicting the traffic situation using traditional centralized prediction methods. This invention proposes a collaborative forecasting method by establishing a prediction model structure with multi-node input and studying the internal mapping relationship among selected nodes and target one, thus improving the performance of the air traffic forecasting method and providing possible guidance for the air traffic management activities in each phase.

SUMMARY OF THE INVENTION

Towards long-range operations, the invention explores the internal mapping relationship of the related sector by analyzing the spatial heterogeneity and nonlinear correlation properties to establish a collaborative forecasting method for the air traffic state in the long- range operating environment.

In order to solve the above technical problems, the technical solution adopted by the invention is as follows:

Extract the data concerning long-range operations and establish a database with basic information;

Collect trajectory data in each sector, and calculate the conflict probability for any pair of aircraft within the sector; 1

According to the calculation result of conflict probability, the air traffic state about safety LUV502895 level measured and uses the unsupervised clustering algorithm to classify the state mode for each sector.

Based on the sector structure, the air traffic state along the predefined long-range flight routes is measured, and the time series data are obtained after repeated observation;

Analyze the spatial heterogeneity and nonlinear correlation properties between sectors through the time lag correlation analysis method to find the sectors that are highly correlated with the targeted ones. The selected sectors work as the distributed nodes for air traffic state prediction of the targeted sector. Take the traffic state of the targeted sector at time 7 as x a and use x! to x denote the traffic state of selected sectors. Assume that the target sector’s traffic state about the safety level at time 7 is connected and formed by the traffic activities which happen in the selected sector along the route, and the internal mapping relationship is assumed as follows:

X= JON NX M x)

Take the historical time series data set of traffic state in related sectors as the training set, which are used to train and determine the Bi-LSTM prediction model: For the trained model, the data set of selected sectors’ traffic states are taken as the input variables and the predicted traffic state of targeted sector is taken as model output ;

Further, the database includes airspace structure data, ADS-B data, and flight-plan data.

Further, the formula for the conflict probability calculation 1s :

Pa =I], Joa (XR Yr> Tr> Xs» Vs» F5 )AV

Where P, is the conflict probability for pair of aircraft, Vu is the conflict zone, La is the probability density function of conflict, (Xp, Vis Zn N(Xg, Vs Z5) is the real-time positions of reference aircraft and the stochastic aircraft respectively.

K-means clustering algorithm is used to identify and classify the traffic state data, and the clustering validity is tested by the calculation of silhouette coefficient, which ranges from -1 to +1, and a high value indicates that the object is well classified.

Further, the time series data set about traffic state is based on the real-life data collected from related sectors, and the refresh frequency is first;

Further, the correlation analysis includes:

The time-lagged cross-correlation is introduced to the correlation between the traffic 2 state time series data obtained from different sectors. The relationship is studied by shifting LU502895 time series data relatively in time, which plays an important role in selecting meaningful features.

Further, the training process of the Bi-LSTM forecasting model includes:

First, select the distributed nodes by considering the time-lagged cross-correlation, and the traffic state time series data in multiple sectors are obtained after repeated observation.

Then, assume the target sector’s traffic state about the safety level is connected and formed by the traffic activities in the selected sector along the route.

The original data set is divided into the training set and test set;

For the current time step, the Bi-LSTM prediction model is proposed. First, the forget gate and input gates are established to check the input value and determine the cell state.

Then, to minimize the loss function, propagate the gradient values backward by the gradient descent method. After iterations, the trained Bi-LSTM prediction model with defined parameters is obtained.

Further, the traffic state time series data set of related sectors saved in the database is taken as the input variable in the trained Bi-LSTM prediction model, and the predicted value of traffic state in the targeted sector is taken as the model’s output;

Compared with the prior art, the beneficial effects achieved by the present invention are:

In order to improve the performance of traffic prediction activities by considering the spatio-temporal correlation of traffic dynamics in the long-haul operating environment, which provides the required guidance for air traffic management activities such as airspace optimization, slot allocation, and so on.

BRIEF DESCRIPTION OF THE DRAWINGS

Fig. 1 is the flow of the collaborative forecasting method,

Fig. 2 is the time-lagged cross-correlation;

Fig. 3 is the structure of the collaborative forecasting model;

Fig. 4 is the statistical chart of silhouette coefficient and cluster number;

Fig. 5 is the air traffic state in sector ARO1;

Fig. 6 is the geographical location of distributed nodes after selection;

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The present invention will be further described with reference to the accompanying 3 drawings. The following examples are only used to illustrate the technical scheme of the LU502895 present invention more clearly, but not to limit the scope of protection of the present invention.

As shown in Figure 1, a collaborative forecasting method for the air traffic state in the context of long-range operation includes the following steps:

Step 1, Extract the data concerning long-range operations and establish a database with basic information;

Step 2, collect trajectory data in each sector, and calculate the conflict probability for any pair of aircraft within the sector;

Step 3, according to the calculation result of conflict probability, the air traffic state about safety level is measured, and using the unsupervised clustering algorithm to classify the state mode for each sector;

Step 4, based on the sector structure, the air traffic state along the predefined long-range flight routes is measured, and the time series data are obtained after repeated observation;

Step 5, analyzes the spatial heterogeneity and nonlinear correlation properties between sectors through the time lag correlation analysis method to find out the sectors which are highly correlated with the targeted one. The selected sectors work as the distributed nodes for air traffic state prediction of the targeted sector. Take the traffic state of the targeted sector at time / as x °” and use x to x denote the traffic state of selected sectors. Assume that the target sector’s traffic state about the safety level at time 7 is connected and formed by the traffic activities which happen in the selected sector along the route, and the internal mapping relationship 1s assumed as follows: = Fx)

Step 6, Take the historical time series data set of traffic state in related sectors as the training set, which are used to train and determine the Bi-LSTM prediction model: For the trained model, the data set of selected sectors’ traffic states are taken as the input variables and the predicted traffic state of targeted sector is taken as model output ;

Step 1 comprises:

Step 1.1: The information stored in the database includes:

Airspace structure data: including sector boundary data, which is embodied in longitude and latitude coordinate data;

ADS-B data: including flight number, departure airport, destination airport, planned 4 departure time, flight altitude (m), flight speed (kt), climb rate (ft/min), longitude, latitude, LU502895 heading angle, and monitoring time;

Flight-plan data: including flight number, planned departure time, planned arrival time, actual departure time, actual arrival time, departure airport, destination airport, aircraft type, and passing waypoint;

Step 2 includes:

Step 2.1: Extract the boundary data of the related sector and the flight trajectory of the aircraft;

Step 2.2: According to the PBN concept, set the values of TSE for en-route applications and calculate the probability of conflict for pair of aircraft in the sector. The calculation formula is shown as:

Fea =| II. Sealy

Where p is the conflict probability for pair of aircraft, V is the conflict zone, f is ca area ca the probability density function of conflict is the real-time p y y ’ (Xp, Veo Ze NXg, Vs, 25) positions of reference aircraft and the stochastic aircraft respectively.

Select the RNP2 for the cruise phase based on the PBN navigation specification, and assume the values of TSE with any system are as the law of normal distribution with zero means. The formula is shown as follows: 2 s 1 € [[——— "dx = 0.95 276

Where s is the aircraft lateral deviations from route centerline, and the standard deviation with the current nominal distribution © is 1.02 nm.

For any pair of aircraft in the sector, defining the reference aircraft and the stochastic aircraft respectively, and their real-time positions are (Xp. Veo Ze) and (Xs. Vg. 2g)

The calculation of conflict probability can be converted into the integration of probability density function within a specific zone; Take the zone as a cylinder, where height is 10km and radius is 300m according to the separation rules. Then, the conflict probability is shown as follows:

Fa =f]. Seal Xp» Yr> Zs Xs> Vs» 25 )AV

Where P, is the conflict probability, Varea is the defined conflict zone, and / is the LU502895 probability density function.

Step 3 includes:

K- means clustering algorithm 1s used to identify and classify the traffic state data, and the clustering validity is tested by the calculation of silhouette coefficient, which ranges from -1 to +1, and a high value indicates that the object is well classified.

The K-means clustering algorithm is explained as follows:

In the initial stage, clustering centers are randomly given, and each sample point is assigned to different centers according to the proximity-first assignment. The center positions are repeatedly updated through iterations until the samples in the clustering set meet the pre- set threshold.

Step 4 includes:

Step 4.1: Determine the temporal and spatial objects within the long-range operating environment, extract the traffic state data of all related sectors in the time range, and construct the traffic state matrix that reflects the space-time information;

Assume the number of related sectors is m and n for the number of time slices, take the i-th sector as an example, which is recorded as: Y() =[X,.X,,.....X,," . For all related sectors, the traffic state matrix is S =[X;.X,....X,,]1 For moment f, the traffic state of all sectors is written as $; =[Xy. Xp... Xp land t=12....n;

Step 5 includes:

Step 5.1: The time-lagged cross-correlation is introduced to the correlation between the traffic state time series data obtained from different sectors. The relationship 1s studied by shifting time series data relatively in time, which plays an important role in selecting meaningful features.

Step 6 includes:

Step 6.1: Select the distributed nodes by considering time-lagged cross-correlation. All selected time series data is saved as y+, which are divided into the training set and testing set;

Divide the historical time series data set y* into the training set x, and testing set x according to the ratio of a:(l-a) where a€(0,1), X an =[X7. Xi X01

Xie = 1X jan Xan UT 6

Step 6.2: The Bi-LSTM network model is composed of the forward LSTM unit and LU502895 backward LSTM unit, respectively. Take the time series data from the selected sector x” as the input of the Bi-LSTM model, and the calculation process of the LSTM unit is as follows:

First, the forget gate determines the cell state G by checking hy and © , and deciding whether to keep this information or not.

F =o(W,-|h_,x,|+b,)

Then, the input gate determines the updated value and cell state.

C, = tanh(W_-[h,_,x,] +b.)

C,=f+C,_ +i *C,

Finally, the output gate determines the output values. 0, = o(W,-[h_,x,|+b,) h =0,*tanh(C,) fi, GC, Ci, %, x and % represent the forget gate, the previous cell state, the current cell state, the output gate, and the input and output at time / respectively; W; , W. and W, represent the matrix weights of forget gate, cell state and output gate respectively; 2s, bc, andb, represent the bias vector of the forget gate, cell state, and output gate respectively; tanh 1s hyperbolic tangent activation function, and © 1s sigmoid function.

At time t, the time series data of traffic state in selected sectors are extracted by different

LSTM units, which is % with the forward LSTM unit and with the backward LSTM unit.

After performing high-dimensional feature extraction, the outputs are given as follows: y, =o [h,h1+b")

Where W" and b* are weight matrix and bias vector , and © is sigmoid function.

The above is only an example of the invention and is not intended to limit the invention.

Any modification, equivalent substitution, improvement, etc. made within the spirit and principles of the invention are included in the scope of the claims of the invention pending approval.

In order to further verify the effectiveness of the proposed method, CSN6882 is selected as the research object, which is the scheduled flights from Guangzhou to Urumqi. The estimated flight duration is 5 hours and 12 minutes, and the flight distance is about 2,274 nautical miles. The sectors along this flight route are taken as the research object, their 7 locations are shown in Table 1. Take the ADS-B data, which was recorded on May 1, 2019, as LU502895 the case, and the samples are shown in Table 2.

Table 1 Sector name and estimated time for CSN6882

Flight Information Estimated flight Accumulated

Number Sector . . . .

Region time flight time 1 ZGGGArROS © 56

GUANGZHOU

2 ZGGGARO3

FIR 0:56 0:56 3 ZGGGAR23 4 ZGGGARI11

ZUUUAR23 6 ZUUUAR22 7 ZUUUARO2 KUNMING FIR 1:19 02:15 8 ZUUUARO4 9 ZUUUARO9

ZUUUARI11 11 ZLLLAROS 12 ZLLLARO1 LANZHOU FIR 1:51 04:06 13 ZLLLARO7 14 ZLLLAR12

URUMOQI FIR

ZWWWARO1 1:06 05:12

Table 2 the format of ADS-B data

Call sign Height Speed Longitude Latitude Time

JT2743 11308.08 772.97 113.67 23.53 i. 14:07:59

JT2743 11308.08 771.38 113.66 23.55 i. 14:08:00

JT2743 11308.08 770.04 113.65 23.57 i. 14:08:01

JT2743 11308.08 767.26 113.64 23.61 i. 14:08:23

JT2743 11308.08 764.61 113.64 23.61 i. 14:08:24

JT2743 11308.08 762.59 113.63 23.64 i. 14:08:25

Taking ZGGGAROS as an example, the active aircraft at a certain time are shown in

Table 3, and the conflict probability for the aircraft pair is shown in Table 4. 8

Table 3 Aircraft number LU502895

Number Call sign 01 GS6451 02 CA733 03 MU2779 04 AK113 05 GS7441 06 ZH8796 07 CZ8545 08 KA886 09 MU5302 3U8782 11 CZ6559

Table 4 Conflict probability for aircraft pair

Num 01 02 03 04 05 06 07 08 09 10 11 ber 4.6E- 01 0 0 0 0 0 0 0 0 0 0 07 3.8E- 4.1E- 7.8E- 1.5E- 02 0 0 0 0 0 0 0 150 86 145 229 3.8E- 3.5E- 8.7E- 7.8E- 5.9E- 7.3E- 03 0 0 0 0 0 150 209 313 154 200 209 04 0 0 0 0 0 0 0 0 0 0 0 4.6E- 05 0 0 0 0 0 0 0 0 0 0 07 1.8E- 06 0 0 0 0 0 0 0 0 0 0 136 3.5E- 07 0 0 0 0 0 0 0 0 0 0 209 4.1E- 8.7E- 1.2E- 6.1E- 08 0 0 0 0 0 0 0 86 313 121 275 7.8E- 7.8E- 1.2E- 8.6E- 09 0 0 0 0 0 0 0 145 154 121 108 1.5E- 5.9E- 6.1E- 8.6E- 10 0 0 0 0 0 0 0 229 200 275 108 9

7.3E- 1.8E- LU502895 11 0 0 209 0 0 136 0 0 0 0 0 © According to the calculation result of conflict probability, the air traffic state about safety level is measured and uses the unsupervised clustering algorithm to classify the state mode for each sector. Considering the randomness of the initial stage for the k-means clustering algorithm, 50 repeated experiments are conducted in each group, respectively. The results are shown in Figure 4, in which scattered points represent the silhouette coefficient in each trial, and the line represents the mean value of silhouette coefficients. The results show that the appropriate number of clusters is 4.

All air traffic states can be divided into different types based on the traffic state embodied in the active aircraft within the sector, which are Level I, Level II, Level III, and

Level IV, the patterns at a certain time are shown in Table 5.

Table 5 Traffic pattern at different times “Time Pattem 8.00.00 Level 8:00:10 Level I 8:00:20 Level I 8:00:30 Level I 8:00:40 Level II 8:00:50 Level II 12:09:00 Level III 12:09:10 Level III 12:09:20 Level III 12:09:30 Level III 12:09:40 Level IV 12:09:50 Level IV

The K-means clustering algorithm classifies the time series data . of sectors along the flight route, and the air traffic state after classification in ZGGGAROS is shown in Figure 5.

According to the time-lagged cross-correlation analysis, multiple sectors are selected as distributed nodes for prediction, which are ZGGGAROI, ZGGGARO02, ZGGGARO4A,

ZGGGARI11, ZUUUARO2, ZUUUAR23, ZUUUARO4, ZUUUARO9, ZLLLARI2,

ZLLLAROS and ZLLLARO7, and ZGGGAROS is selected as the targeted sector. Finally,

establishing the prediction model used to predict traffic state in ZGGGARO5 with information LV502895 collected from distributed nodes. The structure of the targeted sector and distributed nodes is shown in Figure 6.

In order to choose the model that has the best performance, prediction models based on

RNN, LSTM, and Bi-LSTM are established, respectively. With a random seed value of 22, 489,888 training samples and 54,432 test samples are generated, and a fully-connected layer with four classifications is added for learning non-linear combinations of features. Cross-

Entropy loss is selected as the loss function, and ‘softmax’ is used for activation. To avoid overfitting, the dropout layer is applied to the input layer hidden layers, respectively, and the value for dropout is 0.2.

Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), and Accuracy (ACC) are taken as the evaluation metric, which is used to quantify the effectiveness of the forecasting method proposed in the invention. The definitions are shown as follows: 1 # 21

Epuse = NEO —Y,)

LE 4

Enr =v 2h — J

Accuracy = Noe

N

Where V, and J, are the actual and predicted values, N,, is the number of samples with accurate prediction, and N is the total number of samples used for testing.

Considering that parameters would impact the model prediction performance, the grid search method is used to optimize parameters. The optimization process of parameters is shown in Table 6.

Bate 0000000000 06Nn~»/%J[

Learni RMS Learni Learni h RMS RMS ; ng ACC MAE E ng ACC MAE ng ACC MAE size E E rate rate rate © 01 05445 02404 03498 0.1 05573 02353 03585 0.1 05919 02275 03747 120 0.01 0.6665 0.2056 0.3202 0.01 0.6608 0.2084 0.3235 0.01 0.6656 0.2034 0.3231 0.001 0.8004 0.1433 0.2625 0.001 0.8581 0.0990 0.2213 0.001 0.8663 0.0874 0.2142 180 0.1 0.5962 0.2305 0.3469 0.1 0.5738 0.2413 0.3492 0.1 0.5879 0.2312 0.3485 0.01 0.7054 0.1886 0.3072 0.01 0.7163 0.1831 0.3023 0.01 0.7000 0.1893 0.3088 11

0.001 0.8012 0.1454 02616 0.001 08579 0.1006 02226 0.001 08652 0.0885 0LY$P2895 0.1 0.5975 0.2273 0.3557 0.1 0.5630 0.2309 0.3542 0.1 0.5942 0.2293 0.3544 240 0.01 0.7247 0.1819 0.2988 0.01 0.7579 0.1662 0.2847 0.01 0.7571 0.1646 0.2851 0.001 0.8026 0.1464 0.2626 0.001 0.8608 0.0968 0.2202 0.001 0.8671 0.0870 0.2130 0.1 0.5950 0.2334 0.3500 0.1 0.5734 0.2365 0.3456 0.1 0.5977 0.2267 0.3492 300 0.01 0.7494 0.1710 0.2887 0.01 0.7714 0.1574 0.2781 0.01 0.7836 0.1504 0.2715 0.001 0.8010 0.1478 0.2634 0.001 0.8588 0.1003 0.2214 0.001 0.8679 0.0858 0.2126 0.1 0.5791 0.2313 0.3475 0.1 0.5914 0.2442 0.3492 0.1 0.5565 0.2328 0.3497 360 0.01 0.7602 0.1662 0.2834 0.01 0.8050 0.1403 0.2602 0.01 0.7905 0.1469 0.2677 0.001 0.7962 0.1490 0.2658 0.001 0.8582 0.0981 0.2207 0.001 0.8675 0.0868 0.2133 © In order to further demonstrate the advantages of the collaborative prediction method proposed in the invention, ZGGGAROS is taken as the targeted sector, and model performance is observed and compared under different input conditions, which are case 1 and case 2, respectively. In case 1, the time series data from adjacent sectors are introduced as the input variables, which refers to the traffic state time series data only related to ZGGGAROI,

ZGGGARO2, ZGGGARO3, ZGGGARO04, and ZGGGARO6. In case 2, the traffic state time series data related to all distributed nodes are added to the model’s input.

Prediction performance is shown in Table 7. Compared with case 1, it can be clearly observed that the input condition impacts the model’s performance. However, all established models show a decrease in prediction error.

Table 7 Comparison table of prediction accuracy of target security situation model ~~ MAE RMSE ACC Performance —

Input Model

MAE RMSE ACC improvement ~~ RNN 07407 01775 02982 -

Case 1 LSTM 0.8633 0.0943 0.2177 -

Bi-LSTM 0.8679 0.0858 0.2126 -

RNN 0.1775 0.2932 0.7407 A24.7390%

Case 2 LSTM 0.0943 0.2177 0.8633 A45.2389%

Bi-LSTM 0.0858 0.2126 0.8679 A46.0128% 12

Claims

1. A collaborative forecasting method for the air traffic state in the context of long-range LV502895 operation is characterized by comprising the following steps: Extract the data concerning long-range operations and establish a database with basic information; Collect trajectory data in each sector, and calculate the conflict probability for any pair of aircraft within the sector; According to the calculation result of conflict probability, the air traffic states about safety level is measured and uses the unsupervised clustering algorithm to classify the state mode for each sector. Based on the sector structure, the air traffic state along the predefined long-range flight routes is measured, and the time series data are obtained after repeated observation; Analyze the spatial heterogeneity and nonlinear correlation properties between sectors through the time-lagged cross-correlation analysis, to find out the sectors which are highly correlated with the targeted one, the selected sectors work as the distributed nodes for air traffic state prediction of the targeted sector. Take the traffic state of the targeted sector at time / as x °” and use x to x denote the traffic state of selected sectors. Assume that the target sector’s traffic state about the safety level at time 7 is connected and formed by the traffic activities which happened in selected sectors along the route, and the internal mapping relationship 1s assumed as follows: AL) Take the historical time series data set of traffic state in related sectors as the training set, which are used to train and determine the Bi-LSTM prediction model: For the trained model, the data set of selected sectors’ traffic states are taken as the input variables and the predicted traffic state of targeted sector is taken as model output.

2. A collaborative forecasting method for the air traffic state in the context of long-range operation based on claim 1 is characterized in by the database includes airspace structure data, ADS-B data and flight-plan data.

3. A collaborative forecasting method for the air traffic state in the context of long-range operation based on claim 1 is characterized in by the formula for the conflict probability calculation is: Fa ff, Seal Xp» Yr> Zs Xs» Vs» 25 ) dv 13

Where P, is the conflict probability for pair of aircraft, Vu is the conflict zone, La is LU502895 the probability density function of conflict , (Xp Vis Ep Xe, Vso F5) is the real-time positions of reference aircraft and the stochastic aircraft respectively.

4. A collaborative forecasting method for the air traffic state in the context of long-range operation based on claim 1 is characterized in by the traffic state in the sector is quantitatively evaluated based on the conflict probability of aircraft pairs, and the mode of air traffic state 1s effectively classified, including: K- means clustering algorithm is used to identify and classify the traffic state data, and the clustering validity is tested by the calculation of silhouette coefficient, which ranges from -1 to +1, and a high value indicates that the object is well classified.

5. A collaborative forecasting method for the air traffic state in the context of long-range operation based on claim 1 is characterized in by the time series data set about traffic state is based on the real-life data collected from related sectors, and the refresh frequency is first; Take the traffic state of the targeted sector at time # as x“ | and use x to X denote the traffic state of selected sectors. Assume that the target sector’s traffic state about the safety level at time 7 is connected and formed by the traffic activities which happen in the selected sector along the route, and the internal mapping relationship is assumed as follows: X= (XxX x)

6. A collaborative forecasting method for the air traffic state in the context of long-range operation based on claim 1 is characterized in by the correlation analysis method comprises: The time-lagged cross-correlation is introduced to the correlation between the traffic state time series data obtained from different sectors, the relationship is studied by shifting time series data relatively in time, which plays an important role in selecting meaningful features.

7. A collaborative forecasting method for the air traffic state in the context of long-range operation based on claim 1 is characterized in by the training process of the Bi-LSTM forecasting model, which includes: Analyze the spatial heterogeneity and nonlinear correlation properties between sectors through the time-lagged cross-correlation analysis to find out the sectors which are highly correlated with the targeted one. The selected sectors work as the distributed nodes for air traffic state prediction of the targeted sector. The original data set is divided into the training set and test set; 14

For the current time step, the Bi-LSTM prediction model is proposed. The forget gate LU502895 and input gates are established for checking the input value and determining cell state, respectively. To minimize the loss function, propagate the gradient values backward by the gradient descent method. After iterations, the trained Bi-LSTM prediction model with defined parameters is obtained.

8. A collaborative forecasting method for the air traffic state in the context of long-range operation based on claim 1 is characterized in by the traffic state time series data set of related sectors saved in the database is taken as the input variable in the trained Bi-LSTM prediction model, and the predicted value of traffic state in the targeted sector is taken as model’s output.