CN101859146A - Satellite fault prediction method based on predictive filtering and empirical mode decomposition - Google Patents
Satellite fault prediction method based on predictive filtering and empirical mode decomposition Download PDFInfo
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Abstract
The invention relates to a satellite fault prediction method based on predictive filtering and empirical mode decomposition, which belongs to the method for safe operation and fault prediction of the space satellite, and solves the problems of serious noise influence and inaccurate prediction of the fault trend in the traditional satellite fault prediction and diagnosis method. The method comprises the following specific steps: 1, estimating errors of the satellite control system through predictive filtering according to the dynamic relationship of the nonlinear attitude of the satellite, thereby obtaining a system model error; 2, carrying out empirical mode decomposition for the system model error obtained in Step 1 to obtain the IMF component and the residual component of the n-order intrinsic mode function; and 3, establishing a fault trend model related to the residual component obtained in Step 2 through time series analysis, thereby completing the prediction and detection of minor and slow-variation faults. The invention can be applied in the field of fault diagnosis of the satellite attitude control system.
Description
Technical Field
The invention relates to a safe operation and fault prediction method for a space satellite, in particular to a fault prediction method for a satellite attitude control system based on prediction filtering and empirical mode decomposition.
Background
Satellite attitude control is a method and process of acquiring and maintaining the orientation of a satellite in space. At present, when a high-precision three-axis attitude stabilization satellite normally works on a track, a momentum wheel is generally adopted as a main executing mechanism of an attitude control system, and the attitude of the satellite is controlled through momentum exchange between the momentum wheel and the satellite. The reliability of the momentum wheel will directly affect the feasibility and reliability of attitude control of the entire satellite. At present, fault diagnosis and reconstruction of a satellite attitude control system are mainly based on a hardware redundancy method, which is far from enough for a complex satellite attitude control system.
At present, a prediction filtering method is adopted for the safe operation and fault prediction of a satellite, the prediction filtering method is an estimation method suitable for a nonlinear system with unknown input or model errors, the idea of the prediction filtering method is derived from a nonlinear pre-controller provided by Lu from the viewpoint of system control, and on the basis, Crassidis and Markley provide a new real-time filtering algorithm, namely Prediction Filtering (PF), according to a minimum model error criterion. The prediction filtering is used for estimating the model error of the system in real time by comparing the measured output with the predicted output, so that the state of the filter is corrected, and the estimation of the real state is realized. Due to the capability of the prediction filter to simultaneously estimate the model error and the system state, the domestic plum clue and flood axe introduces the prediction filtering method into the field of fault diagnosis by regarding the fault as a special model error. The noise existing in the estimation result of the predictive filtering affects the diagnostic performance, and a low-pass filter method can be adopted to suppress high-frequency noise, but because the characteristics of the noise are unknown, the method for suppressing the noise by adopting the low-pass filter method often fails, so that the fault cannot be accurately predicted, and the further research on the following fault detection and diagnosis is not facilitated. If the satellite fault can be accurately predicted, the feasibility and the reliability of the attitude control of the whole satellite can be improved by estimating the real state before the fault occurs.
Disclosure of Invention
The invention provides a satellite fault prediction method based on prediction filtering and empirical mode decomposition, and aims to solve the problems that a traditional satellite fault prediction method is seriously influenced by noise and cannot accurately predict a fault trend.
The specific process of the invention is as follows:
the method comprises the following steps: estimating the error of a satellite control system by using a prediction filtering method by using the nonlinear attitude dynamics relation of the satellite to obtain a system model error term;
step two: performing empirical mode decomposition on the system model error term obtained in the step one to obtain a first n-order intrinsic mode function IMF component and a residual error component;
step three: and (4) establishing a model of the fault trend of the residual error component obtained in the step two by using a time series analysis method, and completing the prediction and detection of the micro and slowly varying faults.
According to the method, the sum of the fault amount and the model uncertainty is regarded as the model error according to the nonlinear attitude dynamics relation of the satellite, compared with the traditional low-pass filter processing method, the method can effectively eliminate the influence of noise, the model error is estimated by using a prediction filtering method, the model error estimation value obtained by prediction filtering is subjected to empirical mode decomposition, a plurality of internal solid mode components and trend components are obtained, the prediction precision is improved, the trend of the fault is predicted by using a time sequence analysis method, the early-stage gradual change and tiny fault can be accurately predicted and detected, and the method is simple and effective. The method is used for the field of fault diagnosis of the satellite attitude control system.
Drawings
FIG. 1 is a flow chart of a method for satellite fault prediction based on predictive filtering and empirical mode decomposition; FIG. 2 is a flow chart of a third embodiment; FIG. 3 shows the estimation result of the prediction filtering when a slowly varying fault occurs in the pitch axis; FIG. 4 is a result of empirical mode decomposition of the yaw axis (no fault); FIG. 5 is a result of empirical mode decomposition of the pitch axis (creep fault); FIG. 6 is a result of empirical mode decomposition of the roll axis (no fault); FIG. 7 shows the prediction of a slowly varying fault in the pitch axis; fig. 8 shows the result of predicting a slight sudden change failure of the yaw axis.
Detailed Description
The first embodiment is as follows:a satellite fault prediction method based on prediction filtering and empirical mode decomposition comprises the following specific processes:
the method comprises the following steps: estimating the error of a satellite control system by using a prediction filtering method by using the nonlinear attitude dynamics relation of the satellite to obtain a system model error term;
step two: performing empirical mode decomposition on the system model error term obtained in the step one to obtain a first n-order intrinsic mode function IMF component and a residual error component;
step three: and (4) establishing a model of the fault trend of the residual error component obtained in the step two by using a time series analysis method, and completing the prediction and detection of the micro and slowly varying faults.
Empirical Mode Decomposition (EMD) is a new signal decomposition method proposed by the scholars majora in 1998, which can use the change of the internal time scale of the signal to analyze the energy and frequency and expand the signal into a plurality of internal solid mode functions (IMF). Unlike the conventional method using a fixed morphology window as the bounding basis function, the basis function of the EMD is extracted from the signal, i.e., IMF is used as the basis. Whereas IMF must satisfy the following conditions:
1) in the whole function, the number of the extreme points is equal to or different from the number of the zero crossing points by 1;
2) at any instant, the envelope defined by the local extremum envelope has a local mean of zero.
The first condition is similar to the narrow bandwidth requirement of the conventional gaussian smoothing process. The second condition is a new idea: the global requirement is changed to a local requirement so that the instantaneous frequency does not cause unnecessary jitter due to the presence of an asymmetric waveform. The EMD and HHT constructed based on the two conditions are considered to be an adaptive method for strongly processing nonlinear and non-stationary signals, are a great breakthrough in linear and stationary spectrum analysis based on Fourier transform in recent years, and are widely applied. The empirical mode decomposition method can be used for adaptively decomposing the signal into components with different instantaneous frequencies, so that the noise component in the signal can be adaptively eliminated.
Establishing a prediction model of the fault trend is the main content of fault prediction. An autoregressive model (armode) is a common model in time series analysis. The AR model has the advantages of simple modeling, small calculated amount and the like. First order AR models, which have different characteristics than AR (m) where m >1 models, are suitable for stationary stochastic processes, and as a special case of AR models, can predict non-stationary stochastic processes.
The method comprises the following steps of considering the fault as a main part or an important component of a system model error, designing a model error item of a prediction filter estimation system by utilizing a satellite nonlinear attitude dynamics relation, and processing an estimation result by utilizing an empirical mode decomposition method so as to diagnose the micro and mild-varying early fault of a satellite attitude control system.
The purpose of the invention is realized by the following technical scheme: the method comprises the steps of designing a model error item of a prediction filter estimation system by utilizing a satellite nonlinear attitude dynamics relation, carrying out empirical mode decomposition on an estimation result to obtain a plurality of orders of IMFs and a trend item, establishing a model of the trend item by utilizing a time series analysis method, and carrying out prediction and detection on micro and slowly varying faults.
Compared with the prior art, the invention has the following advantages:
1) compared with a low-pass filter processing method, the fault prediction method provided by the invention utilizes an empirical mode decomposition method, can effectively eliminate the influence of noise and extract the trend information of the fault quantity.
2) The fault prediction method provided by the invention utilizes an empirical mode decomposition method to divide signals into a plurality of IMFs and non-stationary residual components, and establishes an AR model on the basis, so that the prediction precision can be improved.
3) Compared with a diagnosis method directly based on a threshold value, the method can improve the sensitivity to the gradual early and tiny faults.
The second embodiment,The embodiment is further described as the first specific embodiment, in the first step, the satellite control system error is estimated by using the satellite nonlinear attitude dynamics relationship and adopting a predictive filtering method, and the process of obtaining the system model error term is as follows:
the model error of the satellite control system is set to be composed of the satellite actuator fault and the model uncertainty, and the measurement equations of the prediction filtering system and the actual system are respectively as follows:
the state equation is as follows:
the prediction filtering equation is:
wherein
In the form of a state vector, the state vector,
is an estimate of the state vector and,is a function of the state that can be made minute,
for the known matrix of the error distribution of the model,
in order to measure the vector of the function,
for estimation of unknown model errors, the measured output of the actual system is in discrete form,
is shown int k The measured value of the time of day,
for measuring noise and settingv k Is a mean of zero and a covariance matrix ofWhite gaussian noise of (1);
in that
And performing Taylor expansion on the measurement function at the moment to obtain:
wherein
Is the sampling period; the sampling period is a constant value and the sampling period is constant,
matrix of
To (1) aiThe elements are as follows:
whereinp i For the first occurrence in Taylor expansiond(t) The order of the differentiation of time is,is composed ofc i Is/are as followskThe order lie derivative;
matrix array
Is a diagonal matrix whose diagonal elements are:
matrix array
Of which the firstiThe elements of the row are:
taking a performance index function:
whereinAnd (3) optimizing the performance index for the positive and semi-fixed weighting matrix by adopting a gradient optimization algorithm, wherein the estimated value of the model error term is obtained by:
estimated value due to model error term
The method has a large noise component, cannot be directly used for fault diagnosis, and needs to be processed in the next step.
The third embodiment,The embodiment is further described with respect to the first specific embodiment, and the process of obtaining the IMF component and the residual component of the first n-th order eigenmode function in the second step is as follows:
setting the estimated value of the error term of the system model as
Time of day
，
Step a, initializing an IMF decomposition process:
and satisfy the relation
Is formed in whichIs as follows
Residual functions remaining after the secondary decomposition;
step b, initializing a screening process:k=1 and satisfies the relation
Is formed in which
Is as followsnSecondary IMF decomposition process throughk－Residual function after 1 screening;
step c, obtaining the estimated value of the system model error item according to the screening program
Through the first stepnThe residual function decomposed by the sub-eigenmode function passes through the firstkResidual function after secondary screening
；
Step d, judging the obtained residual function by adopting a standard deviation criterion
Whether or not the condition of the intrinsic mode function is satisfied, i.e.
Whether or not it is less than the threshold value T,
；
if yes, executing step e, if no, executing step ek=k+1, returning to the step c,
step e, obtainingnIMF component of the sub-eigenmode function
；
Step f, obtaining the estimated value of the error term of the system model
Through the first step
Residual function of sub-eigenmode function decomposition
；
Step g, order
And returning to execute the step b until obtaining the IMF component and the residual component of the first n-th order intrinsic mode function.
The fourth embodiment,The third embodiment is further explained, and the step c obtains the estimated value of the error term of the system model according to the screening programThrough the first step
The residual function decomposed by the sub-eigenmode function passes through the first
Residual function after secondary screening
The process comprises the following steps:
step c1, obtaining system model error terms by utilizing cubic spline function
Through the first stepnThe first trend function of the decomposition of the secondary eigenmode functionk－Residual function after 1-pass screening
Upper and lower envelope curves of (d);
step c2, calculating the residual function
Upper and lower envelope curves in timeMean of inner
；
Step c3, obtaining the estimated value of the system model error term
Through the first step
The first trend function of the decomposition of the secondary eigenmode functionkResidual function after secondary screening
。
The fifth embodiment,The third embodiment is further explained in the present embodiment, and the error term of the system model in step f
4 times of eigenmode function decomposition are carried out to obtain 4 eigenmode function components IMF1, IMF2, IMF3 and IMF 4:(ii) a And obtaining residual error function decomposed by 4 times of eigenmode function
。
The sixth embodiment,The embodiment further explains the first specific implementation, in the third step, a time series analysis method is used to establish a model of the fault trend of the residual error component obtained in the second step, and the process of completing the prediction and detection of the micro and slowly varying faults is as follows:
taking the residual error component as a trend signal, establishing an autoregressive model of the trend signal, wherein the expression is as follows:
wherein,r(t) Is a time series of the function of the residual error,pin order to be the order of the model,a i in order to be the parameters of the model,
is a white noise sequence;
observed value isThe order of the prediction model ispThe following equation set is obtained from the autoregressive model expression:
order:
，
，
the matrix form of the above equation is:
the least squares solution of the model parameters is:
obtaining model parameters from a regression modelAUsing model parametersAAnd (5) fault forecasting and detection are carried out.
The AR model of more than one order is suitable for a stationary random process, the first order AR model has
Different characteristics of the models, as a special case of the AR model, the first-order AR model can predict non-stationary random processes.
The specific implementation of the invention is illustrated by the satellite actuator fault diagnosis simulation example:
executing the step one: and estimating the fault amount of the actuating mechanism by using a prediction filtering method.
The state equation form and the discrete measurement equation of the satellite attitude dynamics are as follows:
in the formula, the state variableIs the attitude angular velocity of the satellite,
is the inertia of the main shaft of the satellite,
is an actuator momentum wheel failure. According to the prediction filtering theory, the obtained fault estimator is as follows:
wherein
To be at
The time pitch axis generating slope is
Actuator creep failure
For example, the failure estimation result of each axis is shown in fig. 3, where the three curves in fig. 3 are the failure estimation values in the x, y, and z coordinate axes (yaw, pitch, and roll axes) in sequence, the abscissa represents time in seconds, and the ordinate represents the failure estimation value in newton meters. Since the estimation result has a large noise component and cannot be directly used for fault diagnosis, the signal must be processed to extractA barrier feature.
And (5) executing the step two: and carrying out empirical mode decomposition on the prediction filtering result to obtain a plurality of IMFs and residual error components.
In order to avoid losing the fault characteristics of the rate gyro, empirical mode decomposition is carried out once after 128 times of sampling. The empirical mode decomposition to layer 4 is completed.
In thatt=19.6sWhen the pitch axis is faulty, the empirical mode decomposition result of the yaw axis (no fault) fault estimator is shown in fig. 4, fig. 5 is the empirical mode decomposition result of the pitch axis fault estimator, and fig. 6 is the empirical mode decomposition result of the roll axis (no fault) fault estimator. Fig. 4, 5, and 6 are the results of empirical mode decomposition of the acquired triaxial yaw, pitch, and roll signals, respectively, each of which includes, from top to bottom, an IMF (intrinsic mode function) component of order 1, 2, 3, 4, and 5 and a residual component after decomposition, respectively, with the abscissa representing time in seconds, and the ordinate representing the IMF component or the residual component in newton meters.
And step three is executed: and establishing an AR model of the residual error component, and performing fault prediction and detection.
And using the first-order AR model as a prediction model of the residual component, and obtaining the model parameter value of the AR model by using the least square estimation method. The results of the predictions of the yaw, pitch and roll axes are shown in figure 7. Fig. 7 shows the fault estimation values in the x, y, and z coordinate axis directions (yaw, pitch, and roll axes) obtained by the method of the present invention for the example described in fig. 3 (where the pitch axis fails at t =19.6 s), where the abscissa represents time in seconds and the ordinate represents the fault estimation value in newton meters. Using an appropriate threshold value of (
) The method can realize the advanced detection of the tiny and early faults.
In addition, the effectiveness of the fault prediction method provided by the invention can also be verified through tiny sudden-change faults. In that
When the yaw axis suddenly breaks down, the amplitude is
The results of the fault prediction of the yaw, pitch and roll axes are shown in fig. 8. Fig. 8 shows the fault estimation values in the x, y, and z coordinate axis directions (yaw, pitch, and roll axes) obtained by the method of the present invention when a sudden fault occurs in which the yaw axis has a width of 0.01n.m at 20s, where the abscissa represents time in seconds and the ordinate represents the fault estimation value in newton meters.
The effectiveness of the fault prediction method provided by the invention can be verified by the fault diagnosis result.
Claims (6)
1. A satellite fault prediction method based on prediction filtering and empirical mode decomposition is characterized by comprising the following specific processes:
the method comprises the following steps: estimating the error of a satellite control system by using a prediction filtering method by using the nonlinear attitude dynamics relation of the satellite to obtain a system model error term;
step two: performing empirical mode decomposition on the system model error term obtained in the step one to obtain a first n-order intrinsic mode function IMF component and a residual error component;
step three: and (4) establishing a model of the fault trend of the residual error component obtained in the step two by using a time series analysis method, and completing the prediction and detection of the micro and slowly varying faults.
2. The method for predicting satellite faults based on the predictive filtering and the empirical mode decomposition according to claim 1, wherein in the first step, the satellite control system errors are estimated by using a satellite nonlinear attitude dynamics relation and adopting a predictive filtering method, and a process of obtaining a system model error term is as follows:
the model error of the satellite control system is set to be composed of the fault of a satellite actuating mechanism and the uncertainty of the model, and the nonlinear state equation and the measurement equation are respectively as follows:
the state equation is as follows:
the prediction filtering equation is:
wherein
In the form of a state vector, the state vector,is an estimate of the state vector and,
is a function of the state that can be made minute,for known model errorsA matrix of a difference distribution is formed,
in order to measure the vector of the function,
for the unknown error of the model to be,
as an estimate of the value of the error,
is shown int k The measured output of the actual system at that moment, in discrete form,
for measuring noise and settingv k Is a mean of zero and a covariance matrix ofWhite gaussian noise of (1);
in that
And performing Taylor expansion on the measurement function at the moment to obtain:
wherein
Is the sampling period; the sampling period is a constant value and the sampling period is constant,
matrix of
To (1) aiThe elements are as follows:
whereinp i For the first occurrence in Taylor expansiond(t) The order of the differentiation of time is,
is composed ofc i Is/are as followskThe order lie derivative;
matrix array
Is a diagonal matrix whose diagonal elements are:
matrix array
Of which the firstiThe elements of the row are:
taking a performance index function:
wherein
And (3) optimizing the performance index for the positive semi-definite weighting matrix by adopting a gradient optimization algorithm to obtain the estimation of a model error item as follows:
3. the method according to claim 2, wherein the step two of obtaining the IMF component and the residual component of the first nth-order eigenmode function is performed by:
setting the error term estimation value of the system model as
Time of day
，
Step a, initializing an IMF decomposition process:
and satisfy the relation
Is formed in which
Is as followsResidual functions remaining after the secondary decomposition;
step b, initializing a screening process:k=1 and satisfies the relation
Is formed in which
Is as followsnSecondary IMF decomposition process throughk－Residual function after 1 screening;
step c, obtaining the error term estimated value of the system model according to the screening program
Through the first stepnThe residual function decomposed by the sub-eigenmode function passes through the firstkResidual function after secondary screening；
Step d, judging the obtained residual function by adopting a standard deviation criterionWhether or not the condition of the intrinsic mode function is satisfied, i.e.
Whether or not it is less than the threshold value T,
；
if yes, executing step e, if no, executing step ek=k+1, returning to the step c,
step e, obtainingnIMF component of the sub-eigenmode function
；
Step f, obtaining the error term estimated value of the system modelThrough the first step
Residual function of sub-eigenmode function decomposition
；
Step g, orderAnd returning to execute the step b until obtaining the IMF component and the residual component of the first n-th order intrinsic mode function.
4. The method according to claim 3, wherein the step c of obtaining the estimated value of the error term of the system model according to the filtering procedure
Through the first step
The residual function decomposed by the sub-eigenmode function passes through the first
Residual function after secondary screening
The process comprises the following steps:
step c1, obtaining system model error term estimation value by utilizing cubic spline function
Through the first stepnThe first trend function of the decomposition of the secondary eigenmode functionk－Residual function after 1-pass screening
Upper and lower envelope curves of (d);
step c2, calculating the residual function
Upper and lower envelope curves in time
Mean of inner
；
Step c3, obtaining the error term estimation value of the system modelThrough the first step
The first trend function of the decomposition of the secondary eigenmode functionkResidual function after secondary screening
。
5. The method of claim 3, wherein the step f is based on an estimation of the error term of the system model4 times of eigenmode function decomposition are carried out to obtain 4 eigenmode function components IMF1, IMF2, IMF3 and IMF 4:
(ii) a And obtaining residual error function decomposed by 4 times of eigenmode function
。
6. The method for predicting satellite faults based on predictive filtering and empirical mode decomposition according to claim 3, wherein a time series analysis method is used in the third step to build a model of the fault trend of the residual components obtained in the second step, and the process of forecasting and detecting the micro and slowly varying faults is as follows:
taking the residual error component as a trend signal, establishing an autoregressive model of the trend signal, wherein the expression is as follows:
wherein,r(t) Is a time series of the function of the residual error,pin order to be the order of the model,a i in order to be the parameters of the model,
is a white noise sequence;
observed value is
The order of the prediction model ispThe following equation set is obtained from the autoregressive model expression:
order:
the matrix form of the above equation is:
the least squares solution of the model parameters is:
obtaining model parameters from a regression modelAUsing model parametersAAnd (5) fault forecasting and detection are carried out.
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