CN110348150B - Fault detection method based on correlation probability model - Google Patents
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Abstract
The invention relates to a fault detection method based on a correlation probability model, which comprises the following steps: selecting a parameter to be detected from a plurality of telemetry parameters; dividing a parameter to be detected into a plurality of working units in time; determining within each unit of work a correlation coefficient between each two of the plurality of telemetry parameters to determine a correlation coefficient vector for the unit of work; establishing a correlation probability model for the plurality of work units to determine a multivariate probability distribution of the plurality of work units; reducing the dimension of the multivariate probability distribution through Principal Component Analysis (PCA) to obtain the univariate probability distribution; and carrying out anomaly detection on the data of the unitary probability distribution to determine an anomaly parameter to be detected. By the method, the parameter abnormality can be detected at early stage of satellite faults, so that the satellite health state monitoring and system maintenance are facilitated.
Description
Technical Field
The invention relates to the field of satellite telemetry data anomaly detection, in particular to a fault detection method based on a correlation probability model.
Background
With the vigorous development of the aerospace industry in China, the number of satellites in research and development and in-orbit operation is increased year by year, and modern satellites are developing from single satellites to satellite networks. Satellites are used as a comprehensive system with high complexity, wide technology and high cost, and due to uncertainty of the space environment and limitation of testing before emission, anomalies or faults are inevitably generated during in-orbit operation, and telemetry parameters are important bases for reflecting the health state of the satellites.
At present, a method for setting a threshold value is widely adopted in China to detect satellite anomalies. The method is simple and effective, has low false detection rate, and is suitable for parameter detection under the condition of final fault occurrence, but the method also has certain disadvantages. Firstly, different models of satellites have different design modes, different working states and different telemetry parameters are set, different thresholds are required to be set according to different conditions, and a large amount of manpower is required to be consumed; secondly, the setting of the threshold value requires abundant expert experience, and the non-ideal setting of the threshold value is extremely easy to cause false alarm or false alarm, and the adopted threshold value range is often too large to reach balance, so that the abnormality cannot be found in the early stage of the fault. The anomaly detection method based on data driving is widely applied in the field of anomaly detection in recent years, and has better expansibility without expert knowledge and accurate mathematical physical model from the data. The anomaly detection method based on data driving mainly comprises the following steps: statistical-based methods and machine-learning-based methods, such as methods based on gaussian models, regression models; neural network-based methods; a method of supporting a vector machine, and the like. But telemetry parameters themselves are insensitive to certain variations and often face threshold selection challenges when making an anomaly decision.
Disclosure of Invention
The invention aims to provide a fault detection method based on a relevant probability model, by which parameter anomalies can be detected rapidly in the early stage of satellite faults, thereby being beneficial to satellite health state monitoring and system maintenance.
According to the invention, this object is achieved by a fault detection method based on a correlation probability model, comprising the steps of:
selecting a parameter to be detected from a plurality of telemetry parameters;
dividing a parameter to be detected into a plurality of working units in time;
determining within each unit of work a correlation coefficient between each two of the plurality of telemetry parameters to determine a correlation coefficient vector for the unit of work;
establishing a correlation probability model for the plurality of work units to determine a multivariate probability distribution of the plurality of work units;
reducing the dimension of the multivariate probability distribution through Principal Component Analysis (PCA) to obtain the univariate probability distribution; and
and carrying out anomaly detection on the data of the unitary probability distribution to determine parameters to be detected of the anomaly.
In a preferred embodiment of the invention, it is provided that the selection of the parameter to be detected from the plurality of telemetry parameters comprises one or more of the following:
dividing telemetry parameters according to satellite subsystems, and detecting telemetry parameters of a single subsystem to distinguish data modes;
separately detecting the numerical data and the non-numerical parameters;
selecting parameters to be detected according to engineering experience, satellite design principle and/or fault plan;
removing telemetry parameters with strong linear correlation; and
the parameters to be detected are selected according to whether the correlation between the telemetry parameters changes before and after the fault occurs or whether the telemetry parameters are related to temperature.
In another preferred embodiment of the present invention, determining a correlation coefficient between each two of the plurality of telemetry parameters within each unit of work to determine a correlation coefficient vector for that unit of work comprises the steps of:
the correlation coefficient between the two parameters a, b is calculated by the following formula:
where n is the length of the time series within a unit of work, a i 、b i The telemetry values of the parameters a, b at a certain moment,
average values of telemetry values of parameters a, b within the unit of work; and
the correlation coefficient for each unit of work is generated to generate a correlation coefficient vector.
In a further preferred embodiment of the invention, it is provided that the establishment of a correlation probability model for the plurality of work units for determining a multivariate probability distribution of the plurality of work units comprises the following steps:
the M p-dimensional correlation coefficient vectors l are determined by the following formula 1 、l 2 、…、l M Wherein p > 1:
wherein μ and Σ are the mean and covariance matrices, respectively, of the p-element normal population, where:
in one embodiment of the invention, the multivariate probability distribution is a multivariate normal distribution and the univariate probability distribution is a univariate normal distribution.
In a preferred embodiment of the invention, it is provided that the anomaly detection of the data of the univariate probability distribution for determining the parameters to be detected for anomalies comprises the following steps:
performing anomaly detection on the data subjected to PCA dimension reduction by a t-test method;
after abnormal data are detected, reconstructing the data in the low-dimensional space into the high-dimensional space, and calculating reconstruction errors of the reconstructed high-dimensional data and the original high-dimensional data and contribution ratio of each component to the reconstruction errors;
determining a component of the contribution ratio exceeding a threshold; and
and determining abnormal parameters to be detected according to the components.
The invention has at least the following beneficial effects: the invention uses the related probability model to detect the faults, and can quickly detect the parameter anomalies in the early stage of satellite faults by identifying the changes of the related parameters of the parameter at the early stage of the anomalies and/or when the slow non-obvious anomalies occur in the parameter, thereby being beneficial to satellite health state monitoring and system maintenance.
Drawings
The invention is further elucidated below in connection with the embodiments with reference to the drawings.
FIG. 1 shows a flow of a fault detection method according to the present invention;
FIG. 2 shows a schematic diagram of a work cell division;
FIG. 3 shows a schematic of fitted unitary normal distribution data; and
fig. 4 shows a schematic diagram of a temperature ramp abnormality.
Detailed Description
It should be noted that the components in the figures may be shown exaggerated for illustrative purposes and are not necessarily to scale. In the drawings, identical or functionally identical components are provided with the same reference numerals.
In the present invention, unless specifically indicated otherwise, "disposed on …", "disposed over …" and "disposed over …" do not preclude the presence of an intermediate therebetween. Furthermore, "disposed on or above" … merely indicates the relative positional relationship between the two components, but may also be converted to "disposed under or below" …, and vice versa, under certain circumstances, such as after reversing the product direction.
In the present invention, the embodiments are merely intended to illustrate the scheme of the present invention, and should not be construed as limiting.
In the present invention, the adjectives "a" and "an" do not exclude a scenario of a plurality of elements, unless specifically indicated.
It should also be noted herein that in embodiments of the present invention, only a portion of the components or assemblies may be shown for clarity and simplicity, but those of ordinary skill in the art will appreciate that the components or assemblies may be added as needed for a particular scenario under the teachings of the present invention.
It should also be noted herein that, within the scope of the present invention, the terms "identical", "equal" and the like do not mean that the two values are absolutely equal, but rather allow for some reasonable error, that is, the terms also encompass "substantially identical", "substantially equal". By analogy, in the present invention, the term "perpendicular", "parallel" and the like in the table direction also covers the meaning of "substantially perpendicular", "substantially parallel".
The numbers of the steps of the respective methods of the present invention are not limited to the order of execution of the steps of the methods. The method steps may be performed in a different order unless otherwise indicated.
In addition, the inventor finds that more than 50% of faults on the satellite are temperature-related, and most of parameter anomalies related to the temperature are gradual anomalies, as shown in fig. 4, when a certain type of satellite measurement and control subsystem has high-power faults.
After the abnormality occurs, the remote measurement parameter value changes slowly until the alarm threshold is exceeded, and a long period of time is needed from the occurrence of the slow-change abnormality to the detection of the slow-change abnormality, so that ground personnel cannot take remedial measures in time, and larger accidents are caused. Therefore, how to quickly and accurately detect the abnormality of the telemetry parameters in the early stage of satellite failure is a problem to be solved.
The invention is based on the data driving method, through analyzing the correlation between satellite parameters, extracting the correlation coefficient vector, establishing a multi-element normal correlation probability model of the correlation coefficient vector, and then carrying out PCA dimension reduction on the correlation coefficient vector to obtain a series of data meeting the unitary normal distribution; and finally, performing anomaly detection on the reduced-dimension data through t-test, and judging the abnormal parameters by calculating the contribution ratio of the reconstruction errors, so as to roughly determine the direction for the subsequent fault diagnosis. The invention can rapidly detect parameter abnormality, especially slow-change abnormality, in early stage of satellite fault, thereby promoting health status monitoring and system maintenance of the satellite.
The invention is further elucidated below in connection with the embodiments with reference to the drawings.
Fig. 1 shows a flow of a fault detection method 100 according to the present invention.
In step 102, a parameter to be detected is selected from a plurality of telemetry parameters.
In step 104, the parameter to be detected is divided into a plurality of work units in time.
At step 106, a correlation coefficient between each two of the plurality of telemetry parameters is determined within each unit of work to determine a correlation coefficient vector for the unit of work.
At step 108, a correlation probability model is built for the plurality of units of work to determine a multivariate probability distribution for the plurality of units of work.
In step 110, the multivariate probability distribution is reduced in dimension by principal component analysis PCA to obtain a univariate probability distribution.
In step 112, anomaly detection is performed on the data of the unitary probability distribution to determine a parameter to be detected for the anomaly.
Details of the steps of the present invention are described in detail below.
Selecting parameters to be detected
A large number of parameters are usually set on the satellite to reflect the running condition and health state of the satellite, if the correlation between all the parameters is calculated, a "dimension disaster" is very easy to be caused, so that selecting an appropriate parameter is also an important ring in anomaly detection. The parameters to be detected may be selected, for example, from the following aspects: 1. dividing parameters according to satellite subsystems, and detecting parameters of a single subsystem; 2. distinguishing data modes, and separately detecting numerical data and non-numerical data; 3. selecting relevant parameters according to engineering experience, satellite design principle and fault plan; 4. the satellite system has a large amount of parameter redundancy, and parameters with strong linear correlation can be removed according to conditions when the parameters are selected; 5. the parameters to be detected can be selected in a targeted manner according to whether the correlation between the parameters changes before and after the occurrence of the fault or whether the parameters are related to temperature.
Dividing units of work
The satellite telemetry parameter is a multiple time series, for example, the satellite can be used for running round the ground to form a working unit, the telemetry parameter is divided, and the length of the working unit can be just the same as the length of one period of most temperature parameters. In this way, the telemetry parameters are divided into a series of units of work, as shown in FIG. 2.
Quantizing the correlation between the parameters and extracting the correlation coefficient vector
Within a unit of work, each telemetry parameter is a unitary time series of equal length. The correlation between the parameters is quantified by calculating pearson correlation coefficients. For the parameter a and the parameter b, the calculation formula of the pearson correlation coefficient between the parameter a and the parameter b is as follows:
wherein n is the length of the time sequence in one working unit, a i 、b i The telemetry values of the parameters a, b at a certain moment,
the average of the telemetry values of the parameters a, b within the unit of operation is given respectively.
And calculating correlation coefficients between every two parameters in a working unit, wherein the correlation coefficients form a correlation coefficient vector of the working unit. Its correlation coefficient vector is extracted for each work cell.
Establishing a correlation probability model
Assuming that M working units are divided, namely, the satellite runs around the ground for M circles, M correlation coefficient vectors are obtained through calculation. Under normal conditions, the scenes of each operation period of the satellite are similar, and the M vectors do not all represent the normal correlation relationship among parameters to be detected in consideration of the influences of on-ground manual operation, uncertain factors of space environment, telemetry data downloading errors and the like. But in general, normal correlation coefficient vectors account for a majority and abnormal correlation coefficient vectors account for only a small portion. As is known from the law of large numbers, when M is sufficiently large, the correlation coefficient vector gradually follows a multivariate normal distribution.
Let 1 1 、l 2 、…、l M M p (p > 1) dimensional correlation coefficient vectors, and the satisfied probability density function is:
where μ and Σ are the mean and covariance matrices, respectively, of the p-element normal population. By l 1 、l 2 、…、l M To estimate the mean and covariance matrix of the population, the method employed here being a maximum likelihood estimation method.
PCA dimension reduction
The feature of maintaining the normality by the linear combination of the multivariate normal distribution is that the data after the multidimensional normal random variable is subjected to dimension reduction is a unitary normal random variable. Fig. 3 shows a fitting unitary normal distribution of a multivariate normal random variable after principal component analysis (Principal Components Analysis, PCA) dimensionality reduction, where the data points are approximately distributed near a straight line, which shows a very strong normalization.
Anomaly detection and determination of anomaly parameters
The invention adopts a t-test method in hypothesis test to detect the abnormality of the data after the PCA dimension reduction. the original and alternative hypotheses for the t-test are respectively:
the test statistics are:
where μ is the average of the population, x i Is an observation of the sample and,
is the mean value of the sample, +.>
Is the standard deviation of the samples, n is the number of sample points. Upon receiving the original assumption, test statistic T obeys a T-distribution with degrees of freedom n-1, and α is typically 0.1,0.05 and 0.01. When |T| > T α/2 And rejecting the original hypothesis, accepting the alternative hypothesis, and judging that the sample distribution and the overall distribution are not consistent and abnormal occurs.
After abnormal data is detected, reconstructing the data in the low-dimensional space into the high-dimensional space, calculating reconstruction errors of the reconstructed high-dimensional data and the original high-dimensional data and contribution ratio of each component to the reconstruction errors, wherein the larger the contribution ratio is, the higher the possibility that the component is abnormal, and the components with larger cross-contrast contribution ratio can approximately determine parameters with abnormality.
The calculation formula of the reconstruction error is as follows:
where X is the original high-dimensional data,
is reconstructed high-dimensional data, +.>
The calculation formula of (2) is as follows:
where a is the conversion matrix and where,
is the mean of the original high latitude data.
Calculating the proportion of reconstruction errors of each component, wherein the formula is as follows:
wherein X is ij Represents the jth component of the ith raw data,
the jth component, U, representing the ith reconstruction data i Representing the reconstruction error of the i-th original data.
While certain embodiments of the present invention have been described herein, those skilled in the art will appreciate that these embodiments are shown by way of example only. Numerous variations, substitutions and modifications will occur to those skilled in the art in light of the present teachings without departing from the scope of the invention. The appended claims are intended to define the scope of the invention and to cover such methods and structures within the scope of these claims themselves and their equivalents.
Claims (5)
1. A fault detection method based on a correlation probability model comprises the following steps:
selecting a parameter to be detected from a plurality of telemetry parameters;
dividing a parameter to be detected into a plurality of working units in time;
determining within each unit of work a correlation coefficient between each two of the plurality of telemetry parameters to determine a correlation coefficient vector for the unit of work;
establishing a correlation probability model for the plurality of work cells to determine a multivariate probability distribution of the plurality of work cells, including determining M p-dimensional correlation coefficient vectors l by the following formula 1 、l 2 、…、l M Wherein p > 1:
where T is the test statistic, which obeys the T-distribution with degrees of freedom n-1, and μ and Σ are the mean and covariance matrices of the p-element normal population, respectively, where:
reducing the dimension of the multivariate probability distribution through Principal Component Analysis (PCA) to obtain the univariate probability distribution; and
and carrying out anomaly detection on the data of the unitary probability distribution to determine parameters to be detected of the anomaly.
2. The method of claim 1, wherein selecting a parameter to be detected from a plurality of telemetry parameters comprises one or more of:
dividing telemetry parameters according to satellite subsystems, and detecting telemetry parameters of a single subsystem to distinguish data modes;
separately detecting the numerical data and the non-numerical parameters;
selecting parameters to be detected according to engineering experience, satellite design principle and/or fault plan;
and
The parameters to be detected are selected according to whether the correlation between the telemetry parameters changes before and after the fault occurs or whether the telemetry parameters are related to temperature.
3. The method of claim 1, wherein determining a correlation coefficient between each two of the plurality of telemetry parameters within each unit of work to determine a correlation coefficient vector for that unit of work comprises the steps of:
the correlation coefficient between the two parameters a, b is calculated by the following formula:
where n is the length of the time series within a unit of work, a i 、b i The telemetry values of the parameters a, b at a certain moment,
average values of telemetry values of parameters a, b within the unit of work; and
the correlation coefficient for each unit of work is generated to generate a correlation coefficient vector.
4. The method of claim 1, wherein the multivariate probability distribution is a multivariate normal distribution and the univariate probability distribution is a univariate normal distribution.
5. The method of claim 1, wherein anomaly detection of the data of the univariate probability distribution to determine parameters to be detected for anomalies comprises the steps of:
performing anomaly detection on the data subjected to PCA dimension reduction by a t-test method;
after abnormal data are detected, reconstructing the data in the low-dimensional space into the high-dimensional space, and calculating reconstruction errors of the reconstructed high-dimensional data and the original high-dimensional data and contribution ratio of each component to the reconstruction errors;
determining a component of the contribution ratio exceeding a threshold; and
and determining abnormal parameters to be detected according to the components.
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| CN112596081B (en) * | 2020-12-03 | 2023-12-01 | 北京航空航天大学 | Health state monitoring method based on correlation health baseline |
| CN112803893B (en) * | 2021-01-21 | 2021-08-10 | 中国科学院微小卫星创新研究院 | Health state monitoring system of satellite power supply system |
| CN113312809B (en) * | 2021-04-06 | 2022-12-13 | 北京航空航天大学 | Spacecraft telemetry data multi-parameter anomaly detection method based on related cluster division |
| CN115184963A (en) * | 2022-07-08 | 2022-10-14 | 国家卫星气象中心(国家空间天气监测预警中心) | Method and system for measuring working state association degree among subsystems in satellite |
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