Flight body attitude angle multi-index fusion identification method based on network target data

Abstract

The invention discloses a flight body attitude angle multi-index fusion identification method based on net target data, and the method comprises the steps: firstly obtaining a real coordinate point set of a net target broken hole contour and a flight body rotation projection contour under a rectangular coordinate system, and extracting a polar coordinate point set from the real coordinate point set; and then, according to the coordinate point sets, calculating a Pearson correlation coefficient, a Hausdorff distance, a PCA principal component axis included angle and a principal component axis length difference, and determining an optimal attitude angle of the flight body through similarity analysis. Besides, the mesh target broken hole contour, the optimal attitude angle and the projection contour of the adjacent attitude angle are displayed in the polar coordinate system, and the principal component axes of the mesh target broken hole contour and the projection contour of the optimal attitude angle are drawn to form a visual graph. According to the method, by means of multi-index fusion, the attitude angle of the flight body can be accurately identified, and powerful technical support is provided for accurate analysis and research of the flight state of the flight body.

Description

Technical Field

[0001] The present application belongs to the technical field of flying body data identification, and specifically relates to a flying body attitude angle multi-index fusion identification method based on target data. Background Art

[0002] In the field of national defense science and technology, irregularly shaped flying objects face complex aerodynamic and atmospheric flight dynamics challenges during flight. The flight attitude, speed, and angle of these objects exhibit a high degree of randomness, and their flight speeds are typically extremely high, often exceeding 4 Ma. Limited by the availability and technical level of high-speed camera equipment, it is difficult to fully and comprehensively record the specific attitude of the flying object as it impacts the target mesh. Furthermore, due to the irregular shape of the flying object itself, the contour of the hole formed after it passes through the target mesh is also irregular. This phenomenon significantly increases the dimensionality of the target mesh data and further amplifies the impact of outliers in the actual collected data, greatly increasing the difficulty of data analysis.

[0003] Existing analysis methods for aircraft posture recognition often rely on simple matching operations based on a single feature. These methods often make numerous assumptions to simplify the aircraft's shape, using only information such as the contour's geometry or spatial positional relationships to identify the aircraft's position and attitude during flight. However, this analysis approach, based on a single feature and simplified assumptions, lacks comprehensive and accurate assessment of contour similarity and cannot meet the practical needs of high-precision analysis.

[0004] At present, there is still a lack of a set of methods that are targeted at practical problems and have high confidence in how to effectively match and analyze the contour data of the hole in the target with the contour data of the projection of the flying body at different attitude angles. Summary of the Invention

[0005] In view of the limitations of traditional analysis methods when processing target data to obtain flight information of flying objects, this application aims to provide a multi-index fusion identification method for flying object attitude angles based on target data. This method aims to effectively eliminate the interference of flying object appearance factors and achieve accurate identification of flying object attitude angles through multi-index fusion, thereby providing reliable technical support for accurate analysis and research of flying object flight status.

[0006] In one aspect of the present application, a method for multi-index fusion identification of a flying object attitude angle based on target data is provided, comprising the following steps:

[0007] Based on the rectangular coordinate system, the real coordinate point set of the net target hole contour and the coordinate point set of the flying body rotation projection contour are respectively obtained, and the polar coordinate point set is extracted according to the coordinate point set of the net target hole contour and the flying body rotation projection contour;

[0008] Based on the coordinate point set and polar coordinate point set of the target hole profile and the rotation projection profile, the Pearson correlation coefficient, Hausdorff distance, PCA principal component axis angle and principal component axis length difference are calculated respectively. Based on the calculation results, similarity analysis is performed to determine the optimal attitude angle of the flying body.

[0009] The net target hole contour, the optimal attitude angle and the projection contour at the attitude angle adjacent to the optimal attitude angle are displayed in the polar coordinate system, and the principal component axes of the net target hole contour and the projection contour at the optimal attitude angle are drawn to construct a visual graph.

[0010] In one embodiment, obtaining a set of real coordinate points of the outline of a hole in the target includes: placing a calibration reference object with a predetermined physical size on the imaging plane of the target, calculating a ratio coefficient between the pixel span of the calibration reference object in the digital image and its physical size, converting the pixel coordinates of the captured image of the outline of the hole in the target into actual length, and obtaining a set of real coordinate points of the outline of the hole in the target.

[0011] In one embodiment, obtaining a set of coordinate points of a rotating projection profile of a flying object includes:

[0012] The three-dimensional data in the body axis coordinate system of the flying body is converted into the earth axis coordinate system through the rotation matrix; wherein the rotation angle covers the full attitude range;

[0013] Perform orthogonal projection on the converted three-dimensional data to generate a two-dimensional projection point cloud;

[0014] The alpha_shapes algorithm is used to extract boundary contours from the two-dimensional projected point cloud and discretize it into an ordered coordinate point set.

[0015] In one embodiment, extracting a polar coordinate point set based on a coordinate point set of a target hole contour and a flying object rotation projection contour includes:

[0016] Convert the coordinate point sets of the target hole contour and the rotation projection contour into polar coordinate parameters respectively;

[0017] Implement Z-score outlier detection and elimination based on predefined standard deviation threshold for polar angle and diameter sequences of polar coordinate parameters;

[0018] For the processed data, IQR outlier points are secondary eliminated based on the interquartile range criterion to obtain the polar coordinate point set.

[0019] In one embodiment, Z-score normalization is performed on the polar angle and polar diameter sequence sets, the Z-score values ​​of the data points are calculated, and data points with an absolute value greater than 3 are identified as abnormal data points and are removed;

[0020] The interquartile range of the data is calculated for the data point set after Z-score processing, and the upper and lower limits of the outliers are determined based on the interquartile range. The abnormal data points outside the upper and lower limits are identified and removed.

[0021] In one embodiment, performing similarity analysis based on the calculation results to determine the optimal attitude angle of the flying object includes:

[0022] Arrange the Pearson correlation coefficient in descending order, and the Hausdorff distance, PCA principal component axis angle, and principal component axis length difference in ascending order;

[0023] Processing is performed based on the relationship between the ratio of the shorter principal component axis to the longer principal component axis of the PCA of the target hole profile and a predetermined threshold value A: a) when the ratio is less than the predetermined threshold value A, a data subset is selected whose Pearson coefficient, Hausdorff distance, and axis length difference are all within the sorting threshold value B, and the posture angle with the smallest PCA principal component axis angle is selected from the subset; b) when the ratio is greater than the predetermined threshold value A, a data subset is selected whose Hausdorff distance, PCA principal component axis angle, and principal component axis length difference are all within the sorting threshold value B, and the posture angle with the largest Pearson correlation coefficient is selected from the subset;

[0024] Obtain the optimal attitude angle of the flying object that matches the hole contour of the net target.

[0025] In one embodiment, the threshold value A is set to 0.7-0.9, and the threshold value B is set to the top 5%-15% in the ranking.

[0026] In one embodiment, displaying the target hole profile, the optimal attitude angle, and the projection profile at attitude angles adjacent to the optimal attitude angle in a polar coordinate system includes:

[0027] Taking the optimal attitude angle as a reference, determining an attitude angle sequence including the optimal attitude angle and adjacent attitude angles within a preset deviation range;

[0028] In the polar coordinate system, the following are simultaneously presented: the discrete coordinate point set of the target hole contour, the projection contour of the flying body corresponding to the optimal attitude angle, and the projection contours corresponding to other attitude angles in the attitude angle sequence.

[0029] In one embodiment, drawing the principal component axes of the target hole contour and the optimal posture angle projection contour includes: performing principal component analysis based on the coordinate point set of the target hole contour and the optimal matching projection contour, and generating a visualization axis with the origin of the coordinate system as the center point and an extension direction consistent with the principal component vector.

[0030] The beneficial effects of this application are:

[0031] 1) Accurately adapt to targets with different appearance characteristics

[0032] This application divides the similarity matching conditions into two types based on the contour and shape characteristics of the target. This targeted division method fully considers the differences between targets with different shapes in the data matching process, so that the similarity judgment can be more in line with the actual target characteristics, and effectively improves the accuracy and adaptability of the data identification of targets with various shapes.

[0033] 2) Improve the comprehensiveness and reliability of similarity judgment

[0034] By reducing the data's dimensionality and employing a combination of similarity metrics for similarity assessment, the limitations of single-metric analysis are overcome. By evaluating the target's hole profile and rotational projection profile from different angles, multiple metrics can more comprehensively mine similarity information from the data, making the final results more reliable and effectively reducing the probability of misjudgments and missed detections.

[0035] 3) Eliminate interference and improve data recognition accuracy

[0036] The interference of the flying body shape is eliminated, and the misleading of the target data identification caused by the flying body shape factors is avoided, so that the data identification can focus on the similarity between the target contour and the rotation projection contour itself, thereby significantly improving the accuracy of data identification and providing high-quality data support for subsequent data analysis and application. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 This is the similarity analysis process of the embodiment of the present application;

[0038] Figure 2 This is a schematic diagram of the shape of an irregular-shaped flying body explosively formed as the research object of the embodiment of the present application;

[0039] Figure 3 This is a schematic diagram of the outline obtained by rotating and projecting the digital model of the flying object in an embodiment of the present application;

[0040] Figure 4 Schematic diagram of the net target of the embodiment of the present application and the outline of the hole after the flying object impacts the net target at a certain attitude angle;

[0041] In the figure: 1-head of the flying body, 2-middle part of the flying body, 3-tail skirt of the flying body, 4-profile of the digital model projection of the flying body, 5-net target. DETAILED DESCRIPTION

[0042] The following will be combined with the drawings in the embodiments of this application to clearly and completely describe the technical solutions in the embodiments of this application. Obviously, the embodiments described are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0043] Traditional analysis methods rely only on single data features or simple distance metrics, making it difficult to accurately reveal the flight information of flying objects contained in different target data. This application uses the alpha_shapes algorithm to extract the contours of the projections of the flying object at various attitude angles, and performs denoising and downsampling on the data. The Pearson coefficient, Hausdorff distance, the angle between the PCA principal component axes, and the length difference of the PCA principal component axes are selected as similarity judgment indicators. According to the shape characteristics of the target hole contour (the ratio of the shorter principal component axis length to the longer principal component axis length of the target is compared with the threshold A), the similarity analysis is divided into two cases: when the principal component axis length ratio of the target is less than the set threshold, the Pearson coefficient, Hausdorff distance, and the PCA principal component axis length difference are used as constraints, and the angle between the PCA principal component axes is used as the judgment indicator; when the principal component axis length ratio of the target is greater than the set threshold, the Hausdorff distance, the angle between the PCA principal component axes, and the PCA principal component axis length difference are used as constraints, and the Pearson coefficient is used as the judgment indicator. After the above similarity judgment, the highest similarity matching result between the net target hole profile and the rotation projection profile is obtained, which is the attitude angle of the flying object when it impacts the net target.

[0044] In one embodiment, referring to Figures 1 to 4 As shown, a multi-index fusion identification method for the attitude angle of a flying body based on target data is provided. The specific implementation plan is as follows:

[0045] 1) Obtain the real coordinate point set of the net target hole contour and the coordinate point set of the flying body rotation projection contour respectively, and extract the polar coordinate point set based on the coordinate point set of the net target hole contour and the flying body rotation projection contour.

[0046] In the specific scenario of an explosively formed flying object impacting a net target, an image of the net target's hole outline is captured using a suitable image acquisition device. The pixel coordinates of the net target hole outline are then converted to coordinates of real length. A reference object of known actual length is placed next to the net target outline and imaged together. The two endpoints of the reference object are then manually selected in the image, and the computer automatically calculates the corresponding pixel lengths, thereby determining the scaling factor (i.e., the real length per pixel). Finally, the pixel coordinates are multiplied by this scaling factor to obtain the coordinate point set of the real length.

[0047] When projecting and extracting the contours of flying objects with different attitude angles, the flying object's coordinate system is first rotated around the x-axis (roll angle), y-axis (pitch angle), and z-axis (yaw angle) by a certain angle to determine the attitude angles and spatial data points (based on the earth's axis system). Then, the flying object data points are projected, and the projection contour is extracted using the alpha_shapes algorithm, which is then discretized to obtain a set of coordinate points.

[0048] The coordinates of the above data points are initially based on the rectangular coordinate system. To facilitate the subsequent similarity analysis, they are converted into polar coordinate parameters, including polar angle and polar diameter sequences, while maintaining the order of the data points in the rectangular coordinate system.

[0049] For polar angle and polar diameter series, Z-score and IQR methods are used to remove outliers respectively. Specifically:

[0050] First, the Z-score method is used to calculate the mean and standard deviation of the data in each dimension, and then the Z value of each data point is calculated using formula (1):

[0051]

[0052] Among them, r is the polar diameter, μ is the mean, and σ is the standard deviation.

[0053] Data points with an absolute Z-score greater than 3 are considered outliers (because in a normal distribution, approximately 99.7% of the data fall within the range of ±3 standard deviations of the mean) and are removed. It's understandable that the theoretical basis for choosing 3 standard deviations is that the data present a normal distribution. However, even if the data doesn't completely conform to a normal distribution, some statistical methods based on the normal distribution can still be approximately applicable if the sample size is large enough—based on the central limit theorem.

[0054] Next, we use the IQR method, or interquartile range, to calculate the 25% value Q1 and 75% value Q3 of the diameter series, and then obtain the interquartile range IQR = Q3 - Q1. We set the lower limit to Q1 - 1.5 × IQR and the upper limit to Q3 + 1.5 × IQR. Diameter data points that fall outside this range are identified as outliers and removed.

[0055] The above data processing method can isolate abnormal data and provide a reliable data basis for subsequent similarity analysis.

[0056] In some embodiments, because the polar angle ranges, x- and y-coordinate ranges, and resolutions of the target hole profile and the rotated projection profile may differ, a custom function is used to align the data. This function sorts the polar angles and uses interpolation to align the polar angle ranges, x- and y-coordinate ranges, and resolutions of the two. This function then generates the aligned polar angle, x- and y-coordinate data for the target hole profile and the rotated projection profile, preventing data from crossing boundaries.

[0057] 2) Based on the coordinate point set and polar coordinate point set of the target hole contour and the rotated projection contour, the Pearson correlation coefficient, Hausdorff distance, PCA principal component axis angle and principal component axis length difference are calculated respectively. Based on the calculation results, similarity analysis is performed to determine the optimal attitude angle of the flying object.

[0058] ① Calculation of Pearson correlation coefficient

[0059] The Pearson correlation coefficient is calculated using the Pearson calculation formula for the horizontal coordinate, vertical coordinate, and polar diameter data between the target hole profile and the rotation projection profile. Specifically, for two variables x1 and x2, where x1 corresponds to the coordinate or polar diameter information of the target hole profile and x2 corresponds to the coordinate or polar diameter information of the rotation projection profile, the linear correlation between the two variables can be accurately measured by calculating the Pearson correlation coefficient. xx The calculation formula is:

[0060]

[0061] Among them, x 1i and x 2i are the i-th observation values ​​of variables x1 and x2, respectively. and are the means of x1 and x2 respectively, and n is the number of observations.

[0062] The data sequences of the target hole profile and the rotation projection profile in the abscissa, ordinate, and polar directions are read from the storage medium. For the target hole profile data and the rotation projection profile data at the same polar angle, the correlation coefficient is calculated in the abscissa, ordinate, and polar dimensions according to the Pearson correlation coefficient calculation formula.

[0063] The Pearson correlation coefficient is a statistic used to measure the linear correlation between two variables. Its value range is usually within the closed interval [-1, 1]. To facilitate comprehensive comparison and analysis of this correlation coefficient with other similarity indicators, a linear transformation method is used to map the correlation coefficient range to the interval [0, 1].

[0064] The specific linear transformation formula used is: y=0.5x+0.5, where x is the original Pearson correlation coefficient and y is the transformed correlation coefficient.

[0065] After completing the normalization processing of the correlation coefficient, the average value of the normalized correlation coefficient is calculated, and this average value is used as an indicator to measure the similarity between the two sets of data of the target hole profile and the rotation projection profile in terms of the linear relationship of the variables.

[0066] When the correlation coefficient is 0, it indicates that there is a completely negative linear correlation between the horizontal coordinate of the target profile and the horizontal coordinate of the projection profile, and between the vertical coordinate of the target profile and the vertical coordinate of the projection profile, that is, an increase in one variable corresponds to an equal proportion decrease in the other variable.

[0067] When the correlation coefficient is 1, it indicates that there is a complete positive linear correlation between the horizontal and vertical coordinates, that is, the changing trends of the two variables are highly consistent, showing the characteristics of increasing and decreasing together.

[0068] When the correlation coefficient is 0.5, it means that the similarity between the horizontal and vertical axes is at a medium level.

[0069] It is understandable that in the actual data processing process, since data point sampling or discretization operations will inevitably introduce errors, it is almost impossible for the correlation coefficient to be exactly 0, 0.5 and 1 in theory.

[0070] ② Hausdorff distance calculation

[0071] The directed Hausdorff distance is calculated for the polar coordinate point sets of the target hole contour and the rotated projection contour. The Hausdorff distance formula is a measure of the similarity between two sets of points. It is a definition of the distance between two sets of points.

[0072] The one-way Hausdorff distance corresponding to the maximum value of the minimum distance between the polar coordinate point set of the net target hole contour and the polar coordinate point set of the rotated projection contour is calculated respectively, and then the maximum value of the one-way Hausdorff distance between the two sets of polar coordinate point sets is taken as the two-way Hausdorff distance. At the same time, the maximum value of the two-way Hausdorff distance between the net target hole contour and the rotated projection contour is calculated.

[0073] Specifically, take two sets A={a1,…a p}, B={b1,…,b p} as an example, the Hausdorff distance between these two point sets is defined as: H(A,B)=max(h(A,B),h(B,A)).

[0074] Among them, the one-way Hausdorff distance Here, ||·|| represents the distance norm between point sets A and B, usually the L2 norm. The bidirectional Hausdorff distance H(A,B) takes the larger value of the unidirectional distance h(A,B) and h(B,A), which measures the maximum mismatch between the two point sets.

[0075] To visualize the Hausdorff distance, this application first calculates the maximum distance between all points in each of the two point sets and the origin. The sum is then used to normalize the Hausdorff distance, ensuring that the normalized Hausdorff distance lies within the [0, 1] interval. A smaller Hausdorff distance indicates a higher degree of similarity between the target hole profile and the rotated projection profile; a smaller Hausdorff distance indicates a lower degree of similarity.

[0076] ③PCA similarity calculation

[0077] Principal Component Analysis (PCA) is a statistical method widely used for data dimensionality reduction and feature extraction. Its core goal is to map the original data onto a new set of orthogonal coordinate axes, known as the principal components of the original data. Each principal component axis corresponds to an eigenvector and an eigenvalue: the eigenvector characterizes the trend of data variation along the principal component axis and clarifies the main direction of the data distribution; the eigenvalue reflects the variance of the data along the principal component axis. Variance is a key indicator of data dispersion; a larger value indicates a more dispersed distribution of the data in that direction, and the corresponding principal component axis length is longer.

[0078] In this application, the data processing of the target hole profile and the rotated projection profile begins by converting the polar coordinates of the target hole profile and the rotated projection profile into rectangular coordinates to unify the data format and facilitate subsequent analysis. Next, principal component analysis (PCA) is used to process the converted rectangular coordinate data to obtain the eigenvalues ​​and eigenvectors of the target hole profile and the rotated projection profile. The eigenvalues ​​quantify the degree of data dispersion along each principal component axis, while the eigenvectors indicate the direction of the principal component axis.

[0079] Specifically, the calculation process of PCA principal component analysis is as follows:

[0080] Suppose there are m 2-net target hole contours and rotation projection contour data point coordinates, with matrix X 2×m =[x1,x2,...,x m ] represents, where each x is a two-dimensional column vector. To eliminate the deviation of the data center, the formula is used Decentralize the data so that the mean is zero.

[0081] By the formula C=XX T / m calculates the corresponding covariance matrix C. The covariance matrix reflects the correlation between the dimensions of the data and is the basis for subsequent feature extraction.

[0082] Perform eigenvalue decomposition on the covariance matrix C to obtain the characteristic matrix (arranged from large to small by eigenvalue). Take the first k columns to form the matrix P 2×k , at this time P is equivalent to a new coordinate system, in which each column is a coordinate axis, and these coordinate axes are the principal component axes.

[0083] Project the original data X into the P coordinate system to obtain the reduced-dimensional data In this way, the data is reduced from two-dimensional space and the main feature information is retained.

[0084] In the present application, in the PCA analysis, in order to unify the data processing method, the polar coordinates of the net target hole profile and the rotated projection profile are converted into rectangular coordinates, and the respective principal component axis vectors and the length and direction of the axis vector orthogonal thereto are calculated. However, when calculating the vector angle, the vector length may interfere with the result, resulting in the inability to accurately reflect the vector direction relationship. Therefore, the vector is normalized so that its modulus is 1. The dot product formula is used to calculate the cosine value of the normalized vector angle, and the angle between the principal component axes between the net target hole profile and the rotated projection profile, and between the rotated projection profile and the rotated projection profile are further obtained (unit: degree). From a geometric point of view, the length of the principal component axis is determined by taking the square root of the corresponding eigenvalue, so that the principal component axis lengths of the net target hole profile and the rotated projection profile can be obtained at the same time.

[0085] In this application, the ratio of the relatively small to relatively large lengths of the principal component axes of the target hole profile is compared with a threshold value A (ranging from 0.7 to 0.9) to determine the combination of weight coefficients for the subsequent similarity criterion. Furthermore, the similarity criterion comprehensively considers factors such as the angle between the principal component axes and the length difference between the principal component axes to assess the similarity between the target hole profile and the rotated projection profile data. This comprehensive evaluation method can more comprehensively and accurately reflect the degree of similarity between the target hole profile and the rotated projection profile data.

[0086] ④ Comprehensive similarity assessment

[0087] Considering the different characteristics of the target contour, the processing process is divided into two cases:

[0088] a) The flying body has prominent head features

[0089] When the head features of the flying object are prominent in the target hole profile, that is, the ratio of the shorter to longer axes of the principal component axes of the target hole profile is less than threshold A (range of 0.7-0.9), the principal component results of the target hole profile have obvious characteristics. In this case, principal component analysis becomes a key step in this application.

[0090] The specific processing process is as follows:

[0091] Data sorting: Arrange the Pearson correlation coefficient between the target hole profile and the rotation projection profile from large to small, and arrange the Hausdorff distance, the angle between the PCA principal component axes, and the length difference between the PCA principal component axes from small to large.

[0092] Preliminary screening: The files are preliminarily screened with the constraint that the Pearson correlation coefficient, Hausdorff distance and PCA principal component axis length difference data are all within threshold B (the first 5%-15% in the arrangement).

[0093] Final judgment: The minimum angle between the PCA principal component axes is used as the final judgment condition. The files that meet the conditions are selected from the initially screened files, and their corresponding posture angles are the final results.

[0094] b) The outline basically shows the characteristics of the tail skirt

[0095] When the ratio of the shorter to longer axes of the target's principal component axes exceeds threshold A (ranging from 0.7 to 0.9), the profile essentially exhibits only tail skirt features, significantly reducing the effectiveness of principal component analysis and causing the length and direction of the principal component axes to become unstable. In this case, the similarity or overlap between the target and the projected profile becomes a key factor. The specific processing steps are as follows:

[0096] Data sorting: Similarly, the Pearson correlation coefficients of the target hole profile and the rotation projection profile are arranged from large to small, and the Hausdorff distance, the angle between the PCA principal component axes, and the length difference of the PCA principal component axes are arranged from small to large.

[0097] Preliminary screening: The files are preliminarily screened with the constraint that the Hausdorff distance, the difference in length of the PCA principal component axes, and the angle between the PCA principal component axes are all within the threshold B (the first 5%-15% in the arrangement).

[0098] Final judgment: Given that the Hausdorff distance is sensitive to the target hole profile data, the maximum value of the Pearson correlation coefficient is used as the final judgment condition. The file that meets the condition is selected from the initially screened files, and its corresponding attitude angle is the final result.

[0099] Through the similarity analysis in the above two cases, the present application can determine the corresponding attitude angle of the rotational projection profile that best matches the net target hole profile, thereby achieving accurate matching of the net target hole profile and the rotational projection profile attitude.

[0100] 3) Display the net target hole contour, the optimal attitude angle, and the projection contour at the attitude angle adjacent to the optimal attitude angle in the polar coordinate system, and draw the principal component axes of the net target hole contour and the projection contour at the optimal attitude angle to construct a visual graph.

[0101] After completing the similarity judgment, in order to intuitively present the matching results between different targets and different projection profiles, this application implements the following visualization steps:

[0102] ① Determination of posture angle list and contour drawing

[0103] With the best-matching attitude angle as the center, a list of nearby attitude angles is determined. Subsequently, the target hole outline, the projection outline at the best-matching attitude angle, and the projection outlines at nearby attitude angles are plotted in a polar coordinate system. This clearly demonstrates the relative position and morphological differences between the target and the projection outlines at different attitude angles.

[0104] ②PCA principal component axis drawing

[0105] In polar coordinates, the principal component axes (PCA) of the target hole profile and the best-matched attitude angle projection profile are plotted. The lengths and directions of the principal component axes are displayed with the origin as their midpoints. The lengths of the principal component axes are displayed based on the actual calculated lengths, their corresponding angles are calculated using vector dot products, and their orientations are determined by the calculated eigenvectors. By plotting the principal component axes, the main characteristic directions and distribution ranges of the target hole profile and the flight object projection profile can be intuitively visualized.

[0106] ③Add legend and save pictures

[0107] Add a legend to the drawn graph, annotating relevant information such as the target hole outline, the best matching attitude angle projection outline, the nearby attitude angle projection outline, and the PCA principal component axes to facilitate understanding of the graph content. Finally, save the drawn visualization image to a designated directory for subsequent analysis and use.

[0108] Comprehensive similarity results display

[0109] In addition to the above visualizations, the matching results between different targets and different projected profiles are specifically output, specifically the maximum value for each similarity criterion. The figure also displays a single target profile, the profile at the angle with the highest similarity after matching, and the rotated projected profile for the angle one step around the best matching profile. Furthermore, the principal component axes orthogonal to each other are plotted, representing the target profile and the profile at the angle with the highest overall similarity.

[0110] In this application, in order to fully evaluate the effectiveness, stability, and anti-interference ability of the method proposed in this application, it is necessary to conduct feasibility verification and sensitivity analysis on the method, and eliminate the interference of the flying object shape on the identification results. The specific implementation steps are as follows:

[0111] a) Feasibility verification

[0112] From a library of contour files extracted from rotating projections of flying objects, several sets of projection contours with different attitude angles were selected. These selected results were used as the target hole contour input, and a series of similarity analyses were performed according to the method described in this application. The feasibility of the similarity method described in this application was verified by comparing the final recognition results with the attitude angles corresponding to the input projection contours. If the recognition results closely matched the input attitude angles, it demonstrated that the method was feasible both theoretically and practically.

[0113] b) Sensitivity analysis

[0114] In the process of using the projected contour as the target hole contour input in step a), a certain degree of perturbation is artificially added or partially reduced. Similarity analysis is then performed again to observe whether the final recognition result is consistent with the pose angle corresponding to the input projected contour. This method evaluates its sensitivity to input data perturbations. If the recognition result remains consistent with the input pose angle despite perturbations, the method demonstrates good stability and anti-interference capabilities.

[0115] c) Elimination of interference from the flight body's shape

[0116] Based on the previous analysis results of explosively formed irregular flying bodies, a geometric model of a rotating body with a similar but regular shape was constructed, and a corresponding rotation projection profile database was established. Using the data in the irregular shape library, a similarity analysis was performed on the projection profiles of regular shapes under certain selected attitude angles. By observing the response of the recognition results to changes in the shape of the flying body, it was determined whether the recognition results remained consistent. If the recognition results can remain stable and consistent with the actual attitude angle under different shape conditions, the interference of the flying body shape on the recognition results can be eliminated, further demonstrating the effectiveness and universality of the method of this application.

[0117] In certain embodiments, the uncertainty in the reliability verification is analyzed.

[0118] During the reliability verification process, the identification results are used as input to examine their consistency. If the identification results are completely consistent, the uncertainty range can be temporarily disregarded. However, in practical applications, various factors can cause the final identification results to not fully match the actual attitude angles. These factors primarily include errors introduced during the extraction of the net target hole profile data, errors in the data processing method, and errors caused by the number of samples.

[0119] According to GB / T 27418-2017 "Evaluation and Expression of Uncertainty in Measurement", the sources of uncertainty can be divided into Class A and Class B. In light of the background of this application, the specific sources of uncertainty are as follows:

[0120] Type A uncertainty is primarily due to random errors, specifically random deviations in the manual extraction of the target hole profile, such as visual errors from clicks and fluctuations in mouse operation. When the same set of target hole profile data is input into the algorithm multiple times, these deviations may cause fluctuations in the output results due to numerical rounding or iterative convergence differences, thus forming Type A uncertainty.

[0121] Type B uncertainty is mainly caused by systematic errors, including operator habitual bias (for example, always marking contour points on the inside or outside of the hole), image resolution limitations (quantization errors caused by pixel size), geometric simplification of the flying body digital model (such as ignoring surface roughness), rotational projection algorithm errors (such as deviations introduced by discrete angle steps), camera lens distortion, perspective distortion caused by the non-parallelism of the target plane and the image, and other factors.

[0122] To determine the above uncertainty, during the feasibility verification process, this application artificially adds or reduces disturbances when extracting the contour of a single net target, obtaining a series of identified attitude angle results and the specific values ​​of the corresponding final judgment conditions (assuming that this is the angle between the PCA principal component axes). First, the mean of these results is calculated using formula (3); second, the experimental standard deviation is calculated according to Bessel formula (4), thereby obtaining the Class A uncertainty u of the single net target hole contour under the final judgment condition value. A (θ). After performing similar operations on each target hole profile, the resulting Type A uncertainty is averaged to obtain the final average Type A uncertainty. This method can more accurately assess the reliability of the identification results.

[0123]

[0124] Among them, θ i It is the respective PCA principal component axis angle value obtained after multiple extractions of single net target hole profile data and similarity analysis, and n is the number of data extractions for a single net target hole profile.

[0125] Calculate the Class B uncertainty value according to the following formula (5):

[0126]

[0127] Where a is the half-width of the confidence interval and k is the confidence factor.

[0128] For the uncertainty of type B, its specific components are determined according to different error types. When extracting the hole contour of the net target, there is a systematic deviation u distributed in a rectangular manner. B1 ; During the digital model projection process, there will be a triangular distribution error u B2 In addition, when the image acquisition device is not parallel to the target, a normally distributed error u will be generated.B3 .

[0129] Comprehensively consider the above errors to synthesize the uncertainty u c Calculation:

[0130]

[0131] Among them, u A Represents the average Type A uncertainty.

[0132] According to the international convention, the confidence factor k = 2, then the interval [q-2u c ,q+2u c ] has a confidence level of about 95%. Substituting k=2 into the formula U=k·u c , the expanded uncertainty U can be obtained.

[0133] In the final judgment condition data, all attitude angles within the expanded uncertainty range, centered around the calculated average value, are accepted. The attitude angle results obtained through data identification constitute a set that meets the specific conditions. The calculation formulas for Class A, Class B, combined uncertainty, and expanded uncertainty are summarized in Table 1.

[0134] Table 1

[0135]

[0136] In summary, this application scientifically divides similarity matching conditions into two types based on the contour features of the target hole. During data processing, dimensionality reduction is performed to reduce data complexity and extract key features. During similarity determination, an innovative combination of multiple similarity indicators is employed, comprehensively considering multi-dimensional information to ensure the accuracy and reliability of the results, which are then used as the ultimate goal.

[0137] Furthermore, to validate the effectiveness and stability of this method, comprehensive and detailed feasibility verification and sensitivity testing were conducted. By simulating various operating conditions and data perturbations, the method's applicability and robustness were verified under various conditions. Furthermore, considering that the shape of the flying object may interfere with the identification results, a correlation analysis was conducted to eliminate this interference factor, ensuring that the accuracy of the identification results depends solely on the similarity between the net target profile and the rotated projection profile itself.

[0138] In terms of uncertainty assessment, an expanded uncertainty range for data identification was determined, providing quantitative error information for the identification results, making them more scientific and reliable. Through this rigorous series of operations and analyses, the similarity between the target profile and the rotational projection profile can be comprehensively and accurately assessed, ultimately completing the target data identification task efficiently and accurately.

Claims

1. A multi-index fusion identification method for flight body attitude angle based on target data, characterized by: include: Based on the rectangular coordinate system, the real coordinate point set of the net target hole contour and the coordinate point set of the flying body rotation projection contour are respectively obtained, and the polar coordinate point set is extracted according to the coordinate point set of the net target hole contour and the flying body rotation projection contour; Based on the coordinate point set and polar coordinate point set of the target hole profile and the rotation projection profile, the Pearson correlation coefficient, Hausdorff distance, PCA principal component axis angle and principal component axis length difference are calculated respectively. Based on the calculation results, similarity analysis is performed to determine the optimal attitude angle of the flying body. The net target hole contour, the optimal attitude angle and the projection contour at the attitude angle adjacent to the optimal attitude angle are displayed in the polar coordinate system, and the principal component axes of the net target hole contour and the projection contour at the optimal attitude angle are drawn to construct a visual graph.

2. The multi-index fusion identification method for flight body attitude angle according to claim 1, characterized in that: Obtaining a set of real coordinate points of the outline of the hole in the target includes: placing a calibration reference object with a predetermined physical size on the imaging plane of the target, calculating a ratio coefficient between the pixel span of the calibration reference object in the digital image and its physical size, converting the pixel coordinates of the captured image of the outline of the hole in the target into actual length, and obtaining a set of real coordinate points of the outline of the hole in the target.

3. The multi-index fusion identification method for flight body attitude angle according to claim 1, characterized in that: The coordinate point set for obtaining the rotating projection profile of the flying object includes: The three-dimensional data in the body axis coordinate system of the flying body is converted into the earth axis coordinate system through the rotation matrix; wherein the rotation angle covers the full attitude range; Perform orthogonal projection on the converted three-dimensional data to generate a two-dimensional projection point cloud; The alpha_shapes algorithm is used to extract boundary contours from the two-dimensional projected point cloud and discretize it into an ordered coordinate point set.

4. The multi-index fusion identification method for flying body attitude angle according to claim 1, characterized in that: The polar coordinate point set is extracted based on the coordinate point set of the target hole contour and the rotating projection contour of the flying body, including: Convert the coordinate point sets of the target hole contour and the rotation projection contour into polar coordinate parameters respectively; Implement Z-score outlier detection and elimination based on predefined standard deviation threshold for polar angle and diameter sequences of polar coordinate parameters; For the processed data, IQR outlier points are secondary eliminated based on the interquartile range criterion to obtain the polar coordinate point set.

5. The multi-index fusion identification method for flying body attitude angle according to claim 4 is characterized in that: Perform Z-score normalization on the polar angle and polar diameter sequence sets, calculate the Z-score values ​​of the data points, and identify data points with absolute values ​​greater than 3 as abnormal data points and eliminate them; The interquartile range of the data is calculated for the data point set after Z-score processing, and the upper and lower limits of the outliers are determined based on the interquartile range. The abnormal data points outside the upper and lower limits are identified and removed.

6. The multi-index fusion identification method for flying body attitude angle according to claim 1, characterized in that: The similarity analysis based on the calculation results determines the optimal attitude angle of the flying body, including: Arrange the Pearson correlation coefficient in descending order, and the Hausdorff distance, PCA principal component axis angle, and principal component axis length difference in ascending order; Processing is performed based on the relationship between the ratio of the shorter principal component axis to the longer principal component axis of the PCA of the target hole profile and a predetermined threshold value A: a) when the ratio is less than the predetermined threshold value A, a data subset is selected whose Pearson coefficient, Hausdorff distance, and axis length difference are all within the sorting threshold value B, and the posture angle with the smallest PCA principal component axis angle is selected from the subset; b) when the ratio is greater than the predetermined threshold value A, a data subset is selected whose Hausdorff distance, PCA principal component axis angle, and principal component axis length difference are all within the sorting threshold value B, and the posture angle with the largest Pearson correlation coefficient is selected from the subset; Obtain the optimal attitude angle of the flying object that matches the hole contour of the net target.

7. The multi-index fusion identification method for flying body attitude angle according to claim 6, characterized in that: The threshold A is set to 0.7-0.9, and the threshold B is set to the top 5%-15% of the ranking.

8. The multi-index fusion identification method for flying body attitude angle according to claim 1, characterized in that: The projection profiles of the target hole, the optimal attitude angle, and the attitude angles adjacent to the optimal attitude angle are displayed in the polar coordinate system, including: Taking the optimal attitude angle as a reference, determining an attitude angle sequence including the optimal attitude angle and adjacent attitude angles within a preset deviation range; In the polar coordinate system, the following are simultaneously presented: the discrete coordinate point set of the target hole contour, the projection contour of the flying body corresponding to the optimal attitude angle, and the projection contours corresponding to other attitude angles in the attitude angle sequence.

9. The multi-index fusion identification method for flying body attitude angle according to claim 1, characterized in that: Drawing the principal component axis of the net target hole contour and the optimal posture angle projection contour includes: performing principal component analysis based on the coordinate point set of the net target hole contour and the optimal matching projection contour, and generating a visualization axis with the origin of the coordinate system as the center point and the extension direction consistent with the principal component vector.

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