Telemetry data anomaly detection method based on b-spline envelope analysis

Abstract

The application discloses a telemetry data anomaly detection method based on B-spline envelope analysis, and specifically relates to the following steps: dividing telemetry data {x1, x2,..., x M} into k+1 segments; obtaining the maximum value P max,i and the minimum value P min,i of each data segment to form a data point set P max , P min ; moving the maximum value P max,i and the minimum value P min,i of each segment to obtain a new data point set P max ', P min '; performing B-spline curve fitting on the points in the data point set P max ', P min ', taking the curve of P max ' as an upper envelope line, taking the curve of P min ' as a lower envelope line, and taking the upper envelope line and the lower envelope line as dynamic thresholds for judging whether data is abnormal to complete anomaly detection of the data. Using the adaptive envelope of B-spline fitting telemetry data as the threshold can help improve the quality and accuracy of signals and reduce the interference of noise. Using the adaptive envelope can better adapt to the dynamic changes of signals, improve the sensitivity and accuracy of fault detection, and has great significance for reducing the loss of spacecraft faults and ensuring the success of space missions.

Description

Technical Field

[0001] The present invention belongs to the technical field of aerospace data processing, and in particular relates to a telemetry data anomaly detection method based on B-spline envelope analysis. Background Art

[0002] In the aerospace sector, telemetry is a key technology that transmits telemetry data from numerous critical devices back to ground-based base stations. In recent years, the demands of space exploration have led to a rapid increase in the functionality of spacecraft systems, resulting in increasingly complex equipment structures and a greater likelihood of equipment failure. These failures often result in significant economic losses and mission failures. Therefore, analyzing telemetry data from critical equipment to troubleshoot equipment failures is of great significance to aerospace missions and scientific research.

[0003] In practice, fault diagnosis methods using fixed thresholds typically do not require complex calculations or algorithms, making them easier to implement. The threshold can be selected based on experience or expert knowledge, ensuring that diagnostic results are tailored to the actual situation. This method is applicable to many fault diagnosis scenarios and has broad applicability. However, fixed threshold methods lack adaptability. They are fixed values ​​set based on experience or theory, unable to automatically adapt to dynamic signal changes. They are also susceptible to subjective factors, potentially leading to missed detections or false alarms. When unknown faults or changes occur in the system, fixed thresholds may not accurately detect and identify these faults.

[0004] Both theory and practice have demonstrated that envelope analysis is an effective method in engineering signal processing, playing a vital role in mechanical fault diagnosis and vibration signal analysis. Adaptive envelope analysis automatically adjusts thresholds based on real-time signal changes, better adapting to signal variations. It also adjusts thresholds based on fault signal strength, improving fault detection rates. Summary of the Invention

[0005] The purpose of the present invention is to provide a telemetry data anomaly detection method based on B-spline envelope analysis, which can accurately identify abnormal data in spacecraft telemetry data, thereby realizing spacecraft fault diagnosis.

[0006] The technical solution adopted by the present invention is a telemetry data anomaly detection method based on B-spline envelope analysis, which is specifically implemented according to the following steps:

[0007] Step 1: Transform the telemetry data {x1, x2, ..., x M} is divided into k+1 segments;

[0008] Step 2: Find the maximum value P on each data segment max,i With the minimum value P min,i , forming a data point set P max , Pmin ;

[0009] Step 3: The maximum value P of each segment max,i With the minimum value P min,i Move and get a new data point set P max ', P min ';

[0010] Step 4: Set the data point set P max ', P min 'B-spline curve fitting is performed on the points in P max ' curve as the upper envelope, and P min The curve of ′ is used as the lower envelope, and the upper and lower envelopes are used as dynamic thresholds to determine whether the data is abnormal, thus completing the data anomaly detection.

[0011] The present invention is also characterized in that:

[0012] In step 1, the telemetry data is {x1, x2, ..., x M}, M is the length of telemetry data, the telemetry data is divided into k data segments of length d, and the remaining length less than d is regarded as the k+1th data segment; in this way, the entire data is divided into k+1 segments, that is, {x 11 , x 12 ,…,x 1d}, {x 21 , x 22 ,…,x 2d},…,{x k1 , x k2 ,…,x kd}, {x (k+1)1 , x (k+1)2 ,…,x (k+1)m}.

[0013] In step 2, the telemetry data {x1, x2, ..., x M} Divide into k+1 segments and find the maximum value P of each data segment max，i With the minimum value P min，i (i=1, 2, ..., k+1), and these points are taken as the data point set P max ={P max，1 , P max，2 ,…,P max，k+1}, P min ={P min，1 , P min，2 ,…,P min，k+1}.

[0014] In step 3, specifically: the first k data segments of length d in step 1 are {x 11 , x12 ,…,x 1d}, {x 21 , x 22 ,…,x 2d},…,{x k1 , x k2 ,…,x kd}, the mean value u of the i-th (i=1, 2, ..., k) segment i , standard deviation σ i The calculation formula is as follows:

[0015]

[0016]

[0017] The last data segment containing m remaining data is {x (k+1)1 , x (k+1)2 ,…,x (k+1)m}, its mean μ k+1 , standard deviation σ k+1 , calculated as follows:

[0018]

[0019]

[0020] The maximum value P of each interval max，i , minimum value P min，i Move the standard deviation σ up and down respectively i , and get P max ′={P max，1 ′,P max，2 ',…,P max，k+1 ′},P max ′={P max，1 ′,P max，2 ′,…,P max，k+1 ′}, as a new set of data points.

[0021] In step 4, specifically:

[0022] Step 4.1, data point set P max The points in ′ can be expressed as: (t max，j , P max，j ′), j=1,2,…,k+1,t max,j P max,j The time corresponding to ′ is fitted using a uniform B-spline curve;

[0023] Step 4.2, data point set P min The point in ' can be expressed as: (t min，j , P min，j′), j=1,2,…,k+1,t min,j P min,j The time corresponding to ′ is fitted using a uniform B-spline curve;

[0024] Step 4.3, by P max 'The B-spline fitting curve obtained from the data point set is used as the upper envelope of the data, P min The B-spline fitting curve obtained from the data point set is used as the lower envelope of the data, and the upper and lower envelopes of the data are used as "dynamic thresholds" to determine whether the data is abnormal. For any set of telemetry data, if the data is within the threshold range, it is judged as normal data; if it is not within the threshold range, it is judged as abnormal data.

[0025] In step 4.1, the fitting process is:

[0026] Step 4.11, T max,0 、T max,,pmax As the data point set P max 'The two time endpoints, T max,0 =t max,1 , T max,pmax =t max,k+1 , and calculate T max,i , T max，i =T max，0 +ih max , i=0,1,…,p max , where p max is the number of fitting segments, h max The time length of each segment,

[0027] Step 4.12, (t max,j ,P max,j ′),j=1,2,…,k+1 and T max,i Substituting into the cubic B-spline equation, we get the matrix T max , as shown below;

[0028]

[0029] Step 4.13, T max Substitute the B-spline optimal fit approximation equation as shown below;

[0030] T max T T max α max =T max T X max

[0031] Among them, X max is(tmax,j ,P max,j ′),j=1,2,…,k+1, α max Is the coefficient matrix to be solved:

[0032] in,

[0033] The solution to the equation is α max =(T max T T max ) -1 T max T X max ;

[0034] Step 4.14, calculate Get the data point set P max 'B-spline fitting curve, where α i is the coefficient matrix α max The i-th element, t is the data point set P max 'Any value in the time interval.

[0035] In step 4.2, the fitting process is:

[0036] Step 4.21, T min,0 、 As the data point set P min 'The two time endpoints, namely T min,0 =t min,1 , And calculate T min,i , T min,i =T min,0 +ih min,i =0,1,…,p min , where p min is the number of fitting segments, h min The time length of each segment,

[0037] Step 4.22, (t min,j ,P min,j ),j=1,2,…,k+1 and T min,i Substituting into the cubic B-spline equation, we get the matrix T min , as shown below;

[0038]

[0039] Step 4.23, T min Substitute the B-spline optimal fit approximation equation as shown below;

[0040] Tmin T T min α min =T min T X min

[0041] Among them, X min is(t min,j ,P min,j ′),j=1,2…,k+1, α min is the coefficient matrix to be solved;

[0042] in,

[0043] The solution to the equation is α min =(T min T T min ) -1 T min T X min ;

[0044] Step 4.24, calculate Get the data point set P min 'B-spline fitting curve, where α i is the coefficient matrix α min The i-th element, t is the data point set P min ’ is any value in the time interval.

[0045] The present invention has the beneficial effect of using the adaptive envelope of telemetry data fitted with B-splines as a threshold, helping to improve signal quality and accuracy while reducing noise interference. The use of the adaptive envelope can better adapt to dynamic signal changes, improve the sensitivity and accuracy of fault detection, and better capture characteristic changes and trends in telemetry data, allowing for early detection of potential fault signs and appropriate maintenance and repair. This is of great significance for reducing spacecraft failure losses and ensuring the success of space missions. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 It is a flow chart of the telemetry data anomaly detection method based on B-spline data envelope of the present invention;

[0047] Figure 2 It is a graph of satellite telemetry data;

[0048] Figure 3 It is a graph of the maximum and minimum values ​​of equally spaced data segments of satellite telemetry data;

[0049] Figure 4It is the result graph after processing the maximum and minimum values ​​of equally spaced data segments of satellite telemetry data;

[0050] Figure 5 This is the result graph of anomaly detection using a fixed threshold;

[0051] Figure 6 is a graph of the adaptive envelope fitted using a polynomial;

[0052] Figure 7 It is a graph of the adaptive envelope fitted using B-spline;

[0053] Figure 8 This is a graph showing anomaly detection using the adaptive envelope obtained by B-spline fitting as the threshold. DETAILED DESCRIPTION

[0054] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0055] Example 1

[0056] The present invention is based on the telemetry data anomaly detection method of B-spline envelope analysis, such as Figure 1 As shown, please follow the steps below:

[0057] Step 1: Assume that the telemetry data sequence is {x1,x2,…,x M}, M is the length of telemetry data, the telemetry data sequence is divided into k data segments of length d, and the remaining length less than d is regarded as the k+1th data segment; in this way, the entire data is divided into k+1 segments, that is, {x 11 ,x 12 ,…,x 1d},{x 21 ,x 22 ,…,x 2d},…,{x k1 ,x k2 ,…,x kd},{x (k+1)1 ,x (k+1)2 ,…,x (k+1)m};

[0058] For the telemetry data sequence {x1, x2, ..., x M}, take data of length d as a segment, divide d by M, the quotient is k, and the remainder is m, divide the entire data into k data segments with an interval of d and the last m data less than d as the k+1th segment, so that the entire data is divided into k+1 segments;

[0059] Step 2: Find the maximum value P on each data segment (i.e., the i-th data segment) max,i With the minimum value Pmin,i , these points constitute the data point set P max , P min ;

[0060] In step 1, the given telemetry data sequence {x1, x2, ..., x M} Divide into k+1 segments and find the maximum value P of each data segment max,i With the minimum value P min , i (i = 1, 2, ..., k + 1), and these points are taken as the data point set P max ={P max，1 , P max，2 ,…,P max，k+1}, P min ={P min，1 , P min，2 ,…,P min，k+1}.

[0061] Step 3: Calculate the standard deviation σ of each data segment i , its size reflects the degree of fluctuation of the data, and the segment corresponds to the maximum value P max,i With the minimum value P min,i Move up and down respectively, and the standard deviation of the moving distance σ i , get a new data point set P max ', P min ';

[0062] The first k data segments of length d given in step 1 are {x 11 , x 12 ,…,x 1d}, {x 21 , x 22 ,|…,x 2d},…,{x k1 , x k2 ,…,x kd}, the mean value u of the i-th (i=1, 2, ..., k) segment i , standard deviation σ i The calculation formula is as follows:

[0063]

[0064]

[0065] The last data segment containing m remaining data is {x (k+1)1 , x (k+1)2 ,…,x (k+)m}, its mean μ k+1 , standard deviation σ k+1 , calculated as follows:

[0066]

[0067]

[0068] The maximum value P of each interval max,i , minimum value P min,i Move the standard deviation σ up and down respectively i , and get P max ′={P max，1 ′,P max，2 ′,…,P max，k+1 ′},P max ′={P max，1 ′,P max，2 ′,…,P max，k+1 ′}, as a new set of data points.

[0069] Step 4: Set the data point set P max ', P min 'B-spline curve fitting is performed on the points in P max 'The curve is the upper envelope of the data, corresponding to P min The curve of ' is used as the lower envelope of the data, and the upper and lower envelopes of the data are used as the "dynamic thresholds" to determine whether the data is abnormal, thereby completing the abnormality detection of the data;

[0070] Step 4.1, data point set P max The point in ' can be expressed as: (t max，j , P max，j ′), j=1,2,…,k+1,t max,j P max,j The time corresponding to ′ is fitted using a uniform B-spline curve; specifically:

[0071] Step 4.11, T max,0 、 As the data point set P max 'The two time endpoints, T max,0 =t max,1 , T max,pmax =t max,k+1 , and calculate T max,i , T max，i =T max，0 +ih max，i =0, 1, ..., p max , where p max is the number of fitting segments (p max <k),h max The time length of each segment,

[0072] Step 4.12, (tmax，j , P max，j ′), j=1, 2, ..., k+1 and T max,i Substituting into the cubic B-spline equation, we get the matrix T max , as shown below;

[0073]

[0074] The cubic B-spline is defined as follows:

[0075]

[0076] Step 4.13, T max Substitute the B-spline optimal fit approximation equation as shown below;

[0077] T max T T max α max =T max T X max

[0078] Among them, X max is(t max，j , P′ maxj ), j = 1, 2, ..., k + 1, α max Is the coefficient matrix to be solved:

[0079] in,

[0080] The solution to the equation is α max =(T max T T max ) -1 T max T X max ;

[0081] Step 4.14, calculate Get the data point set P max 'B-spline fitting curve, where α i is the coefficient matrix α max The i-th element, t is the data point set P max 'Any value in the time interval, that is, t max,1 ≤t≤t max,k+1 ;

[0082] Step 4.2, data point set P min The point in ' can be expressed as: (t min，j , P′ minj ), j = 1, 2, ..., k + 1, tmin,j P min,j The time corresponding to ′ is fitted using a uniform B-spline curve, as follows:

[0083] Step 4.21, T min,0 、T min,pmin As the data point set P min 'The two time endpoints, namely T min,0 =t min,1 , T min,pmin =t min,k+1 , and calculate T min,i , T min，i =T min，0 +ih min , i=0,1,…,p min , where p min is the number of fitting segments (p min <k),h min The time length of each segment,

[0084] Step 4.22, (t min，j , P min，j ′), j=1, 2, ..., k+1 and T min,i Substituting into the cubic B-spline equation, we get the matrix T min , as shown below;

[0085]

[0086] Step 4.23, T min Substitute the B-spline optimal fit approximation equation as shown below;

[0087] T min T T min α min =T min T X min

[0088] Among them, X min is(t min，j , P min，j ′), j = 1, 2, ..., k + 1, α min is the coefficient matrix to be solved;

[0089] in,

[0090] The solution to the equation is α min =(T min T T min ) -1 Tmin T X min ;

[0091] Step 4.24, calculate Get the data point set P min 'B-spline fitting curve, where α i is the coefficient matrix α min The i-th element, t is the data point set P min 'Any value in the time interval, that is, t min,1 ≤t≤t min,k+1 .

[0092] Step 4.3, by P max 'The B-spline fitting curve obtained from the data point set is used as the upper envelope of the data, P min The B-spline fitting curve obtained from the data point set is used as the lower envelope of the data, and the upper and lower envelopes of the data are used as "dynamic thresholds" to determine whether the data is abnormal. For any set of telemetry data, if the data is within the threshold range, it is judged as normal data; if it is not within the threshold range, it is judged as abnormal data;

[0093] Traditional fixed threshold anomaly detection is only applicable to normal working conditions or certain special working conditions. If the threshold is set too large, it cannot accurately detect anomalies. If the threshold is set too small, it will cause misjudgment. The dynamic threshold proposed in this invention can improve the sensitivity and detection ability of anomalies, and has a certain degree of adaptability. The accuracy of anomaly detection is higher and closer to actual engineering problems.

[0094] Example 2

[0095] The present invention is based on a telemetry data anomaly detection method based on B-spline envelope analysis. The telemetry data is first divided into data segments, and the maximum and minimum values ​​of each data segment are obtained as the data point sets of the upper and lower envelopes. The data point sets are respectively moved upward and downward, and the moving distance is the standard deviation of the corresponding data segment to obtain a new data point set. The new data point set is fitted with a B-spline curve to obtain the upper and lower envelopes, and finally a data envelope with a certain threshold is obtained. The envelope can follow the trend changes of the telemetry data, so as to accurately capture whether the telemetry data is abnormal.

[0096] Example 3

[0097] This embodiment uses the telemetry data of a certain satellite to conduct analysis experiments. The data is as follows: Figure 2 As shown; telemetry data (t i , x i), i = 1, 2, ..., M. Under normal circumstances, the change curve has a certain regularity. If a fault occurs, it will obviously not conform to the change trend of the curve. Therefore, a certain threshold can be set to judge whether a fault has occurred. If a fixed threshold T is set to judge whether an abnormality has occurred, if the threshold is set too large, it will not be able to accurately detect abnormal values. If the threshold is set too small, it will cause misjudgment. Therefore, the fixed threshold cannot accurately capture data anomalies;

[0098] First, the data is divided into k+1 data segments, and the maximum and minimum values ​​of the k+1 interval data are obtained as the data point sets of the upper and lower envelopes. The results are as follows: Figure 3 As shown, the data point set is moved up and down respectively, and the moving distance is the standard deviation of the corresponding data segment data to obtain a new data point set. The result is as follows Figure 4 As shown;

[0099] Using the fixed threshold obtained according to the 3σ principle to perform anomaly detection may result in missed detection. The results are as follows Figure 5 As shown, the upper and lower envelope fitting curves are obtained by fitting the new data point set using polynomial fitting. The results are shown in Figure 6 The B-spline algorithm is used to fit the new data point set, and the fitting curves of the upper and lower envelopes are obtained. The results are shown in Figure 7 As shown. Using B-spline to fit the telemetry data adaptive envelope as the threshold for anomaly detection, the results are shown in Figure 8 shown.

[0100] Now define the following indicators to compare the data envelope obtained by traditional polynomial fitting with the method proposed in this invention. The indicators are defined as follows:

[0101] 1. Interval coverage

[0102] Interval coverage rate (ICP) refers to the probability that the true value falls into the interval. The larger the ICP value, the more the interval constructed by the model can cover all true values ​​to the maximum extent. ICP can be used to evaluate the accuracy and reliability of the interval.

[0103]

[0104] Among them, N represents the number of samples, CP i It is a Boolean value indicating whether the i-th sample falls within the interval.

[0105]

[0106] Among them, x i is the true value of the sample, U i and L i are the lower and upper bounds of the interval.

[0107] 2. Average interval width percentage

[0108] The width percentage IMWP is the average of the interval width and the percentage of the true value of the sample;

[0109]

[0110] Where N represents the number of samples, x i is the true value of the sample, U i and L i are the lower and upper bounds of the interval.

[0111] This indicator measures the average percentage of the interval width corresponding to each sample value to the actual observation value. The smaller the IMWP value, the more the model can meet the actual needs. The interval width is generally correlated with the sample value. Therefore, using the IMWP indicator can give a more reasonable evaluation of the interval width.

[0112] 3. Average bandwidth error

[0113] Mean Width Deviation (MWD) is an important metric used to measure the accuracy of dynamic threshold predictions. The smaller the MWD value, the higher the model's accuracy. A sufficiently small MWD value indicates a high probability that the true sample value falls within the dynamic threshold range, improving anomaly detection effectiveness.

[0114] The average bandwidth error is measured using the following formula:

[0115]

[0116]

[0117] Where N is the number of samples, x i is the true value of the sample, U i and L i are the upper and lower bounds of the interval, WD i is the bandwidth error of the sample.

[0118] Table 1 compares the results of the polynomial fitting method and the method of the present invention in terms of interval coverage, average interval width percentage, and average bandwidth error:

[0119] Table 1 Comparison of indicators of the two methods

[0120] Interval coverage Average interval width percentage Average bandwidth error Polynomial fitting method 0.7559 0.1744 0.0482 B-spline fitting method 0.9862 0.1648 0.0041

[0121] Table 1 shows that the present invention outperforms traditional polynomial fitting methods in all three metrics, demonstrating that the present invention has better detection capabilities for telemetry data anomalies. The above analysis demonstrates that the proposed anomaly detection method based on B-spline envelope analysis can accurately detect anomalies in telemetry data.

Claims

1. Based on The telemetry data anomaly detection method based on spline envelope analysis is characterized in that: Please follow the steps below to implement it: Step 1: Telemetry data Divided into fragments; Step 2: Find the maximum value of each data segment With minimum value , i =1,2,… k +1; constitutes a data point set , , and these points are taken as the data point set ; Step 3: The maximum value of each segment With minimum value Move to get a new set of data points , ; Specifically: Before step 1 The length is The data fragment is , No. i The mean of the segments , standard deviation The calculation formula is as follows, i =1,2,… k ; The last one contains The remaining data segments are , its mean , standard deviation , calculated as follows: The maximum value of each interval , minimum Move the standard deviation up and down respectively ,get , as a new set of data points; Step 4: Set the data points , Points in Spline curve fitting, The curve is taken as the upper envelope, The curve is used as the lower envelope, and the upper and lower envelopes are used as dynamic thresholds to determine whether the data is abnormal, completing the data anomaly detection; specifically: Step 4.1, data point set The points in can be represented as: , for The corresponding time is uniform The spline curve is fitted; the fitting process is: Step 4.11, 、 As a set of data points The two time endpoints, , , and calculate , ,in is the number of fitting segments, The time length of each segment, ; Step 4.12, and Substitute three times In the spline equation, we get the matrix , as shown below; Step 4.13, Substitution The spline optimal fit approximation equation is shown below; in, for The matrix composed of Is the coefficient matrix to be solved: in, ; The solution to the equation is ; Step 4.14, calculate , get the data point set of The spline fitting curve, where is the coefficient matrix No. elements, For the data point set Any value in the time interval; Step 4.2, data point set The points in can be represented as: , for The corresponding time is uniform Spline curve fitting; Step 4.3, by The data point set obtained The spline fitting curve is used as the upper envelope of the data. The data point set obtained The spline fitting curve is used as the lower envelope of the data, and the upper and lower envelopes of the data are used as "dynamic thresholds" to determine whether the data is abnormal. For any set of telemetry data, if the data is within the threshold range, it is judged as normal data; if it is not within the threshold range, it is judged as abnormal data.

2. The method according to claim 1 The telemetry data anomaly detection method based on spline envelope analysis is characterized in that: In step 1, the telemetry data is , is the telemetry data length, and the telemetry data is divided into The length is The remaining length of the data segment is insufficient. is considered as the first data fragments; thus, the entire data is divided into fragments, i.e. .

3. The method according to claim 1 The telemetry data anomaly detection method based on spline envelope analysis is characterized in that: In step 4.2, the fitting process is: Step 4.21, 、 As a set of data points The two time endpoints of , , and calculate , ,in is the number of fitting segments, The time length of each segment, ; Step 4.22, and Substitute three times In the spline equation, we get the matrix , as shown below; Step 4.23, Substitution The spline optimal fit approximation equation is shown below; in, for The matrix composed of is the coefficient matrix to be solved; in, The solution to the equation is ; Step 4.24, calculate , get the data point set of The spline fitting curve, where is the coefficient matrix No. elements, For the data point set Any value in the time interval.

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