A terminal area airspace traffic flow spatial pattern mining method considering abnormal trajectories

Abstract

The application relates to the technical field of flight trajectory pattern recognition, and discloses a terminal area airspace traffic flow space pattern mining method considering abnormal trajectories, which comprises the following steps: acquiring historical flight trajectories of an airport terminal area airspace, constructing an airspace description matrix T of the airport terminal area after pretreatment of the terminal area flight trajectories; establishing a deep self-encoding model; optimizing the deep self-encoding model, and extracting a normal trajectory set Y from the airspace description matrix T; and extracting the space pattern of the normal trajectory set Y to support the decision of airspace management. The method can avoid the influence of abnormal trajectories on the clustering results of terminal airspace data, avoid the influence of high-dimensional information on the discrimination ability of a clustering model, and guarantee the clustering effect of the clustering model.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of flight trajectory pattern mining, and particularly relates to a terminal area airspace traffic flow spatial pattern mining method considering abnormal trajectories. BACKGROUND

[0002] In the process of airport traffic flow management, the terminal area airspace is regarded as a key airspace unit affecting the flight safety of aircrafts due to its significant characteristics such as small space, complex routes and frequent activity disturbances. Rapid and accurate identification and characterization of the spatial pattern of the terminal area airspace traffic flow is of great significance to the decision support of airspace management. The spatial pattern mining of the terminal area airspace traffic flow is essentially to divide the flight trajectories of the terminal area airspace into representative cluster structures, that is, to assign a group of similar flight trajectories to the same cluster, and the cluster is regarded as a typical traffic flow spatial pattern of the terminal area airspace.

[0003] Currently, the existing technology usually uses a density-based clustering model to process the terminal airspace data and extract the traffic flow spatial pattern of the terminal area airspace. However, the cluster structure of the density-based clustering algorithm is largely dependent on the distance metric function, so the discrimination ability in high-dimensional space is limited. At the same time, the abnormal trajectories in the terminal area airspace data also affect the extraction of the traffic flow spatial pattern of the terminal area airspace by the clustering model, resulting in poor decision-making effect for airspace management, and further causing the overall efficiency of airport operation to be reduced.

[0004] Therefore, how to provide a scheme capable of overcoming the above problems is a problem that those skilled in the art need to solve urgently. SUMMARY

[0005] The present application aims to improve the existing clustering algorithm in the prior art, which has limited discrimination ability in high-dimensional space, and the abnormal trajectories in the terminal area airspace data have a great influence on the clustering model when processing the terminal airspace data, resulting in poor decision-making effect for airspace management, and further causing the overall efficiency of airport operation to be reduced. The present application provides a terminal area airspace traffic flow spatial pattern mining method considering abnormal trajectories, comprising the following steps:

[0006] S1, obtaining flight trajectories in a historical airport terminal area airspace, and constructing an airspace description matrix T of the airport terminal area airspace after preprocessing the flight trajectories in the airport terminal area airspace;

[0007] S2, establishing a deep auto-encoding model, and extracting a normal trajectory set Y from the airspace description matrix T by using the deep auto-encoding model;

[0008] S3, extracting the airport terminal area airspace traffic flow spatial pattern of the normal trajectory set Y by using the encoder of the deep auto-encoder in cooperation with the K-means algorithm to support the decision-making of airspace management.

[0009] The step S1 of the method converts originally complex, high-dimensional, heterogeneous flight trajectory data into regular and standard numerical matrix by preprocessing and constructing a unified spatial domain description matrix T, realizes the structuring and standardization of flight trajectory data, the step S2 filters out abnormal trajectories in the spatial domain description matrix by using the encoder and decoder of the deep auto-encoding model, leaves the normal trajectory set Y for the subsequent process, so that the subsequent process is not disturbed by abnormal trajectories, and the step S3 extracts the low-dimensional representation of the normal trajectory set by using the encoder of the auto-encoding model, and then clusters the low-dimensional representation by using the K-means algorithm, thereby relieving the problem that the discrimination ability of the clustering algorithm in the traditional method is limited in high-dimensional space.

[0010] Further, the S1 specifically comprises collecting a flight trajectory data set X={F g} in an airport terminal area airspace, and obtaining an airport terminal area airspace description matrix T after normalizing the data in the airport terminal area airspace flight trajectory data set X, the spatial domain description matrix T being an n*m dimensional matrix, wherein n is the number of airport terminal area airspace flight trajectories in the spatial domain description matrix, and m is the data dimension of a single airport terminal area airspace flight trajectory.

[0011] In the above implementation process, the different physical meanings and dimensional characteristics in the flight trajectory are unified to the same scale by normalizing the data in the airport terminal area airspace flight trajectory data set X, so that the deep auto-encoding model can uniformly learn the content of all features, and an n*m dimensional spatial domain description matrix T is constructed to meet the input rules of the subsequent deep auto-encoding model.

[0012] Further, the deep auto-encoding model in the S2 specifically comprises an input layer, an encoder, a decoder and an output layer.

[0013] The encoder comprises a first Dense layer, a second Dense layer and a third Dense layer connected in sequence, and the output end of the input layer is connected to the input end of the first Dense layer.

[0014] The decoder comprises a fourth Dense layer, a fifth Dense layer and a sixth Dense layer connected in sequence, the input end of the fourth Dense layer receives the output of the third Dense layer, the output end of the fifth Dense layer is connected to the input end of the sixth Dense layer, and the output end of the sixth Dense layer is connected to the input end of the output layer.

[0015] In the above implementation, a deep structure with multiple stacked dense layers is adopted. Each layer performs non-linear processing on the output of the previous layer, enabling the model to learn complex patterns in flight trajectory data. The encoder gradually compresses the high-dimensional input into a low-dimensional representation. The low-dimensional representation preserves the most important and representative features of the high-dimensional input. When the K-means algorithm processes the low-dimensional representation, it avoids the limitation of the discrimination ability of clustering algorithms in high-dimensional space in traditional methods. The decoder receives the low-dimensional representation output by the encoder and then reconstructs the high-dimensional data. By comparing the reconstructed trajectory with the original trajectory, it is possible to measure whether the deep autoencoder model has been sufficiently learned, further improving the accuracy of subsequent spatial pattern mining models.

[0016] Furthermore, in step S2, extracting the set of normal trajectories Y from the spatial description matrix T specifically includes the following steps:

[0017] Step S2-1: When t≥1, learnable parameter vector based on the (t-1)th period. Calculate the reconstructable matrix R for the t-th period. t ;

[0018] Step S2-2: Based on the reconstructable matrix R of the t-th period t Constructing the performance function for anomaly trajectory monitoring in the t-th period The performance function of the abnormal trajectory monitoring is used to determine whether the learnable parameter vector θ should be saved. t and the non-reconstructable matrix N opt ;

[0019] Step S2-3: Based on the non-reconstructable matrix N saved in step S2-2 opt Extract the set of normal trajectories Y.

[0020] In the above implementation process, the optimal learnable parameter vector, reconstructable matrix, and non-reconstructable matrix are gradually found by updating the learnable parameter vector, reconstructable matrix, and non-reconstructable matrix in each cycle. A first convergence threshold is set to determine whether to save the current learnable parameter vector and non-reconstructable matrix in a timely manner. After obtaining the non-reconstructable matrix, the normal trajectory set Y is extracted from the spatial description matrix T using the zero vector judgment process for subsequent training, while abnormal trajectories are discarded. This method can simply and effectively remove abnormal trajectories from the spatial description matrix, avoiding the impact of abnormal trajectories on the clustering model when processing terminal spatial data.

[0021] Further, step S2-1 specifically includes:

[0022] When t≥1, based on the (t-1)th period And reconstructable matrix Rt-1 Calculate the learnable parameter vector for the t-th period ,as follows:

[0023]

[0024] Where α is the first learning rate, 0 < α ≤ 0.1, R is a reconstructable matrix in the (t-1)th period. t-1 The encoder error accumulation function is calculated as follows:

[0025]

[0026] in, Let be the learnable parameter vector of the encoder in the (t-1)th cycle, and let be the encoder equipped with the learnable parameter vector in the (t-1)th cycle. ;

[0027] R is a reconstructable matrix in the (t-1)th period. t-1 The decoder error accumulation function is calculated as follows:

[0028]

[0029] in, Represents the learnable parameter vector carried in the (t-1)th cycle. The decoder, R t-1 Represents the reconstructable matrix of the (t-1)th period;

[0030] Using the learnable parameter vector of the t-th cycle The deep autoencoder model calculates the reconstructable matrix R for the (t-1)th period. t-1 Reconstruction results for the t-th cycle:

[0031]

[0032] Using the reconstruction result S of the t-th cycle t The intermediate matrix M of the t-th period is calculated using the spatial description matrix T. t as follows:

[0033]

[0034] Using M t For the (t-1)th period, the non-reconstructable matrix N t-1 The update yields the non-reconstructable matrix N for the t-th period. t as follows:

[0035]

[0036] wherein, is a near-epoch gradient descent learning rate, ; is the non-reconstructable matrix N t of the i-th row and r-th column in the matrix N is the intermediate matrix M t of the i-th row and r-th column in the matrix M

[0037] calculates the reconstructable matrix R t of the t-th cycle using the spatial domain description matrix T, and the calculation method is as follows:

[0038]

[0039] wherein, N t is the non-reconstructable matrix of the t-th cycle, and R t is the reconstructable matrix of the t-th cycle.

[0040] In the above implementation process, by simultaneously iterating and optimizing the learnable parameter vector and the reconstructable matrix, the updated learnable parameter vector is obtained by using the gradient descent method in each cycle using the learnable parameter vector and the reconstructable matrix of the previous cycle, and then the non-reconstructable matrix and the reconstructable matrix are calculated using the deep self-encoding model carrying the updated learnable parameter vector. This updating method using gradient descent can avoid large fluctuations in parameter updating during learning, and is conducive to converging to a good non-reconstructable matrix and a deep self-encoding model with better robustness.

[0041] Further, the step S2-2 comprises the following steps:

[0042] constructs the anomaly trajectory detection performance function of the t-th cycle is represented as:

[0043]

[0044] wherein, N t is the non-reconstructable matrix of the t-th cycle; is the element of the i-th row and r-th column in the non-reconstructable matrix, r=1,...,m and i=1,...,n; β represents the performance weight; represents the L2,1 norm of N t ;

[0045] a first convergence threshold is given, if , the learnable parameter vector of the t-th cycle is saved as is recorded as , and the non-reconstructable matrix Nt denoted as N opt .

[0046] In the above implementation process, the abnormal trajectory monitoring performance function is composed of and , wherein measures the reconstruction error of the deep auto-encoding model with the learnable parameter vector in the t-th period on the reconstructible matrix in the t-th period, and minimizes , that is, the deep auto-encoding model is forced to continuously improve the reconstruction capability, and is used to measure the sparsity of the non-reconstructible matrix, and minimizes , so that the non-reconstructible matrix is more sparse, that is, the screening of the abnormal trajectory is more reasonable, and the function optimizes the learning effect of the model and ensures that the abnormal value is not detected too much. By introducing the first convergence threshold , and judging the change amount of the abnormal trajectory monitoring performance function of the two consecutive periods, when the change is less than the threshold, the training is stopped, which can effectively avoid the model convergence problem caused by premature stopping and the overfitting problem caused by late stopping.

[0047] Further, the step S2-3 extracts the normal trajectory set Y, specifically:

[0048] whether each row vector of the non-reconstructible matrix N opt is a zero vector, if the i-th row of the non-reconstructible matrix N opt is a zero vector, the i-th row flight trajectory in the spatial domain description matrix T is added to the normal trajectory set Y, and the formula is represented as:

[0049]

[0050] wherein, i=1,...,n; T(i,:) represents the flight trajectory of the i-th row in the spatial domain description matrix T; represents any i value; ||N opt (i,:)||2 represents that the i-th row of N opt is a zero vector.

[0051] In the above implementation process, whether the row vector N opt of the non-reconstructible matrix is a zero vector can directly judge whether the spatial domain description matrix is an abnormal trajectory in the row corresponding to the non-reconstructible matrix, and such a way has higher computational efficiency compared to additional training of a classifier.

[0052] Further, the step S3 includes the following steps:

[0053] Sq1, when When ≥1, based on the first Each cycle Calculate the first Cluster allocation results for each cycle ;

[0054] Sq2, using the Cluster allocation results for each cycle With the Cluster allocation results for each cycle When comparing, Then the first Cluster allocation results for each cycle Preserving the spatial pattern of airspace traffic flow in the airport terminal area is crucial; otherwise, it would... And continue with step Sq1.

[0055] In the above implementation process, the iteration stops when the cluster allocation results of two consecutive iteration cycles, namely g and g-1, are completely consistent. This method is more direct and reliable than setting the number of iterations or observing the loss function curve.

[0056] Further, step Sq1 specifically includes:

[0057] when At that time, using the first Each cycle and cluster center set Calculate the first Each cycle and cluster center set :

[0058]

[0059] Where j = 1, 2, ..., c; As the second learning rate, ; ;

[0060] Using the first Learnable parameter vector for each period After updating the learnable parameters in the deep autoencoder model, the encoder updated in the i-th cycle is obtained. The extracted i-th... The set of low-dimensional representation vectors of the normal trajectory set Y with each period :

[0061]

[0062] Where k = 1, 2, ..., v, and v is the number of elements in the normal trajectory set Y;

[0063] Calculate the first Low-dimensional representation vector of normal trajectory set of the i-th period Belonging to the j-th Period clustering center Probability of belonging to the cluster :

[0064]

[0065] wherein, represents the square of the Euclidean distance of and ;

[0066] Calculate the low-dimensional representation vector of the normal trajectory set of the i-th period using the probability : Belonging to the j-th Period clustering center Target probability of belonging to the cluster :

[0067]

[0068] KL divergence defines a distance metric function :

[0069]

[0070] Calculate the cluster assignment result of the i-th period based on and : :

[0071]

[0072] wherein, represents the Euclidean distance of and .

[0073] In the above implementation process, the encoder is initialized by using the optimized learnable parameter vector, and the initial low-dimensional representation of the normal trajectory set Y is extracted by using the encoder, and the low-dimensional representation is sent into the K-means algorithm to obtain the initial clustering center, which alleviates the problem that the discrimination ability of the clustering algorithm in the traditional method is limited in high-dimensional space. After the initial clustering center is extracted, the KL divergence calculated by the distribution probability and the target probability constitutes the loss , and the clustering center and the learnable parameter vector of the deep autoencoder are updated simultaneously using the gradient descent method according to the loss, so that the final feature mode and the clustering mode reach a high degree of optimality.

[0074] ​​In summary, compared with the prior art, the beneficial effects of the present invention are as follows: The present invention constructs an airspace description matrix T (high-dimensional information) of the airport terminal area by preprocessing the historical terminal area airspace flight trajectories of the airport, and then maps the airspace description matrix into low-dimensional information through the encoder of a deep autoencoder model. The low-dimensional information is then decoded. Reconstruction is the result of reconstruction S t (High-dimensional information), using the reconstruction result S t Multi-period iterative removal of abnormal trajectories from the spatial description matrix, feeding only the set of normal trajectories into subsequent calculations, not only preserves the spatial characteristics of the original data using high-dimensional information, but also minimizes the impact of abnormal trajectories on the terminal spatial data clustering results, thus utilizing the low-dimensional information... Clustering is performed to avoid the impact of high-dimensional information on the discrimination ability of the clustering model, thus ensuring the clustering effect of the clustering model, improving the support of the spatial pattern of airspace traffic flow in the terminal area for airspace management decisions, and thereby improving the overall efficiency of airport operations. Attached Figure Description

[0075] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0076] Figure 1 This is a flowchart illustrating a method for mining spatial patterns of terminal area airspace traffic flow that considers abnormal trajectories, as described in the embodiments.

[0077] Figure 2 This is a structural diagram of the deep autoencoder model in a terminal area airspace traffic flow spatial pattern mining method that considers abnormal trajectories, as described in the embodiment. Detailed Implementation

[0078] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0079] It should be noted that similar reference numerals and letters refer to like items throughout the accompanying drawings, and once an item is defined in one drawing, it is not necessary to further define and explain it in the subsequent drawings. Also, in the description of the present application, the terms "first", "second", and the like are used only to distinguish different descriptions, and cannot be understood as indicating or implying relative importance, or implying any such actual relationship or order between these entities or operations. In addition, the terms "connected", "connected", and the like can be direct connection between elements, or indirect connection via other elements.

[0080] Referring to Figure 1 , the embodiment provides a terminal area airspace traffic flow spatial pattern mining method considering abnormal trajectories, specifically including steps S1 to S3:

[0081] S1, acquire historical flight trajectories in the terminal area airspace, and construct an airspace description matrix T of the airport terminal area after preprocessing the flight trajectories in the terminal area airspace.

[0082] A one-month flight trajectory dataset X={F g} in the airport terminal area airspace is collected from an automatic dependent surveillance-broadcast (ADS-B) system, wherein g=1,...,n; n is the number of flights appearing in the airport terminal area airspace within a month; each flight trajectory F g contains 200 position points, and is specifically represented as F g ={p i,g}, wherein i=1,...,200; each position point has longitude lon, latitude lat, and height alt three-dimensional features, and is represented as , wherein represents the longitude feature of p i,g position point, represents the latitude feature of pi,g position point, represents the height feature of p i,g position point, since each flight trajectory F g contains 200 position points, and each position point has three-dimensional features, so the dimension of a flight trajectory F g is 600.

[0083] The data in the airport terminal area airspace flight trajectory dataset X is normalized to obtain the airport terminal area airspace description matrix T. It is easy to understand that a flight trajectory data F gThe dimension of the airspace description matrix T is 600, and there are n flight trajectory data in the flight trajectory dataset X. Therefore, the dimension of the obtained airspace description matrix T is n*600.

[0084] S2. Establish a deep autoencoder model and use the deep autoencoder model to extract the set of normal trajectories Y from the spatial description matrix T.

[0085] See Figure 2 The deep autoencoder model includes an input layer, an encoder, a decoder, and an output layer. The encoder includes a first Dense layer, a second Dense layer, and a third Dense layer. The input of the first Dense layer receives the output of the input layer, the output of the first Dense layer is connected to the input of the second Dense layer, and the output of the second Dense layer is connected to the input of the third Dense layer. The output dimensions of the first Dense layer, the second Dense layer, and the third Dense layer are 300, 150, and 75, respectively.

[0086] The decoder includes a fourth Dense layer, a fifth Dense layer, and a sixth Dense layer. The input of the fourth Dense layer receives the output of the third Dense layer, the output of the fourth Dense layer is connected to the fifth Dense layer, the output of the fifth Dense layer is connected to the sixth Dense layer, and the output of the sixth Dense layer is connected to the output layer. The output dimensions of the fourth Dense layer, the fifth Dense layer, and the sixth Dense layer are 150, 300, and 600, respectively.

[0087] S2-1. At the initial time (t=0), construct the initial non-reconstructable matrix N. 0 and the initial reconstructable matrix R 0 , where N 0 =0 n*600 That is, the initial non-reconstructable matrix N 0 Given an n*600 dimension zero matrix, the initial reconstructable matrix R 0 =T; Initialize the deep autoencoder model, and denote the initial learnable parameter vector of the deep autoencoder model as T. ,in, Let be the initial learnable parameter vector of the encoder, and let be the encoder carrying the initial learnable parameter vector. ; Let be the initial learnable parameter vector of the decoder, and let be the decoder carrying the initial learnable parameter vector. .

[0088] It should be noted that the initialization method for the deep autoencoder model is existing technology and is not related to the subject matter of this invention, so it will not be described in detail.

[0089] S2-2, When t≥1, based on the (t-1)th period And reconstructable matrix R t-1 Calculate the learnable parameter vector for the t-th period ,as follows:

[0090]

[0091] Where α is the first learning rate, 0 < α ≤ 0.1, R is a reconstructable matrix in the (t-1)th period. t-1 The encoder error accumulation function is calculated as follows:

[0092]

[0093] in, Let be the learnable parameter vector of the encoder in the (t-1)th cycle, and let be the encoder equipped with the learnable parameter vector in the (t-1)th cycle. .

[0094] R is a reconstructable matrix in the (t-1)th period. t-1 The decoder error accumulation function is calculated as follows:

[0095]

[0096] in, Represents the learnable parameter vector carried in the (t-1)th cycle. The decoder, R t-1 Represents the reconstructable matrix for the (t-1)th period.

[0097] It is worth mentioning that when t=1, the reconstructable matrix R of the (t-1)th period is... t-1 This is the initial reconstructable matrix R in step S3-1. 0 , for ,and for ;

[0098] As an example when the period t=1, since t=1 then t-1=0, the following calculation process is easy to understand:

[0099] Based on the initial learnable parameter vector of the t=0 period And reconstructable matrix R 0 Calculate the learnable parameter vector for the first cycle. ,as follows:

[0100]

[0101] Where α is the first learning rate, 0 < α ≤ 0.1, The reconstructable matrix R at the initial time step 0 The encoder error accumulation function is calculated as follows:

[0102]

[0103] The reconstructable matrix R at the initial time step 0 The decoder error accumulation function is calculated as follows:

[0104]

[0105] Easy to understand Represents the initial learnable parameter vector. The encoder, Represents the initial learnable parameter vector. The decoder.

[0106] As an example when the period t=2, since t=2 then t-1=1, the following calculation process is easy to understand:

[0107] Based on a period of t=1 And reconstructable matrix R 1 Calculate the learnable parameter vector for the second cycle. ,as follows:

[0108]

[0109] Where α is the first learning rate, 0 < α ≤ 0.1, The first periodic reconstructable matrix R 1 The encoder error accumulation function is calculated as follows:

[0110]

[0111] The decoder error accumulation function of the reconstructable matrix R1 in the first period The calculation method is as follows:

[0112]

[0113] in, This represents the first learnable parameter vector in the first cycle. The encoder, This represents the first learnable parameter vector in the first cycle. The decoder.

[0114] It should be noted that, as can be seen from the example, the initial non-reconstructable matrix N defined in step S3-1...0 Initial reconstructable matrix R 0 The initial learnable parameter vector of the encoder and the initial learnable parameter vector of the decoder The learnable parameter vector used at t=1 is only substituted into the calculation, while the learnable parameter vector used at t=2 is calculated at t=1.

[0115] The reconstructable matrix R of the (t-1)th period t-1 Input to the learnable parameter vector carrying the t-th cycle In the deep autoencoder model, the reconstruction result S of the t-th cycle is obtained. t The specific process is as follows:

[0116] 1) Input layer: Receives the reconstructable matrix R for the (t-1)th period. t-1 The input, where R t-1 The dimension is n*600.

[0117] 2) Encoder: The input of the first Dense layer is connected to the output of the input layer, mapping the n*600-dimensional matrix output by the input layer to an n*300-dimensional matrix;

[0118] The input of the second Dense layer is connected to the output of the first Dense layer, mapping the n*300-dimensional matrix output by the first Dense layer to an n*150-dimensional matrix.

[0119] The input of the third Dense layer is connected to the output of the second Dense layer, mapping the n*150-dimensional matrix output by the second Dense layer to an n*75-dimensional matrix;

[0120] The encoder is used to reconstruct the matrix R in the (t-1)th period. t-1 Feature extraction and dimensionality compression are performed to obtain R. t-1 The low-dimensional representation vector set Z t-1 The low-dimensional representation vector set Z t-1 It is an n*75 dimension matrix.

[0121] 3) Decoder: The input of the fourth Dense layer is connected to the output of the third Dense layer, mapping the n*75-dimensional matrix output by the third Dense layer to an n*150-dimensional matrix;

[0122] The input of the fifth Dense layer is connected to the output of the fourth Dense layer, mapping the n*150-dimensional matrix output by the fourth Dense layer to an n*300-dimensional matrix.

[0123] The input of the sixth Dense layer is connected to the output of the fifth Dense layer, mapping the n*300-dimensional matrix output by the fifth Dense layer to an n*600-dimensional matrix;

[0124] The decoder is used to process the low-dimensional representation vector set Z of the (t-1)th period output by the encoder. t-1 Reconstruction is performed to obtain the intermediate result S for the t-th period. t .

[0125] 4) Output layer: Outputs the reconstruction result S of the t-th period. t , where is an n*m dimension matrix, where n is the number of flight numbers in a month, m is the dimension of the flight trajectory feature vector, and there are a total of 600 dimensions.

[0126] The above process can be expressed by the following formula:

[0127]

[0128] Among them, the reconstruction result S of the t-th cycle t It is an n*600 dimensional matrix.

[0129] Using the reconstruction result S of the t-th cycle t The intermediate matrix M of the t-th period is calculated using the spatial description matrix T. t as follows:

[0130]

[0131] Wherein, the intermediate matrix M of the t-th period t Given an n*600 dimensional matrix, it can be understood that the spatial description matrix T is an n*600 dimensional matrix, and the reconstruction result S... t It is also an n*600 dimensional matrix, so the difference between the two is M. t It is also an n*600 dimensional matrix.

[0132] Using M t For the (t-1)th period, the non-reconstructable matrix N t-1 The update yields the non-reconstructable matrix N for the t-th period. t as follows:

[0133]

[0134] in, The learning rate for proximal gradient descent. ; N is a non-reconstructable matrix with period t. t The element in the i-th row and r-th column, M is the intermediate matrix of the t-th period. tThe element in the i-th row and r-th column, i=1,...,n; r=1,...,m and m=600.

[0135] Calculate the reconstructable matrix R for the t-th period using the spatial description matrix T. t The calculation method is as follows:

[0136]

[0137] Where, N t Let R be a non-reconstructable matrix with period t. t Let be the reconstructable matrix for the t-th period.

[0138] S2-3, Construct a performance function for abnormal trajectory monitoring.

[0139] The performance function for anomaly trajectory detection in the t-th period is expressed as:

[0140]

[0141]

[0142]

[0143] Where, N t Let be a non-reconstructable matrix in the t-th period; Let be the element in the i-th row and r-th column of the non-reconstructable matrix, where r = 1, ..., m and i = 1, ..., n, m = 600; β represents the performance weight, β = 0.1; ||N t || 2,1 Represents finding N t The L2,1 norm.

[0144] like Then let t=t+1 and continue executing steps S2-2 to S2-3, where, The first convergence threshold, ;

[0145] Otherwise, save the learnable parameter vector for the t-th period. and the non-reconstructable matrix N t They are respectively denoted as and N opt Then proceed to step S3-4, as shown in the following formula:

[0146]

[0147]

[0148]

[0149] S2-4. Based on the non-reconstructable matrix N saved in step S2-3 opt Extracting the normal trajectory set Y, specifically:

[0150] Sequentially determine the non-reconstructable matrix N opt Is each row vector a zero vector? If so, matrix N cannot be reconstructed. opt If the i-th row is the zero vector, then the flight trajectory in the i-th row of the airspace description matrix T is added to the normal trajectory set Y, as expressed by the formula:

[0151]

[0152] Where i=1,...,n; T(i,:) represents the flight trajectory in the i-th row of the airspace description matrix T; ||Nopt(i,:)||2 represents any value of i; opt The i-th row is a vector of zeros.

[0153] For example, consider the airspace description matrix of the airport terminal area. The non-reconstructable matrix of the t-th period Obviously, N t The second row of the matrix is ​​a non-zero vector, while the first and third rows are zero vectors. Therefore, the airport terminal area airspace description matrix T and the non-reconstructable matrix N are considered to be... t The flight trajectory corresponding to the non-zero vector is added to the normal trajectory set Y, then .

[0154] S3. Use the encoder of the deep autoencoder model in conjunction with the K-means algorithm to extract the spatial pattern of airspace traffic flow in the airport terminal area of ​​the normal trajectory set Y.

[0155] At the initial moment At that time, the learnable parameter vector saved in step S3-3 is used. Initialize the encoder and use the initialized encoder. Extracting the initial low-dimensional representation of the normal trajectory set Y Let Z be the set. 0 :

[0156]

[0157] Where k = 1, 2, ..., v, and v is the number of elements in the normal trajectory set Y.

[0158] The initial set of cluster centers is obtained using the K-means algorithm. :

[0159]

[0160] Where j=1,2,...,c and in this embodiment c=8, in actual application the value of c is the reference route number of the standard instrument approach map of the airport terminal area airspace; represents the initial cluster centers; Kmeans() represents the K-means algorithm.

[0161] Compute the initial low-dimensional representation Belongs to the initial cluster center probability of belonging to a cluster :

[0162]

[0163] Using probability Compute the initial low-dimensional representation Belongs to the initial cluster center Target probability of the cluster :

[0164]

[0165] Defining a distance metric function using KL divergence The calculation method is as follows:

[0166]

[0167] in accordance with Determine the initial spatial pattern extraction performance function. :

[0168]

[0169] Wherein, γ is the weight coefficient of the distance metric function. In this embodiment, γ=0.4 because the reconstruction capability of the deep autoencoder model is the key evaluation point, and 0<γ<1.

[0170] when At that time, based on the first Each cycle and cluster center set Calculate the first Each cycle and cluster center set :

[0171] Where j = 1, 2, ..., c; As the second learning rate, ; ;

[0172] Using the first Learnable parameter vector for each period After updating the learnable parameters in the deep autoencoder model, the encoder updated in the i-th cycle is obtained. The extracted i-th... The set of low-dimensional representation vectors of the normal trajectory set Y with each period :

[0173]

[0174] Where k = 1, 2, ..., v, and v is the number of elements in the normal trajectory set Y;

[0175] based on and Calculate the first Cluster allocation results for each cycle :

[0176]

[0177] in, represent and The Euclidean distance.

[0178] Using the first Cluster allocation results for each cycle With the Cluster allocation results for each cycle If a comparison is made, Then calculate the first Low-dimensional representation vector of a set of periodic normal trajectories Belongs to the Cluster centers of each period probability of belonging to a cluster :

[0179]

[0180] in, represent and The square of the Euclidean distance.

[0181] Using probability Calculate the first A low-dimensional representation vector of the set of normal trajectories in each period. Belongs to the first Periodic cluster centers Target probability of the cluster :

[0182]

[0183] KL divergence is defined as a distance metric function. :

[0184]

[0185] like Then the first Cluster allocation results for each cycle As a spatial pattern of airspace traffic flow in the terminal area, it is used to support airspace management decisions.

[0186] It should be noted that the cycle The period t is not related to each other. That is, step S3 will be executed only after step S2 is completed. In other words, step S3 will be executed only after step S2 is completed and the normal trajectory set Y is obtained. During the execution of step S3, the value of the normal trajectory set Y will not change. That is, the value of the normal trajectory set Y will remain fixed after step S2 is completed.

[0187] In the above process, an encoder network is used to transform high-dimensional trajectory data (600 dimensions, i.e., the normal trajectory set Y of the i-th period) into a low-dimensional representation vector (75 dimensions, i.e., the low-dimensional representation vector of the normal trajectory set of the i-th period). Following this, spatial pattern mining has the following advantages:

[0188] 1) Mitigating the curse of dimensionality: Low-dimensional representation is data with redundant information removed, mapping trajectory data to a more compact space, reducing the difficulty of spatial pattern mining models, and suppressing the risk of overfitting.

[0189] 2) Low-dimensional representation can reduce the computational cost of spatial learning models, making spatial pattern mining models easier to deploy on resource-constrained devices.

[0190] 3) Raw high-dimensional trajectory data often contains noise or redundant information. By learning the inherent structure of the data, noise and redundancy can be filtered out, thereby enhancing the robustness and generalization ability of the data features.

[0191] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for mining spatial patterns of terminal area traffic flow considering abnormal trajectories, characterized in that, The method comprises the following steps: S1, obtaining historical flight trajectories in an airport terminal airspace, and constructing an airspace description matrix T of the airport terminal airspace after preprocessing the flight trajectories in the airport terminal airspace; S2, establishing a deep auto-encoding model, and extracting a normal trajectory set Y from the airspace description matrix T by using the deep auto-encoding model; The deep auto-encoding model in S2 comprises an input layer, an encoder, a decoder and an output layer; The encoder comprises a first Dense layer, a second Dense layer and a third Dense layer connected in sequence, and an output end of the input layer is connected to an input end of the first Dense layer; The decoder comprises a fourth Dense layer, a fifth Dense layer and a sixth Dense layer connected in sequence, an input end of the fourth Dense layer receives an output of the third Dense layer, an output end of the fifth Dense layer is connected to an input end of the sixth Dense layer, and an output end of the sixth Dense layer is connected to an input end of the output layer; In S2, the normal trajectory set Y is extracted from the airspace description matrix T, and the extraction specifically comprises the following steps: Step S2-1, when t≥1, based on the learnable parameter vector of the (t-1)th period computing the reconstructable matrix R of the tth period t ; Step S2-2, reconstructing the matrix R based on the tth cycle t Constructing a performance function for the tth cycle anomaly trajectory monitoring Using the performance function of the anomaly trajectory monitoring to determine whether to save the learnable parameter vector θ t and the non-reconstructable matrix N t If saved, the non-reconstructable matrix N t is denoted as N opt , θ t is denoted as θ opt ; Step S2-3, based on the non-reconstructable matrix N saved in step S2-2 opt extracting a normal trajectory set Y; S3, extracting an airport terminal airspace traffic flow spatial pattern of the normal trajectory set Y by using the encoder of the deep auto-encoder and cooperating with a K-means algorithm to support decision-making of airspace management.

2. The method of claim 1, wherein the method comprises: The S1 is specifically collecting flight trajectory data set X={F g} in the airport terminal airspace, and obtaining an airport terminal airspace description matrix T after normalizing the data in the airport terminal airspace flight trajectory data set X. The airspace description matrix T is an n*m-dimensional matrix, where n is the number of airport terminal airspace flight trajectories in the airspace description matrix, and m is the data dimension of a single airport terminal airspace flight trajectory.

3. The method of claim 1, wherein the method further comprises: The step S2-1 is specifically: At t≥1, based on the (t−1)th cycle and the reconstructable matrix R t-1 computing the learnable parameter vector of the tth cycle as follows: wherein a is a first learning rate, 0 < a < 0.1, Rt-1is the reconstructable matrix R of the t-1th cycle t-1 The encoder error accumulation function of the following formula is calculated: wherein, is the vector of learnable parameters of the encoder at the t-1th cycle, and the encoder with the vector of learnable parameters of the t-1th cycle is denoted as ; Rt-1, the reconstructable matrix for the t-1th cycle t-1 decoder error accumulation function, calculated as follows: wherein, represents a decoder of the learnable parameter vector of the t-1th cycle R t-1 represents a reconstructable matrix of the t-1th cycle; using a deep auto-encoding model with learnable parameter vector of the t-1th cycle t-1 reconstruction result of the tth cycle using the reconstruction result S of the t-th cycle t and the spatial domain description matrix T to calculate an intermediate matrix M of the t-th cycle t as follows: M t Nt-1= Nt-2- M t-1 Nt= Nt-1- M t Nt= Nt-1- M wherein, is a near-end gradient descent learning rate, ; is the non-reconstructable matrix N of the t-th cycle t is the element in the i-th row and r-th column of the matrix N, is the intermediate matrix M of the t-th cycle t is the element in the i-th row and r-th column of the matrix M, i = 1,..., n; r = 1,..., m; The reconstructable matrix R of the tth cycle is calculated using the spatial description matrix T t in the following way: where N t is the non-reconstructable matrix for the tth cycle, R t is the reconstructable matrix for the tth cycle.

4. The method of claim 3, wherein the method further comprises: The step S2-2 comprises the following steps: Constructing the anomaly trajectory detection performance function for the tth cycle is expressed as: where N t is the non-reconstructable matrix for the tth cycle; is the element of the non-reconstructable matrix in the ith row and rth column, r = 1,..., m and i = 1,..., n; β represents the performance weight; represents the L2,1 norm of N t ; Given a first convergence threshold , if , save the learnable parameter vector of the t-th cycle denoted by , save the non-reconstructable matrix N of the t-th cycle t denoted by N opt .

5. The method of claim 4, wherein the method further comprises: In the step S2-3, the normal trajectory set Y is extracted, and the extraction is specifically: In succession, it is judged whether each row vector of the non-reconstructable matrix N opt is a zero vector. If the i-th row of the non-reconstructable matrix N opt is a zero vector, the i-th row flight trajectory in the spatial description matrix T is added to the normal trajectory set Y, which is expressed by the following formula: where i = 1,..., n; T(i, :) represents the flight trajectory of the i-th row of the spatial domain description matrix T; represents any take one i value; ||N opt (i, :) represents the flight trajectory of the i-th row of the spatial domain description matrix T; opt the i-th row of the spatial domain description matrix T is a zero vector.

6. The method of claim 5, wherein the method further comprises: The step S3 comprises the following steps: Sq1, when At that time, based on the first Each cycle Calculate the first Cluster allocation results for each cycle ; Sq2, using the Cluster allocation results for each cycle With the Cluster allocation results for each cycle When comparing, Then the first Cluster allocation results for each cycle Preserving the spatial pattern of airspace traffic flow in the airport terminal area is crucial; otherwise, it would... And continue with step Sq1.

7. The method of claim 6, wherein the method further comprises: The step Sq1 is specifically: When the first set of and cluster centers for the first set of and cluster centers is calculated: wherein j = 1, 2,..., c; is a second learning rate, ; ; γ is a weight coefficient of the distance metric function; using the updated low-dimensional representation vector set Y of the normal trajectory set Y of the first cycle the updated low-dimensional representation vector set Y of the normal trajectory set Y of the first cycle the updated low-dimensional representation vector set Y of the normal trajectory set Y of the first cycle the updated low-dimensional representation vector set Y of the normal trajectory set Y of the first cycle the updated low-dimensional representation vector set Y of the normal trajectory set Y of the first cycle wherein k = 1, 2, …, v, and v is the number of elements in the normal trajectory set Y. Compute the low-dimensional representation vectors for the set of normal trajectories of the period belonging to the cluster center of the period : wherein representing and the square of the Euclidean distance of Utilizing probabilities Computing a low-dimensional representation vector of the normal trajectory set for the period Belonging to the period cluster center Target probability of the cluster to which it belongs : KL divergence defines a distance metric function : Based on and calculating the cluster allocation result of the period : wherein representing and Euclidean distance.

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