A short-term forecasting method for airport traffic based on quadratic decomposition and integration

Abstract

The present invention discloses a short-term airport traffic forecasting method based on quadratic decomposition and integration, comprising the following steps: S1, obtaining historical airport operation data, and performing standardization processing on the airport arrival and departure traffic data within the airport statistical period to obtain an original time series; S2, using the STL algorithm model to decompose the original time series of step S1 to obtain three components: trend term, seasonal term, and residual term; S3, calculating the sample entropy values of the three components in step S2. Unlike time series forecasting methods, the present invention, guided by the "decomposition and integration methodology," constructs a quadratic decomposition and integration forecasting model, decomposing complex time series into several low-complexity component time series for forecasting. The method of the present invention has a fast calculation speed, with an arrival traffic forecast accuracy of over 97% and a departure traffic forecast accuracy of over 99%, providing a scientific basis for accurately grasping airport traffic trends and precisely implementing traffic management measures.

Description

Technical Field

[0001] The present invention relates to the technical field of flow management of air traffic management, and in particular to a short-term prediction method for airport flow based on secondary decomposition and integration. Background Art

[0002] With the continuous development of my country's social economy, the demand for civil aviation transportation has grown steadily, and the growth rate of air traffic flow has been significant. When the flight flow exceeds the guarantee capacity, flight delays often occur, and the workload of controllers increases dramatically, which not only threatens operational safety but also reduces system efficiency. The airport's arrival and departure traffic flow is an important part of air traffic flow. Accurately predicting airport traffic flow provides support for the scientific formulation of airport operation planning schemes, the reasonable setting of the launch rate of controlled operations, and the precise implementation of traffic management measures, thereby effectively ensuring operational safety and alleviating flight delays.

[0003] Airport traffic forecasts are divided into medium- and long-term forecasts and short-term forecasts. Medium- and long-term forecasts are usually based on years, months, and days as the forecast scale, and are mainly used in the strategic stage. Short-term airport traffic forecasts are based on hours and minutes as the forecast scale, and are usually based on the number of flights arriving and departing within 6 hours. They are often used in the tactical traffic management stage and are more instructive for safe and efficient operations.

[0004] For the short-term prediction of airport arrival and departure traffic, existing technologies mainly focus on airport traffic time series as the research object, using traditional time series prediction methods such as AR and ARAIM, or single intelligent prediction methods such as support vector machine (SVM), long short-term memory neural network (LSTM), extreme gradient boosting (XGboost), or weighted combinations of different methods. These methods usually have high requirements for data characteristics and data volume. At the same time, air traffic flow has nonlinear chaotic and fractal characteristics, and the high complexity results in low prediction accuracy. Summary of the Invention

[0005] The purpose of the present invention is to provide a short-term prediction method for airport traffic based on quadratic decomposition integration to solve the problem that the existing technology usually has high requirements for data characteristics and data volume, and at the same time, air traffic flow has nonlinear chaotic and fractal characteristics, and the high complexity causes low accuracy of prediction results.

[0006] To achieve the above object, the present invention provides the following technical solution: comprising the following steps:

[0007] S1. Obtain historical airport operation data and normalize the airport arrival and departure traffic data within the airport statistical period to obtain the original time series;

[0008] S2. Use the STL algorithm model to decompose the original time series in step S1 to obtain three components: trend term, seasonal term and residual term;

[0009] S3, calculating the sample entropy values of the three components in step S2, and dividing the samples into two categories according to the size of the sample entropy values;

[0010] S4, performing a secondary decomposition based on the GA-VMD method on the component with the larger sample entropy value in step S3 to obtain components;

[0011] S5. Apply the XGboost method to predict the components obtained by the secondary decomposition in step S4 and the components with smaller sample entropy values in step S3, and then perform integrated prediction by accumulation.

[0012] Preferably, the standardization process in step S1 includes:

[0013] S101. Sort the flights according to the actual departure date and time, and obtain the airport departure flow time series according to the specified statistical period;

[0014] S102. Sort the flights according to the order of actual landing dates and landing times, and obtain the airport arrival flow time series according to the prescribed statistical period.

[0015] Preferably, the statistical period of step S1 includes 60 minutes.

[0016] Preferably, the historical airport operation data in step S1 includes: flight number, registration number, departure airport, destination airport, planned departure time, actual departure time, planned landing time and actual landing time data.

[0017] Preferably, the GA-VMD in step S4 refers to applying the GA method to optimize the penalty factor α and the number of decomposition levels K of the VMD method, and the steps include:

[0018] S401, α and K are randomly generated within their respective value ranges, and the chromosome is composed of the combination of [α, K];

[0019] S402. Using envelope entropy as the fitness function for optimization, select the better chromosomes to enter the next generation of evolution;

[0020] S403. When the optimal fitness of each generation tends to be stable, [α, K] is the optimized value.

[0021] Compared with the prior art, the present invention has the following beneficial effects:

[0022] 1. The present invention uses the STL method to decompose the original time series into three components: trend term, seasonal term and remainder term, calculates the sample entropy values of the three components, and divides them into two categories according to the size of the sample entropy values. The VMD method is used to perform secondary decomposition on the components with larger sample entropy values, and the XGBoost method is used to predict each component. Then, an integrated prediction is performed by accumulation. Different from the time series prediction method, a secondary decomposition integrated prediction model is constructed under the guidance of "decomposition and integration methodology", which decomposes the complex time series into several low-complexity component time series for prediction. The method of the present invention has a fast calculation speed, and the accuracy of approach flow prediction reaches more than 97%, and the accuracy of departure flow prediction reaches more than 99%, providing a scientific basis for accurately grasping the airport traffic situation and accurately implementing flow management measures. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 This is a flow chart of a method for short-term airport traffic prediction based on secondary decomposition and integration according to the present invention;

[0024] Figure 2 This is a schematic diagram of the original sequence of hourly airport arrival and departure traffic in a method for short-term airport traffic prediction based on secondary decomposition integration of the present invention;

[0025] Figure 3 This is a schematic diagram of the STL decomposition results of the airport approach flow in a short-term airport flow prediction method based on secondary decomposition integration of the present invention;

[0026] Figure 4 This is a schematic diagram of the STL decomposition results of airport departure traffic in a method for short-term airport traffic prediction based on secondary decomposition integration of the present invention;

[0027] Figure 5 This is a schematic diagram of the VMD decomposition results of the trend term of the arrival traffic time series in the airport traffic short-term prediction method based on secondary decomposition integration of the present invention;

[0028] Figure 6 This is a schematic diagram of the VMD decomposition results of the residual term of the arrival traffic time series in a method for short-term airport traffic prediction based on quadratic decomposition integration of the present invention;

[0029] Figure 7 This is a schematic diagram of the VMD decomposition results of the departure traffic time series trend item in the airport traffic short-term prediction method based on secondary decomposition integration of the present invention;

[0030] Figure 8 This is a schematic diagram of the VMD decomposition results of the residual term of the departure traffic time series in a method for short-term airport traffic prediction based on quadratic decomposition integration according to the present invention;

[0031] Figure 9This is a schematic diagram of the Beijing Capital International Airport approach traffic forecast results;

[0032] Figure 10 This is a schematic diagram of the departure traffic forecast results for Beijing Capital Airport. DETAILED DESCRIPTION

[0033] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0034] In recent years, decomposition-integration forecasting methods have become a cutting-edge concept in the field of complex nonlinear time series forecasting. This method decomposes the complex original time series into several low-complexity components, then predicts each component and integrates the predictions. This effectively improves forecast accuracy and has been successfully applied in fields such as short-term power load forecasting and ground transportation forecasting. Existing methods all use traditional single-step decomposition, but some components may still have high complexity due to insufficient decomposition and require further decomposition. Furthermore, the application of decomposition-integration forecasting methods to short-term airport traffic forecasting has not been reported. This paper uses this as inspiration to construct a short-term airport traffic forecasting method based on secondary decomposition and integration.

[0035] See also Figure 1-10 The present invention provides a technical solution: the calculation method first establishes a calculation system, which is composed of software modules. The first module installs a primary decomposition module for original time series data, and uses the STL method to decompose the original time series into three components: trend term, seasonal term, and residual term. The second module installs a sample entropy calculation module, calculates the sample entropy values of the three components decomposed by the first module, and divides them into two categories according to the size of the sample entropy values. The third module installs a secondary decomposition module, and uses the VMD method to perform secondary decomposition on the components with larger sample entropy values calculated by the second module. The fourth module installs a component prediction module, uses the XGBoost method to predict each component, and then performs integrated prediction by accumulation. The primary decomposition module for original time series data and the component prediction module are used as an implementation platform for the short-term prediction method of sector traffic based on the integrated methodology; the primary decomposition module, the sample entropy calculation module, the secondary decomposition module, and the component prediction module are connected in sequence.

[0036] The specific method includes the following steps:

[0037] S1. Obtain historical airport operation data and normalize the airport arrival and departure traffic data within the airport statistical period to obtain the original time series. The statistical period is 60 minutes, 30 minutes, or 15 minutes. The following description focuses on the 60-minute period. Historical airport operation data includes: flight number, registration number, departure airport, destination airport, planned takeoff time, actual takeoff time, planned landing time, and actual landing time data.

[0038] Standardization includes:

[0039] S101. Date conversion: convert the airport arrival and departure flow data to the first day of the measurement month, and perform linear interpolation according to the time to obtain the airport arrival and departure flow data with equal time intervals;

[0040] S102. Format conversion: convert the airport arrival and departure traffic data into a Dataframe format, that is, a combination format of date and value.

[0041] Reference Figure 2 ,Taking the actual operation data from January 2 to January 30, 2020 as an example, ,according to the 60-min statistical scale, the arrival and departure traffic ,time series are constructed respectively, which consist of 696 data, ,respectively.

[0042] S2. Use the STL algorithm model to decompose the original time series of step S1 to obtain three components: trend term, seasonal term and residual term.

[0043] The core content of the STL algorithm is the iterative process of locally weighted regression (Loess), which is divided into an inner loop and an outer loop.

[0044] 1. The inner circulation process is as follows:

[0045] 1) Variable initialization: k is the number of iterations, is the seasonal item data at time t of the k-th iteration;

[0046] 2) Detrending: Using robust weight ρ t Get the new Loess adjustment value x t ;

[0047] 3) Cyclic subsequence smoothing: Each seasonal term subsequence without trend term is smoothed to obtain temporary seasonal term

[0048] 4) Low-pass filtering: After three sliding averages and one Loess process, we get

[0049] 5) Smooth detrending to obtain the seasonal term sequence after the kth cycle:

[0050] 6) Remove seasonal items:

[0051] 7) Trend smoothing term: The Loess process is performed again on the obtained seasonal terms to obtain the trend term sequence after the kth cycle

[0052] 8) Check whether the maximum number of iterations is met, or Check whether the result has converged. If not, repeat the process (2)-(8) again.

[0053] 2. The main function of the outer loop is to calculate the robust weight ρ t , as shown in formula (1).

[0054]

[0055] Where h = 6 × medtan(|R t |), medtan(*) means taking the median. |R t | represents the absolute value of the remainder at time t, B(x) represents the bisquare function, and its expression is shown in formula (3), and x represents the input parameter.

[0056]

[0057] At this point, the original time series data is decomposed into trend term, seasonal term and residual term, as shown in formula (3). t Represents the observation value of the time series data at time t; T t 、S t 、R t They represent the values of trend term, seasonal term and residual term at time t respectively.

[0058] x t =T t +S t +R t t=1,2...N (3)

[0059] Reference Figure 3 , STL is applied to decompose the original arrival flow time series data, and finally three components of arrival flow trend term, seasonal term and residual term are obtained.

[0060] Reference Figure 4 , STL is applied to decompose the original departure flow time series data, and finally three components of departure flow trend term, seasonal term and residual term are obtained.

[0061] S3. Calculate the sample entropy values of the three components in step S2 and divide the samples into two categories according to their entropy values.

[0062] The calculation method of sample entropy is as follows:

[0063] Step 1: Convert the original time series {x i According to formula (4), construct a new vector X(i)

[0064] X(i)=[x i , x i+1 ,...,x i+(m-1) ],i=N-m+1 (4)

[0065] Where m is the embedding dimension and N is the length of the time series.

[0066] Step 2: Calculate the maximum distance between any two vectors X(i) and X(j) according to formula (5)

[0067] d ij =max(x i+k -x j+k ) (5)

[0068] Where k = 0, 1, 2, ..., m-1, i ≠ j

[0069] Step 3: Given a tolerance value r, count the d corresponding to each i value ij <Number of r(d ij <r), and find its quotient B with the total number of vectors i m (r), see formula (6)

[0070] B i m (r)=num(d ij <r) / (Nm) (6)

[0071] Where, 1≤j≤Nm, j≠i

[0072] Step 4: Calculate B according to formula (7) m (r)

[0073]

[0074] Step 5: Let m = m + 1, repeat steps 1-4, and calculate B m+1 (r)

[0075] Step 6: Calculate the sample entropy SE(m, r) according to formula (8). In practical application, it can be approximately calculated according to formula (9):

[0076]

[0077] SE(m, r, N) = -ln[B m+1 (r) / B m (r)](9).

[0078] Refer to Table 1 to calculate the component sample entropies for the arrival and departure traffic decomposition. In this technical solution, sample entropy values greater than 1 indicate high complexity and require further decomposition. As can be seen from the table, only the seasonal term has low complexity; the other two components are highly complex and both require VMD secondary decomposition. Both the trend term and the remainder term have high sample entropy values, requiring secondary decomposition to reduce complexity.

[0079] S4. Perform a secondary decomposition based on the GA-VMD method on the component with the larger sample entropy value in step S3 to obtain a component. GA-VMD refers to applying the GA method to optimize the penalty factor α and the number of decomposition levels K of the VMD method. The steps include:

[0080] S401, α and K are randomly generated within their respective value ranges, and the chromosome is composed of a combination of [α, K];

[0081] S402. Using envelope entropy as the fitness function for optimization, select the better chromosomes to enter the next generation of evolution;

[0082] S403. When the optimal fitness of each generation tends to be stable, [α, K] at this time is the optimized value.

[0083] The specific steps of the time series secondary decomposition based on the GA-VMD method are as follows;

[0084] Step 1: During initialization, the value range of α is 10-1000, and the value range of k is 4-20. The minimum envelope entropy is used as the optimization index, and the optimized α and K are obtained using the genetic algorithm GA;

[0085] Step 2: Set k = 0, number of iterations n = 0, and initialize the time series component Frequency center of the component Component Lagrange operator

[0086] Step 3: n=n+1, iterate

[0087] Step 4: Update according to formula (10) and formula (11) and ω k (ω), until the number of decompositions reaches K, the inner iteration stops

[0088]

[0089]

[0090] in, is the time series under the independent variable ω, u k (ω) is the decomposed single-component AM / FM signal, ^ represents the estimated value, ω is the independent variable, dω represents the derivative of ω, λ(ω) is the Lagrange operator under the independent variable ω, is the frequency center of the component under the independent variable ω.

[0091] Step 5: Iterate λ according to formula (12)

[0092]

[0093] Where γ is the noise margin.

[0094] Step 6: Given the accuracy ε, stop if the stopping condition of formula (13) is satisfied, otherwise go to step (10) to continue iteration.

[0095]

[0096] The VMD parameters optimized by GA are shown in Table 2, and the decomposition results are shown in Figure 5-Figure 8 As shown in Figure 2, the components of the second decomposition of the arrival traffic time series trend term and the residual term are 15 and 16 respectively, and the components of the second decomposition of the departure traffic time series trend term and the residual term are 14 and 16 respectively.

[0097] S5. Apply the XGboost method to predict the components obtained by the secondary decomposition in step S4 and the components with smaller sample entropy values in step S3, and then perform integrated prediction by accumulation.

[0098] The basic idea of this algorithm is to correct the existing prediction errors by continuously adding new trees, and finally weight the prediction results of the decision tree. The iterative process of XGboost is shown in formula (14):

[0099]

[0100] in, is the predicted value of the i-th sample at the t-th iteration. The algorithm iterates and retains the t-1-th predicted value and introduces a new function f t (x i ) to fit the remaining residuals.

[0101] The accuracy of the prediction is determined by calculating the mean absolute error (MAE), mean square error (MSE), and equalization coefficient (EC). The calculation formulas are shown in equations (15)-(17). MAE represents the mean deviation of the predicted value from the actual value, MSE reflects the degree to which the predicted value deviates from the actual value, and EC reflects the overall accuracy of the prediction.

[0102]

[0103]

[0104]

[0105] in are the actual value and predicted value at the first moment respectively; L is the number of predictions. The smaller the MAE and MSE, the smaller the prediction error. They can be used for comparative analysis between different prediction methods. EC is used to analyze the accuracy of prediction results. The closer it is to 1, the more accurate the prediction.

[0106] For each component time series, the last 6 data points are used for verification, and the first 690 data points are used for training. Each group consists of 12 data points, and one data point is slid back each time, resulting in a total of 679 data points. After the model is trained with the first 678 data points, the 679th data point is used for prediction. A multi-step prediction is used, with only one value predicted each time. The new predicted value is used as input to roll forward the next value. Since the model predicts short-term traffic within 6 hours, a total of 6 steps are used, resulting in 6 predicted values for each component time series. The prediction results of each component after the secondary decomposition are summed and integrated, and compared with the actual values used for verification to analyze the prediction accuracy.

[0107] Reference Figure 9 、 Figure 10 As shown in Table 4, the EC values for the arrival flow forecast are above 0.97, and the EC values for the departure flow forecast are above 0.99. Both the RMSE and MAE indicators are small, indicating good forecasting performance, with the departure flow forecast performing even better. The calculation time on the MATLAB platform is only approximately 120 seconds, fully meeting the real-time requirements of short-term forecasting.

[0108] Referring to Table 4, data from Shanghai Pudong and Hongqiao Airports and Guangzhou Baiyun Airport in January 2020 were collected to construct a traffic time series with a 60-minute statistical scale. Short-term forecasts of 1 to 6 hours were performed. The EC values of the approach traffic forecast were all above 0.98, and the EC values of the departure traffic forecast were all above 0.99.

[0109] Table 1 Entropy values of each component sample of STL decomposition results

[0110] type Trend Items Seasonal items Remaining items Approach 1.37208 0.47812 2.21186 Exit 1.03463 0.73393 2.73055

[0111] Table 2 GA optimized VMD parameters

[0112]

[0113] Table 3 Evaluation indicators of prediction results at the 60-minute scale

[0114] index Approach Exit EC 0.9703 0.9959 RMSE (flights) 1.1808 0.2848 MAE (flights) 1.3009 0.2486

[0115] Table 4 Prediction results of each airport

[0116]

[0117] As can be seen from the above table, the method of the present invention has a fast calculation speed, the accuracy of approach traffic prediction reaches more than 97%, and the accuracy of departure traffic prediction reaches more than 99%, providing a scientific basis for accurately grasping the airport traffic situation and accurately implementing traffic management measures.

[0118] The present invention fully combines the advantages of STL and VMD, applies STL to decompose the seasonal term, trend term and residual term into three components, and calculates the sample entropy of each component. The sample entropy value of the seasonal term component is small, indicating that the complexity is small and it is easy to predict, while the sample entropy value of the trend term and residual term components is large, indicating that the complexity is large. Applying VMD for secondary decomposition can reduce the complexity of the components and improve the prediction accuracy.

[0119] Through secondary decomposition, components with high complexity and high prediction difficulty contribute less to the variance of the original time series, while components with low complexity and low prediction difficulty contribute more to the variance. Therefore, components with high variance contributions are easier to predict and have higher prediction accuracy. Their prediction accuracy directly affects the accuracy of the final integrated prediction, resulting in higher overall prediction accuracy.

[0120] It should be noted that, in this document, relational terms such as first and second, etc., are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "comprises," "comprising," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that includes a list of elements includes not only those elements but also other elements not explicitly listed, or elements inherent to such process, method, article, or apparatus.

[0121] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to these embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the appended claims and their equivalents.

Claims

1. A short-term airport traffic forecasting method based on secondary decomposition integration, characterized by: The following steps are involved: S1. Obtain historical airport operation data and normalize the airport arrival and departure traffic data within the airport statistical period to obtain the original time series; S2. Use the STL algorithm model to decompose the original time series in step S1 to obtain three components: trend term, seasonal term and residual term; S3, calculating the sample entropy values of the three components in step S2, and dividing the samples into two categories according to the size of the sample entropy values; S4. Perform a secondary decomposition based on the GA-VMD method on the component with the larger sample entropy value in step S3 to obtain a component. GA-VMD refers to applying the GA method to optimize the penalty factor α and the number of decomposition levels K of the VMD method. The steps include: S401, α and K are randomly generated within their respective value ranges, and the chromosome is composed of the combination of [α, K]; S402. Using envelope entropy as the fitness function for optimization, select the better chromosomes to enter the next generation of evolution; S403. When the optimal fitness of each generation tends to be stable, [α, K] is the optimized value; The specific steps of the time series secondary decomposition based on the GA-VMD method are as follows: Step 1: During initialization, the value range of α is 10-1000, and the value range of k is 4-20. The minimum envelope entropy is used as the optimization index, and the optimized α and K are obtained using the genetic algorithm GA; Step 2: Set k = 0, number of iterations n = 0, and initialize the time series component Frequency center of the component Component Lagrange operator Step 3: n=n+1, iterate; Step 4: Update according to formula (10) and formula (11) and ω k (ω), until the number of decompositions reaches K, the inner iteration stops in, is the time series under the independent variable ω, u k (ω) is the decomposed single-component AM / FM signal, ^ represents the estimated value, ω is the independent variable, dω represents the derivative of ω, λ(ω) is the Lagrange operator under the independent variable ω, is the frequency center of the component under the independent variable ω; Step 5: Iterate λ according to formula (12) Where, γ is the noise tolerance; Step 6: Given the accuracy ε, stop if the stopping condition of formula (13) is satisfied, otherwise go to step (10) to continue iterating: S5. Apply the XGboost method to predict the components obtained by the secondary decomposition in step S4 and the components with smaller sample entropy values in step S3, and then perform integrated prediction by accumulation. The iterative process of XGboost is shown in formula (14): in, is the predicted value of the i-th sample at the t-th iteration. The algorithm iterates and retains the t-1-th predicted value and introduces a new function f t (x i ) to fit the remaining residuals; The accuracy of the prediction is determined by calculating the mean absolute error (MAE), mean square error (MSE), and equalization coefficient (EC). The calculation formulas are shown in equations (15)-(17). MAE represents the mean deviation of the predicted value from the actual value, MSE reflects the degree to which the predicted value deviates from the actual value, and EC reflects the overall accuracy of the prediction. in are the actual value and predicted value at the first moment respectively; L is the number of predictions. The smaller the MAE and MSE, the smaller the prediction error. They can be used for comparative analysis between different prediction methods. EC is used to analyze the accuracy of prediction results. The closer it is to 1, the more accurate the prediction.

2. The method for short-term airport traffic flow prediction based on secondary decomposition integration according to claim 1 is characterized by: The step S1 standardization process includes: S101. Sort the flights according to the actual departure date and time, and obtain the airport departure flow time series according to the specified statistical period; S102. Sort the flights according to the order of actual landing dates and landing times, and obtain the airport arrival flow time series according to the prescribed statistical period.

3. The method for short-term airport traffic flow prediction based on secondary decomposition integration according to claim 1 is characterized by: The statistical period of step S1 is 60 minutes.

4. The method for short-term airport traffic flow prediction based on secondary decomposition integration according to claim 1 is characterized by: The historical airport operation data in step S1 includes: flight number, registration number, departure airport, destination airport, planned departure time, actual departure time, planned landing time and actual landing time data.

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