CN110555192B - Method for eliminating delay effect of self-powered neutron detector based on digital circuit - Google Patents
Method for eliminating delay effect of self-powered neutron detector based on digital circuit Download PDFInfo
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Abstract
A method for eliminating the delay effect of a self-powered neutron detector based on a digital circuit comprises the following design steps: writing a relational expression of current I (t), the quantity of each nuclide and neutron flux density phi (t) according to the physical process of the emitter material of the detector in a neutron field; obtaining impulse response of the detector, and further performing Laplace transform on the impulse response function of the detector to obtain a delay response transfer function G(s) ═ I (s)/phi(s) of the detector; then, the inverse function is calculated to obtain the delay correction transfer function G‑1(s) ═ 1/g(s); according to transfer function G‑1And(s) ═ I (s)/phi(s) corresponding time domain iterative equations of all links design a digital delay compensation program. The system can correct the delayed current signal of the self-powered neutron detector, and overcomes the signal delay caused by the half-life period of the intermediate nuclide; compared with a method for correcting signal delay by an analog circuit, the system also has the advantages of flexible parameter adjustment and difficulty in interference of external link factors.
Description
Technical Field
The invention belongs to the technical field of neutron detection, and particularly relates to a method for eliminating a delay effect of a self-powered neutron detector based on a digital circuit.
Background
Nuclear energy is the most promising future energy source for humans. In a nuclear reactor, neutron flux density is the physical quantity that most intuitively represents reactor power and reactor status, and one also controls the reactor by controlling neutron flux density within the reactor. Due to the particularity of nuclear reactors and the importance of safe operation of nuclear reactors, neutron detection is of paramount importance in the detection of various particles and rays within the reactor.
The detection environment inside the reactor core is complex, the requirement on neutron detectors is high, high temperature resistance and irradiation resistance are required, and the reactor core is simple in structure and small in size. Currently, the commonly used neutron detectors can be classified into gas detectors, semiconductor detectors, scintillator detectors, and self-powered detectors according to their operation mechanisms. The gas detector is resistant to high temperature and radiation, but is still insufficient for the detection environment of high temperature and high pressure in the stack. The semiconductor detector is only suitable for measuring the fast neutron energy spectrum of the reactor, and has little application value to the existing thermal neutron reactor. The scintillator detector has high requirements for the stability of a high-voltage power supply and is difficult to realize in a reactor core.
The self-powered detector is particularly suitable for detecting the high neutron flux of the reactor core due to the characteristics of no external bias voltage, simple structure, small volume, overall solidification, simple electronic equipment and the like. However, in the current self-powered detectors, mainly103Rh (rhodium) detector,51V (vanadium) detector and59the detection principle of a self-powered detector of a Co (cobalt) detector is shown in the attached figure 2, the detector is placed in a reactor core, electrons are emitted through several different ways after the detector absorbs neutrons, and when the electrons are collected, current is generated in a loop; the current intensity is related to the neutron flux density in the stack, i.e. the neutron flux can be measured by measuring the current and subjecting it to some kind of processing.
In the case of the present self-powered detector,103rh detectors are widely used, but because103The isotope formed by Rh after absorbing neutrons in the neutron field decays with a certain half-life to generate electrons (or gamma rays which are converted into electrons through interaction with matter) to form a current signal of the detector. Clearly, due to the half-life limitation, the current signal does not reflect the neutron flux change in time. For example, by placing a self-powered detector suddenly in a constant neutron field, the current signal takes several minutes to reach a stable value. This is clearly not in line with the requirement for real-time monitoring of the neutron flux in the reactor core.
For the103Rh is said, the generation mechanism of the detector current signal in the neutron field is shown in fig. 2. In the composition of the detector current, three parts should be included in principle: 1) the first part is from103Rh absorbs neutrons and reacts instantaneously (n, gamma), the released gamma ray reacts with matter to generate electron by photoelectric effect or Compton effect, the current is instantaneous component, 2) the second part comes from104mRh is caused by withdrawal of104Gamma ray and substance released from RhElectrons generated by the proton-generating photoelectric effect or the compton effect; 3) the third part is from104Electrons generated by the decay of Rh β. The latter two terms are among the retarding components because of the half-life limitations of the Rh isotope.
At present, many scholars at home and abroad have many researches on a rhodium self-powered detector to obtain many achievements, and meanwhile, the rhodium self-powered detector has some defects: 1) the related art often includes only the first and third portions, and omits the second portion, which is not a main component of Rh, but the effect of Rh is not negligible in consideration of the effect of correcting the delay. 2) Some documents use two-dimensional matrix filters based on an optimal estimation method, where the matrix operation is very complicated and not user-friendly. 3) The laplace transform is significantly too complex to be understood. 4) The analog circuit method has high requirements on the precision of the component parameters, and once determined, the method is not easy to change according to the burn-up condition. In contrast, digital circuits can avoid the above problems, are easy to understand, and are highly adaptable.
Disclosure of Invention
In order to solve the problems in the prior art, the invention aims to provide a method for eliminating the delay effect of a self-powered neutron detector based on a digital circuit, 1) a digital delay compensation program can realize delay correction on current signals generated by the self-powered neutron detector such as rhodium, and the like, so that the problem of current signal delay caused by half-life limit is solved; 2) the digital delay compensation program is constructed by using the time domain iterative equation corresponding to the typical link in the delay compensation transfer function, and the digital delay compensation program has the advantages of intuition, simplicity and convenience.
In order to achieve the above purpose, the invention adopts the following technical scheme:
a method for eliminating delay effect of a self-powered neutron detector based on a digital circuit comprises the following steps:
step 1: drawing a reaction mechanism schematic diagram according to the reaction physical process of the self-powered detector material in a neutron field;
step 2: writing a differential equation system (1) of the number N (t) of the intermediate nuclides in a unit volume of the energy-saving neutron detector and the neutron flux density phi (t) according to the generation and decay relations of all nuclides related to the reaction mechanism schematic diagram drawn in the step 1, and writing an expression (2) of detection current I (t) and the number of the intermediate nuclides and the neutron flux density phi (t); the intermediate nuclide in the unit volume of the self-powered neutron detector refers to an unstable nuclide generated after a neutron is captured by a nuclide emitted by the self-powered neutron detector, and an unstable nuclide generated after the generated unstable nuclide is continuously decayed or is de-excited;
wherein
i represents the ith intermediate nuclide and takes the value of 1 to m;
j represents the jth intermediate nuclide and takes the value from 1 to i-1 or i +1 to m; if i-1<1, there is no item 3 to the right of the system of differential equations (1); if i +1> m, then there is no item 4 to the right of system of differential equations (1);
m represents a total of m intermediate nuclides;
t represents time;
Σia macroscopic cross-section for reaction to produce an ith intermediate nuclide within a unit volume of the self-powered neutron detector;
fiefficiency of generating an instantaneous current for the production of the ith intermediate nuclide in the self-powered neutron detector;
jigenerating efficiency for current when the ith intermediate nuclide in the self-powered neutron detector is de-excited or decayed;
λiis the decay constant of the ith intermediate nuclear species;
λjis the decay constant of the jth intermediate species;
Ni(t) is the number of species per unit volume of the ith intermediate species;
Nj(t) is the unit volume of the jth intermediate nuclideThe number of nuclides;
phi (t) is the neutron flux density at time t;
i (t) is the detection current output by the detector at the time t.
And step 3: the neutron flux density phi (t) is assumed as a unit pulse signal delta (t), and the nuclide number N in the unit volume of the ith intermediate nuclide of the self-powered neutron detector is specifically deduced according to an expression (3)i(t) expression (4) and detection current i (t) and time t expression (5), so that the detection current responding to the unit pulse signal input is the unit impulse response of the self-powered neutron detector, as shown in expression (6);
in the formula:
i represents the ith intermediate nuclide and takes the value of 1 to m;
t represents time;
∑ia macroscopic cross-section for reaction to produce an ith intermediate nuclide within a unit volume of the self-powered neutron detector; n is a radical ofi(t) is the number of species per unit volume of the ith intermediate species;
λiis the decay constant of the ith intermediate nuclear species;
phi (t) is the neutron flux density at time t;
i (t) is the detection current output by the detector at the time t;
h (t) is the unit impulse response of the self-powered neutron detector;
aiand biThe parameter factor is given by a specific self-powered neutron detector;
and 4, step 4: for neutron flux density φ (t), the probe current I (t) has the convolution expression (7):
I(t)＝φ(t)*h(t) (7)
and 5: performing Laplace transform on an expression (6) of the impulse response function of the detector to obtain a transfer function G(s) from neutron flux to detection current, wherein the expression is (8):
obtaining a delay compensation transfer function G by an inverse function method-1(s) expressed as (9):
according to sigmai、λi、jiThe values of (2) can be obtained for each parameter in equation (9);
wherein:
∑ia macroscopic cross-section for reaction to produce an ith intermediate nuclide within a unit volume of the self-powered neutron detector;
λiis the decay constant of the ith intermediate nuclear species;
jiefficiency of current generation for the i-th intermediate species within a unit volume of the detector to de-excite or decay;
g(s) is a transfer function of neutron flux to probe current;
s is an independent variable in a complex frequency domain;
p is the form of the transient part of the detector signal after Laplace transformation, and is a transient component, so a proportionality coefficient is represented in a transfer function;
bithe proportional coefficient of the ith first-order inertia element in the delay response transfer function;
G-1(s) a delay compensation transfer function;
k0is the proportionality coefficient of the proportionality link;
kithe proportional coefficient of the ith first-order inertia link in the delay compensation transfer function is calculated;
Tithe time constant of the ith first-order inertia element in the delay compensation transfer function is obtained;
step 6: according to the formula (9): the delay compensation transfer function is composed of a proportion link and two first-order inertia links, and a mathematical expression of a digital delay compensation program can be designed according to time domain iterative equations corresponding to the proportion link and the first-order inertia links;
the time domain iterative equation corresponding to the proportion link is as follows:
cb(t)＝k0rb(t) (10)
wherein:
k0is the proportionality coefficient of the proportionality link;
rb(t) is the input quantity of the system at the time t;
cb(t) is the output quantity of the proportional link at the time t;
the time domain difference iterative equation of the first-order inertia link is as follows:
wherein:
r (t) is the input quantity of the digital delay compensation program at the time t;
Δ t is the time interval of the input data, i.e. the sampling step length;
Tiis the time constant of the ith first-order inertial element;
ci(t) is the output quantity of the ith first-order inertia link at the time t;
ci(t-delta t) is the output quantity of the ith first-order inertia link at the time of t-delta t; obtaining a mathematical table of the output quantity of the digital delay compensation program at the time t according to the delay compensation transfer function in the formula (9)The expression is as follows:
wherein:
k0is the proportionality coefficient of the proportionality link;
kithe proportionality coefficient of the ith first-order inertia link;
r (t) is the input quantity of the digital delay compensation program at the time t;
ci(t) is the output quantity of the ith first-order inertia link at the time t;
o (t) is the output quantity of the digital delay compensation program at the time t;
and 7: the digital delay compensation program expressed by the mathematical expression of the formula (12) is realized by a computer language, and the basic operation logic of the computer program is as follows:
reading the detection current data at the time t as the input quantity r (t) of a program at the time t; respectively putting the input quantity r (t) at the time t into a proportional link subfunction and subfunctions of a plurality of first-order inertia links, and obtaining the output quantity c of the subfunctions after operationb(t)、ci(t); adding the output quantity of the sub-function into the accumulated main function to obtain the output quantity O (t) of the whole digital delay compensation program at the time t;
the detection current signal output by the detector is input into the digital delay compensation program, and the obtained output quantity O (t) reflects the true value of the neutron flux density detected by the detector at the time t, namely the delay effect of the delayed self-powered neutron detector is eliminated.
Compared with the prior art, the invention has the following advantages:
and 6, solving a time domain equation of the digital delay compensation program according to a time domain iterative equation corresponding to a typical link on the basis of the delay compensation transfer function, wherein the method is visual and simple.
The digital delay compensation program obtained in the step 6 has a better compensation effect on the self-powered detector.
The digital delay compensation program obtained in the step 6 has good stability, and avoids the harsh requirements on the parameter precision of components and the working environment.
Drawings
FIG. 1 is a schematic flow chart of the present invention.
Fig. 2 is a diagram of a typical neutron-dependent reaction process detected by the detector (taking rhodium as an example of a self-powered detector).
FIG. 3 is a logic block diagram of a computer program designed according to the digital delay compensation program time domain equation.
Fig. 4 is a diagram illustrating the effect of the digital delay compensation procedure on the delay compensation of the step neutron flux signal.
Fig. 5 is a diagram illustrating the effect of the digital delay compensation procedure on the delay compensation of the neutron flux signal in the ramp.
Fig. 6 is a graph of the effect of the digital delay compensation procedure on the delay compensation of a continuous mixed neutron flux signal.
Detailed Description
The invention is described in further detail below with reference to the following figures and specific embodiments.
Here, Rh-103 is taken as an example, and is a self-powered neutron detector which generates two intermediate nuclides after capturing neutrons, and the specific process is shown in fig. 1.
Step 1: drawing a reaction mechanism schematic diagram according to the reaction physical process of the self-powered detector material in a neutron field; for a self-powered neutron detector that generates two intermediate species after capturing a neutron, a rhodium self-powered neutron detector (a typical self-powered neutron detector that generates two intermediate species after capturing a neutron) is shown in schematic form in fig. 2.
Step 2: writing a differential equation system (1) of the number N (t) of the intermediate nuclides in a unit volume of the energy-saving neutron detector and the neutron flux density phi (t) according to the generation and decay relations of all nuclides related to the reaction mechanism schematic diagram drawn in the step 1, and writing an expression (2) of detection current I (t) and the number of the intermediate nuclides and the neutron flux density phi (t); the intermediate nuclide in the unit volume of the self-powered neutron detector refers to an unstable nuclide generated after a neutron is captured by a nuclide emitted by the self-powered neutron detector, and an unstable nuclide generated after the generated unstable nuclide is continuously decayed or is de-excited;
wherein
i represents the ith intermediate nuclide and takes the value of 1 to m;
j represents the jth intermediate nuclide and takes the value from 1 to i-1, or i +1 to m; if i-1<1, there is no item 3 to the right of the system of differential equations (1); if i +1> m, then there is no item 4 to the right of system of differential equations (1);
m represents a total of m intermediate nuclides;
t represents time;
Σia macroscopic cross-section for reaction to produce an ith intermediate nuclide within a unit volume of the self-powered neutron detector;
fiefficiency of generating an instantaneous current for the production of the ith intermediate nuclide in the self-powered neutron detector;
jigenerating efficiency for current when the ith intermediate nuclide in the self-powered neutron detector is de-excited or decayed;
λiis the decay constant of the ith intermediate nuclear species;
λjis the decay constant of the jth intermediate species;
Ni(t) is the number of species per unit volume of the ith intermediate species;
Nj(t) is the number of species in the unit volume of the jth intermediate species;
phi (t) is the neutron flux density at time t;
i (t) is the detected current value output by the detector at the time t.
And step 3: the neutron flux density phi (t) is assumed as a unit pulse signal delta (t), and the nuclide number N in the unit volume of the ith intermediate nuclide of the self-powered neutron detector is specifically deduced according to an expression (3)i(t) expression (4) and detection current i (t) and time t expression (5), so that the detection current responding to the unit pulse signal input is the unit impulse response of the self-powered neutron detector, as shown in expression (6);
in the formula:
i represents the ith intermediate nuclide and takes the value of 1 to m;
t represents time;
∑ia macroscopic cross-section for reaction to produce an ith intermediate nuclide within a unit volume of the self-powered neutron detector; n is a radical ofi(t) is the number of species per unit volume of the ith intermediate species;
λiis the decay constant of the ith intermediate nuclear species;
h (t) is the unit impulse response of the self-powered neutron detector;
phi (t) is the neutron flux density at time t;
i (t) is a detection current value output by the detector at the time t;
aiand biThe parameter factor is given by a specific self-powered neutron detector;
and 4, step 4: for a typical neutron flux density φ (t), the probe current I (t) has the relationship (7), and the convolution expression is:
I(t)＝φ(t)*h(t) (7)
for a rhodium self-powered neutron detector, the detector unit impulse response can be written in the form of equation (7-1):
in the formula:
phi (t) is the neutron flux density at time t;
i (t) is a detection current value output by the detector at the time t;
h (t) is the unit impulse response of the self-powered neutron detector;
∑1a macroscopic cross-section for generating a first intermediate species for an (n, γ) reaction per unit volume of the self-powered neutron detector;
∑2a macroscopic cross-section for generating a second intermediate species for producing an (n, γ) reaction per unit volume of the self-powered neutron detector;
λ1is the decay constant of the first intermediate species;
λ2is the decay constant of the second intermediate species;
j1efficiency of generating current for de-excitation or decay of a first intermediate species per unit volume of the self-powered neutron detector;
j2efficiency of generating current for de-excitation or decay of a second intermediate species per unit volume of the self-powered neutron detector;
p is an instantaneous component in the probe current.
And 5: performing Laplace transform on an expression (6) of the impulse response function of the detector to obtain a transfer function G(s) from neutron flux to detection current, wherein the expression is (8-1):
and obtaining a delay compensation transfer function G'(s) by an inverse function method, wherein the expression is (9-1):
according to sigma1、Σ2、λ1、λ2、j1、j2The values of (2) can be obtained for the values of the parameters in the formula (9-1);
the specific process is as follows:
first, a generalized form of the delay compensation transfer function is written, as shown in equation (9-2):
the expression of the delay compensation transfer function directly obtained by the inverse function is shown as (9-3):
in order to solve the analysis form of each parameter in the expression (9-1), the expressions (9-1) and (9-2) are processed by the conversion method and the comparison coefficient method. First, in order to simplify the writing form of expression (9-3), the complicated variable in expression (9-3) is replaced with parameters m and n, and m is made to be p (λ)1+λ2)+j1λ1Σ1+j2λ2Σ2n＝pλ1λ2+λ1λ2(j1Σ1+j2Σ2+j2Σ1) Then the delay compensating transfer function G-1(s) can be abbreviated as a form of formula (9-4):
by comparing the coefficients, the solution k can be obtained0、k1、k2、T1、T2The system of equations of (1):
solving the equation set in formula (9-5) to obtain k0、k1、k2、T1、T2Analytic form of several parameters:
will be ∑1、Σ2、λ1、λ2、j1、j2Substituting the value of p into k0、k1、k2、T1、T2In an analytical expression of several parameters, k can be found0、k1、k2、T1、T2The specific numerical value of (1).
Wherein:
∑1a macroscopic cross-section for generating a first intermediate species for an (n, γ) reaction per unit volume of the detector;
∑2macroscopic cross-section for generating a second intermediate species for an (n, γ) reaction per unit volume of the detector; is the decay constant of the first intermediate species;
λ2is the decay constant of the second intermediate species;
j1efficiency of current generation for de-excitation (or decay) of the first species in a unit volume of the detector;
j2efficiency of current generation for de-excitation (or decay) of the second species per unit volume of the detector;
g(s) is a transfer function of neutron flux to probe current;
s is an independent variable in a complex frequency domain;
p is the form of the transient part of the detector signal after Laplace transformation, and is a transient component, so a proportionality coefficient is represented in a transfer function;
G-1(s) is the transfer function of the probe current to the compensated neutron flux;
k0is a proportional ringThe proportionality coefficient of the node;
k1is the proportionality coefficient of the first order inertia element;
k2is the proportionality coefficient of the second first-order inertia element;
T1is the time constant of the first order inertial element;
T2is the time constant of the second first-order inertial element;
m is an intermediate variable number one, and the expression is as follows: m ═ p (λ)1+λ2)+j1λ1Σ1+j2λ2Σ2；
n is an intermediate variable with the expression: n ═ p λ1λ2+λ1λ2(j1Σ1+j2Σ2+j2Σ1)。
Step 6:
as can be seen from the formula (9-1): the delay compensation transfer function is composed of a proportional element and two first-order inertia elements. A mathematical expression of the digital delay compensation program can be designed according to a time domain iterative equation corresponding to the proportion link and the first-order inertia link.
The time domain iterative equation corresponding to the proportion link is as follows:
cb(t)＝k0rb(t) (10)
wherein:
k0is the proportionality coefficient of the proportionality link;
rb(t) is the input quantity of the system at the time t;
cband (t) is the output quantity of the proportional element at the time t.
The time-domain difference iterative equation for the first-order inertial element can be written as:
wherein:
r (t) is the input quantity of the system at the time t;
Δ t is the time interval (sampling step) of the input data;
Tiis the time constant of the ith first-order inertial element;
ci(t) is the output quantity of the ith first-order inertia link at the time t;
ci(t-delta t) is the output quantity of the ith first-order inertia link at the time of t-delta t;
from the delay compensation transfer function in equation (9), the mathematical expression of the output quantity of the digital delay compensation program at time t can be obtained as follows:
O(t)＝k0r(t)+k1c1(t)+k2c2(t) (12)
wherein:
k0is the proportionality coefficient of the proportionality link;
k1the proportionality coefficient of the 1 st-order inertia link;
k2the proportionality coefficient of the 2 nd first-order inertia link;
r (t) is the input quantity of the system at the time t;
c1(t) is the output quantity of the 1 st first-order inertia link at the time t;
c2(t) is the output quantity of the 2 nd first-order inertia link at the time t;
o (t) is the output of the digital delay compensation procedure at time t.
And 7: the digital delay compensation program expressed by the mathematical expression of the formula (12) is realized by a computer language, and the basic operation logic of the computer program is as follows:
as shown in fig. 3, reading the detection current data at the time t as the input amount r (t) of the program at the time t; respectively putting the input quantity r (t) at the time t into a proportional link subfunction and subfunctions of a plurality of first-order inertia links, and obtaining the output quantity c of the subfunctions after operationb(t)、ci(t); adding the output quantity of the sub-function into the accumulated main function to obtain the output quantity O (t) of the whole digital delay compensation program at the time t;
the detection current signal output by the detector is input into the digital delay compensation program, and the obtained output quantity O (t) reflects the true value of the neutron flux density detected by the detector at the time t, namely the delay effect of the delayed self-powered neutron detector is eliminated.
Application example:
in order to remarkably eliminate the time delay effect, the compensation effect of the detector on the detection current when the neutron flux is a step signal such as startup and shutdown of a reactor is examined, and when t is 20 seconds, the neutron flux is changed from phi to 0 (cm)2·s)-1Suddenly changes to phi 1 (cm)2·s)-1And is maintained after 20 seconds. In the simulation process, each relevant parameter is evaluated according to the specific implementation mode and the situation described in the evaluation description part, and the current sampling time step Ts0.1 second. Wherein the values of the parameters are as follows:
Σ1＝0.8165cm-1
Σ2＝10.0207cm-1
λ1＝0.00268s-1
λ2＝0.01650s-1
j1＝4.583×10-22A·s·cm3
j2＝5.956×10-21A·s·cm3
p＝f1Σ1+f2Σ2＝3.6×10-21A·s·cm2
the result of eliminating the delay effect is shown in fig. 4. As shown by the thin dashed line in fig. 4, the current signal with a delay component from the powered detector takes more than 180 seconds to reach 90% of the steady level, i.e. if the neutron flux density is displayed solely from the current data there will be a significant delay, and if this method is used, the monitoring of the reactor neutron flux density is also of no significance; in contrast, the neutron flux density obtained by adopting the elimination delay algorithm and the delay elimination circuit is well matched with the actual neutron flux density. As can be seen from the thick solid line in fig. 4 and fig. 6, the delay is perfectly corrected, so that the real-time monitoring of the neutron flux density in the reactor can be realized, and the safety control of the reactor is more facilitated.
Examining the compensation effect of the detector on the detection current when the neutron flux is a ramp signal, such as the slow increase and decrease of the reactor power, and the neutron flux is changed from phi to 0 (cm) when t is 20 seconds2·s)-1Becomes 1 (cm) at 300 seconds in the form of a linear function2·s)-1The process of (1). In the simulation process, each relevant parameter is evaluated according to the specific implementation mode and the situation described in the evaluation description part, and the current sampling time step Ts0.1 second. Wherein the values of the parameters are as follows:
Σ1＝0.8165cm-1
Σ2＝10.0207cm-1
λ1＝0.00268s-1
λ2＝0.01650s-1
j1＝4.583×10-22A·s·cm3
j2＝5.956×10-21A·s·cm3
p＝f1Σ1+f2Σ2＝3.6×10-21A·s·cm2
the result of eliminating the delay effect is shown in fig. 5. As shown by the thin dashed line in fig. 5, the current signal with the delay component from the powered detector is in the form of a curve with a gradually increasing slope, i.e. there will be a large delay if the neutron flux density is shown solely from the current data; in contrast, the neutron flux density obtained by adopting the elimination delay algorithm and the delay elimination circuit is well matched with the actual neutron flux density.
The compensation effect of the detector on the detection current under an actual working condition is examined, and the neutron flux is changed from phi to 0 (cm) when t is 20 seconds2·s)-1The change phi of the projection is 1 (cm)2·s)-1(ii) a Neutron flux is defined by phi 1 (cm) at t-320 seconds2·s)-1Becomes phi 2 (cm) in the form of a linear function2·s)-1This process takes 300 seconds; at t 620 seconds, the neutron flux is defined by 2 (cm)2·s)-1The change phi of the projection is 1 (cm)2·s)-1(ii) a Neutron flux is defined by phi 1 (cm)2·s)-1The change phi of the projection is 0 (cm)2·s)-1. In the simulation process, each relevant parameter is evaluated according to the specific implementation mode and the situation described in the evaluation description part, and the current sampling time step Ts0.1 second. Wherein the values of the parameters are as follows:
Σ1＝0.8165cm-1
Σ2＝10.0207cm-1
λ1＝0.00268s-1
λ2＝0.01650s-1
j1＝4.583×10-22A·s·cm3
j2＝5.956×10-21A·s·cm3
p＝f1Σ1+f2Σ2＝3.6×10-21A·s·cm2
the result of eliminating the delay effect is shown in fig. 6: the neutron flux density obtained by adopting the elimination delay algorithm and the delay elimination circuit is well matched with the actual neutron flux density.
While the present invention has been described with reference to exemplary embodiments, it is understood that the terminology used is intended to be in the nature of words of description and illustration, rather than of limitation. As the present invention may be embodied in several forms without departing from the spirit or essential characteristics thereof, it should also be understood that the above-described embodiments are not limited by any of the details of the foregoing description, but rather should be construed broadly within its spirit and scope as defined in the appended claims, and therefore all changes and modifications that fall within the meets and bounds of the claims, or equivalences of such meets and bounds are therefore intended to be embraced by the appended claims.
Claims (2)
1. A method for eliminating the delay effect of a self-powered neutron detector based on a digital circuit is characterized in that: the method comprises the following steps:
step 1: drawing a reaction mechanism schematic diagram according to the reaction physical process of the self-powered detector material in a neutron field;
step 2: writing a differential equation system (1) of the number N (t) of the intermediate nuclides in a unit volume of the energy-saving neutron detector and the neutron flux density phi (t) according to the generation and decay relations of all nuclides related to the reaction mechanism schematic diagram drawn in the step 1, and writing an expression (2) of detection current I (t) and the number of the intermediate nuclides and the neutron flux density phi (t); the intermediate nuclide in the unit volume of the self-powered neutron detector refers to an unstable nuclide generated after a neutron is captured by a nuclide emitted by the self-powered neutron detector, and an unstable nuclide generated after the generated unstable nuclide is continuously decayed or is de-excited;
wherein
i represents the ith intermediate nuclide and takes the value of 1 to m;
j represents the jth intermediate nuclide and takes the value from 1 to i-1 or i +1 to m; if i-1<1, there is no item 3 to the right of the system of differential equations (1); if i +1> m, then there is no item 4 to the right of system of differential equations (1);
m represents a total of m intermediate nuclides;
t represents time;
Σia macroscopic cross-section for reaction to produce an ith intermediate nuclide within a unit volume of the self-powered neutron detector;
fiefficiency of generating an instantaneous current for the production of the ith intermediate nuclide in the self-powered neutron detector;
jigenerating efficiency for current when the ith intermediate nuclide in the self-powered neutron detector is de-excited or decayed;
λiis the decay constant of the ith intermediate nuclear species;
λjis the decay constant of the jth intermediate species;
Ni(t) is the number of species per unit volume of the ith intermediate species;
Nj(t) is the number of species in the unit volume of the jth intermediate species;
phi (t) is the neutron flux density at time t;
i (t) is the detection current output by the detector at the time t;
and step 3: the neutron flux density phi (t) is assumed as a unit pulse signal delta (t), and the nuclide number N in the unit volume of the ith intermediate nuclide of the self-powered neutron detector is specifically deduced according to an expression (3)i(t) expression (4) and detection current i (t) and time t expression (5), so that the detection current responding to the unit pulse signal input is the unit impulse response of the self-powered neutron detector, as shown in expression (6);
in the formula:
i represents the ith intermediate nuclide and takes the value of 1 to m;
t represents time;
Σia macroscopic cross-section for reaction to produce an ith intermediate nuclide within a unit volume of the self-powered neutron detector; n is a radical ofi(t) is the number of species per unit volume of the ith intermediate species;
λiis the decay constant of the ith intermediate nuclear species;
phi (t) is the neutron flux density at time t;
i (t) is the detection current output by the detector at the time t;
h (t) is the unit impulse response of the self-powered neutron detector;
aiand biThe parameter factor is given by a specific self-powered neutron detector;
and 4, step 4: for neutron flux density φ (t), the probe current I (t) has the convolution expression (7):
I(t)＝φ(t)*h(t) (7)
and 5: performing Laplace transform on an expression (6) of the impulse response function of the detector to obtain a transfer function G(s) from neutron flux to detection current, wherein the expression is (8):
obtaining a delay compensation transfer function G by an inverse function method-1(s) expressed as (9):
according to sigmai、λi、jiThe values of (2) can be obtained for each parameter in equation (9);
wherein:
∑ia macroscopic cross-section for reaction to produce an ith intermediate nuclide within a unit volume of the self-powered neutron detector;
λiis the decay constant of the ith intermediate nuclear species;
jiefficiency of current generation for the i-th intermediate species within a unit volume of the detector to de-excite or decay;
g(s) is a transfer function of neutron flux to probe current;
s is an independent variable in a complex frequency domain;
p is the form of the transient part of the detector signal after Laplace transformation, and is a transient component, so a proportionality coefficient is represented in a transfer function;
bithe proportional coefficient of the ith first-order inertia element in the delay response transfer function;
G-1(s) a delay compensation transfer function;
k0is the proportionality coefficient of the proportionality link;
kithe proportional coefficient of the ith first-order inertia link in the delay compensation transfer function is calculated;
Tithe time constant of the ith first-order inertia element in the delay compensation transfer function is obtained;
step 6: according to the formula (9): the delay compensation transfer function is composed of a proportion link and two first-order inertia links, and a mathematical expression of a digital delay compensation program can be designed according to time domain iterative equations corresponding to the proportion link and the first-order inertia links;
the time domain iterative equation corresponding to the proportion link is as follows:
cb(t)＝k0rb(t) (10)
wherein:
k0is the proportionality coefficient of the proportionality link;
rb(t) is the input quantity of the system at the time t;
cb(t) is the output quantity of the proportional link at the time t;
the time domain difference iterative equation of the first-order inertia link is as follows:
wherein:
r (t) is the input quantity of the digital delay compensation program at the time t;
Δ t is the time interval of the input data, i.e. the sampling step length;
Tiis the time constant of the ith first-order inertial element;
ci(t) is the output quantity of the ith first-order inertia link at the time t;
ci(t-delta t) is the output quantity of the ith first-order inertia link at the time of t-delta t;
according to the delay compensation transfer function in the equation (9), the mathematical expression of the output quantity of the digital delay compensation program at the time t is obtained as follows:
wherein:
k0is the proportionality coefficient of the proportionality link;
kithe proportionality coefficient of the ith first-order inertia link;
r (t) is the input quantity of the digital delay compensation program at the time t;
ci(t) is the output quantity of the ith first-order inertia link at the time t;
o (t) is the output quantity of the digital delay compensation program at the time t;
and 7: the digital delay compensation program expressed by the mathematical expression of the formula (12) is realized by a computer language, and the basic operation logic of the computer program is as follows:
reading the detection current data at the time t as the input quantity r (t) of a program at the time t; respectively putting the input quantity r (t) at the time t into a proportional link subfunction and subfunctions of a plurality of first-order inertia links, and obtaining the output quantity c of the subfunctions after operationb(t)、ci(t); adding the output quantity of the sub-function into the accumulated main function to obtain the output quantity O (t) of the whole digital delay compensation program at the time t;
the detection current signal output by the detector is input into the digital delay compensation program, and the obtained output quantity O (t) reflects the true value of the neutron flux density detected by the detector at the time t, namely the delay effect of the delayed self-powered neutron detector is eliminated.
2. The method of claim 1, wherein: the digital delay compensation program in the step 6 can compensate the delay effect of the self-powered neutron detector; the digital delay compensation program and the establishment method thereof are suitable for any self-powered neutron detector with delay effect and any form of neutron flux function, and the difference is only the change of parameters.
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