CN103871525B - Rhodium self-powered detector signal delay removing method based on Kalman filtering - Google Patents
Rhodium self-powered detector signal delay removing method based on Kalman filtering Download PDFInfo
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Abstract
The present invention relates to nuclear reactor core and measure system detector signal processing technology field, specifically disclose a kind of rhodium self-powered detector signal delay removing method based on Kalman filtering.Concretely comprising the following steps of the method: 1, set up the nuclear reaction model of rhodium and neutron;2, Kalman filter model is set up;3, Kalman filtering is utilized to make rhodium self-power neutron detector current signal to postpone to eliminate;3.1, obtain the systematic procedure white noise variance matrix Q in Kalman filtering algorithm and systematic observation white noise variance matrix is R;3.2, gather rhodium self-powered detector current value, after carrying out analog digital conversion, utilize Kalman filtering to make rhodium self-power neutron detector current signal to postpone to eliminate;A kind of rhodium self-powered detector signal delay removing method based on Kalman filtering of the present invention, can carry out noise reduction process to measuring current signal, it is ensured that in the case of response time is sufficiently small, noise amplification suppresses at 1 ~ 8 times.
Description
Technical field
The invention belongs to nuclear reactor core and measure system detector signal processing technology field, be specifically related to a kind of based on card
The rhodium self-powered detector signal delay removing method of Kalman Filtering.
Background technology
As the rhodium self-power neutron detector of detector, its sensitive material rhodium and neutron in advanced In-core Instrumentation system heap
The secondary nucleic that reaction produces occurs decay to produce electric current, and under stable situation, this size of current is directly proportional to position flux,
Therefore its position neutron flux can be deduced by measurement rhodium self-powered detector.Owing to such detector current mainly becomes
Divide and produced by the decay of secondary nucleic, under reactor transient condition (situation of neutron-flux level change), such detection
Device electric current can not reflect the change of flux level in real time, but has certain delay, and delay time parameter declines with secondary nucleic
Become consistent.Therefore, rhodium self-power neutron detector is utilized to make the advanced reactor core measuring system of neutron measurement device, in ensureing
The accuracy of sub-flux measurement, needs the current signal that rhodium self-sufficiency can be visited device to make to postpone Processing for removing.
Owing to being always attended by noise (process noise and measurement noise) during actual measurement, utilize direct mathematical reverse
Method of drilling is made to postpone elimination and can detector current signal noise be amplified, and maximum is scalable to 20 times, the precision that impact is measured.Cause
This is during postponing Processing for removing, it is desirable to have the amplification of effect suppression noise.
Kalman filtering belongs to a kind of software filtering method, and its basic thought is: with least mean-square error as best estimate
Criterion, uses the state-space model of signal and noise, utilizes the estimated value of previous moment and the observation of current time to come more
The new estimation to state variable, obtains the estimated value of current time, algorithm according to the system equation set up and observational equation to need
Signal to be processed makes the estimation meeting least mean-square error.
Summary of the invention
It is an object of the invention to be to provide a kind of rhodium self-powered detector signal delay based on Kalman filtering to disappear
Except method, can carry out the current signal of rhodium self-power neutron detector postponing Processing for removing, and effectively suppress noise so that
Rhodium self-power neutron detector also can normally use when reactor transient condition.
Technical scheme is as follows: a kind of rhodium self-powered detector signal delay elimination side based on Kalman filtering
Method, the method specifically includes following steps:
Step 1, set up the nuclear reaction model of rhodium and neutron;
Under reactor transient condition, the change of flux causes change the difference of rhodium self-power neutron detector electric current
Step, the latter has certain delayed compared with the former, and the concrete formula describing above-mentioned reaction is as follows:
I (t)=cn (t)+λ1m1(t) (3)
Wherein, m1(t), m2T () represents detector104Rh and104mThe current component that Rh directly causes, n (t) represents detector
Detector current under the detector poised state that place's neutron flux is corresponding;λ1, λ2Represent104Rh and104mThe decay constant of Rh;c
Represent the transient response composition of detector current;a1、a2Represent respectively104Rh and104mThe electric current share that Rh causes;I (t) represents rhodium
Self-supporting energy electric current;
Step 2, set up Kalman filter model;
For the system of a discrete control process, this system can describe with a state equation:
X (k+1)=F (k+1 | k) X (k)+GW (k) (4)
The measured value of system:
Z (k)=H (k) X (k)+IV (k) (5)
System amount to be asked:
Y (k)=LX (k) (6)
Wherein, X (k) is that the n of kth time sampled point ties up state vector, W (k) systematic procedure white noise, and its variance matrix is Q,
V (k) is systematic observation white noise, its variance matrix be R, F (k+1 | k) be n*n state-transition matrix, Z (k) is kth time sampling
The m of point ties up measured value, and H (k) is m*n observing matrix, and G is n*n control system matrix, and I is the noise control matrix of m*n.Y (k) is l
Tieing up and wait to seek vector, L is that l*n ties up matrix;
Step 3, utilize Kalman filtering to rhodium self-power neutron detector current signal make postpone eliminate;
Step 3.1, the systematic procedure white noise variance matrix Q obtained in Kalman filtering algorithm and systematic observation white noise
Variance matrix is R;
Obtain the white noise variance R and systematic procedure white noise variance matrix Q of self-supporting moderate energy neutron detector measurement electric current;
Step 3.2, collection rhodium self-powered detector current value, after carrying out analog digital conversion, utilize Kalman filtering to rhodium certainly
Make to postpone to eliminate to moderate energy neutron detector current signal;
Formula (1), formula (2), formula (3) are made Laplace transform, obtain following equation:
During equilibrium state, equation becomes:
Then formula (7) becomes:
Formula (9) is carried out inverse Laplace transformation, obtains following state equation:
I (t)=[c, c, c] X (t) (12)
Wherein,
Initial value:
Discrete state equations is:
I (k)=[c c c] X (k) (17)
N (k)=[1 0 0] X (k) (18)
Wherein,
Initial value:
Formula (4) in formula (16), (17), (18) the most corresponding Kalman model, (5), (6).Then postpone to eliminate step
Rapid as follows:
Collection k moment rhodium self-powered detector current value I (k), the Z (k) of corresponding formula (5), continuation below step:
Carry out pre-estimation:
XP (k+1)=F (k+1 | k) X (k) (21)
Obtain covariance matrix
P (k+1)=F (k+1 | k) P (k) * F (k+1 | k) '+G*Q*G'(22)
Obtain Kalman gain
K (k+1)=P (k+1) * H (k) ' * (H (k) * P (k+1) * H (k) '+R)-1 (23)
Obtain next step state value
X (k+1)=XP (k+1)+K (k+1 | k) * (Z (k+1)-H (k) * XP (k+1)) (24)
Update covariance matrix
P (k+2)=P (k+1)-K (k+1) * H (k) * P (k+1) (25)
Calculating obtains amount to be asked
Y (k)=LX (k) (26)
Wherein, Y (k) is k moment rhodium self-powered detector current value I(k) corresponding postpone the value after eliminating.
In described step 3.1, the white noise variance R of electric current measured by self-power neutron detector is defeated by state of statistical control
The white noise exporting electric current under artificial situation obtains.
Systematic procedure white noise variance matrix Q in described step 3.1 particularly as follows:
Q is 3*3 matrix, is process white noise Variance matrix, w here1(k), w2K () is 0, w3
K () is the increment of k sample moment n (k), therefore Q has a following form:
Wherein, q here11、q22Close to 0, for formula (1), the model variance of formula (2), q33Increment side for n (k)
Difference.
The remarkable result of the present invention is: a kind of rhodium self-powered detector based on Kalman filtering of the present invention is believed
Number delay eliminating method, can carry out noise reduction process to measuring current signal, it is ensured that in the case of response time is sufficiently small,
Noise amplification suppresses at 1 ~ 8 times.
Accompanying drawing explanation
Fig. 1 is a kind of rhodium self-powered detector signal delay removing method stream based on Kalman filtering of the present invention
Cheng Tu.
Detailed description of the invention
Below in conjunction with the accompanying drawings and the present invention is described in further detail by specific embodiment.
As described in Figure 1, a kind of rhodium self-powered detector signal delay removing method based on Kalman filtering, it specifically walks
Rapid as follows:
Step 1, set up the nuclear reaction model of rhodium and (hot) neutron;
Under reactor transient condition, the change of flux causes change the difference of rhodium self-power neutron detector electric current
Step, the latter has certain delayed compared with the former, and the concrete formula describing above-mentioned reaction is as follows: Formula 1 Formula 2
I (t)=cn (t)+λ1m1(t) formula 3
Wherein, m1(t), m2T () represents detector104Rh and104The current component that mRh directly causes, n (t) represents detector
Detector current under the detector poised state that place's (hot) neutron flux is corresponding;λ1, λ2Represent104Rh and104mThe decay of Rh is normal
Number (λ1=ln2/42.3s-1=0.016386s-1,λ2=ln2/4.34/60s-1=0.00266186s-1);C represents detector current
Transient response composition;a1、a2Represent respectively104Rh and104m(a kind of situation is c=0.06 to the electric current share that Rh causes, a1=0.879,
a2=0.061);I (t) represents SPND electric current.
Step 2, set up Kalman filter model
For the system of a discrete control process, this system can describe with a state equation:
X (k+1)=F (k+1 | k) X (k)+GW (k) formula 4
The measured value of system:
Z (k)=H (k) X (k)+IV (k) formula 5
System amount to be asked:
Y (k)=LX (k) formula 6
Wherein, X (k) is the n dimension state vector of kth time sampled point, W (k) systematic procedure white noise (n dimension), its variance square
Battle array be Q, V (k) be systematic observation white noise (n dimension), its variance matrix be R, F (k+1 | k) be n*n state-transition matrix, Z (k)
M for kth time sampled point ties up measured value, and H (k) is m*n observing matrix, and G is n*n control system matrix, and I is that m*n is noise control
Matrix.Y (k) is that l ties up and waits to ask vector, and L is that l*n ties up matrix.
Step 3, utilize Kalman filtering to rhodium self-power neutron detector current signal make postpone eliminate
Step 3.1, the systematic procedure white noise variance matrix Q arranged in Kalman filtering algorithm and systematic observation white noise
Variance matrix is R, wherein,
R: be the white noise variance of self-power neutron detector measurement electric current, in the case of this value can be exported by state of statistical control
The white noise of output electric current is obtained.
Q:Q is 3*3 matrix, is process white noise Variance matrix, w here1(k), w2K () is 0,
w3K () is the increment of k sample moment n (k), therefore Q has a following form:
Wherein, q here11、q22Close to 0, for formula 1, the model variance of formula 2, q33Increment variance for n (k).
Step 3.2, collection rhodium self-powered detector current value, and utilize Kalman filtering to rhodium self-power neutron detector
Current signal is made to postpone to eliminate
Formula 1, formula 2, formula 3 are made Laplace transform, obtain following equation:
During equilibrium state, equation becomes:
Then formula 8 becomes:
Formula 10 is carried out inverse Laplace transformation, obtains following state equation:
I (t)=[c, c, c] X (t) formula 13
Wherein,
Initial value:
Discrete state equations is:
I (k)=[c c c] X (k) formula 18
N (k)=[1 0 0] X (k) formula 19
Wherein,
Initial value: Formula 20
Formula 4,5,6 in the most corresponding Kalman model of formula 17,18,19.Then postpone removal process as follows:
Collection k moment rhodium self-powered detector current value I (k), the Z (k) of corresponding formula 5, continuation below step:
Carry out pre-estimation:
XP (k+1)=F (k+1 | k) X (k) formula 22
Obtain covariance matrix
P (k+1)=F (k+1 | k) P (k) * F (k+1 | k) '+G*Q*G' formula 23
Obtain Kalman gain
K (k+1)=P (k+1) * H (k) ' * (H (k) * P (k+1) * H (k) '+R)-1 formula 24
Obtain next step state value
X (k+1)=XP (k+1)+K (k+1 | k) * (Z (k+1)-H (k) * XP (k+1)) formula 25
Update covariance matrix
P (k+2)=P (k+1)-K (k+1) * H (k) * P (k+1) formula 26
Calculating obtains amount to be asked
Y (k)=LX (k) formula 27
Wherein, Y (k) is k moment rhodium self-powered detector current value I(k) corresponding postpone the value after eliminating.
Claims (3)
1. a rhodium self-powered detector signal delay removing method based on Kalman filtering, it is characterised in that: the method has
Body comprises the steps:
Step 1, set up the nuclear reaction model of rhodium and neutron;
Under reactor transient condition, the change of flux causes the change of rhodium self-powered detector electric current asynchronous, and the latter is relatively
The former has certain delayed, and the concrete formula describing above-mentioned reaction is as follows:
I (t)=cn (t)+λ1m1(t) (3)
Wherein, m1(t), m2T () represents detector respectively104Rh and104mThe current component that Rh directly causes, n (t) represents detector
Detector current under the detector poised state that place's neutron flux is corresponding;λ1, λ2Represent respectively104Rh and104mThe decay of Rh is normal
Number;C represents the transient response composition of detector current;a1、a2Represent respectively104Rh and104mThe electric current share that Rh causes;I (t) table
Show rhodium self-powered detector electric current;
Step 2, set up Kalman filter model;
For the system of a discrete control process, this system can describe with a state equation:
X (p+1)=F (p+1 | p) X (p)+GW (p) (4)
The measured value of system:
Z (p)=H (p) X (p)+IV (p) (5)
System amount to be asked:
Y (p)=LX (p) (6)
Wherein, X (p) is that the n of pth time sampled point ties up state vector, and W (p) systematic procedure white noise, its variance matrix is Q, V (p)
For systematic observation white noise, its variance matrix be R, F (p+1 | p) be n*n state-transition matrix, Z (p) is the m of pth time sampled point
Dimension measured value, H (p) is m*n observing matrix, and G is n*n control system matrix, and I is the noise control matrix of m*n, and Y (p) is that l dimension is treated
Seeking vector, L is that l*n ties up matrix;
Step 3, utilize Kalman filtering to rhodium self-powered detector current signal make postpone eliminate;
Step 3.1, the systematic procedure white noise variance matrix Q obtained in Kalman filtering algorithm and systematic observation white noise variance
Matrix is R;
Obtain rhodium self-powered detector and measure the white noise variance R and systematic procedure white noise variance matrix Q of electric current;
Step 3.2, collection rhodium self-powered detector current value, after carrying out analog digital conversion, utilize Kalman filtering to rhodium self-sufficiency energy
Detector current signal is made to postpone to eliminate;
Formula (1), formula (2), formula (3) are made Laplace transform, obtain following equation:
During equilibrium state, equation becomes:
Then formula (7) becomes:
Formula (9) is carried out inverse Laplace transformation, obtains following state equation:
I (t)=[c, c, c] X (t) (12)
Wherein,
Initial value:
Discrete state equations is:
I (k)=[c c c] X (k) (17)
N (k)=[1 0 0] X (k) (18)
Wherein,
Initial value:
Formula (4) in formula (16), (17), (18) the most corresponding Kalman model, (5), (6), then postpone removal process such as
Under:
Collection k moment rhodium self-powered detector current value I (k), the Z (k) of corresponding formula (5), continuation below step:
Carry out pre-estimation:
XP (k+1)=F (k+1 | k) X (k) (21)
Obtain covariance matrix
P (k+1)=F (k+1 | k) P (k) F (k+1 | k) '+G Q G'(22)
Obtain Kalman gain
K (k+1)=P (k+1) H (k) ' (H (k) P (k+1) H (k) '+R)-1 (23)
Obtain next step state value
X (k+1)=XP (k+1)+K (k+1 | k) (Z (k+1)-H (k) XP (k+1)) (24)
Update covariance matrix
P (k+2)=P (k+1)-K (k+1) H (k) P (k+1) (25)
Calculating obtains amount to be asked
Y (k)=LX (k) (26)
Wherein, Y (k) is the value after delay corresponding for k moment rhodium self-powered detector current value I (k) eliminates.
A kind of rhodium self-powered detector signal delay removing method based on Kalman filtering the most according to claim 1,
It is characterized in that: in described step 3.1, the white noise variance R of electric current measured by rhodium self-powered detector is defeated by state of statistical control
The white noise exporting electric current under artificial situation obtains.
A kind of rhodium self-powered detector signal delay removing method based on Kalman filtering the most according to claim 1,
It is characterized in that: systematic procedure white noise variance matrix Q in described step 3.1 particularly as follows:
Q is 3*3 matrix, is systematic procedure white noiseVariance matrix, w here1(k), w2K () is 0, w3
K () is the increment of k sample moment n (k), therefore Q has a following form:
Wherein, q here11、q22Close to 0, respectively formula (1), the model variance of formula (2), q33Increment side for n (k)
Difference.
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