CN108170955A - Consider robust state monitoring and the fault detection method of random sensor saturation effect - Google Patents
Consider robust state monitoring and the fault detection method of random sensor saturation effect Download PDFInfo
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Abstract
The invention discloses a kind of robust state monitoring for considering random sensor saturation effect and fault detection method, including step s1. system state space model foundations；Step s2. Robust Estimator Designs, the design of step s3. fault detects strategy.Include following design content in step s2：State estimator initial value is set, calculates intermediate variable, calculates the one-step prediction state estimation error covariance upper bound, calculates state estimator gain, the state estimation error covariance upper bound is calculated, in line computation state estimation：State estimation initial value is set, calculates a step status predication value, new breath is calculated, calculates state estimation；Include following design content in step s3：Residual error is calculated, calculates fault detect statistic, calculates the residual error second moment upper bound, calculates failure determination threshold value, sets fault detection logic.The present invention can monitor system running state and detection failure, to ensure that modern project system safety and steady is run simultaneously by the combination between above-mentioned steps.
Description
Technical field
The present invention relates to a kind of robust state monitoring for considering random sensor saturation effect and fault detection methods.
Background technology
With the rapid development of automatic technology and computer technology, the scale and complexity of modern project system increase
Add, the generation of any small fault may all cause chain reaction, cause casualties and economic loss, even result in calamity
Consequence.Therefore, it is necessary to real time on-line monitoring state and detection failure, with safeguards system safety.
In practical applications, due to physics or technology restriction, sensor saturated phenomenon is very universal.Standing state monitor with
Saturation effect is usually considered as that bounded is non-linear to be handled by fault detection method.However, due to environmental change or sensor event
Reasons, the sensors such as barrier can often occur random saturated phenomenon, existing method caused to fail.
On the other hand, modern project system operating conditions are severe, and running environment is complicated and changeable, and model uncertainty is stronger,
Requirement is proposed to the robustness of status monitoring and fault detect.However, existing method can only be to model uncertainty structure
The system known carries out status monitoring and fault detect, and does not consider random saturated phenomenon.
Based on the above situation, in order to meet practical application request, there is an urgent need for a kind of Shandongs for considering random sensor saturation effect
Stick status monitoring and fault detection method, while system running state and detection failure are monitored, ensure modern project system safety
Even running.
Invention content
It is an object of the invention to propose that a kind of robust state monitoring for considering random sensor saturation effect is examined with failure
Survey method, to solve the disadvantage that standing state monitoring and fault detection method, effective guarantee practical application request.
The present invention to achieve these goals, adopts the following technical scheme that：
Robust state monitoring and the fault detection method of random sensor saturation effect are considered, including step：
S1. system state space model foundation
Establish system state space model：
Wherein,For system mode,It inputs in order to control,It is exported to measure；
For process noise,For measurement noise；
For procedure parameter,For measurement parameter；
It is uncertain for procedure parameter,For measurement parameter not
Certainty；
For actuator failures；
For saturation coefficient, g ():For saturation function；
nx、nu、nySystem mode dimension is represented respectively, and control input dimension measures output dimension；
N is represented respectivelyxTie up real vector space, nuTie up real vector space, nyIt is empty to tie up real vector
Between；
N is represented respectivelyx×nxTie up real number matrix space, nx×nuTie up real number matrix space, ny
×nxTie up real number matrix space；
Saturation coefficient Λ (k) concrete forms are as follows：
Wherein, λi(k) i-th of component of saturation coefficient is represented,It is 1 to nyInteger set；
Given vectorSaturation function g () concrete form is as follows：
Wherein sgn ():For sign function,For saturation boundary, | | qi||2For qi
Two norms；
Above-mentioned stochastic variable meets following condition：
The mean value of initial system state x (0) isCovariance is P0, second moment Σ0；
The mean value of noise w (k), v (k) are zero, and covariance is respectively Σw(k), Σv(k)；
Parameter uncertainty Aδ(k),Bδ(k),Cδ(k) mean value is zero, and covariance is respectively
The mean value of Λ (k) is Λc(k), second moment ΣΛ(k)；
S2. Robust Estimator Design
Offline design state estimator gain：
Set state estimator initial value：
Wherein,Represent the mean value of initial system state x (0)；
Σx(0)Represent the second moment of initial system state x (0)；
Represent the initial estimation error covariance upper bound；
Calculate intermediate variable：
Wherein,For one-step prediction state estimation；
α1For arbitrary arithmetic number；
For Cc(k) second moment of x (k)；
Wherein, α2Represent arbitrary arithmetic number,Represent (Cc(k)+Cδ(k)) second moment of x (k)；
Wherein, α3、α4、α5And α6Represent arbitrary arithmetic number；
It representsIt is equal
Value；
Represent Cδ(k) second moment of x (k)；
Represent the one-step prediction state estimation error covariance upper bound；
Calculate the one-step prediction state estimation error covariance upper bound：
Wherein,Represent the state estimation error covariance upper bound；
Represent Aδ(k-1) second moment of x (k-1)；
Represent Bδ(k-1) second moment of u (k-1)；
Calculate state estimator gain Kx(k)：
Calculate the state estimation error covariance upper bound
In line computation state estimation：
Set state estimation initial value
Calculate a step status predication value：
The new breath r of calculating (k | k-1)：
Calculate state estimation
S3. fault detect strategy designs
Calculate residual error r (k)：
Calculate fault detect statistic TD(k)：
Wherein, nwRepresenting time slip-window length, r (n) represents residual error,Represent square of two norm of residual error；
Calculate residual error second moment upper bound Jth(k)：
Wherein, β1、β2、β3、β4、β5、β6、β7、β8Arbitrary arithmetic number is represented respectively；
It representsMark；
It representsMean value；
It representsMark；
It representsSecond moment；
It representsMark；
It representsMark；
It represents
Mean value；
tr(Σv(k)) represent Σv(k)Mark；
Calculate failure determination threshold value JD(k)：
Set fault detection logic：
If fault detect statistic is less than or equal to the failure determination threshold value, i.e. TD(k)≤JD(k) when, then system is normal；
If fault detect statistic is more than the failure determination threshold value, i.e. TD(k) ＞ JD(k) when, then the system failure.
The invention has the advantages that：
The robust state monitoring of the random sensor saturation effect of the considerations of present invention addresses and fault detection method, including
Three steps, i.e. step s1. system state spaces model foundation；Step s2. Robust Estimator Designs, step s3. failures
Inspection policies design.Wherein, include following design content in step s2：State estimator initial value is set, calculates intermediate variable,
The one-step prediction state estimation error covariance upper bound is calculated, calculates state estimator gain, calculates state estimation error covariance
The upper bound, in line computation state estimation：State estimation initial value is set, calculates a step status predication value, new breath is calculated, calculates state
Estimated value；Include following design content in step s3：Residual error is calculated, calculates fault detect statistic, calculates residual error second moment
The upper bound calculates failure determination threshold value, sets fault detection logic.The method of the present invention, can by the combination between above-mentioned steps
System running state and detection failure are monitored simultaneously, to ensure that modern project system safety and steady is run.
Description of the drawings
Fig. 1 is that the robust state monitoring of random sensor saturation effect and the flow of fault detection method are considered in the present invention
Figure；
Fig. 2 is system virtual condition 1 and the curve graph of estimated state 1 in the present invention；
Fig. 3 is system virtual condition 2 and the curve graph of estimated state 2 in the present invention；
Fig. 4 is the curve graph of system state estimation mean square error in the present invention；
Fig. 5 is system failure detection statistic and the curve graph of failure determination threshold value in the present invention.
Specific embodiment
Below in conjunction with the accompanying drawings and specific embodiment is described in further detail the present invention：
As shown in Figure 1, robust state monitoring and the fault detection method of random sensor saturation effect are considered, including step
Suddenly：
S1. system state space model foundation
Establish system state space model：
Wherein,For system mode,It inputs in order to control,It is exported to measure；
For process noise,For measurement noise；
For procedure parameter,For measurement parameter；
It is uncertain for procedure parameter,For measurement parameter not
Certainty；
For actuator failures；
For saturation coefficient, g ():For saturation function；
nx、nu、nySystem mode dimension is represented respectively, and control input dimension measures output dimension；
N is represented respectivelyxTie up real vector space, nuTie up real vector space, nyIt is empty to tie up real vector
Between；
N is represented respectivelyx×nxTie up real number matrix space, nx×nuTie up real number matrix space, ny
×nxTie up real number matrix space.
Saturation coefficient Λ (k) concrete forms are as follows：
Wherein, λi(k) i-th of component of saturation coefficient is represented,It is 1 to nyInteger set.
I-th of component λi(k) following Bernoulli Jacob's distributions are obeyed：
Given vectorSaturation function g () concrete form is as follows：
Wherein sgn ():For sign function,For saturation boundary, | | qi||2For
qiTwo norms.
Above-mentioned stochastic variable meets following condition：
The mean value of initial system state x (0) isCovariance is P0, second moment Σ0；
The mean value of noise w (k), v (k) are zero, and covariance is respectively Σw(k), Σv(k)；
Parameter uncertainty Aδ(k),Bδ(k),Cδ(k) mean value is zero, and covariance is respectively
The mean value of Λ (k) is Λc(k), second moment ΣΛ(k)。
S2. Robust Estimator Design
Offline design state estimator gain：
Set state estimator initial value：
Wherein,Represent the mean value of initial system state x (0)；
Σx(0)Represent the second moment of initial system state x (0)；
Represent the initial estimation error covariance upper bound.
Calculate intermediate variable：
Wherein,For one-step prediction state estimation；
α1For arbitrary arithmetic number；
For Cc(k) second moment of x (k).
Wherein, α2Represent arbitrary arithmetic number,Represent (Cc(k)+Cδ(k)) second moment of x (k).
Wherein, α3、α4、α5And α6Represent arbitrary arithmetic number；
It representsIt is equal
Value；
Represent Cδ(k) second moment of x (k)；
Represent the one-step prediction state estimation error covariance upper bound.
Calculate the one-step prediction state estimation error covariance upper bound：
Wherein,Represent the state estimation error covariance upper bound；
Represent Aδ(k-1) second moment of x (k-1)；
Represent Bδ(k-1) second moment of u (k-1).
Calculate state estimator gain Kx(k)：
Calculate the state estimation error covariance upper bound
In line computation state estimation：
Set state estimation initial value
Calculate a step status predication value：
The new breath r of calculating (k | k-1)：
Calculate state estimation
S3. fault detect strategy designs
Calculate residual error r (k)：
Calculate fault detect statistic TD(k)：
Wherein, nwRepresenting time slip-window length, r (n) represents residual error,Represent square of two norm of residual error.
Calculate residual error second moment upper bound Jth(k)：
Wherein, β1、β2、β3、β4、β5、β6、β7、β8Arbitrary arithmetic number is represented respectively；
It representsMark；
It representsMean value；
It representsMark；
It representsSecond moment；
It representsMark；
It representsMark；
It represents
Mean value；
Represent Σv(k)Mark.
Calculate failure determination threshold value JD(k)：
Set fault detection logic：
If fault detect statistic is less than or equal to the failure determination threshold value, i.e. TD(k)≤JD(k) when, then system is normal；
If fault detect statistic is more than the failure determination threshold value, i.e. TD(k) ＞ JD(k) when, then the system failure.
In order to verify the validity of the above method, the present invention gives following experiment, and parameter value is as follows：
Procedure parameter and measurement parameter are：
Procedure parameter uncertainty covariance and procedure parameter uncertainty covariance are：
The mean value of initial system state x (0) isCovariance is P0=1.5I2×2×10-6, second moment is
Σ0=1.5I2×2×10-6；The covariance of noise w (k), v (k) are respectively Σw(k)=1.4I2×2×10-6, Σv(k)=1.6I2×2
×10-6；Saturation boundary is s=[0.10.1]T；The mean value of saturation coefficient Λ (k) is Λc(k)=diag (0.1,0.2), second order
Square is ΣΛ(k)=diag (0.1,0.2,0.1,0.2).
Actuator failures are：
Experimental result is as shown in Figures 2 to 5.Wherein：
Experimental system virtual condition 1 is as shown in Figure 2 with estimated state 1；System virtual condition 2 and such as Fig. 3 institutes of estimated state 2
Show；System state estimation mean square error is as shown in Figure 4；System failure detection statistic and failure determination threshold value are as shown in Figure 5.
According to experimental result it can be seen that the method for the present invention can effectively monitor system mode and detecting system failure.
Certainly, described above is only presently preferred embodiments of the present invention, should the present invention is not limited to enumerate above-described embodiment
When explanation, any those skilled in the art are all equivalent substitutes for being made, bright under the introduction of this specification
Aobvious variant, all falls within the essential scope of this specification, ought to be protected by the present invention.
Claims (1)
1. consider robust state monitoring and the fault detection method of random sensor saturation effect, which is characterized in that including step：
S1. system state space model foundation
Establish system state space model：
Wherein,For system mode,It inputs in order to control,It is exported to measure；
For process noise,For measurement noise；
For procedure parameter,For measurement parameter；
It is uncertain for procedure parameter,It is not known for measurement parameter
Property；
For actuator failures；
For saturation coefficient,For saturation function；
nx、nu、nySystem mode dimension is represented respectively, and control input dimension measures output dimension；
N is represented respectivelyxTie up real vector space, nuTie up real vector space, nyTie up real vector space；
N is represented respectivelyx×nxTie up real number matrix space, nx×nuTie up real number matrix space, ny×nx
Tie up real number matrix space；
Saturation coefficient Λ (k) concrete forms are as follows：
Wherein, λi(k) i-th of component of saturation coefficient is represented,It is 1 to nyInteger set；
Given vectorSaturation function g () concrete form is as follows：
WhereinFor sign function,For saturation boundary, | | qi||2For qiTwo models
Number；
Above-mentioned stochastic variable meets following condition：
The mean value of initial system state x (0) isCovariance is P0, second moment Σ0；
The mean value of noise w (k), v (k) are zero, and covariance is respectively Σw(k), Σv(k)；
Parameter uncertainty Aδ(k),Bδ(k),Cδ(k) mean value is zero, and covariance is respectively
The mean value of Λ (k) is Λc(k), second moment ΣΛ(k)；
S2. Robust Estimator Design
Offline design state estimator gain：
Set state estimator initial value：
Wherein,Represent the mean value of initial system state x (0)；
Σx(0)Represent the second moment of initial system state x (0)；
Represent the initial estimation error covariance upper bound；
Calculate intermediate variable：
Wherein,For one-step prediction state estimation；
α1For arbitrary arithmetic number；
For Cc(k) second moment of x (k)；
Wherein, α2Represent arbitrary arithmetic number；
Represent (Cc(k)+Cδ(k)) second moment of x (k)；
Wherein, α3、α4、α5And α6Represent arbitrary arithmetic number；
It representsMean value；
Represent Cδ(k) second moment of x (k)；
Represent the one-step prediction state estimation error covariance upper bound；
Calculate the one-step prediction state estimation error covariance upper bound：
Wherein,Represent the state estimation error covariance upper bound；
Represent Aδ(k-1) second moment of x (k-1)；
Represent Bδ(k-1) second moment of u (k-1)；
Calculate state estimator gain Kx(k)：
Calculate the state estimation error covariance upper bound
In line computation state estimation：
Set state estimation initial value
Calculate a step status predication value：
The new breath r of calculating (k | k-1)：
Calculate state estimation
S3. fault detect strategy designs
Calculate residual error r (k)：
Calculate fault detect statistic TD(k)：
Wherein, nwRepresenting time slip-window length, r (n) represents residual error,Represent square of two norm of residual error；
Calculate residual error second moment upper bound Jth(k)：
Wherein, β1、β2、β3、β4、β5、β6、β7、β8Arbitrary arithmetic number is represented respectively；
It representsMark；
Represent Λ (k)Mean value；
It representsMark；
It representsSecond moment；
It representsMark；
It representsMark；
It represents's
Mean value；
tr(Σv(k)) represent Σv(k)Mark；
Calculate failure determination threshold value JD(k)：
Set fault detection logic：
If fault detect statistic is less than or equal to the failure determination threshold value, i.e. TD(k)≤JD(k) when, then system is normal；
If fault detect statistic is more than the failure determination threshold value, i.e. TD(k) ＞ JD(k) when, then the system failure.
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| CN109978252A (en) * | 2019-03-22 | 2019-07-05 | 山东科技大学 | A kind of high-power integrated fuel cell system running state prediction and evaluation method |
| CN110580035A (en) * | 2019-09-02 | 2019-12-17 | 浙江工业大学 | motion control system fault identification method under sensor saturation constraint |
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