Flight path analysis method and system fusing frequency domain features and multi-dimensional evaluation indexes

Abstract

The invention discloses a flight path analysis method and system fusing frequency domain features and multi-dimensional evaluation indexes. The method comprises the following steps: performing abnormal flight number filtering on flight path data acquired by a flight path data acquisition device; second track data are obtained through fast Fourier transform, and high-frequency energy features and peak frequency features are extracted; through a unified standardization processing method, target track data needing to be analyzed is screened out; adaptively determining an interval in which the optimal clustering cluster number is located; traversing each clustering cluster number in the interval, determining an optimal clustering cluster number K according to the contour coefficient and the Devens-Pall index, and performing clustering analysis through a K-Means + + algorithm according to the optimal clustering cluster number K; and carrying out visual display on a clustering analysis result of the target track data. The method can provide a theoretical reference for the clustering analysis of the arrival and departure tracks of the aircrafts in the terminal area through the analysis method fusing the frequency domain features and the multi-dimensional evaluation indexes, enables the optimization result to fit the reality, and has the practical application potential.

Description

Technical Field

[0001] The present invention relates to the technical field of air traffic management, and in particular to a track analysis method and system integrating frequency domain features with multi-dimensional evaluation indicators. Background Art

[0002] With the rapid development of my country's civil aviation industry, the flight density of route transport aircraft in the airspace has increased rapidly, and the continuous growth of flight traffic has made the terminal airspace a prone area for airspace congestion, flight delays and flight accidents. In this context, a variety of terminal area aircraft track analysis technologies have emerged, which aims to optimize the layout of air traffic networks and improve the smoothness and safety of air traffic through data mining and analysis. Aircraft track analysis technology assists air traffic controllers in monitoring the flight trajectory of aircraft by depicting the movement of aircraft in the air, and promptly discovers and handles potential abnormal tracks and flight conflicts.

[0003] However, traditional clustering methods, such as HDBSCAN and spectral clustering, mostly rely on single time-domain feature information, which is time-consuming to calculate and has unsatisfactory results. In addition, the flight trajectories collected in the terminal area have complex characteristics such as large data volume, strong time series, and high anomaly rate, so they have certain limitations in processing.

[0004] Therefore, people in this field are in urgent need of finding a new technical solution to solve the above problems. Summary of the invention

[0005] In order to overcome the problems existing in the related art, the present invention discloses a track analysis method and system which integrates frequency domain features and multi-dimensional evaluation indicators.

[0006] According to a first aspect of the disclosed embodiments of the present invention, a track analysis method integrating frequency domain features and multi-dimensional evaluation indicators is provided, the method comprising:

[0007] Filtering the track data collected by the track data acquisition device for abnormal flight numbers to obtain filtered first track data, where the first track data is arranged in time sequence;

[0008] traversing the first track data by fast Fourier transform, performing frequency domain conversion on the first track data, acquiring second track data, and extracting high-frequency energy features and peak frequency features in the second track data;

[0009] Through a unified and standardized processing method, the target track data required for analysis is screened out from the high-frequency energy characteristics and peak frequency characteristics;

[0010] Adaptively determine the interval where the optimal number of clusters is located according to the number of label data in the target track data;

[0011] By traversing each cluster number in the interval through a fusion traversal algorithm, an optimal cluster number K is determined according to a silhouette coefficient and a Davis-Balding index, so as to perform cluster analysis on the target track data through a K-Means++ algorithm according to the optimal cluster number K;

[0012] The cluster analysis results of the target track data are visualized.

[0013] Optionally, filtering the track data collected by the track data acquisition device for abnormal flight numbers to obtain the filtered first track data includes:

[0014] For the flight number corresponding to each track node in the track data, extract the flight number and the corresponding feature label data;

[0015] Fill the flight number and the corresponding feature label into the created empty dictionary;

[0016] After the empty dictionary is filled, the number of label data corresponding to the flight number in the filled dictionary is detected by a dictionary search algorithm;

[0017] If the number of the tag data is greater than 1, the flight number is determined to be an abnormal flight number;

[0018] Abnormal flight numbers in the track data are filtered to obtain first track data.

[0019] Optionally, traversing the first track data by fast Fourier transform, performing frequency domain conversion on the first track data, acquiring second track data, and extracting high-frequency energy features and peak frequency features in the second track data include:

[0020] The first track data is traversed by fast Fourier transform is the sequence length of the first track data;

[0021] Perform frequency domain conversion on the first track data to obtain second track data It can be expressed by the following formula:

[0022]

[0023]

[0024] in, is the first frequency components, is an imaginary unit, From 0 to The frequency index of is the FFT result of an even-indexed vector, is the FFT result of the odd-indexed vector, is the rotation factor in FFT;

[0025] Extract the high-frequency energy feature in the second track data, the high-frequency energy feature ε high It can be expressed by the following formula:

[0026]

[0027] in, and are the lower and upper limit indices of the high frequency cutoff frequency respectively;

[0028] Extract the peak frequency feature in the second track data, the peak frequency feature It can be expressed by the following formula:

[0029]

[0030] in, yes Maximum value index, is the sampling frequency.

[0031] Optionally, the target track data required for analysis is screened out from the high-frequency energy features and the peak frequency features by a unified standardized processing method, including:

[0032] Based on the combination of the high-frequency energy features and the combination of the peak frequency features, calculating the mean and standard deviation of the features in each combination;

[0033] For each feature, the difference is obtained by subtracting the mean corresponding to the feature from the feature, and then the difference is divided by the standard deviation corresponding to the feature to obtain the quotient, so as to obtain the target track data filtered out from the high-frequency energy features and peak frequency features according to the quotient corresponding to each feature.

[0034] Optionally, the traversing each cluster number in the interval by a fusion traversal algorithm and determining the optimal cluster number K according to the silhouette coefficient and the Davis-Balding index includes:

[0035] Traverse each cluster number in the region, and calculate the silhouette coefficient and Davis-Baulding index of each cluster number, wherein the silhouette coefficient SC is represented by the following formula:

[0036]

[0037] in, SC(n) represents the silhouette coefficient of data point n, SC(n)∈[-1,1], represents the average distance from data point n to other data points in the same cluster, It represents the minimum value of the average distance from data point n to all data points in other clusters, M is the number of clusters,

[0038] The Davis-Balding Index DBI is represented by the following formula:

[0039]

[0040] in, represents the average distance from the data point in each cluster k to the cluster center, Represents the distance between different clusters k and m, represents the spread of each cluster k, It represents the maximum value of the dispersion of cluster k and all other clusters m, and M represents the number of clusters;

[0041] A weighted score is calculated according to the silhouette coefficient and the Davis-Baulding index to determine the optimal number of clusters K according to the weighted score, wherein the weighted score WS is represented by the following formula:

[0042] WS = ω1*SC-ω2*DBI,

[0043] Among them, ω1+ω2=1,ω1,ω2>0.

[0044] Optionally, the method further includes:

[0045] The effect of cluster analysis was evaluated by adjusted Rand coefficient and normalized mutual information.

[0046] Optionally, the visual display of the cluster analysis result of the target track data includes:

[0047] The cluster analysis results of the target track data are visualized in terms of visual changes, the number of tracks in each cluster, and the track plane and spatial distribution of each cluster.

[0048] According to a second aspect of the disclosed embodiment of the present invention, a track analysis system integrating frequency domain features and multi-dimensional evaluation indicators is provided, the system comprising:

[0049] An abnormal flight number filtering module filters the track data collected by the track data acquisition device for abnormal flight numbers, and obtains filtered first track data, where the first track data is arranged in time sequence;

[0050] a frequency domain conversion module, connected to the abnormal flight number filtering module, traversing the first track data through fast Fourier transform, performing frequency domain conversion on the first track data, acquiring second track data, and extracting high-frequency energy features and peak frequency features in the second track data;

[0051] A track data screening module is connected to the frequency domain conversion module, and screens target track data required for analysis from high-frequency energy features and peak frequency features through a unified standardized processing method;

[0052] An optimal cluster number determination module is connected to the track data screening module and adaptively determines the interval of the optimal cluster number according to the number of label data in the target track data;

[0053] A cluster analysis module is connected to the optimal cluster number determination module, and traverses each cluster number in the interval through a fusion traversal algorithm, and determines the optimal cluster number K according to the silhouette coefficient and the Davis-Balding index, so as to perform cluster analysis on the target track data through the K-Means++ algorithm according to the optimal cluster number K;

[0054] The visualization display module is connected to the cluster analysis module and performs visualization on the cluster analysis results of the target track data.

[0055] Optionally, the abnormal flight number filtering module includes:

[0056] A label data extraction unit, for extracting the flight number and corresponding feature label data corresponding to each track node in the track data;

[0057] An empty dictionary filling unit, connected to the label data extraction unit, fills the flight number and the corresponding feature label into the created empty dictionary;

[0058] A dictionary search unit, connected to the empty dictionary filling unit, detects the number of label data corresponding to the flight number in the filled dictionary through a dictionary search algorithm after the empty dictionary is filled;

[0059] an abnormal flight number determination unit, connected to the dictionary search unit, and determining the flight number as an abnormal flight number if the number of the tag data is greater than 1;

[0060] The abnormal flight number filtering unit is connected to the abnormal flight number determining unit, and filters the abnormal flight numbers in the track data to obtain the first track data.

[0061] Optionally, the track data screening module includes:

[0062] A mean standard deviation calculation unit, which calculates the mean and standard deviation of the features in each combination based on the combination of high-frequency energy features and the combination of peak frequency features;

[0063] The track data screening unit is connected to the mean standard deviation calculation unit. For each feature, the difference is obtained by subtracting the mean corresponding to the feature from the feature, and then the difference is divided by the standard deviation corresponding to the feature to obtain the quotient. According to the quotient corresponding to each feature, the target track data screened out from the high-frequency energy feature and the peak frequency feature is obtained.

[0064] In summary, the technical solution disclosed in the present invention can bring the following beneficial effects:

[0065] (1) The terminal area track analysis method that integrates frequency domain characteristics and multi-dimensional evaluation indicators can provide a theoretical reference for the cluster analysis of the arrival and departure tracks of aircraft in the terminal area. The frequency domain characteristics of the aircraft flight track are taken into account, making the optimization results more realistic and more potential for practical application.

[0066] (2) Frequency domain analysis can more accurately reflect the periodic characteristics contained in the track, providing richer information for track feature analysis, thereby optimizing the accuracy and efficiency of the analysis;

[0067] (3) It can clearly distinguish and reflect the flight trajectories in all directions, and can efficiently identify abnormal trajectories, showing a high clustering effect and credibility.

[0068] Other features and advantages disclosed in the present invention will be described in detail in the following detailed description. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] The accompanying drawings are used to provide a further understanding of the present disclosure and constitute a part of the specification. Together with the following specific embodiments, they are used to explain the present disclosure but do not constitute a limitation of the present disclosure. In the accompanying drawings:

[0070] Figure 1 It is a flowchart of a track analysis method based on the fusion of frequency domain features and multi-dimensional evaluation indicators;

[0071] Figure 2 A schematic diagram of the principle diagram of track data acquisition and collection;

[0072] Figure 3 Schematic diagram of searching and mapping of track data labels and filtering of abnormal flight numbers;

[0073] Figure 4 It is a schematic diagram of adaptive re-clustering analysis for multi-dimensional attribute tracks;

[0074] Figure 5A structural diagram showing the multi-level visualization of the terminal area track clustering results;

[0075] Figure 6 is a graph showing how the silhouette coefficient and the Davis-Balding index vary with the number of clusters in the example;

[0076] Figure 7 is a distribution diagram of the number of tracks contained in each cluster in the example;

[0077] Figure 8 It is a two-dimensional plane display diagram of some track clusters in the example;

[0078] Fig. 9 A three-dimensional display diagram of some track clusters in the example;

[0079] Fig.10 is a structural block diagram of a track analysis system integrating frequency domain features and multi-dimensional evaluation indicators according to an exemplary embodiment;

[0080] Fig.11 is based on Fig.10 A structural block diagram of an abnormal flight number filtering module is shown;

[0081] Fig.12 is based on Fig.10 A structural block diagram of a track data screening module is shown. DETAILED DESCRIPTION

[0082] The specific embodiments disclosed in the present invention are described in detail below in conjunction with the accompanying drawings. It should be understood that the specific embodiments described herein are only used to illustrate and explain the present disclosure, and are not used to limit the present disclosure.

[0083] Figure 1 It is a flow chart of a track analysis method that integrates frequency domain features and multi-dimensional evaluation indicators, such as Figure 1 As shown, the method includes:

[0084] In step 101, the track data collected by the track data acquisition device is filtered for abnormal flight numbers to obtain the filtered first track data.

[0085] The first track data is arranged in time sequence.

[0086] For example, Figure 2 As shown, the first track data arranged in time series is collected and input through the data acquisition device. The track data consists of a large number of time-series track nodes. Each track node contains multi-dimensional attributes, such as "flight number", "x-coordinate", "y-coordinate", "z-coordinate", "timestamp", etc. The multi-dimensional attributes of the track node constitute the track vector of this track node.

[0087] Specifically, for the flight number corresponding to each track node in the track data, extract the flight number and the corresponding feature label data; fill the flight number and the corresponding feature label into the created empty dictionary; after the empty dictionary is filled, detect the number of label data corresponding to the flight number in the filled dictionary through a dictionary search algorithm; if the number of label data is greater than 1, determine the flight number as an abnormal flight number; filter the abnormal flight numbers in the track data to obtain the first track data.

[0088] For example, Figure 3 As shown, a label search mapping is performed on the track data, and a dictionary search algorithm is used in the disclosed embodiment of the present invention to filter abnormal flight numbers. The multidimensional attributes of the track node constitute the track vector of this track node, and each flight number has a number of characteristic label data. Check whether there is a label in the first track data. If so, create an "empty dictionary" to store the label list corresponding to each flight number. A label search mapping is performed on the first track data, that is, for each track data, the current flight number and its label data are extracted, and the label corresponding to this flight number is filled into the empty dictionary, and the corresponding result is output (it should be noted that when a label is detected, the data is the verification set data; when it is detected that there is no label, the data is the training set data, that is, the input data can be automatically judged as training set data or verification set data through the disclosed embodiment of the present invention). A dictionary search algorithm is used to filter abnormal flight numbers. That is, after the empty dictionary is filled, the dictionary search algorithm is used to check the number of tags held by all the track data in the dictionary. If the number of tags held is greater than 1, the track data is determined as an abnormal flight number that needs to be filtered. The above method can extract all non-abnormal flight numbers from the original data for filtering.

[0089] In step 102, the first track data is traversed by fast Fourier transform, the first track data is converted into a frequency domain, the second track data is obtained, and the high-frequency energy characteristics and peak frequency characteristics in the second track data are extracted.

[0090] Specifically, the first track data is traversed by fast Fourier transform is the sequence length of the first track data; the first track data is converted into the frequency domain to obtain the second track data It can be expressed by the following formula:

[0091]

[0092] in, is the first frequency components, is an imaginary unit, From 0 to The frequency index of is the FFT result of an even-indexed vector, is the FFT result of the odd-indexed vector, is the rotation factor in FFT; extract the high-frequency energy feature in the second track data, the high-frequency energy feature ε high It can be expressed by the following formula:

[0093]

[0094] in, and are the lower and upper limit indices of the high frequency cutoff frequency respectively;

[0095] Extract the peak frequency feature in the second track data, the peak frequency feature It can be expressed by the following formula:

[0096]

[0097] in, yes Maximum value index, is the sampling frequency.

[0098] For example, the second track data after filtering abnormal flight numbers is processed by the Fast Fourier Transform (FFT) method, the time domain data is converted into frequency domain data, and the frequency domain features in all directions are extracted. In the disclosed embodiment of the present invention, all filtered track data are automatically traversed, and the FFT method is applied to the multi-dimensional attributes of each second track data to perform a unified frequency domain conversion, and then the high-frequency energy characteristics and peak frequency characteristics of the data points in the three spatial dimensions of "x, y, z" are extracted to construct feature vectors. The fast Fourier transform technology is introduced to utilize its unique advantages in frequency domain analysis, such as reducing noise interference, capturing subtle differences, reducing computational complexity and enhancing the robustness of the algorithm, in order to break through the limitations of existing track analysis methods.

[0099] It should be noted that DFT (Discrete Fourier Transform, referred to as DFT) is a mathematical tool that converts signals from time domain to frequency domain, which can analyze the frequency components of signals. FFT is an algorithm that efficiently calculates discrete Fourier transform and its inverse transform. The emergence of FFT algorithm has greatly improved the calculation efficiency of DFT, making it possible to quickly perform frequency domain analysis in practical applications.

[0100] The basic principle of the DFT algorithm is: for a length of sequence Its DFT is:

[0101]

[0102] in, is the first frequency components, is an imaginary unit, is the frequency index (from 0 to ).

[0103] The basic principle of FFT algorithm is to reduce the computational complexity of DFT from Reduce to The specific implementation of the Cooley-Tukey-based track vector FFT divide-and-conquer algorithm is shown in Table 1:

[0104] Table 1 FT divide-and-conquer algorithm flow for track vectors

[0105]

[0106] FFT reduces the number of multiplications and additions by using butterfly operations. Butterfly operations are a specific type of complex multiplication and addition operations that combine the results of two smaller DFTs to construct a larger DFT. The FFT result of the sequence By combining the length The FFT results of the two subsequences are:

[0107]

[0108] in, is the FFT result of an even-indexed vector, is the FFT result of the odd-indexed vector, are the rotation factors in the FFT.

[0109] For example, in the flight trajectory of an aircraft, high-frequency components are often associated with rapidly changing motion characteristics, such as sudden turns, acceleration or deceleration, etc. These characteristics are crucial to understanding the dynamic behavior of the aircraft; peak frequencies can indicate major vibration or motion patterns, helping to identify specific flight modes or abnormal behaviors.

[0110] High-frequency energy usually refers to the sum of the energy of the signal in the high-frequency part. In the frequency domain, the energy of the signal can be obtained by calculating the square of the modulus of the FFT result. If It's a signal The FFT result of the signal is The energy of the frequency component in It is The magnitude of the frequency components. and They are the lower and upper limit indexes of the high frequency cutoff frequency respectively, and in the actual calculation process, only the sum of the frequency energy of the part with an absolute value of the frequency greater than 0.1 is calculated.

[0111] The peak frequency refers to the frequency component with the largest signal energy. In the FFT result, the peak frequency corresponds to the index of the frequency component with the largest energy. Its peak frequency Indicates that the The largest The actual value of the peak frequency can be obtained by passing the index Convert to actual frequency to get. is the sampling frequency, is the number of FFT points, then The actual frequency of the frequency component

[0112] In step 103, the target track data required for analysis is screened out from the high-frequency energy features and the peak frequency features through a unified standardization processing method.

[0113] Specifically, based on the combination of the high-frequency energy features and the combination of the peak frequency features, the mean and standard deviation of the features in each combination are calculated; for each feature, the difference is obtained by subtracting the mean corresponding to the feature, and then the difference is divided by the standard deviation corresponding to the feature to obtain the quotient, so as to obtain the target track data filtered out from the high-frequency energy features and the peak frequency features according to the quotient corresponding to each feature.

[0114] Enter and select feature data for cluster analysis. First, select the multidimensional frequency domain features that need cluster analysis, and filter out the frequency domain feature quantities that need to be analyzed from the peak frequency and high-frequency energy to further analyze the terminal area track characteristics under different problem scenarios. Then the selected multidimensional frequency domain features need to be standardized, that is, based on the above selected feature quantity combination, calculate the mean and standard deviation of each feature quantity. For each value in each feature quantity, subtract the mean of its feature quantity from the value, and then divide it by the standard deviation of the feature quantity. The data processed in this way will have a mean of 0 and a unit standard deviation, realizing the standardization of features. The standardization of multidimensional frequency domain feature quantities facilitates the calculation and comparison of subsequent multidimensional evaluation indicators.

[0115] In step 104, the interval of the optimal number of clusters is adaptively determined according to the number of label data in the target track data.

[0116] For example, if a large amount of track data is to be clustered, the optimal number of track clusters needs to be determined. According to the number of labels of the track data (validation set data), the interval of the optimal number of clusters K is adaptively determined to facilitate subsequent track clustering analysis.

[0117] like Figure 4 As shown in the figure, the interval to which the number of clusters of track clustering belongs is adaptively determined, and the optimal number of clusters is found by integrating the traversal algorithm and multi-dimensional evaluation indicators. Then, the K-Means++ algorithm is used to perform cluster analysis on the track data. According to the scenario of the analysis problem, the appropriate type of frequency domain features are selected and standardized to unify the dimension; then, the selection range of the number of clusters k is determined according to the number of labels in the track data set (validation set data), that is, the interval in which the k value is located; then, the traversal search method is applied, combined with the track clustering effect comprehensive evaluation system of multi-dimensional evaluation indicators, to find the optimal number of clusters K in the above k value interval, and the selected track frequency domain features are subjected to K-Means++ cluster analysis with this K value.

[0118] In step 105, each cluster number in the interval is traversed by a fusion traversal algorithm, and the optimal cluster number K is determined according to the silhouette coefficient and the Davis-Balding index, so as to perform cluster analysis on the target track data according to the optimal cluster number K by using the K-Means++ algorithm.

[0119] For example, after obtaining the interval in which the number of clusters is located, the method for determining the optimal number of clusters based on traversal search can traverse each number of clusters in the interval, and evaluate the track clustering effect under each cluster number by applying a comprehensive evaluation system of track clustering effects based on multi-dimensional evaluation indicators, output the optimal number of clusters, and use it to perform clustering analysis of the tracks.

[0120] Specifically, each cluster number in the region is traversed, and the silhouette coefficient and Davis-Baulding index of each cluster number are calculated, wherein the silhouette coefficient SC is expressed by the following formula:

[0121]

[0122] in, SC(n) represents the silhouette coefficient of data point n, SC(n)∈[-1,1], represents the average distance from data point n to other data points in the same cluster, It represents the minimum value of the average distance from data point n to all data points in other clusters, M is the number of clusters,

[0123] The Davis-Balding Index DBI is expressed by the following formula:

[0124]

[0125] in, represents the average distance from the data point in each cluster k to the cluster center, Represents the distance between different clusters k and m, represents the spread of each cluster k, It represents the maximum value of the dispersion of cluster k and all other clusters m, and M represents the number of clusters;

[0126] A weighted score is calculated according to the silhouette coefficient and the Davis-Baulding index to determine the optimal number of clusters K according to the weighted score, wherein the weighted score WS is represented by the following formula:

[0127] WS = ω1*SC-ω2*DBI,

[0128] Among them, ω1+ω2=1,ω1,ω2>0.

[0129] The comprehensive evaluation system of track clustering effect based on multi-dimensional evaluation indicators includes the internal evaluation indicators of Silhouette Coefficient (SC), Davis-Bouldin Index (DBI) and Weighted Score (WS); as well as the calculation and evaluation of external evaluation indicators such as Adjusted Rand Index (ARI) and Normalized Mutual Information (NMI).

[0130] SC is a widely recognized metric in cluster analysis, which is used to evaluate the similarity and separation of samples in different clusters. The coefficient ranges from -1 to 1, where 1 means that the sample is closely connected to the samples in its cluster and is clearly separated from the samples in other clusters, indicating that the clustering effect is ideal. On the contrary, a value of -1 indicates that the sample may be incorrectly assigned to the current cluster, and the clustering effect is poor. An SC value close to 0 means that the sample is on the decision boundary between the two clusters, and the clustering effect is average. Assume that for each data point n, its average distance to all other points in the same cluster is the cohesion within the cluster; the minimum value of the average distance from data point n to all points in other clusters is the separation between clusters.

[0131] DBI is an important tool for measuring the performance of clustering algorithms. It evaluates the clustering effect by calculating the ratio of the intra-cluster distance to the inter-cluster distance. The lower the DBI value, the tighter the samples in the cluster and the higher the separation between clusters, thus achieving better clustering results. The calculation of the DBI index involves the average distance of samples within the cluster and the average distance between different clusters, providing an intuitive quantitative measure of the performance of the clustering algorithm.

[0132] Considering that a single indicator may not be able to fully reflect the comprehensive performance of the clustering algorithm, the disclosed embodiment of the present invention introduces WS for comprehensive evaluation. By combining SC and DBI and assigning them appropriate weights ω1 and ω2, a more comprehensive clustering quality evaluation is provided. The calculation method of the weighted score takes into account the importance and influence of different indicators, so as to more accurately reflect the performance of the clustering algorithm in different aspects.

[0133] In addition, the method also includes: evaluating the effect of cluster analysis by using adjusted Rand coefficient and normalized mutual information.

[0134] It should be noted that the calculation of internal evaluation indicators (SC, DBI, WS) is mainly used to find the optimal number of clusters for track clustering analysis, while the calculation of external indicators (ARI, NMI) is used to evaluate the final clustering effect of track data (validation set data). Among them, ARI is the adjusted Rand Index (RI), which is an indicator for evaluating clustering effects. The value range is from -1 to 1. The higher the value, the more consistent the clustering result is with the true label.

[0135] The calculation of ARI is based on the confusion matrix, which contains two clustering results: the true label (T) and the cluster label (C). The elements in the confusion matrix are The true label is And the cluster label is The number of samples, through this matrix can calculate the following four values: is the number of sample pairs that are in the same cluster and belong to the same class in the true label; is the number of sample pairs that are in the same cluster but not in the same class in the true label; is the number of sample pairs that are not in the same cluster but belong to the same class in the true label; is the number of sample pairs that are not in the same cluster and are not in the same class in the true label.

[0136]

[0137] in, is the expected value of RI, and max(RI) is the possible maximum value of RI, which is usually 1.

[0138] Normalized mutual information is also an indicator for evaluating clustering effects. Its value ranges from 0 to 1. The higher the value, the more consistent the clustering result is with the true label. The calculation of NMI is based on mutual information (MI) and information entropy. MI measures the mutual dependence between two random variables, while information entropy measures the uncertainty of a random variable. NMI normalizes the mutual information so that the result is not affected by the size of the data, so that the similarity of different data sets or different clustering results can be compared.

[0139]

[0140] in, is the mutual information, representing the random variable and The mutual information between and They are and The information entropy of is a random variable Value and Value The joint probability of and They are and The marginal probability of .

[0141] In order to more clearly illustrate the calculation method in this step, an example is given below:

[0142] In order to determine the weights of the two coefficients in the comprehensive score of the clustering results, the present invention applies three weight combinations of ω1=0.6, ω2=0.4; ω1=0.5, ω2=0.5; ω1=0.4, ω2=0.6 respectively in the case analysis process, and performs a visual analysis on the clustering results, and finally determines the weight combination of ω1=0.5, ω2=0.5. This weight combination has the following advantages: balanced evaluation: it can balance the cohesion within the cluster and the separation between clusters, ensuring that the clustering results are both tight and have good separation. Comprehensiveness: The combination of the two indicators can more comprehensively reflect the complexity and multidimensional characteristics of the track data, thereby improving the accuracy and reliability of the clustering evaluation. Flexibility: In different situations, the weights can be adjusted to adapt to different clustering requirements and data characteristics, thereby improving the flexibility of the clustering evaluation. Therefore, setting the weights of the silhouette coefficient and the Davis coefficient to 0.5 can ensure that the clustering evaluation takes into account both the tightness within the cluster and the separation between clusters, making the clustering effect evaluation more scientific and accurate. For the optimal number of clusters k, the present invention sets the iteration space of the k value to [2,60] in the model testing phase based on the maximum number of labels of the data.

[0143] Based on the above analysis, the frequency domain feature of the track data (validation and data) is mined and analyzed, and the analysis results of the following three indicators can be obtained. The changes of each indicator with the number of clusters are as follows: Figure 6 shown.

[0144] Analysis of the silhouette coefficient (SC):

[0145] like Figure 6 As shown in the figure, as the number of clusters increases, the silhouette coefficient initially shows an upward trend. This is because when the number of clusters is small, the samples within the cluster may not be tight enough, but as k increases, the samples are more carefully assigned to smaller clusters with higher similarity, thereby enhancing the cohesion within the cluster. When k is in the interval [26,30], the value of SC does not fluctuate significantly, and its range (maximum value minus minimum value) is 0.0044, which is almost negligible, indicating that the clustering effect in this interval is excellent. When k = 30, SC reaches a maximum value of 0.8159, which indicates that under this number of clusters, the cohesion within the cluster and the separation between clusters have reached the best balance. Thereafter, as the number of clusters continues to increase, when k is in the interval [33,59], there is a sharp fluctuation. This fluctuation shows that in this interval, the clustering effect is constantly adjusted and optimized, but it has never exceeded the SC value when k = 30. Thereafter, when k continues to increase, the number of samples in each cluster decreases, resulting in a decrease in the cohesion within the cluster, so the SC value shows a downward trend instead.

[0146] Analysis of the Davis-Balding Index (DBI):

[0147] like Figure 6 As shown in the figure, it is observed that the DBI value shows a trend of first decreasing and then increasing with the increase of k. This phenomenon reveals a clustering principle: increasing the number of clusters within a certain range can enhance the separation between clusters, but when the number of clusters increases beyond a certain threshold, too many clusters may lead to a decrease in the separation of data points within the cluster, thereby reducing the overall performance of clustering. At the beginning, as the number of clusters increases, the DBI value gradually decreases, the clustering effect continues to improve, and reaches the minimum value when k is in the interval [23,30]. When k = 30, the DBI value drops to the lowest point of 0.4008, indicating that the clustering effect is optimized under this number of clusters. However, when the k value continues to increase, the DBI value instead shows a fluctuating upward trend. This may be because the excessive number of clusters leads to a decrease in the separation of data points within the cluster, resulting in too few data points within the cluster, and it is impossible to effectively distinguish different clusters, thus resulting in a poor clustering effect.

[0148] From the relationship between DBI and the number of clusters k, we can conclude that the clustering effect is optimal when k = 30. This number of clusters not only ensures the compactness of data points within the cluster, but also maintains the distinction between clusters, achieving the optimal performance of the clustering algorithm.

[0149] Analysis of weighted score (WS):

[0150] It is too one-sided to determine the optimal number of clusters only from the perspective of a single indicator. The present invention determines the optimal number of clusters k based on the comprehensive weighted score of SC and DBI. By analyzing the relationship between the weighted score (WS) and the number of clusters k, we found that WS shows a trend of first decreasing and then increasing with the increase of k, which shows that the number of clusters has a significant impact on the clustering performance. When k is small, increasing the number of clusters helps to improve the cohesion within the cluster (SC increases) and the separation between clusters (DBI decreases). As k gradually increases, WS also continues to increase, and when k=30, WS reaches a maximum value of 0.2076, which shows that under this number of clusters, after comprehensively considering SC and DBI, the clustering effect is the best. As the k value further increases, when the number of clusters exceeds the optimal range that can be supported by the intrinsic structure of the data, the number of samples in each cluster decreases, resulting in a decrease in the similarity within the cluster, and the distinction between clusters also decreases. This excessive subdivision phenomenon weakens the distinguishing ability of the clustering algorithm, thereby damaging the overall clustering effect, which is reflected in the weighted score (WS) and manifested as a decrease in performance.

[0151] By carefully analyzing the relationship between WS and the number of clusters k, it can be concluded that when k = 30, the weighted score reaches 0.2076, at which time SC = 0.8159 and DBI = 0.4008 are at their respective optimal levels. Therefore, after comprehensive evaluation, it can be concluded that when the number of clusters k = 30, the clustering effect is best. Using the optimal number of clusters K = 30, the frequency domain feature quantities of the track data (validation set data) are finally clustered and analyzed, and external indicators are calculated, which can obtain ARI = 0.3705 and NMI = 0.6718. Therefore, it can be considered that the results of track clustering have high accuracy and credibility to a certain extent, and the performance of the two external indicators is sufficient for further data analysis and decision support.

[0152] like Figure 7 As shown in Figure 2, some management insights can be obtained by analyzing the number distribution of tracks in different clusters. See Table 2. Cluster 1 contains 2755 tracks, which accounts for about 23.29% of the total number of flights. Due to the large number of such tracks, they occupy an important position in the overall flight flow and have an important impact on air traffic management and route planning. Therefore, it is necessary to focus on the aircraft operation activities here.

[0153] Table 2 Distribution of the number of tracks in each cluster

[0154]

[0155] like Figure 8-Figure 9 As shown, the present invention selects some representative clusters, and uses plane and three-dimensional visualization technology to intuitively present the clustering results of the approach and departure tracks of aircraft in the terminal area. Through this intuitive display method, we can clearly observe that after applying this clustering method to analyze the approach and departure tracks of aircraft in the terminal area, the flight tracks of each aircraft in their respective approach or departure directions are clearly reflected and distinguished. The clustered tracks show a high degree of concentration and show an obvious clustering trend, which indicates that the clustering effect is significant. The tracks within each cluster are closely connected, while the tracks between clusters are relatively independent. This phenomenon of high separation further confirms the effectiveness of clustering. In addition, through this method, we can also efficiently identify abnormal tracks in various directions. These abnormal tracks often appear as outliers in the clustering diagram, which provides convenience for further analysis and processing.

[0156] In step 106, the cluster analysis results of the target track data are visualized.

[0157] For example, Figure 5 As shown, the track clustering results are visualized at multiple levels, including but not limited to the two-dimensional plane and three-dimensional distribution of the tracks contained in each cluster, the number of tracks contained in each cluster, and the changes in multi-dimensional evaluation indicators with the number of clusters.

[0158] Specifically, Figure 8 It is a two-dimensional plane visualization display of the track, such as Figure 8 As shown in the figure, through two-dimensional plane analysis, the rationality of route setting can be intuitively analyzed. For example, Figure 8 -e)8-f) The flight paths in clusters 21 and 27 are very messy, and aircraft often fly around, indicating that the arrival and departure routes are not set reasonably, and may need to be re-evaluated and re-planned; Figure 8 The tracks contained in clusters 0 and 18 shown in Figures 8-a) and 8-d) are relatively regular. Although cluster 0 also has some detour tracks, it can be generally said that the route setting here is reasonable, and aircraft can get reasonable route allocation and flight activities here. In addition, through the two-dimensional visualization of the track clustering results, abnormal tracks can be identified more quickly, such as Figure 8 -b) and 8-c) can clearly and intuitively display the outliers and abnormal tracks of clusters 5 and 16, which can provide support for further analysis of the causes of the abnormalities.

[0159] Fig. 9 It is a three-dimensional visualization display of the track, such as Fig. 9 As shown in the figure, only studying the plane characteristics of the flight trajectory will ignore the multi-dimensional characteristics of the trajectory points, and will also lead to limitations in further exploring the abnormal trajectory of the aircraft. Therefore, while combining the plane analysis, it is also necessary to conduct research on the three-dimensional spatial distribution of the aircraft's flight trajectory. Taking cluster 0 as an example, since it has a considerable number of trajectories, more detailed trajectory management and flow control strategies are required to avoid potential conflicts and improve airspace utilization. However, as Figure 8 -a), observation only from two-dimensional angles is too messy and not conducive to further analysis. Fig. 9 -a) to perform multi-level analysis, so that the flight trajectory of the aircraft can be fully understood. In addition, from the two-dimensional display of cluster 18 ( Figure 8 -d)), its track is relatively concentrated and regular; but from a three-dimensional perspective ( Fig. 9 -d)) analysis shows that cluster 18 still has a considerable amount of circumnavigation, which can only be better displayed in three-dimensional space. For cluster 21, even though its two-dimensional track is relatively messy, it is still relatively concentrated and regular in three-dimensional space. For clusters 15 and 16, three-dimensional analysis supplemented by clustering results can also identify abnormal tracks more quickly and efficiently. Therefore, only analyzing the two-dimensional clustering results of the track has certain limitations, which can easily mislead the analysis and lead to wrong conclusions.

[0160] Fig.10 is a structural block diagram of a track analysis system that integrates frequency domain features and multi-dimensional evaluation indicators according to an exemplary embodiment. Fig.10 As shown, the track analysis system 1000 includes:

[0161] The abnormal flight number filtering module 1010 filters the track data collected by the track data acquisition device for abnormal flight numbers, and obtains the filtered first track data, which is arranged in time sequence;

[0162] The frequency domain conversion module 1020 is connected to the abnormal flight number filtering module 1010, traverses the first track data through fast Fourier transform, performs frequency domain conversion on the first track data, obtains second track data, and extracts high-frequency energy features and peak frequency features in the second track data;

[0163] The track data screening module 1030 is connected to the frequency domain conversion module 1020, and screens the target track data required for analysis from the high-frequency energy characteristics and the peak frequency characteristics through a unified standardization processing method;

[0164] The optimal cluster number determination module 1040 is connected to the track data screening module 1030, and adaptively determines the interval of the optimal cluster number according to the number of label data in the target track data;

[0165] The cluster analysis module 1050 is connected to the optimal cluster number determination module 1040, and traverses each cluster number in the interval through a fusion traversal algorithm, and determines the optimal cluster number K according to the silhouette coefficient and the Davis-Balding index, so as to perform cluster analysis on the target track data through the K-Means++ algorithm according to the optimal cluster number K;

[0166] The visualization display module 1060 is connected to the cluster analysis module 1050 and performs visualization on the cluster analysis result of the target track data.

[0167] Fig.11 is based on Fig.10 The structural block diagram of an abnormal flight number filtering module is shown in FIG. Fig.11 As shown, the abnormal flight number filtering module 1010 includes:

[0168] The label data extraction unit 1011 extracts the flight number and the corresponding feature label data for the flight number corresponding to each track node in the track data;

[0169] The empty dictionary filling unit 1012 is connected to the label data extraction unit 1011, and fills the flight number and the corresponding feature label into the created empty dictionary;

[0170] A dictionary search unit 1013 is connected to the empty dictionary filling unit 1012, and after the empty dictionary is filled, detects the number of label data corresponding to the flight number in the filled dictionary through a dictionary search algorithm;

[0171] The abnormal flight number determination unit 1014 is connected to the dictionary search unit 1013, and if the number of the tag data is greater than 1, the flight number is determined as an abnormal flight number;

[0172] The abnormal flight number filtering unit 1015 is connected to the abnormal flight number determining unit 1014, and filters the abnormal flight numbers in the track data to obtain the first track data.

[0173] Fig.12 is based on Fig.10 A structural block diagram of a track data screening module is shown in FIG. Fig.12 As shown, the track data screening module 1030 includes:

[0174] A mean standard deviation calculation unit 1031 calculates the mean and standard deviation of the features in each combination based on the combination of the high-frequency energy features and the combination of the peak frequency features;

[0175] The track data screening unit 1032 is connected to the mean standard deviation calculation unit 1031. For each feature, the difference is obtained by subtracting the mean corresponding to the feature from the feature, and then the difference is divided by the standard deviation corresponding to the feature to obtain the quotient. According to the quotient corresponding to each feature, the target track data screened out from the high-frequency energy features and the peak frequency features is obtained.

[0176] In summary, the present invention discloses a track analysis method and system that integrates frequency domain features and multi-dimensional evaluation indicators, including: filtering abnormal flight numbers on track data collected by track data acquisition equipment; acquiring second track data through fast Fourier transform, extracting high-frequency energy features and peak frequency features; screening out target track data required for analysis through a unified standardized processing method; adaptively determining the interval where the optimal number of clusters is located; traversing each number of clusters in the interval, determining the optimal number of clusters K according to the silhouette coefficient and the Davis-Balding index, and performing cluster analysis according to the optimal number of clusters K through the K-Means++ algorithm; and visually displaying the cluster analysis results of the target track data. The method can provide a theoretical reference for cluster analysis of the approach and departure tracks of aircraft in the terminal area through an analysis method that integrates frequency domain features and multi-dimensional evaluation indicators, so that the optimization results are in line with reality and have more practical application potential.

[0177] The preferred embodiments of the present disclosure are described in detail above in conjunction with the accompanying drawings; however, the present disclosure is not limited to the specific details in the above embodiments. Within the technical concept of the present disclosure, a variety of simple modifications can be made to the technical solution of the present disclosure, and these simple modifications all fall within the protection scope of the present disclosure.

[0178] It should also be noted that the various specific technical features described in the above specific embodiments can be combined in any suitable manner without contradiction. In order to avoid unnecessary repetition, the present disclosure will not further describe various possible combinations.

[0179] In addition, various embodiments of the present disclosure may be arbitrarily combined, and as long as they do not violate the concept of the present disclosure, they should also be regarded as the contents disclosed by the present disclosure.

Claims

1. A track analysis method integrating frequency domain features and multi-dimensional evaluation indicators, characterized in that: The method comprises: Filtering the track data collected by the track data acquisition device for abnormal flight numbers to obtain filtered first track data, where the first track data is arranged in time sequence; traversing the first track data by fast Fourier transform, performing frequency domain conversion on the first track data, acquiring second track data, and extracting high-frequency energy features and peak frequency features in the second track data; Through a unified and standardized processing method, the target track data required for analysis is screened out from the high-frequency energy characteristics and peak frequency characteristics; Adaptively determine the interval where the optimal number of clusters is located according to the number of label data in the target track data; By traversing each cluster number in the interval through a fusion traversal algorithm, an optimal cluster number K is determined according to a silhouette coefficient and a Davis-Balding index, so as to perform cluster analysis on the target track data through a K-Means++ algorithm according to the optimal cluster number K; The cluster analysis results of the target track data are visualized.

2. The terminal area track analysis method integrating frequency domain features and multi-dimensional evaluation indicators according to claim 1 is characterized in that: The step of filtering the track data collected by the track data acquisition device by abnormal flight numbers to obtain the filtered first track data includes: For the flight number corresponding to each track node in the track data, extract the flight number and the corresponding feature label data; Fill the flight number and the corresponding feature label into the created empty dictionary; After the empty dictionary is filled, the number of label data corresponding to the flight number in the filled dictionary is detected by a dictionary search algorithm; If the number of the tag data is greater than 1, the flight number is determined to be an abnormal flight number; Abnormal flight numbers in the track data are filtered to obtain first track data.

3. The track analysis method integrating frequency domain features and multi-dimensional evaluation indicators according to claim 1 is characterized in that: The method of traversing the first track data by fast Fourier transform, performing frequency domain conversion on the first track data, acquiring second track data, and extracting high-frequency energy features and peak frequency features in the second track data includes: The first track data is traversed by fast Fourier transform is the sequence length of the first track data; Perform frequency domain conversion on the first track data to obtain second track data It can be expressed by the following formula: in, is the first frequency components, i is an imaginary unit, From 0 to The frequency index of is the FFT result of an even-indexed vector, is the FFT result of the odd-indexed vector, is the rotation factor in FFT; Extract the high-frequency energy feature in the second track data, the high-frequency energy feature ε high It can be expressed by the following formula: in, and are the lower and upper limit indices of the high frequency cutoff frequency respectively; Extract the peak frequency feature in the second track data, the peak frequency feature It can be expressed by the following formula: in, yes Maximum value index, is the sampling frequency.

4. The track analysis method integrating frequency domain features and multi-dimensional evaluation indicators according to claim 1 is characterized in that: The target track data required for analysis is screened out from the high-frequency energy characteristics and peak frequency characteristics through a unified standardized processing method, including: Based on the combination of the high-frequency energy features and the combination of the peak frequency features, calculating the mean and standard deviation of the features in each combination; For each feature, the difference is obtained by subtracting the mean corresponding to the feature from the feature, and then the difference is divided by the standard deviation corresponding to the feature to obtain the quotient, so as to obtain the target track data filtered out from the high-frequency energy features and peak frequency features according to the quotient corresponding to each feature.

5. The track analysis method integrating frequency domain features and multi-dimensional evaluation indicators according to claim 1 is characterized in that: The method of traversing each cluster number in the interval by a fusion traversal algorithm and determining the optimal cluster number K according to the silhouette coefficient and the Davis-Balding index includes: Traverse each cluster number in the region, and calculate the silhouette coefficient and Davis-Baulding index of each cluster number, wherein the silhouette coefficient SC is represented by the following formula: in, SC(n) represents the silhouette coefficient of data point n, SC(n)∈[-1,1], represents the average distance from data point n to other data points in the same cluster, It represents the minimum value of the average distance from data point n to all data points in other clusters, M is the number of clusters, The Davis-Balding Index DBI is represented by the following formula: in, represents the average distance from the data point in each cluster k to the cluster center, Represents the distance between different clusters k and m, represents the spread of each cluster k, It represents the maximum value of the dispersion of cluster k and all other clusters m, and M represents the number of clusters; A weighted score is calculated according to the silhouette coefficient and the Davis-Baulding index to determine the optimal number of clusters K according to the weighted score, wherein the weighted score WS is represented by the following formula: WS = ω1*SC-ω2*DBI, Among them, ω1+ω2=1,ω1,ω2>0.

6. The method for determining the optimal number of clusters based on traversal search according to claim 5, characterized in that: The method further comprises: The effect of cluster analysis was evaluated by adjusted Rand coefficient and normalized mutual information.

7. The track analysis method integrating frequency domain features and multi-dimensional evaluation indicators according to claim 1 is characterized in that: The visual display of the cluster analysis results of the target track data includes: The cluster analysis results of the target track data are visualized in terms of visual changes, the number of tracks in each cluster, and the track plane and spatial distribution of each cluster.

8. A track analysis system integrating frequency domain features and multi-dimensional evaluation indicators, characterized in that: The system comprises: An abnormal flight number filtering module filters the track data collected by the track data acquisition device for abnormal flight numbers, and obtains filtered first track data, where the first track data is arranged in time sequence; a frequency domain conversion module, connected to the abnormal flight number filtering module, traversing the first track data through fast Fourier transform, performing frequency domain conversion on the first track data, acquiring second track data, and extracting high-frequency energy features and peak frequency features in the second track data; A track data screening module is connected to the frequency domain conversion module, and screens target track data required for analysis from high-frequency energy features and peak frequency features through a unified standardized processing method; An optimal cluster number determination module is connected to the track data screening module and adaptively determines the interval of the optimal cluster number according to the number of label data in the target track data; A cluster analysis module is connected to the optimal cluster number determination module, and traverses each cluster number in the interval through a fusion traversal algorithm, and determines the optimal cluster number K according to the silhouette coefficient and the Davis-Balding index, so as to perform cluster analysis on the target track data through the K-Means++ algorithm according to the optimal cluster number K; The visualization display module is connected to the cluster analysis module and performs visualization on the cluster analysis results of the target track data.

9. The track analysis system integrating frequency domain features and multi-dimensional evaluation indicators according to claim 8 is characterized in that: The abnormal flight number filtering module includes: A label data extraction unit, for extracting the flight number and corresponding feature label data corresponding to each track node in the track data; An empty dictionary filling unit, connected to the label data extraction unit, fills the flight number and the corresponding feature label into the created empty dictionary; A dictionary search unit, connected to the empty dictionary filling unit, detects the number of label data corresponding to the flight number in the filled dictionary through a dictionary search algorithm after the empty dictionary is filled; an abnormal flight number determination unit, connected to the dictionary search unit, and determining the flight number as an abnormal flight number if the number of the tag data is greater than 1; The abnormal flight number filtering unit is connected to the abnormal flight number determining unit, and filters the abnormal flight numbers in the track data to obtain the first track data.

10. The track analysis system integrating frequency domain features and multi-dimensional evaluation indicators according to claim 8, characterized in that: The track data screening module comprises: A mean standard deviation calculation unit, which calculates the mean and standard deviation of the features in each combination based on the combination of high-frequency energy features and the combination of peak frequency features; The track data screening unit is connected to the mean standard deviation calculation unit. For each feature, the difference is obtained by subtracting the mean corresponding to the feature from the feature, and then the difference is divided by the standard deviation corresponding to the feature to obtain the quotient. According to the quotient corresponding to each feature, the target track data screened out from the high-frequency energy feature and the peak frequency feature is obtained.

Images