A method for monitoring the health status of a spacecraft control system based on polygon similarity

Abstract

A method for monitoring the health status of a spacecraft control system based on polygon similarity includes: normalizing spacecraft data; performing feature extraction based on principal component analysis on the data after normalization; constructing a polygon by connecting vertices with each other with each feature as a vertex; calculating the similarity of the polygon to perform spacecraft health monitoring. By analyzing errors such as the perimeter of the polygon and the peak value, difference value, and absolute value of the curves indicated by each vertex, the present invention measures the similarity of the polygon in all aspects, ensuring the accuracy of spacecraft health status monitoring. At the same time, the correlation relationship between multi-dimensional data is presented in the form of a polygon, which can be presented very simply and intuitively when abnormal signs appear, improving the visualization level of spacecraft health monitoring.

Description

Technical Field

[0001] The present invention belongs to the field of aerospace and relates to a method for monitoring the health status of a spacecraft control system based on polygon similarity. Background Art

[0002] Although the current spacecraft health status monitoring can achieve full-parameter monitoring, it generally uses the single-parameter threshold detection method. The threshold is generally determined in the design stage by the method of "ground normal test + fault mode analysis", and is not optimized according to the telemetry data during the actual on-orbit process, and the coupling situation of multi-dimensional parameters is not considered, which results in low accuracy of spacecraft health status monitoring or untimely alarm. For example, in China, there was a case where a certain service was suddenly interrupted due to the failure of a momentum wheel. It was found afterwards that each parameter of the momentum wheel was within the threshold range, but through the collaborative analysis of multiple parameters, the abnormality of the product could be detected nearly 20 hours in advance. Summary of the Invention

[0003] The technical problem solved by the present invention is: to overcome the deficiencies of the prior art, a method for monitoring the health status of a spacecraft control system based on polygon similarity, to realize the extraction of implicit features and the collaborative analysis between multi-dimensional data, and to improve the visualization degree and accuracy of multi-parameter health status monitoring of spacecraft.

[0004] The technical solution of the present invention is: a method for monitoring the health status of a spacecraft control system based on polygon similarity, and the steps are as follows:

[0005] 1) Normalize the spacecraft data;

[0006] 2) Perform feature extraction based on principal component analysis on the data after normalization;

[0007] 3) Use each feature as a vertex, and construct a polygon by connecting the vertices;

[0008] 4) Calculate the similarity of the polygon to perform spacecraft health monitoring.

[0009] The specific process of the step 1) is:

[0010] Assume that the dimension of the spacecraft data to be monitored is N, and normalize the spacecraft data:

[0011]

[0012] Where: x i represents the i-th dimension data of the spacecraft, i = 1, 2,..., N, represents the data after normalization, x i,minrepresents the minimum value of the i-th dimensional data of the spacecraft within a limited time period under normal conditions, x i,max represents the maximum value of the i-th dimensional data of the spacecraft within a limited time period under normal conditions.

[0013] The specific process of step 2) is as follows:

[0014] Assume that the sample matrix mentioned after the normalization of the normal data of the spacecraft is X ∈ R M × N , where M is the number of observed samples and N is the number of variables. Feature extraction is performed on the sample matrix X:

[0015] 2a. Calculate the covariance matrix of the sample matrix X:

[0016]

[0017] where: COV(X) represents the covariance matrix of matrix X, and C ij represents the element in the i-th row and j-th column of the covariance matrix C, i = 1, 2,..., n, j = 1, 2,..., m;

[0018] 2b. Calculate the eigenvalues λ i and the corresponding eigenvectors u i , where i = 1, 2,..., N;

[0019] 2c. Arrange the eigenvalues in descending order, and calculate the cumulative contribution rate of the first k principal components according to the following formula:

[0020]

[0021] 2d. When the calculated cumulative contribution rate is greater than the threshold, extract the eigenvectors corresponding to the first k eigenvalues including this principal component to form the transformation matrix P k :

[0022] P k = [u1 u2 … u k , k < N;

[0023] where: u l represents the l-th eigenvector of P k , l = 1, 2,..., k.

[0024] The specific process of step 3) is as follows:

[0025] Assume that the data after feature extraction is Y = XP k = [y1 y2 … y k , where y lDenote the l-th eigenvector of Y, where l = 1, 2,..., k. For the j-th feature of the m-th sample, where m = 1, 2,..., M and j = 1, 2,..., k, calculate its position according to the following formula:

[0026] a m,j = y m,j cosθ

[0027] b m,j = y m,j sinθ

[0028] where y m,j denotes the m-th row of y j and θ = 2π / k;

[0029] Taking a m,j as the horizontal axis and b m,j as the vertical axis, determine the position of the j-th feature in the m-th sample, and then construct a polygon by connecting the vertices with lines between the vertices;

[0030] In the spacecraft health status monitoring, each feature has a maximum value under normal circumstances; assume x r = [1 1 …1], and the data after feature extraction is y r = x r P k , and according to obtain the position when each feature takes the maximum value, and then get the polygon formed by taking the maximum value at each vertex, which we call the reference polygon.

[0031] The specific process of step 4) is as follows:

[0032] For the constructed polygon, calculate the similarity S error between the polygon of the m-th sample and the reference polygon in real time according to the perimeter error L perk of the polygon, the peak error E error,perk of the polygon, the difference error E error of the polygon, and the absolute error E error of the polygon. When the polygon similarity exceeds the threshold, it is considered that the spacecraft has an anomaly, otherwise it is considered that the spacecraft is normal.

[0033] The similarity of the polygon where δ i represents the weight coefficient, i = 1, 2, 3, 4, satisfying 0 ≤ δ i ≤ 1 and δ1 + δ2 + δ3 + δ4 = 1.

[0034] The calculation method of the perimeter error L error of the polygon is as follows:

[0035] Let Li,j Denote the length between vertex \(i\) and vertex \(j\), which is calculated by the following formula:

[0036]

[0037] Then the perimeter \(L\) of the polygon is \(L = L 1,2 +L 2,3 + \cdots+L k,1 .

[0038] The perimeter error obtained by comparing with the reference polygon is:

[0039] L error =L - L r

[0040] where \(L r denotes the perimeter of the reference polygon.

[0041] The calculation method of the peak error \(E\) of the polygon perk is as follows:

[0042]

[0043] where \(y max =\max(y m,1 ,y m,2 ,\cdots,y m,k ), \(y min =\min(y m,1 ,y m,2 ,\cdots,y m,k ), \(y r,max =\max(y r,1 ,y r,2 ,\cdots,y r,k ), \(y r,min =\min(y r,1 ,y r,2 ,\cdots,y r,k ).

[0044] The calculation method of the difference error \(E error,perk is as follows:

[0045]

[0046] where \(y error,max =\max(y m,1 - y r,1 ,y m,2 - y r,2 ,\cdots,y m,k - y r,k ), \(y error,min =\min(y m,1 - y r,1 ,y m,2 - yr,2 ,…, y m,k -y r,k )。

[0047] The absolute error E error is calculated as follows:

[0048]

[0049] where

[0050] The advantages of the present invention compared with the prior art are as follows:

[0051] (1) The correlation relationship between multi-dimensional data is presented in a vivid and intuitive way of a polygon. When abnormal signs appear, it can be presented very simply and intuitively, improving the visualization level of spacecraft health monitoring.

[0052] (2) By analyzing the perimeter of the polygon and the peak values, differences, and absolute values of the curves shown by each vertex, etc., the similarity of the polygon is measured comprehensively, ensuring the accuracy of spacecraft health status monitoring. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 is a flowchart of the method of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0054] As Figure 1 shown, the steps of the present invention are specifically as follows:

[0055] (1) Normalization processing of spacecraft data.

[0056] (2) Feature extraction based on principal component analysis for the data after normalization processing.

[0057] (3) Construct a polygon by connecting the vertices with each feature as a vertex.

[0058] (4) Calculate the similarity of the polygon and perform spacecraft health monitoring.

[0059] Specifically as follows:

[0060] (1) Embodiment of Step 1:

[0061] Assume that the dimension of the spacecraft data to be monitored is N. First, normalize the data:

[0062]

[0063] where: x i represents the i-th dimensional data of the spacecraft (i = 1, 2,..., N), Represents the normalized data, x i,min Represents the minimum value of the i-th dimensional data of the spacecraft within a finite time period under normal conditions, x i,max Represents the maximum value of the i-th dimensional data of the spacecraft within a finite time period under normal conditions. It should be noted that the spacecraft data considered in this patent is stationary data.

[0064] (2) Implementation method of Step 2:

[0065] Assume that the sample matrix mentioned after the normalization process of the spacecraft normal data is X ∈ R M×N (M is the number of observation samples, N is the number of variables), and the following steps are used to extract features from the sample matrix X:

[0066] a. Calculate the covariance matrix of the sample matrix X:

[0067]

[0068] Where: COV(X) represents the covariance matrix of matrix X, C ij Represents the element in the i-th row and j-th column of the covariance matrix C (i = 1, 2,..., n, j = 1, 2,..., m).

[0069] b. Calculate the eigenvalues λ i and the corresponding eigenvectors u i , where i = 1, 2,..., N.

[0070] c. Arrange the eigenvalues in descending order, and calculate the cumulative contribution rate of the first k principal components according to the following formula:

[0071]

[0072] d. When the calculated cumulative contribution rate is greater than the threshold, extract the eigenvectors corresponding to the first k eigenvalues including this principal component to form the transformation matrix P k :

[0073] P k = [u1 u2…u k , k < N

[0074] Where: u l Represents the l-th eigenvector of P k , l = 1, 2,..., k.

[0075] The cumulative contribution rate is used to measure the degree of information preservation of the new component to the original data. Generally, it is required that the cumulative contribution rate threshold is greater than 85%.

[0076] (3) Implementation method of Step 3:

[0077] Assume that the data after feature extraction is Y = XP k = [y1 y2 … y k (y l represents the l-th eigenvector of Y, l = 1, 2,..., k). For the feature j of the m-th sample (m = 1, 2,..., M, j = 1, 2,..., k), calculate its position according to the following formula:

[0078] a m,j = y m,j cosθ

[0079] b m,j = y m,j sinθ

[0080] where, y m,j represents the m-th row of y j , θ = 2π / k.

[0081] Taking a m,j as the horizontal axis and b m,j as the vertical axis, determine the position of feature j in the m-th sample, and then construct a polygon by connecting the vertices with each other with each feature as a vertex.

[0082] In the spacecraft health state monitoring, each feature has a maximum value under normal circumstances. Assume x r = [1 1 …1], and the data after feature extraction is y r = x r P k , and according to obtain the position when each feature takes the maximum value, and then get the polygon formed by taking the maximum value at each vertex, which we call the reference polygon.

[0083] During the spacecraft health state monitoring process, observe the change of the polygon. When it exceeds the range of the reference polygon, it is considered that the spacecraft has an anomaly, realizing the visual monitoring of multiple parameters of the spacecraft.

[0084] (4) Implementation method of step four:

[0085] For the constructed polygon, use the following calculation formula to calculate the similarity S between the polygon of the m-th sample and the reference polygon in real time error , when the polygon similarity exceeds the threshold, it is considered that the spacecraft has an anomaly, otherwise it is considered that the spacecraft is normal (this threshold is generally given by experts).

[0086] a. Perimeter error of the polygon.

[0087] Let L i,jDenote the length between vertex \(i\) and vertex \(j\), which is calculated using the following formula:

[0088]

[0089] Then the perimeter \(L\) of the polygon is \(L = L\) 1,2 + \(L\) 2,3 + \(\cdots\) + \(L\) k,1 .

[0090] The perimeter error compared with the reference polygon is:

[0091] \(L\) error = \(L - L\) r

[0092] where \(L\) r represents the perimeter of the reference polygon, and its calculation formula is similar to that of \(L\).

[0093] b. Peak error, difference error and absolute error of the polygon

[0094] Split the polygon into curves, and calculate the peak error, difference error and absolute error by comparing with the curves shown in the reference polygon.

[0095] The formula for calculating the peak error is as follows:

[0096]

[0097] The formula for calculating the difference error is as follows:

[0098]

[0099] The formula for calculating the absolute error is as follows:

[0100]

[0101] where \(y\) max = \(\max(y\) m,1 , \(y\) m,2 , \(\cdots\), \(y\) m,k ), \(y\) min = \(\min(y\) m,1 , \(y\) m,2 , \(\cdots\), \(y\) m,k ), \(y\) r,max = \(\max(y\) r,1 , \(y\) r,2 , \(\cdots\), \(y\) r,k ), \(y\) r,min = \(\min(y\) r,1 , \(y\) r,2 , \(\cdots\), \(y\) r,k ), \(y\) error,max = \(\max(y\) m,1 - \(y\) r,1 , \(y\)m,2 -y r,2 ,…,y m,k -y r,k ), y error,min = min(y m,1 -y r,1 , y m,2 -y r,2 ,…,y m,k -y r,k ),

[0102] c. Similarity of the polygon

[0103]

[0104] wherein, δ i represents the weight coefficient (i = 1, 2, 3, 4), satisfying 0 ≤ δ i ≤ 1 and δ1 + δ2 + δ3 + δ4 = 1, and the specific value of δ i is generally determined by the attention degrees of the perimeter error, peak error, difference error and absolute error.

[0105] Although the present invention has been disclosed above with preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make possible changes and modifications to the technical solution of the present invention without departing from the spirit and scope of the present invention. Therefore, any simple modification, equivalent change and modification made to the above embodiments according to the technical essence of the present invention without departing from the technical solution of the present invention shall fall within the protection scope of the technical solution of the present invention.

Claims

1. A method for monitoring the health status of a spacecraft control system based on polygon similarity, characterized in that The steps are as follows: 1) Normalize the spacecraft data; 2) Perform feature extraction based on principal component analysis on the data after normalization to form a transformation matrix; 3) Use each feature as a vertex and construct a polygon and a reference polygon through the connections between vertices; 4) Calculate the similarity of the polygon and perform health monitoring of the spacecraft based on this similarity; The specific process of the normalization in step 1) is as follows: Assume that the dimension of the spacecraft data to be monitored is N, and normalize the spacecraft data: where: x i represents the i-th dimensional data of the spacecraft, i = 1, 2, ..., N, represents the data after normalization, x i,min represents the minimum value of the i-th dimensional data of the spacecraft within a finite time period under normal conditions, x i,max represents the maximum value of the i-th dimensional data of the spacecraft within a finite time period under normal conditions; The specific process of the feature extraction and forming the transformation matrix in step 2) is as follows: Let the sample matrix after normalizing the normal data of the spacecraft be \(X\in R\) M×N , where \(M\) is the number of observation samples and \(N\) is the number of variables; 2a. Calculate the covariance matrix of the sample matrix X; Where: COV(X) represents the covariance matrix of matrix X, and C ij represents the element in the i-th row and j-th column of the covariance matrix C, where i = 1, 2, ..., n and j = 1, 2, ..., m; 2b. Calculate the eigenvalues λ of the covariance matrix C i and the corresponding eigenvectors u i , where i = 1, 2,..., N; 2c. Arrange the eigenvalues in descending order and calculate the cumulative contribution rate of the first k principal components according to the following formula: 2d. When the calculated cumulative contribution rate is greater than the threshold value, extract the eigenvectors corresponding to the first k eigenvalues including this principal component to form the transformation matrix P k : P k = [ u1 u2 … u k , k < N; where: u l represents the l-th eigenvector of P k , where l = 1, 2, ..., k; The specific process of constructing the polygon in step 3) is as follows: Let the data after feature extraction be Y = XP k = [y1 y2 … y k , where yl represents the l-th eigenvector of Y, l = 1, 2, ..., k. For the feature j of the m-th sample, m = 1, 2, ..., M, j = 1, 2, ..., k, then the position of the feature j of the m-th sample is: a m,j = y m,j cos θ b m,j = y m,j sin θ where y m,j represents the m-th row of y j , θ = 2π / k; With a m,j as the horizontal axis and b m,j as the vertical axis, determine the position of feature j in the m-th sample, and then construct a polygon with each feature as a vertex by connecting the vertices. In the health state monitoring of spacecraft, each feature has a maximum value; assume x r = [11…1], and the data after feature extraction is y r = x r P k , obtain the positions when each feature takes the maximum value, and then obtain the polygon formed by each vertex taking the maximum value, which is the reference polygon.

2. The method for monitoring the health state of a spacecraft control system based on polygon similarity according to claim 1, characterized in that: The specific process of step 4) is as follows: For the constructed polygon, the perimeter error L of the polygon is calculated in real time error , the peak error E of the polygon perk , the difference error E error,perk , the absolute error E error , and the similarity S between the polygon of the m-th sample and the reference polygon is calculated error . When the polygon similarity exceeds the threshold, it is considered that the spacecraft is abnormal; otherwise, the spacecraft is considered normal.

3. The health state monitoring method of a spacecraft control system based on polygon similarity according to claim 2, characterized in that: Similarity of the polygon where δ i represents the weight coefficient, i = 1, 2, 3, 4, and satisfies 0 ≤ δ i ≤ 1 and δ1 + δ2 + δ3 + δ4 = 1.

4. A method for monitoring the health status of a spacecraft control system based on polygon similarity according to claim 2, characterized in that: The perimeter error L of the polygon error is calculated as follows: Let L i,j represent the length between vertex i and vertex j, which is calculated using the following formula: Then the perimeter L of the polygon is L 1,2 +L 2,3 +…+L k,1 ; The perimeter error obtained compared with the reference polygon is: L error = L - L r Among them, L r represents the perimeter of the reference polygon.

5. The method for monitoring the health state of a spacecraft control system based on polygon similarity according to claim 2, wherein: The peak error E of the polygon perk is calculated as follows: where y max = max(y m,1 , y m,2 , …, y m,k ), y min = min(y m,1 , y m,2 , …, y m,k ), y r,max = max(y r,1 , y r,2 , …, y r,k ), y r,min = min(y r,1 , y r,2 , …, y r,k ).

6. The method for monitoring the health state of a spacecraft control system based on polygon similarity according to claim 2, characterized in that: The said difference error E error,perk is calculated as follows: where y error,max = max(y m,1 - y r,1 , y m,2 - y r,2 , …, y m,k - y r,k ), y error,min = min(y m,1 - y r,1 , y m,2 - y r,2 , …, y m,k - y r,k ).

7. A method for monitoring the health status of a spacecraft control system based on polygon similarity according to claim 2, characterized in that: The absolute error E error is calculated as follows: Among them

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