Principal component bisection K-means clustering method suitable for flight takeoff and landing type identification

Abstract

The invention provides a principal component bisection K-means clustering method suitable for flight takeoff and landing type identification, and belongs to the field of flight data processing, and the method comprises the steps: obtaining original flight takeoff and landing data, and carrying out the preprocessing of the data, and obtaining a flight parameter data set; calculating correlation coefficients between the flight parameters in the flight parameter data set to obtain a correlation coefficient matrix, screening the correlation coefficient matrix according to a correlation coefficient threshold to obtain required flight parameters, and forming a principal component analysis flight parameter data matrix by the required flight parameters and the discrimination parameters; calculating a correlation coefficient matrix of the principal component analysis flight parameter data matrix and performing eigendecomposition to obtain principal component eigenvalues and eigenvectors, sorting the principal component eigenvalues, obtaining principal component contribution rates according to the principal component eigenvalues, and determining principal components by accumulating the principal component contribution rates; and bisecting K-means clustering is carried out on the principal components, two-dimensional space distribution of flight takeoff and landing in any two principal components is obtained, and flight takeoff and landing type identification is carried out according to the two-dimensional space distribution and discrimination parameters.

Description

Technical Field

[0001] This application belongs to the field of flight data processing, and specifically relates to a principal component binary K-means clustering method suitable for flight take-off and landing type identification. Background Technology

[0002] In the aircraft development phase, life design and verification based on design load spectra are no longer sufficient to meet the requirements for completeness of results throughout the entire aircraft lifecycle. This is due to the increased operational severity of modern aircraft following the adoption of new training syllabi, and the discrepancies between actual and expected use. Furthermore, significant differences exist between different flight operations, including takeoffs and landings, resulting in considerable dispersion in flight parameters and structural damage even within the same flight path. Therefore, a method for identifying and classifying flight takeoff and landing types is needed to meet the requirements for analyzing and evaluating differences in flight missions and for compiling baseline usage load spectra.

[0003] In flight takeoff and landing type identification methods, traditional methods include representative takeoff and landing screening and mission profile merging. These are qualitative and semi-quantitative methods that combine human experience. Although they can classify flight takeoffs and landings to a certain extent, their simple processing of data features and relatively subjective screening criteria can easily lead to insufficient classification accuracy. This limitation is particularly evident when there are many types of flight missions and complex data dimensions.

[0004] Takeoff and landing screening methods typically classify data based on simple thresholds for a specific flight parameter (such as altitude or speed). This approach ignores the multidimensional nature of flight data, leading to biased classification results. While mission profile merging can consider more flight parameters, it still faces the curse of dimensionality when processing multidimensional data and requires manually setting parameter thresholds, making it highly subjective. As the complexity and volume of flight data continue to increase, the limitations of traditional methods become apparent, making it difficult to meet the demands of modern aviation missions. Summary of the Invention

[0005] The purpose of this application is to provide a principal component binary K-means clustering method suitable for flight take-off and landing type identification, in order to solve or alleviate at least one of the problems in the background art.

[0006] The technical solution of this application is: a principal component binary K-means clustering method suitable for flight takeoff and landing type identification, including:

[0007] S10: Obtain raw flight takeoff and landing data, and preprocess the raw flight takeoff and landing data to obtain flight parameter dataset;

[0008] S20, calculate the correlation coefficient between each flight parameter in the flight parameter dataset to obtain the correlation coefficient matrix, and select the required flight parameters from the correlation coefficient matrix according to the correlation coefficient threshold, and construct the principal component analysis flight parameter data matrix with the required flight parameters and the discrimination parameters.

[0009] S30, calculate the correlation coefficient matrix of the principal component analysis flight parameter data matrix and perform eigenvalue decomposition to obtain the principal component eigenvalues ​​and eigenvectors of the principal component analysis flight parameter data matrix, sort the principal component eigenvalues ​​and corresponding eigenvectors, obtain the principal component contribution rate based on the principal component eigenvalues, and determine the principal components and their number by accumulating the principal component contribution rate.

[0010] S40: Perform binary K-means clustering on the principal components to obtain a two-dimensional spatial distribution of flight takeoffs and landings formed by any two principal components. Based on the two-dimensional spatial distribution and discrimination parameters, identify the flight takeoff and landing type.

[0011] In a preferred embodiment of this application, step S20 specifically includes:

[0012] S21. Based on the n mission profiles and m corresponding flight parameters in the preprocessed flight parameter dataset, the flight parameters are normalized. The maximum and minimum values ​​of all flight parameters under each mission profile are set to 1 and -1, respectively. The values ​​of the remaining flight parameters under the mission profile are scaled proportionally to obtain a flight parameter vector with n elements for each flight parameter.

[0013] S22, perform preliminary sorting of the flight parameters after standard normalization, take the flight parameter with the largest value as the starting flight parameter, and calculate the correlation coefficient between different flight parameters using the standard normalized flight parameter vector;

[0014] S23, assuming that p flight parameters remain after initial screening, select the flight parameter with the largest value from the initial screening as the first flight parameter, and calculate the correlation coefficient between the remaining p-1 flight parameter vectors and the first flight parameter vector respectively; take the flight parameter with the smallest absolute value of the correlation coefficient as the second flight parameter under this task profile, and then calculate the correlation coefficient between the remaining p-2 flight parameter vectors and the first two flight parameter vectors respectively; take the flight parameter with the smallest absolute value of the correlation coefficient as the third flight parameter, and so on, filtering and sorting the p flight parameters in sequence, removing flight parameters with correlation coefficients above the threshold;

[0015] S24, the flight parameters and discriminant parameters that do not exceed the correlation coefficient threshold form the principal component analysis flight parameter data matrix.

[0016] In a preferred embodiment of this application, the generalized correlation coefficient method based on the mean inequality and Euclidean distance is used to calculate the correlation coefficient between various flight parameters. The calculation method is as follows:

[0017]

[0018]

[0019] Where: r1, r2, ..., r k The Pearson correlation coefficients between specified flight parameters and the remaining flight parameters;

[0020] k is the number of flight parameters;

[0021] R is the average of the squared correlation coefficients between the parameter with the largest value and each of the remaining flight parameters.

[0022] In a preferred embodiment of this application, the correlation coefficient threshold is not less than 0.9.

[0023] In a preferred embodiment of this application, step S30 specifically includes:

[0024] S31, using the required flight parameters as independent variables x and the discriminant parameters as dependent variables y, standardize the independent variables x and dependent variables y using z-score, including:

[0025] Let x be the average value of the j-th column of the independent variable x. mj The standard deviation of the j-th column in the independent variable x is x. si The standardized matrix of the independent variable x is x*. The standardized matrix x* is used as the new independent variable. In the formula, x j Let x be the data in the j-th column of the independent variable. This represents the data in the j-th column of matrix x*.

[0026] Let the mean of the dependent variable y be y m The standard deviation is y s The standardized matrix of the dependent variable y is y*. The standardized matrix y* is used as the new independent variable. ;

[0027] S32, according to the correlation coefficient calculation method, the correlation coefficient matrix of the principal component analysis flight parameter data matrix is ​​obtained, and eigenvalues ​​and corresponding eigenvectors are obtained by eigenvalue decomposition. The obtained eigenvalues ​​are arranged in descending order, and the corresponding eigenvectors are also arranged. The eigenvalues ​​are... Its corresponding feature vector is ;

[0028] Let the contribution rate of the j-th indicator be... ;

[0029] Let the cumulative contribution of the first p indicators be... ;

[0030] If the cumulative contribution rate of the first p indicators is greater than the contribution rate threshold, then the first p principal components can comprehensively reflect the indicators. The first p principal components are the determined principal components, and the number of principal components is p.

[0031] In a preferred embodiment of this application, the contribution rate threshold is not less than 75%.

[0032] In a preferred embodiment of this application, step S40 specifically includes:

[0033] S41, use the multiple principal components obtained in step S30 as input data for bipartite K-means clustering;

[0034] S42, the principal components are clustered using the binary K-means clustering algorithm. The process includes:

[0035] S421, Random Initialization: Given a flight parameter dataset X={x1,x2,...,x...} n Let the target number of clusters be K. Treat all flight parameter data points as an initial cluster and add them to the cluster list S.

[0036] S422, Initial Split: Split on the Flight Parameter Dataset Perform a binary search, that is, divide it into two clusters C1 and C2, and use the basic k-means algorithm to perform the binary search, and add the result to the cluster list S;

[0037] S423, Select the optimal binary search: Select a cluster C1 from the cluster list S, perform a binary search on it, calculate the sum of squared errors SSE for each binary search result, select the cluster C1' with the smallest SSE in the binary search result and add it to the cluster list S. Similarly, repeat the above process for cluster C2 to obtain the cluster C2' with the smallest SSE in the binary search result, and add cluster C2' to the cluster list S. Remove the original clusters C1 and C2 from the list S to update the cluster list and complete the cluster update of the optimal binary search result.

[0038] The formula for calculating the sum of squared errors (SSE) is as follows:

[0039]

[0040] In the formula, Ci is the centroid of the i-th cluster, i∈K, and x is a sample in the cluster;

[0041] S424, Repeated Iteration: Repeatedly distribute data points in the flight parameter dataset and update the cluster list for clustering until the number of clusters in the cluster list S reaches K, or the maximum number of iterations is reached. Finally, the K clusters in the cluster list S are the final clustering result.

[0042] S43. After clustering is completed, the clusters are distributed on the principal components to obtain the flight take-off and landing in a two-dimensional spatial distribution formed by any two principal components. Flight take-off and landing are identified based on the two-dimensional spatial distribution and the discrimination parameters.

[0043] The principal component binary K-means clustering method provided in this application for flight takeoff and landing type identification offers a feasible theoretical method and practical case for single-aircraft tracking and evaluation of aircraft usage load, and provides a feasible method for compiling benchmark usage load spectra. Attached Figure Description

[0044] To more clearly illustrate the technical solutions provided in this application, the accompanying drawings will be briefly described below. Obviously, the drawings described below are merely some embodiments of this application.

[0045] Figure 1 This is a schematic diagram of the principal component binary K-means clustering method applicable to flight take-off and landing type identification in this application.

[0046] Figure 2 This is a schematic diagram of a binary K-means clustering distribution according to an embodiment of this application. Detailed Implementation

[0047] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions in the embodiments of this application will be described in more detail below with reference to the accompanying drawings.

[0048] Based on a large amount of flight takeoff and landing data, this application uses principal component analysis and multiple regression analysis to linearly transform the dimensionality of the massive flight parameter dataset. It then uses the generalized correlation coefficient method to further reduce the dimensionality of the flight parameter data. Finally, it selects the bipartite K-means clustering algorithm to perform cluster analysis on the principal component comprehensive index obtained after dimensionality reduction, calculates the equivalent damage of each takeoff and landing, and completes the flight takeoff and landing clustering based on principal component analysis.

[0049] like Figure 1 As shown, this application provides a principal component binary K-means clustering method suitable for flight takeoff and landing type identification, including:

[0050] S10: Obtain raw flight takeoff and landing data, and preprocess the raw flight takeoff and landing data to obtain flight parameter dataset.

[0051] Raw flight takeoff and landing data typically consists of a data matrix with several flight parameters (such as directional overload, lateral overload, flight speed, engine speed, etc.) as columns and multiple mission profiles (i.e., flight conditions) as rows. After obtaining the raw flight takeoff and landing data, the data format is converted and the flight parameters of each mission profile are preprocessed through methods such as backfilling, rainflow, and filtering to remove outliers and invalid values, thus obtaining the flight parameter dataset.

[0052] This embodiment of the application uses 95 raw flight takeoff and landing data points from an aircraft's baseline usage spectrum as an example for illustration. By preprocessing the flight parameters from the acquired 95 raw flight takeoffs and landings, a flight parameter dataset for the 95 flight takeoffs and landings can be obtained.

[0053] S20: Calculate the correlation coefficient between each flight parameter in the flight parameter dataset to obtain the correlation coefficient matrix. Select the required flight parameters from the correlation coefficient matrix according to the correlation coefficient threshold. Use the required flight parameters and the discriminant parameters to form the principal component analysis flight parameter data matrix.

[0054] Step S20 in this application specifically includes the following steps:

[0055] S21. Based on the n mission profiles and m corresponding flight parameters in the preprocessed flight parameter dataset, the flight parameters are normalized. The maximum and minimum values ​​of all flight parameters under each mission profile are set to 1 and -1, respectively. The values ​​of the remaining flight parameters under the mission profile are scaled proportionally, so that each flight parameter can obtain a flight parameter vector with n elements.

[0056] S22. The flight parameters after standard normalization are initially sorted, and the flight parameter with the largest value is used as the starting flight parameter. The correlation coefficient between different flight parameters is calculated using the standard normalized flight parameter vector.

[0057] In this application, the generalized correlation coefficient method based on the mean inequality and Euclidean distance is used to calculate the correlation coefficient between various flight parameters. The calculation method is as follows:

[0058] (1)

[0059] (2)

[0060] Where: r1, r2, ..., r k The Pearson correlation coefficient is given between the specified flight parameter and the remaining flight parameters; k is the number of flight parameters; R is the average of the squared correlation coefficients between the parameter with the largest value and each of the remaining flight parameters.

[0061] S23, assuming p flight parameters remain after initial screening, select the flight parameter with the largest value from the initially screened flight parameters as the first flight parameter. Calculate the vectors of the remaining p-1 flight parameters and the vector A of the first flight parameter. α1 The generalized correlation coefficient is calculated; the flight parameter with the smallest absolute value of the generalized correlation coefficient is taken as the second flight parameter α2 under the mission profile, and the generalized correlation coefficients of the remaining p-2 flight parameter vectors and the first two flight parameter vectors are calculated respectively; the flight parameter with the smallest absolute value of the generalized correlation coefficient is taken as the third flight parameter, and the p flight parameters are screened and sorted in turn.

[0062] Based on the aforementioned sorting results, flight parameters 1, 2, 3, ..., p are sequentially selected to form a flight parameter sequence. Multiple linear regression is then used to invert the flight parameters of the test set to determine if the inversion accuracy requirements are met. If not, flight parameters are added until the last flight parameter p is reached. Simultaneously, the inversion accuracy after changing the first flight parameter is compared, until all the initially selected p flight parameters are used as the first flight parameter to complete the above iterative calculation, thereby completing the calculation of the correlation coefficient matrix.

[0063] Finally, flight parameters with a correlation coefficient threshold above 0.9 are removed. In a preferred embodiment of this application, the correlation coefficient threshold is not lower than 0.9, meaning that flight parameters exceeding the correlation coefficient threshold of 0.9 are removed. The higher the correlation coefficient, the more redundant the selection.

[0064] S24. The flight parameters and discrimination parameters obtained from the above process are used to form a new principal component analysis flight parameter data matrix.

[0065] In a preferred embodiment of this application, takeoff and landing equivalent damage is selected as the discrimination parameter. Therefore, in this embodiment of the application, after removing some flight parameters based on a correlation coefficient threshold of 0.9 or higher, the remaining 8 flight parameters are obtained—namely, directional overload n. x Lateral overload n y Normal overload n z Air pressure altitude H p Flight speed v z Ninety-five flight takeoffs and landings, including roll rate P, pitch rate Q, and yaw rate R, along with nine other parameters (takeoff and landing equivalent damage), constituted a principal component analysis flight parameter data matrix as input for subsequent steps, as shown in Table 1.

[0066] Table 1 Required flight parameters and takeoff and landing equivalent damage

[0067]

[0068] S30: Calculate the correlation coefficient matrix of the flight parameter data matrix of principal component analysis and perform eigenvalue decomposition to obtain the principal component eigenvalues ​​and eigenvectors of the flight parameter data matrix of principal component analysis. Sort the principal component eigenvalues ​​and corresponding eigenvectors. Obtain the principal component contribution rate based on the principal component eigenvalues. Determine the principal components and their number by accumulating the principal component contribution rate.

[0069] This embodiment of the application takes the eight flight parameters and takeoff and landing equivalent damage obtained above as examples. The independent variable is x, which is a matrix composed of 1*n columns. Taking each mission profile analysis as an example, n=8 is taken, which corresponds to the heading overload n. x Lateral overload n y Eight flight parameters were considered. The dependent variable was y, which corresponds to takeoff and landing equivalent damage, represented as a 1x1 column matrix. The number of mission profiles, or samples, totaled 95. These 95 data sets were concatenated to form a 95x8 matrix of independent variable x and a 95x1 matrix of dependent variable y. The z-score was then used to standardize both the independent variable x and the dependent variable y.

[0070] Let x be the average value of the j-th (j∈1~n) column of the independent variable x. mj The standard deviation of the j-th column in the independent variable x is x. si The standardized matrix of the independent variable x is x*. We then use the standardized matrix x* as the new independent variable: In the formula, x j Let x be the data in the j-th column of the independent variable. This represents the data in the j-th column of matrix x*.

[0071] Let the mean of the dependent variable y be y m The standard deviation is y s The standardized matrix of the dependent variable y is y*. The standardized matrix y* is used as the new independent variable: ;

[0072] Similarly, following the correlation coefficient calculation method, the correlation coefficient matrix of the flight parameter data matrix from principal component analysis is obtained. Then, eigenvalues ​​and corresponding eigenvectors are obtained through eigenvalue decomposition. The obtained eigenvalues ​​are arranged in descending order, and the corresponding eigenvectors are also arranged. The eigenvalues ​​are... Its corresponding feature vector is .

[0073] Let the contribution rate of the j-th indicator be... ;

[0074] Let the cumulative contribution of the first p indicators be... .

[0075] If the cumulative contribution rate of the first p indicators is greater than the contribution rate threshold, then these p principal component analyses (PCA) can be considered to comprehensively reflect the indicators. In a preferred embodiment of this application, the contribution rate threshold can be set to approximately 80% or not less than 75%.

[0076] In this application, the amount of data information depends on the variance contribution rate of the principal components, and the number of principal components is determined based on the cumulative contribution rate of the variance. Taking the principal component analysis flight parameter data matrix in Table 1 as an example, the principal component analysis flight parameter data matrix, consisting of 8 flight parameters and takeoff and landing equivalent damage values ​​(a total of 9 parameters), is used to determine the correlation coefficient matrix according to the generalized correlation coefficient method, and eigenvalues ​​are calculated and arranged in descending order, along with the corresponding eigenvectors. Table 2 shows the eigenvalues ​​and their contribution rates in this embodiment of the application, and Table 3 shows the principal component analysis eigenvectors in this embodiment of the application.

[0077] Table 2. Eigenvalues ​​and cumulative contribution rates of the flight parameter data matrix from principal component analysis.

[0078] Table 3. Eigenvectors from Principal Component Analysis

[0079] The variance contribution rate data corresponding to the eigenvalues ​​shows that most of the variance contribution rate is contained in the first few principal components, with the first three principal components covering nearly 80% of the variance contribution rate. Therefore, in this embodiment of the application, the first principal component PCA1, the second principal component PCA2, and the third principal component PCA3 are selected as the basis for classification, which can represent the characteristics of the original eight flight parameters and takeoff and landing equivalent damage. As shown in Table 3, the first three principal components are as follows:

[0080] PCA1 = -0.199n x -0.257n y +0.906n z +0.185H p +0.134v z +0.057P+0.061Q+0.113R+0.029D;

[0081] PCA2 = -0.408n x +0.091n y -0.029n z -0.122H p +0.398v z +0.203P-0.636Q-0.212R-0.401D;

[0082] PCA3 = -0.405n x +0.028ny -0.053n z +0.376H p -0.485v z -0.537P-0.361Q+0.191R+0.027D.

[0083] As can be seen from the above equation, the normal overload n in the first principal component PCA1 z Lateral overload n y , heading overload n x Altitude H p and flight speed v z The value is relatively large, which mainly reflects the normal overload n. z Lateral overload n y , heading overload n x Altitude H p and flight speed v z Changes in pitch rate Q, landing equivalent damage D, and yaw overload n in the second principal component PCA2 x Flight speed v z The roll rate P is relatively large, and it mainly reflects the pitch rate Q, landing equivalent damage D, and yaw overload n. x Flight speed v z and the change in roll angular velocity P; the roll angular velocity P and flight velocity v in the third principal component PCA3 z , heading overload n x Altitude H p And the change in pitch rate Q. The third principal component PCA3 mainly reflects the roll rate P and flight speed v. z , heading overload n x Altitude H p And the change in pitch angular velocity Q.

[0084] As can be seen from the above analysis, this application transforms the original nine-dimensional flight take-off and landing clustering problem into a three-dimensional principal space classification problem through principal component analysis, thus simplifying the classification difficulty.

[0085] S40: Perform binary K-means clustering on the principal components to obtain a two-dimensional spatial distribution of flight takeoffs and landings formed by any two principal components. Based on the two-dimensional spatial distribution and discrimination parameters, identify the flight takeoff and landing type.

[0086] Specifically, step S40 in this application includes:

[0087] S41, the multiple principal components PCA1~PCA obtained in step S30 are... n As input data for binary K-means clustering, this input data can be represented as a matrix, where each row corresponds to a sample and each column corresponds to a principal component.

[0088] For example, in this embodiment of the application, the multiple principal components are the first principal component PCA1 to the third principal component PCA3 determined by the above process.

[0089] S42, the principal components are clustered using the binary K-means clustering algorithm. The process includes:

[0090] S421, Random Initialization: Given a flight parameter dataset X={x1,x2,...,x...} n Let K be the target number of clusters. Treat all flight parameter data points as an initial cluster and add them to the cluster list S.

[0091] S422, Initial Split: Split on the Flight Parameter Dataset Perform a binary search, dividing the data into two clusters, C1 and C2, using the basic k-means algorithm, and add the results to the cluster list S.

[0092] S423, Select the optimal binary search: Select a cluster C1 from the cluster list S, perform a binary search on it, calculate the sum of squared errors (SSE) for each binary search result, select the cluster C1' with the smallest SSE in the binary search results and add it to the cluster list S. Similarly, repeat the above process for cluster C2 to obtain the cluster C2' with the smallest SSE in the binary search results, and add cluster C2' to the cluster list S as well. Remove the original clusters C1 and C2 from the list S to update the cluster list and complete the cluster update of the optimal binary search result.

[0093] In this application, the formula for calculating the sum of squared errors (SSE) is as follows:

[0094]

[0095] In the formula, Ci is the centroid of the i-th cluster, i∈K, and x is a sample in the cluster, i.e., flight take-off and landing data;

[0096] S424, Repeated Iteration: Repeatedly distribute data points in the flight parameter dataset and update the cluster list for clustering until the number of clusters in the cluster list S reaches K, or the maximum number of iterations is reached. Finally, the K clusters in the cluster list S are the final clustering result.

[0097] S43. After clustering is completed, the clusters are distributed on the principal components to obtain the flight take-off and landing in a two-dimensional spatial distribution formed by any two principal components. Flight take-off and landing are identified based on the two-dimensional spatial distribution and the discrimination parameters.

[0098] By examining the distribution of each cluster in the clustering distribution, we can confirm the number of samples in different clusters and their positions on the principal components PCA1~PCA1. nThe clustering analysis focuses on the central location of each cluster to understand its representative characteristics. For example, if a cluster has a large PCA1 value, it is likely composed primarily of samples with high PCA1 scores. The clustering results are then visualized using two-dimensional or three-dimensional scatter plots, where samples are labeled with different colors according to their cluster affiliation.

[0099] Figure 2 The figure shows the two-dimensional principal space distribution of the 95 flight take-off and landing clustering results in this embodiment of the application, corresponding to the first principal component PCA1 and the second principal component PCA2. The horizontal axis is the first principal component PCA1 and the vertical axis is the second principal component PCA2. Figure 2 Each point in the diagram represents a flight takeoff and landing, and different images or symbols represent the clustering categories into which they are grouped. The different categories in the diagram (such as solid circles, solid triangles, solid rhombuses, hollow circles, hollow rhombuses, hollow triangles, etc.) show the clustering results of bipartite K-means clustering for different takeoff and landing events (based on the magnitude of the takeoff and landing equivalent damage value). It can be observed from the diagram that some categories (such as solid circles) exhibit a relatively dense distribution, indicating that these flight takeoffs and landings have similar characteristics in the principal component two-dimensional space; some categories (such as hollow triangles) are distributed more widely, indicating that their takeoff and landing characteristics differ significantly from other categories. Therefore, the bipartite K-means clustering method of this application can effectively cluster and identify flight takeoff and landing data according to a given number of clusters or categories.

[0100] Based on the calculation results of the landing equivalent damage D in Table 1, the landing equivalent damage values ​​corresponding to the 10 flight landings with the largest landing equivalent damage, from largest to smallest, are 3849.9, 2978.3, 1891.5, 1808.2, 1576.4, 1200, 1099.1, 1069, 1050.7, and 1021.4, respectively. The landing equivalent damage values ​​corresponding to these 10 flight landings in Table 1 and the results of the binary K-means clustering of the above process are summarized in Table 4.

[0101] Table 4. Top 10 most damaging takeoff and landing injuries and their clustering results.

[0102] As can be seen from Table 4, the 10 flights with the greatest takeoff and landing equivalent damage were divided into 3 classes / clusters (i.e., category 1, type 3, and category 5) using the binary K-means clustering method in this application.

[0103] Based on the calculation results of landing equivalent damage in Table 2, the damage values ​​corresponding to the five landings with the smallest landing equivalent damage, from smallest to largest, are 7, 10.3, 13.2, 15.8, and 16.2, respectively. The damage values ​​and the clustering results of these five landings in Table 5 are summarized in Table 5. As can be seen from Table 5, the five flights with the smallest landing equivalent losses are clustered into the same class.

[0104] Table 5. Five landing and takeoff damage types with the least damage and their clustering results.

[0105] It should be noted that if high-damage takeoffs and landings are concentrated in a few categories, these categories can be considered to represent high-risk flight takeoff and landing patterns. By observing the intervals between categories, the degree of difference between different types of takeoff and landing events can be determined. For example, if the high-damage takeoff and landing category and the low-damage category are far apart in the principal component two-dimensional space, it indicates that the characteristics of these two types of takeoffs and landings are significantly different, which may be related to different flight conditions or operating methods.

[0106] This application establishes a flight takeoff and landing clustering method based on principal component analysis (PCA) based on equivalent damage theory. Driven by data, it employs bipartite K-means clustering to classify flight takeoff and landing types, reducing the local optima problem that may occur with traditional K-means clustering. Furthermore, to address the need for processing high-dimensional, multi-feature flight parameters, this application proposes a generalized correlation coefficient to better reduce data dimensionality and applies principal component analysis (PCA) to extract key features, focusing on critical dynamic changes during takeoff and landing, thus improving the targeting and effectiveness of clustering analysis. The combination of PCA and bipartite K-means enables automated data segmentation, automatically identifying and classifying takeoff and landing phases in different flight stages, reducing the need for manual intervention and improving process automation and efficiency. PCA scientifically and effectively reduces noise and redundant flight parameters, making the clustering results more robust; simultaneously, the bipartite K-means algorithm is more robust and stable when processing complex flight parameter information. This method is adaptable to various aircraft data, has strong versatility, and can be applied to different types of aircraft data, providing a new technical means for aircraft condition monitoring and analysis.

[0107] The principal component binary K-means clustering method of this application, applicable to flight takeoff and landing type identification, has the following advantages compared to existing technologies:

[0108] 1) Efficiency improvement: In the flight parameter data acquired by actual single-machine tracking, there are many types of parameters. Principal component regression combines the ideas of principal component extraction (dimensionality reduction) and multivariate regression analysis. It emphasizes obtaining a set of features with obvious physical or statistical significance through feature transformation. It is suitable for situations where there are many variables and the number of samples is less than the dimensionality of the variables. The method in this application can screen out important parameter types and improve analysis efficiency.

[0109] 2) Improved classification accuracy: The generalized correlation coefficient in this application optimizes the selection of flight parameters, highlighting the comprehensive correlation between one variable and multiple variables. When extracting the main features of flight data to complete dimensionality reduction, it maximizes the representation of the number of takeoffs and landings under various flight conditions.

[0110] 3) Cost reduction: The computational complexity of the binary K-means clustering in this application is relatively low. During the analysis process, it does not rely on given categories or thresholds to divide the data, which can effectively utilize limited computing resources and divide the data into several categories based on the similarity and difference of the data.

[0111] 4) Wide applicability: The combination of principal component analysis (PCA) and binary K-means can be applied to large-scale datasets and specific designs for various aircraft takeoff and landing classifications, providing a more applicable new technical means for aircraft condition monitoring and analysis.

[0112] The above description is merely a specific embodiment of this application, but the scope of protection of this application 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 this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A principal component dichotomous K-means clustering method suitable for take-off and landing type identification, characterized in that, The method comprises the following steps: S10, obtaining original flight data, and preprocessing the original flight data to obtain a flight parameter data set; S20, calculating the correlation coefficient between each flight parameter in the flight parameter data set to obtain a correlation coefficient matrix, screening the required flight parameters from the correlation coefficient matrix according to a correlation coefficient threshold, and constructing a principal component analysis flight parameter data matrix with the required flight parameters and a discriminant parameter; S30, calculating the correlation coefficient matrix of the principal component analysis flight parameter data matrix and performing eigenvalue decomposition to obtain the principal component eigenvalues and eigenvectors of the principal component analysis flight parameter data matrix, sorting the principal component eigenvalues and the corresponding eigenvectors, obtaining the principal component contribution rate according to the principal component eigenvalues, and determining the principal components and the number thereof by accumulating the principal component contribution rate; S40, performing two-means clustering on the principal components to obtain a two-dimensional space distribution of flight takeoff and landing formed by any two principal components, and performing flight takeoff and landing type identification according to the two-dimensional space distribution and the discriminant parameter.

2. The principal component dichotomous K-means clustering method suitable for flight landing type identification according to claim 1, characterized in that, Step S20 specifically comprises: S21, performing standard normalization processing on the flight parameters according to n task profiles and corresponding m flight parameters in the preprocessed flight parameter data set, setting the maximum value and the minimum value of all flight parameters under each task profile as 1 and -1, and scaling the values of the remaining flight parameters under the task profile in proportion, so as to obtain a flight parameter vector with n elements for each flight parameter; S22, performing preliminary sorting on the standard normalized flight parameters, taking the flight parameter with the largest value as the starting flight parameter, and calculating the correlation coefficient between different flight parameters according to the standard normalized flight parameter vector; S23, assuming that there are p flight parameters remaining after preliminary screening, selecting the flight parameter with the largest value in the preliminary screened flight parameters as the first flight parameter, calculating the correlation coefficient between the remaining p-1 flight parameter vectors and the first flight parameter vector, taking the flight parameter corresponding to the minimum absolute value of the correlation coefficient as the second flight parameter under the task profile, and calculating the correlation coefficient between the remaining p-2 flight parameter vectors and the first two flight parameter vectors, and taking the flight parameter corresponding to the minimum absolute value of the correlation coefficient as the third flight parameter, and sequentially screening and sorting the p flight parameters to remove the flight parameters with a correlation coefficient higher than the threshold; S24, the flight parameters not exceeding the correlation coefficient threshold and the discriminant parameter form a principal component analysis flight parameter data matrix.

3. The principal component dichotomous K-means clustering method suitable for flight landing type identification according to claim 2, wherein, The correlation coefficient between each flight parameter is calculated by using the generalized correlation coefficient method based on the mean inequality and the Euclidean distance, and the calculation method is as follows: wherein: r1, r2,..., r k to designate the Pearson correlation coefficient between the respective flight parameter and the remaining flight parameters; K is the number of flight parameters; R is the average value of the square of the correlation coefficient between the parameter with the largest value in the flight parameters and each of the remaining flight parameters.

4. The principal component dichotomous K-means clustering method suitable for flight landing type identification according to claim 3, characterized in that, The correlation coefficient threshold is not less than 0.

9.

5. The principal component dichotomous K-means clustering method suitable for flight landing type identification according to claim 4, wherein, Step S30 specifically comprises: S31, taking the required flight parameters as the independent variable x and the discriminant parameter as the dependent variable y, and using z-score to standardize the independent variable x and the dependent variable y, including: Let the mean of the jth column in the independent variable x be x mj , the standard deviation of the jth column in the independent variable x be x si , the standardized matrix of the independent variable x be x , in which x j is the jth column data in the independent variable x, is the jth column data in the matrix x Let the mean of the dependent variable y be y m , the standard deviation be y s , the matrix of the dependent variable y after standardization be y ; S32, obtaining the correlation coefficient matrix of the principal component analysis flight parameter data matrix according to the calculation method of the correlation coefficient, and performing characteristic decomposition to obtain the characteristic value and the corresponding characteristic vector, arranging the obtained characteristic value in descending order, and arranging the corresponding characteristic vector at the same time, the characteristic value is , and the corresponding characteristic vector is ; Let the jth indicator contribution rate be denoted by ; Let the cumulative contribution of the first p indicators be denoted by ; If the cumulative contribution rate of the first p indexes is greater than the contribution rate threshold, the first p principal components can comprehensively reflect the indexes, and the first p principal components are the determined principal components, and the number of the principal components is p.

6. The principal component dichotomous K-means clustering method suitable for flight landing type identification according to claim 5, wherein, The contribution rate threshold is not less than 75%.

7. The principal component dichotomous K-means clustering method suitable for flight landing type identification according to claim 5, wherein, The step S40 specifically comprises: S41, taking the plurality of principal components obtained in the step S30 as input data of the bisecting K-means clustering; S42, clustering the principal components by the bisecting K-means clustering algorithm, and the process comprises: S421, random initialization: given the flight parameter dataset X = {x1, x2,..., x n}, let the target number of clusters be K, consider all flight parameter data points as an initial cluster, and add the cluster to the cluster list S; S422, initial split: on the flight parameter dataset Split into two clusters, C1 and C2, using the basic k-means algorithm and add the result to the cluster list S; S423, selecting an optimal bisecting: selecting a cluster C1 from a cluster list S, bisecting the cluster C1, calculating an error sum of squares SSE of each time for the bisecting results, selecting a cluster C1' with the minimum SSE in the bisecting results and adding the cluster C1' to the cluster list S, and repeating the above process for the cluster C2 to obtain a cluster C2' with the minimum SSE in the bisecting results, adding the cluster C2' to the cluster list S, removing the original cluster C1 and the cluster C2 from the cluster list S, updating the cluster list, and completing the cluster updating of the optimal bisecting result; wherein, Ci is a centroid of the i-th cluster, i∈K, and x is a sample in the cluster; S424, repeating iteration: repeating the distribution of the data points in the flight parameter data set and the updating of the cluster list until the number of clusters in the cluster list S reaches K or the maximum iteration number is reached, and the K clusters in the final cluster list S are the final clustering results; S43, after the clustering, distributing the clustered clusters on the principal components to obtain a two-dimensional space distribution of the flight and landing in any two principal components, and identifying the flight and landing according to the two-dimensional space distribution and the discrimination parameter. ​

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