CN113627523B - Satellite micro fault detection method - Google Patents
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Abstract
The invention discloses a satellite micro fault detection method, which adopts a sliding window to extract on-orbit samples, then uses linear discriminant analysis for each extracted on-orbit sample, calculates an optimal projection vector between the on-orbit sample and a historical normal sample, obtains a detection threshold according to the historical normal data and the optimal projection vector, calculates the deviation between the on-orbit sample and the historical normal sample, and compares the deviation with the detection threshold to judge whether a fault occurs.
Description
Technical Field
The invention relates to the technical field of aerospace, in particular to a satellite micro fault detection method.
Background
Along with the reduction of rocket launching cost and satellite manufacturing cost, the number of satellites running in orbit is increased year by year, and great economic benefits are brought to society. However, due to severe space operating environments and artifacts, some anomalies or malfunctions may occur in critical modules or components of the orbiting satellites. If the micro faults in the early stage can be detected and processed in time, the loss and damage caused by the faults can be effectively reduced. Therefore, a minute fault detection technology, which is one of key technologies for ensuring normal operation of satellites, is increasingly receiving attention.
The current common satellite fault detection method is to directly compare the on-orbit telemetry parameters with a preset threshold. The fault detection method is suitable for detecting faults with abrupt changes and larger fault amplitude, but the detection effect on micro faults may be poor. This is because the telemetry parameters that fail in a minor manner may not change significantly from those of a normal state. If the set fault detection threshold value is too small, the fault detection method is sensitive to noise so as to cause frequent false alarms; if the set threshold value is too large, the detection of some early failure symptoms is missed. In addition, because the production batch of satellites is not completely the same, the process and the operation environment are not completely the same, different fault detection thresholds may need to be designed for different satellites, and the efficiency of manually setting the proper detection threshold for each telemetry parameter is low.
Compared with a simple threshold comparison method, the satellite fault detection method based on the model is more intelligent, and generally integrates the functions of fault detection, positioning, recovery and the like. However, with the rapid development of technology, a great deal of new technology, new materials, high integration devices, etc. are applied to satellites. The complex coupling relation exists among all devices of the satellite, and the unfamiliar of modeling staff on the generation mechanism, performance, influence and the like of various faults can lead to the difficulty of establishing an accurate and comprehensive fault model, so that the application of the satellite fault detection method based on the model is limited.
The fault detection method based on data driving has the advantages of low expert participation, high modeling efficiency, strong expansibility and the like, and becomes a research hot spot in recent years. At present, the fault detection method based on data driving is mainly divided into two main types: a fault detection method based on unsupervised learning and a fault detection method based on supervised learning. The core idea of the fault detection method based on unsupervised learning is deviation. The method utilizes the satellite ground test or the historical normal data which is reserved during the in-orbit operation to automatically establish a model capable of representing the normal state of the satellite, and when the actual in-orbit data and the model representing the normal data have larger deviation, the model is considered to have faults. Since there are many ground test data and in-orbit data of satellites, fault detection methods based on unsupervised learning are more studied and applied, and typical fault detection methods include IMS, OS-SVM, GPR, PCA, LOF, LSTM, and the like. Although these fault detection methods are different from each other in terms of the principle on which they build the normal model, they all have in common that the normal model for detecting faults is obtained by learning historical normal data. After learning and training are completed, no matter what kind of faults occur in actual on-orbit data, the methods detect the faults by adopting a fixed and unchanged model, and do not perform targeted optimization or adjustment on the faults which may occur in actual.
The core idea of the fault detection method based on supervised learning is classification. The method learns and establishes a classifier on historical normal data and various real fault data or simulation fault data which are reserved when the satellite runs in orbit. When the on-orbit data is classified into normal types after being classified by the classifier, the artificial on-orbit data does not have faults; on the contrary, when the on-orbit data is classified into a certain fault class after being classified by the classifier, the on-orbit data is considered to have a certain fault class. Representative fault detection methods such as LDA, SVM, neural network, etc. However, since satellites are generally highly reliable, the telemetry data collected by actual satellite operation and maintenance systems is mostly normal data, with very few faulty samples. In addition, classification models built using failure samples of different satellites may not be generic, thus impeding the application of supervised learning based failure detection methods in the satellite domain.
Disclosure of Invention
Aiming at part or all of the problems in the prior art, the invention provides a satellite micro-fault detection method based on dynamic linear discriminant analysis, which comprises the following steps:
extracting an on-orbit sample by adopting a sliding window;
obtaining an optimal projection vector between the on-orbit sample and the historical normal sample by using linear discriminant analysis (linear discriminant analysis, LDA);
establishing a normal model by using the historical normal data and the optimal projection vector to obtain a detection threshold;
calculating an objective function value between the on-orbit sample and the historical normal sample, comparing the objective function value with the detection threshold, and judging whether a fault occurs or not; and
and sliding the interactive window back to extract a new on-orbit sample, and repeating the steps.
Further, the window length of the sliding window is a fixed value.
Further, the detection method further comprises Z-score normalization of each parameter of the historical normal samples and the on-orbit samples before calculating the optimal projection vector.
Further, the detection threshold is obtained through non-central F distribution test.
The invention provides a satellite micro fault detection method, which uses dynamic linear discriminant analysis (linear discriminant analysis, LDA) to search an optimal projection vector capable of separating on-orbit data and historical normal data in real time, then establishes a normal model by utilizing the historical normal data and the optimal projection vector, and finally judges whether a fault occurs by checking whether the deviation between the real-time on-orbit telemetry data and the normal model exceeds a threshold. Since LDA itself has a property of being insensitive to variance, the detection method can be applied to detect a failure of the mean increase or decrease type of the parameter. And it has been verified that when detecting micro faults, the detection method has obvious advantages in fault detection rate and false alarm rate compared with the common fault detection methods such as PCA, IForest, OS-SVM, KNN, LOF and the like, and is a brand new and effective fault detection method.
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To further clarify the above and other advantages and features of embodiments of the present invention, a more particular description of embodiments of the invention will be rendered by reference to the appended drawings. It is appreciated that these drawings depict only typical embodiments of the invention and are therefore not to be considered limiting of its scope. In the drawings, for clarity, the same or corresponding parts will be designated by the same or similar reference numerals.
FIG. 1 shows a schematic diagram of a linear discriminant analysis method;
FIG. 2 is a schematic diagram of a satellite micro-fault detection method according to an embodiment of the present invention;
FIG. 3 is a flow chart of a method for detecting satellite micro-faults according to an embodiment of the present invention;
FIG. 4 shows comparison of the detection results of 8 kinds of fault detection methods in the prior art and a satellite micro-fault detection method according to an embodiment of the present invention for a simulation fault 1;
FIG. 5 shows comparison of the detection results of 8 kinds of fault detection methods in the prior art and a satellite micro-fault detection method according to an embodiment of the present invention for a simulation fault 2;
FIG. 6 shows comparison of the detection results of the simulation fault 3 by 8 fault detection methods in the prior art and a satellite micro-fault detection method according to an embodiment of the present invention; and
fig. 7 shows comparison of detection results of different fault magnitudes by 8 fault detection methods in the prior art and a satellite micro-fault detection method according to an embodiment of the present invention.
Detailed Description
In the following description, the present invention is described with reference to various embodiments. One skilled in the relevant art will recognize, however, that the embodiments may be practiced without one or more of the specific details, or with other alternative and/or additional methods, materials, or components. In other instances, well-known structures, materials, or operations are not shown or described in detail to avoid obscuring aspects of the invention. Similarly, for purposes of explanation, specific numbers, materials and configurations are set forth in order to provide a thorough understanding of the embodiments of the invention. However, the invention is not limited to these specific details. Furthermore, it should be understood that the embodiments shown in the drawings are illustrative representations and are not necessarily drawn to scale.
Reference throughout this specification to "one embodiment" or "the embodiment" means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the present invention. The appearances of the phrase "in one embodiment" in various places in the specification are not necessarily all referring to the same embodiment.
Aiming at the defects of the existing satellite fault detection method, the invention provides a satellite micro fault detection method combining the deviation ideas in the unsupervised learning fault detection method and the classification ideas in the supervised learning fault detection method. Wherein the classification concept is used to find an optimal projection vector separating the on-orbit telemetry data and the historical normal data. Specifically, the fault detection problem is regarded as a classification problem: the historical normal data is in one class, and the on-orbit telemetry data to be detected is in another different class, so that the on-orbit telemetry data and the historical normal data on the optimal projection vector have the largest degree of distinction; and the bias concept is used to detect if the on-orbit telemetry data is truly faulty: after the optimal projection vector is obtained, a normal model is established by utilizing the historical normal data and the optimal projection vector, and finally whether a fault occurs is judged by checking whether the deviation between the real-time on-orbit telemetry data and the normal model exceeds a threshold.
Based on the classification concept described above, in one embodiment of the invention, a linear discriminant analysis (linear discriminant analysis, LDA) is optimized and finally data classification is achieved. The linear discriminant analysis is also called Fisher discriminant analysis, is a supervised dimension reduction and classification method, and has wide application in the pattern recognition field, such as the pattern image recognition field of face recognition, naval vessel recognition and the like. Taking two classifications as an example, a given datasetWherein x is i Column vector, z, consisting of multidimensional telemetry parameters i Is x i A corresponding class label. z i Only two values, z i E {0,1}. Let n j 、X j 、μ j 、Σ j The sample number, the sample set, the mean vector and the covariance matrix of the j < th > E {0,1} type samples are respectively represented. Wherein,
let the projection vector be w, for any sample x i Its projection on vector w is w T x i . Mean vector μ of two classes 0 Sum mu 1 The projections on vector w are w T μ 0 And w T μ 1 And respectively usingAnd->Representing and defining the divergence of each class after projection on vector w as +.>
The LDA method expects that the more separated the sample points of different classes are after projection on the vector w, the better the aggregate the sample points of the same class are. In other words, the larger the difference of the mean values, the better the hash value, and thus, the objective function J (w) of LDA can be constructed as follows:
wherein:
S b ＝(μ 0 -μ 1 )(μ 0 -μ 1 ) T and (b)
2 w ＝Σ 0 +Σ 1 ，
Then the goal of LDA is to find the projection vector w that maximizes J (w). Let w T 2 w w=1, the finding of the w problem that maximizes J (w) can be translated into an optimization problem as shown below:
the optimization problem can be solved by a Lagrangian multiplier method and is obtained:
from the solution of the obtained values and the relation between the eigenvalues and eigenvectors, the projection vector w is a matrixAnd w for maximizing J (w) is the matrix +.>A feature vector corresponding to the maximum feature value of (a).
In the traditional LDA method, the training data contains multiple types of samples, and when various samples in the training set are determined, a classifier, such as an optimal projection straight line for two classifications or a projection hyperplane suitable for multiple classifications, can be obtained through the one-time LDA method, and the data to be classified can be divided through the classifier, so that a classification result is finally obtained. In satellite fault detection, as shown in fig. 1, real-time on-orbit data of a data bit satellite to be classified is classified into two classes by adopting an LDA method based on a history normal sample and a fault sample, so that whether the real-time on-orbit data belongs to normal data or fault data is judged.
However, in practice, there are often few historical failure samples, which are insufficient to support the LDA for learning and training. Based on this, as shown in fig. 2, in one embodiment of the present invention, the learning and training samples are first adjusted, specifically, the historical normal data is taken as a class 0 sample, the on-track data to be detected is taken as a class 1 sample, and then an optimal projection vector w is found that separates the historical normal data from the real-time on-track data as far as possible. Second, in an embodiment of the present invention, the on-track data is extracted by sliding windows, for on-track data X within each sliding window k An optimal projection vector w is obtained by using a one-time LDA method k Due to on-track data X in different windows k May be different, so that the optimal projection vector w is obtained each time using the LDA method k And compared with the traditional LDA method, the LDA method adopted in the embodiment of the invention can be regarded as a dynamic LDA method, and because the optimal projection vector obtained by each calculation in the dynamic LDA method can be adjusted according to the change of real-time on-orbit data, the method has stronger adaptability to potential faults.
In the embodiment of the invention, whether the on-track data is abnormal or not is judged through the deviation between the on-track data and the historical normal data, and once the deviation exceeds the normal fluctuation range, the on-track data can be considered to be faulty. In one embodiment of the present invention, as shown in fig. 2, an objective function of LDA is used as a measure of deviation, a normal model is first established by historical normal data and an optimal projection vector to obtain a detection threshold, and then the objective function is calculated and compared with the detection threshold to determine whether an abnormality occurs. Specifically, the determination of the detection threshold includes:
first, it is assumed that the history normal data X 0 And on-track data X k Respectively obey mutually independent m-dimensional joint Gaussian distributionThen X is known from the properties of the m-dimensional joint Gaussian distribution 0 And X k In the optimal projection vector w k The data f and g after projection obey a one-dimensional Gaussian distribution +.>Andthen the objective function J (w k ) Can be expressed as:
next, due to historical normal data X 0 Is fixed and known data, and therefore its mean vector mu 0 Sum covariance matrix Σ 0 Can also be regarded as fixed known data, and the optimal projection vector w k Is obtained by dynamic LDA calculation in the previous step, and can be regarded as fixed known data and is matched with X k Related mean vector mu k Sum covariance matrix Σ k Is unknown and variable, based on which, let w k T μ 0 ＝c 1 ，w k T Σ 0 w k ＝c 2 Wherein c 1 ,c 2 Are all constant. Then the objective function J (w k ) Can be used forTo be simplified as:
next, in order to obtain on-track data X k X is normal data k And X is 0 Deviation between J (w) k ) Is assumed to be X 0 And X is k Belonging to the same class and X k By the method of X 0 The obeyed joint Gaussian distribution is sampled, then due to X k In the optimal projection vector w k The data g after upper projection obeys one-dimensional Gaussian distribution g-N (w k T μ k ,w k T Σ k w k ) Wherein w is k T μ k ，w k T Σ k w k Respectively X k At vector w k The mean and variance of the projected samples are set to w k T μ 0 ，w k T Σ 0 w k Respectively X 0 In straight line w k The overall mean and the overall covariance after projection, X is known from the nature of the one-dimensional Gaussian distribution k At vector w k Mean value w of projected samples k T μ k Obeying a one-dimensional gaussian distribution, the sample variance w k T Σ k w k Subject to degree of freedom n 1 Chi-square distribution of-1:
due to the sample mean value w k T μ k Obeys a one-dimensional gaussian distribution, and therefore, w k T μ k Subtracting constant term c 1 W at the back k T μ k -c 1 Also obey oneThe wigas distribution, i.eAlso because of-> Thus (2)The variable +.>After normalization, the ∈Rev can be obtained>
From the relationship between the standard normal distribution and the chi-square distribution,thus G 1 (w k ) Satisfy the following requirementsAt the same time due to w k T Σ 0 w k ＝c 2 Therefore there is->Thus obtaining G 2 (w k ) Satisfy the following requirementsThen for the deviation J (w k ) In other words, due to denominator term G 2 (w) is a non-centered chi-square distribution, and G 1 (w k ) And G 2 (w) are independent of each other, and from the relationship between chi-square distribution and F distribution, the relationship between chi-square distribution and F distribution indicates->Subject to degrees of freedom n 1 -1 and 1, non-central parameter c 2 Non-central F distribution of (c):
thus, non-central F distribution can be used to verify X k Whether or not a fault has indeed occurred, i.e. can be obtained by non-central F distribution checking given a confidence level αIs set to be a detection threshold epsilon of (2) k . Specifically, it means:
if it isThe value of (2) is greater than or equal to ε k Then it can be considered that X 0 And X is k Belongs to the same class, at this time X k No failure occurred; and
if it isHas a value less than ε k When it is considered X 0 And X is k Belonging to different classes, where X k A fault occurred.
Based on the above-mentioned ideas, as shown in fig. 3, the method for detecting satellite micro-faults provided by the invention comprises the following steps:
first, in step 301, an on-track sample is extracted. Using a window length n 1 Is to extract on-track sample X k ；
Next, in step 302, an optimal projection vector is calculated. Using LDA to find the optimal projection vector between the on-track sample and the historical normal sample, in one embodiment of the invention, before calculating the optimal projection vector, further comprises the step of comparing the historical normal sample X 0 Is Z-score normalized for each parameter of (2)For on-orbit sample X k Performing Z-score normalization to obtain +.>Then calculate the optimal projection vector w between the normalized normal samples and the on-orbit samples by LDA k ；
Next, in step 303, a detection threshold is calculated. Establishing a normal model by using the historical normal data and the optimal projection vector according to the method to obtain a detection threshold n 1 ε k ；
Next, at step 304, a fault diagnosis is performed. Calculate the objective function value J (w) k ) And is in contact with the detection threshold n 1 ε k Comparison:
if it isThen consider on-track sample X k A fault occurs; and
if it isThen consider on-track sample X k Normal performance; and
finally, in step 305, the sliding window is slid back. Sliding window continues to slide backwards to extract new X k The foregoing steps are then repeated.
To verify the effectiveness of the algorithm presented herein, the inventors first conducted a simulation test in which 8 telemetry data to be monitored, x= [ X 1 ,x 2 ,x 3 ,x 4 ,x 5 ,x 6 ,x 7 ,x 8 ] 3 Wherein each data is modeled as follows:
wherein [ s ] 1 ,s 2 ,s 3 ,s 4 ,s 5 ] T And [ e ] 1 ,e 2 ,e 3 ,e 4 ,e 5 ,e 6 ,e 7 ,e 8 ] T 5 signal sources, 8 noise sources, and all source signals are independent and all obey a standard normal distribution N (0, 1);
in addition, three simulated faults [ f ] are designed 1 ,f 2 ,f 3 ] T Since offset faults occur with a high frequency in practice, f 1 ,f 2 ,f 3 Is an offset fault and does not occur simultaneously:
IFore, OS-SVM, KNN, LOF, HBOS, PCA +T are adopted respectively 2 The method in the embodiment of the invention detects faults by PCA+SPE, PCA+ fai and adopts Fault Detection Rate (FDR), false Alarm Rate (FAR), F1 value and AUC value as evaluation criteria of fault detection results:
FDR＝prob{2core(w k )>n 1 ε k |H 1 }，
FAR＝prob{2core(w k )>n 1 ε k |H 0 }，
FPR＝prob{H 0 |2core(w k )>n 1 ε k }，
when the detection method in the embodiment of the invention is adopted, 200 windows are respectively obtained after the historical normal data and the on-orbit data are extracted through the sliding window, wherein the first 100 windows in the 200 windows of the on-orbit data are normal data windows, the last 100 windows are fault data windows, the experimental signal-to-noise ratio is set to be 30dB, and the confidence level is set to be 0.005. For comparison, the parameters monitored by the other eight methods are the average value of the data of each sliding window, instead of the original value, and the 5 methods such as IFore, OS-SVM, KNN, LOF, HBOS and the like are all realized by using an open source program PYOD, except that the rotation parameter is uniformly set to 0.05, the other parameters are all default settings of PYOD, the cumulative variance contribution rate is 90% in the three methods related to PCA, and the statistic confidence is set to 95%.
FIG. 4 shows the results of the 9 fault detection methods for simulated fault 1, as shown in OS-SVM, KNN, LOF, PCA +T 2 The 6 methods such as PCA+ fai and the algorithm provided herein have good detection effect on the fault 1, and the IFore, HBOS and PCA+SPE methods have slightly poorer detection results on the fault 1;
fig. 5 shows the detection results of the 9 fault detection methods on the simulated fault 2, and as shown in the figure, the detection effects of the first 8 fault detection methods on the fault 2 are not ideal, and in the detection results of the 8 methods, the abnormality index of the fault window is not obviously different from the abnormality index of the normal window. In the detection result of the fault 2 (third row of third graph), the J (w) value of the fault window is obviously much larger than the J (w) value of the normal window, and the J (w) values of all the fault windows are larger than the detection threshold, so that the fault detection rate is up to 100%;
fig. 6 shows the detection results of the 9 fault detection methods on the simulated fault 3, and as shown in the drawing, similar to the fault 2, the detection effect of the first 8 fault detection methods on the fault 3 is poor, but the fault detection rate of the detection method in the embodiment of the invention is still as high as 100%.
Because the Gaussian source and the noise source in the numerical simulation experiment have certain randomness, in order to further verify the effect of the detection method provided by the invention, the inventor randomly simulates 3 faults for 100 times respectively, and then takes the average value of fault detection results, and the results are shown in table 1. As can be seen from Table 1, for 3 simulated faults f 1 ,f 2 ,f 3 The False Alarm Rates (FAR) of the 9 fault detection algorithms are all concentrated around 5% -7%, so the results in table 1 can be considered as comparison results under the condition of similar false alarm rates. From the viewpoint of Fault Detection Rate (FDR), the detection method in the embodiment of the invention aims at fault f 1 ,f 2 ,f 3 Is ranked 4 th, 1 st and 1 st in 9 methods, respectively. For fault f 1 The detection method in the embodiment of the invention is only 0.27% lower than the first name although the detection method is ranked fourth. For fault f 2 And f 3 The fault detection rate of the detection method in the embodiment of the invention is 91.31% and 88.12% higher than that of the second name. From the viewpoint of F1 value, the detection method in the embodiment of the invention aims at fault F 1 ,f 2 ,f 3 The failure detection rates of (1) are ranked 3 rd, 1 st and 1 st, respectively, in 9 methods, respectively. From the perspective of AUC values, the detection method in the embodiment of the invention is specific to the fault f 1 ,f 2 ,f 3 The failure detection rates of (2) are all ranked 1 in 9 methods, respectively.
TABLE 1
In order to verify the detection capability of the detection method provided by the invention on small-amplitude faults, the inventor uses the fault f 3 Further experiments were performed for the example, which retained the aforementioned simulation environment and experimental parameter settings, but changed f 3 Will f 3 Starting from 0.0015, increasing by 0.0015 each time, and finally increasing to 0.225. And at each fault amplitude, 30 times of average value taking are simulated as statistical results. Under different fault amplitudes, the change of the F1 value and the AUC value of the detection results of different methods is shown in FIG. 7, and it can be seen that as F 3 The F1 value and AUC value of the detection results of the above 9 methods also increase gradually, however, the rising speeds of the different methods are different. The F1 value and the AUC value of the detection result of the detection method provided by the invention are rapidly increased along with the increase of the fault amplitude and are kept near the highest value. The rise rates of both PCA+SPE and PCA+ fai are low, but still much slower than the detection methods provided by the present invention.
As can be seen from fig. 7, for faults with larger amplitudes, the detection effect of the detection method provided by the present invention may not be advantageous; however, in the case of detecting a small-amplitude fault, the advantage is very remarkable compared with the other 8 fault detection methods. This is mainly because, when the dynamic LDA extremely optimal projection vector is adopted, the fault parameters are amplified and other parameters are suppressed. The amplification of the fault parameters can improve the detection capability of the algorithm on small-amplitude faults, the suppression of other parameters can reduce the influence of noise of other parameters on detection results, and the traditional fault detection method does not have the processes of amplifying the fault parameters and suppressing irrelevant parameters, so that compared with the traditional detection method, the detection method provided by the invention can be suitable for detecting satellite micro faults and has more comprehensive fault detection capability on different fault amplitudes.
While various embodiments of the present invention have been described above, it should be understood that they have been presented by way of example only, and not limitation. It will be apparent to those skilled in the relevant art that various combinations, modifications, and variations can be made therein without departing from the spirit and scope of the invention. Thus, the breadth and scope of the present invention as disclosed herein should not be limited by any of the above-described exemplary embodiments, but should be defined only in accordance with the following claims and their equivalents.
Claims (6)
1. The satellite micro fault detection method is characterized by comprising the following steps:
extracting an on-orbit sample by adopting a sliding window;
calculating an optimal projection vector between the on-orbit sample and the historical normal sample by using linear discriminant analysis;
obtaining a detection threshold through non-center F distribution detection according to the historical normal data and the optimal projection vector:
obtaining obeying degree of freedom n through non-central F distribution inspection 1 -1 and 1, and the non-central parameter is c 2 Is non-central F distribution of (C)Is set to be a detection threshold epsilon of (2) k Wherein:
and
n 1 -1 is X k At vector w k Freedom of chi-square distribution obeyed by the projected sample variance;
according to an objective function J (w k ) Calculating the deviation between the on-orbit sample and the historical normal sample, comparing the deviation with the detection threshold, and judging whether a fault occurs or not; and
sliding window back to pick up new on-orbit sample, repeating the above steps.
2. The method of claim 1, wherein the window length of each sample of the sliding window is a fixed value.
3. The method of claim 1, further comprising Z-score normalizing each parameter of the historical normal samples and the on-orbit samples prior to calculating the optimal projection vector.
4. The detection method according to claim 1, wherein the deviation is based on an objective function J (w k ) And (3) calculating to obtain:
wherein,
μ 0 、∑ 0 respectively mean vector and covariance matrix of the history normal data;
μ k 、Σ k respectively mean vector and covariance matrix of the on-orbit data; and
ω k is the best projection vector.
5. The method of detecting as claimed in claim 4, wherein said determining of the fault comprises:
if it isThen the on-track sample is considered to be faulty; and
if it isThe on-track sample is considered to be behaving normally.
6. A satellite employing the detection method according to any one of claims 1 to 5.
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