CN109243637B - Method and system for reconstructing reactor space-time distribution model - Google Patents
Method and system for reconstructing reactor space-time distribution model Download PDFInfo
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Abstract
S1, sampling a given detector sample set for many times according to the weight of each detector sample to obtain a sampling detector sample set; s2, using a reconstruction function for the sampling detector sample set to obtain a space-time distribution function of the sampling detector sample set; s3, calculating and obtaining a calculated value of each detector sample in a given detector sample set under the distribution by utilizing a space-time distribution function; s4, calculating the reliability of the reconstruction function according to the calculated value of each detector sample; s5, when the reliability is smaller than a preset reference value, updating the weight of each detector sample in the given detector sample set until the reliability of the reconstruction function is larger than the reference value; and S6, obtaining a final reconstruction function according to the reconstruction function of the past iteration. The invention can obviously improve the accuracy of the reconstruction function.
Description
Technical Field
The invention relates to the field of monitoring and measuring of nuclear reactors, in particular to a method and a system for reconstructing a reactor space-time distribution model.
Background
Currently, core monitoring or core operation diagnosis (or accident diagnosis) depends on various measuring devices, or probes, and typical probes include: the measurement of various temperatures, pressures, liquid levels or neutron fluxes or neutron spectra of the first and second loop systems of the nuclear power plant reactor also includes other physical quantity measuring instruments such as related measuring instruments required for monitoring the radiation dose of the power plant.
First, each type of detector has its own limitations. Such as measurement accuracy issues of the detector, and spatial distribution of the detector, etc. I.e. the detector cannot be accurate to the hundred percent and it is not possible to arrange the detector at all positions of the known area of influence.
Secondly, the physical quantities characterized by the detectors are not the physical quantities of real interest to the nuclear power plant. For example, detectors typically obtain measured current or voltage signals, etc., and power plants may be concerned with the intrinsic source of their signals, such as neutron flux levels, etc. A conversion factor between physical quantities needs to be defined. Obviously, the conversion factor can only be calculated by theoretical calculation or a large number of empirical data fitting formulas.
Again, the physical quantities that need to be detected themselves have large differences in specific properties and are often not known in advance. For example, some physical quantities themselves vary relatively slowly in space or time, and are characterized by smoothness or continuity in the partial derivatives of their characteristic functions, etc. Some physical quantities themselves exhibit jumps or sharp changes in space or time. The unknown property greatly increases the monitoring requirement, and typically most reconstruction functions and the like can effectively reconstruct the slowly changing space-time distribution, but more processing is required for the severely changing space-time distribution (typically, space-time transformation and the like are required to make the space-time distribution smoother).
Finally, after the characteristics of the detector limitation, the inherent property of the physical quantity, the physical quantity conversion relation and the like are comprehensively considered, a global reconstruction function needs to be defined. The algorithm converts the detector signal into a spatio-temporal distribution of physical quantities for core monitoring or diagnostics. For example, accident diagnosis, after obtaining the space-time measured value of some local characteristic physical quantities, the space-time distribution or probability distribution of the accident characteristics of the potential source is calculated according to the algorithm. For another example, in the core operation monitoring, after the detector measurement of the core local measurement point is obtained, the three-dimensional space-time distribution of the attention feature quantity is calculated and obtained through the reconstruction function.
In order to improve the accuracy of the time-space distribution of the physical quantities related to the core operation monitoring or accident monitoring, two aspects are usually taken from the following points:
(1) from the detector perspective: the accuracy of the detector is improved, and a measured value with higher accuracy is obtained. The detector is more reasonable to arrange.
(2) From the perspective of the reconstruction function, an optimization algorithm with higher efficiency or higher precision is adopted, and the like, so that a more accurate algorithm or an algorithm which is more practical after being weighed is obtained.
In engineering applications, various types of reconstruction functions have been developed based on various principles and assumptions, and these algorithms have respective advantages and disadvantages: some algorithms can effectively reduce the uncertainty of the detector and simulate the overall change trend of a full-time space region, but ignore the local high-order fine change; some algorithms can simulate the local trend of the height distortion change, but are particularly sensitive to the arrangement of the detector and the failure of the detector; some algorithms can realize the simulation of high-precision time-space regions, but a large amount of computing resources need to be consumed or the computing convergence is not good enough; some algorithms are suitable for scenes in which the trend of the reactor is not obvious; some algorithms can be applied to the change of the abnormal operation condition of the reactor.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a method and a system for reconstructing a reactor space-time distribution model, wherein the method and the system gradually increase the weight of a detector with larger error and reduce the weight of a detector with smaller error, thereby improving the precision of space-time distribution of a reconstruction result.
In order to solve the technical problem, the invention provides a method for reconstructing a reactor space-time distribution model, which comprises the following steps:
step S1, sampling a given detector sample set for multiple times according to the weight of each detector sample to obtain a sampling detector sample set;
step S2, a reconstruction function is used for the sampling detector sample set to obtain a space-time distribution function of the sampling detector sample set;
step S3, calculating and obtaining a calculated value of each detector sample in the given detector sample set under the distribution by utilizing the space-time distribution function;
step S4, calculating the reliability of the reconstruction function according to the calculated value of each detector sample;
step S5, when the reliability is smaller than a preset reference value, updating the weight of each detector in the given sample set, and repeating the steps S1-S4 until the reliability of the reconstruction function is larger than the reference value;
and step S6, obtaining a final reconstruction function according to the reconstruction functions of the past iterations.
Wherein the method further comprises:
the given set of detector samples is acquired and the initial weight of each detector sample in the given set of detector samples is assumed to be equal.
Wherein, the step S3 specifically includes: obtaining a computed value for each detector sample in the given set of detector samples using:
wherein the content of the first and second substances,
for a computed value of the kth detector sample in a given set of detector samples, Z (s, t) is the spatio-temporal distribution function, f 1 Is the fission reaction cross-section distribution of the kth probe.
Wherein the step S4 specifically includes the steps of,
step S41, calculating the reliability of the calculated value of each detector sample in the given detector sample set according to the calculated value of each detector sample;
and step S42, calculating the reliability of the reconstruction function according to the reliability of the calculated value of each detector sample.
Wherein, the step S41 specifically includes:
wherein sig k Is the reliability of the calculated value of the kth detector sample in a given set of detector samples, U k Is the value of the kth detector sample in a given set of detector samples,
for the computed value of the kth detector sample in a given set of detector samples, δ is a given fitting error value.
Wherein the step S42 specifically includes calculating the reliability of the reconstruction function using the following formula
Wherein epsilon n Is the reliability of the nth reconstruction function, p k The weight of the kth one of the given detector samples.
Wherein the optimizing the reconstruction function specifically includes:
updating the weight of each detector sample in the given sample set according to the reliability of each detector sample in the given sample set.
Wherein the updating the weight of each detector sample according to the reliability of each detector sample specifically includes:
wherein alpha is n Is a function of the weight of the image,
is the updated weight of the kth detector sample in the given set of detector samples,
is the current weight of the kth detector sample in the given set of detector samples.
Wherein the final reconstruction function is calculated using the following equation:
wherein f is the final reconstruction function, N is the number of iterations of the past, f n Is the reconstruction function for the nth iteration.
The invention also provides a system for reconstructing a reactor space-time distribution model, which comprises:
the acquisition module is used for sampling a given detector sample set for multiple times according to the weight of each detector sample to obtain a sampling detector sample set;
the space-time distribution function calculation module is used for using a reconstruction function for the sampling detector sample set to obtain a space-time distribution function of the sampling detector sample set;
a first calculation module, configured to calculate, by using the spatio-temporal distribution function, a calculation value of each detector sample in the given set of detector samples under the distribution;
the second calculation module is used for calculating the reliability of the reconstruction function according to the calculated value of each detector sample;
the reconstruction function optimization module is used for optimizing the reconstruction function when the reliability is smaller than a preset reference value, and substituting the optimized reconstruction function into the first calculation module for calculation until the reliability of the reconstruction function is larger than the reference value;
and the reconstruction function calculation module is used for obtaining a final reconstruction function according to the reconstruction function of the past iteration.
The embodiment of the invention has the beneficial effects that: in the process of obtaining the reconstruction function, the embodiment of the invention gradually strengthens the weight of the detector with larger error and reduces the weight of the detector with smaller error, thereby reducing the overall error globally, secondly, starting from the essence of the detector, the algorithm increases the weight of the high-quality detector and reduces the weight of the detector with larger uncertainty, and from the space distribution of the detector, the algorithm increases the weight of a reasonable detector arrangement area, and finally, through a mode of sampling for many times, the measurement uncertainty of the detector can be effectively reduced through an average means, the influence of an overfitting phenomenon during the space fitting of the reconstruction function is reduced, thereby leading the space-time distribution of the final reconstruction result to have higher precision.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a schematic main flow chart of a method for reconstructing a reactor space-time distribution model based on multiple reconstruction functions according to an embodiment of the present invention.
Detailed Description
The following description of the embodiments refers to the accompanying drawings, which are included to illustrate specific embodiments in which the invention may be practiced.
Referring to fig. 1, a method for reconstructing a reactor spatio-temporal distribution model includes the following steps:
and step S1, sampling the given detector sample set for multiple times according to the weight of each detector sample in the given detector sample set to obtain a sampling detector sample set.
Wherein, before the step S1, the method further includes: the given set of detector samples is acquired and the initial weights of the detector samples in the given set of detector samples are assumed to be the same.
In particular, assume that there are 50 samples in a given set of detector samples, denoted as U respectively 1 、U 2 、……、U 50 Then the initial weights of these 50 samples are all equal to 1/50, assuming that the number of repeated sampling is 50, each sampling results in one sample, if during the course of 50 samplings, it is assumed that U is 1 -U 10 Are all sampled 2 times, and U 11 -U 40 Are all sampled in sequence, the sampling sample set is composed of 2U 1 -U 10 And 1U 11 -U 40 And (4) forming.
And step S2, a reconstruction function is used for the sampling detector sample to obtain a space-time distribution function of the sampling detector sample.
Given the measured values of each type of detector and the reconstruction function, the spatio-temporal distribution or probability distribution of the characteristic quantities can be obtained as: z i (s, t) ═ f (d (t), nature (d)), i ═ 1, …, K, where s denotes a spatial sequence, t denotes a temporal sequence, and f is a reconstruction function (or recovery algorithm). The argument of f includes two parts, namely the measurement d (t) of the detector itself, and the other is the intrinsic property of the detector (d), such as the spatial distribution or the physical nature and intrinsic error of the signal conversion factor of the detector. Using the detector signal through a reconstruction function f i The spatio-temporal distribution or probability distribution Z can be calculated i (s,t)。
Specifically, assume that the sample set is { U } l And L is 1,2, … L, where L is the number of samples in the sampled sample set, and the reconstruction function is used on the sampled sample set to obtain the reconstructed sample setIts corresponding space-time distribution function Z i (s, t). Obviously, the reconstruction function obtained is different depending on the sampling set.
And step S3, calculating and obtaining a calculation value of each detector sample in the given detector sample set under the space-time distribution function by utilizing the space-time distribution function.
Specifically, the calculated value for each detector sample in the given set of detector samples is calculated using the following equation:
wherein the content of the first and second substances,
calculated value for the kth detector sample in a given set of detector samples, Z k (S, t) is the space-time distribution function calculated in said step S2, f 1 Is the fission reaction cross-section distribution of the kth probe.
And step S4, calculating the reliability of the reconstruction function according to the calculated value of each detector sample.
Wherein, the step S4 specifically includes:
step S41, calculating the reliability of the calculated value of each detector sample in the given detector sample set according to the calculated value of each detector sample;
and step S42, calculating the reliability of the reconstruction function according to the reliability of the calculated value of each detector sample.
Wherein, the step S41 specifically includes:
wherein, sig k Is the reliability of the calculated value of the kth detector sample in a given set of detector samples, U k Is the kth detector sample in a given set of detector samplesThe value of the current value is that,
for the computed value of the kth detector sample in a given set of detector samples, δ is a given fitting error value.
Specifically, by comparing the relationship between the calculated value of each detector sample in a given detector sample set and the initial given value, the reconstruction accuracy of reconstructing the detector sample by using the reconstruction function can be determined, and when the difference between the calculated value and the initial given value is greater than a set threshold, it indicates that the accuracy of the detector sample reconstructed by using the reconstruction function does not meet the requirement, and the reconstruction function needs to be further optimized.
Wherein the step S42 specifically includes: the reliability of the reconstruction function is calculated using the following equation:
wherein epsilon n Is a first reconstruction function f n Reliability of p k The weight of the kth one of the given detector samples. The reliability of the reconstruction function reflects the difference between the reconstruction function and the expected reconstruction function.
Step S5, when the reliability is smaller than a preset reference value, updating the weight of each detector sample in the given detector sample set, and repeating the steps S1-S4 until the reliability of the reconstruction function is larger than the reference value.
Specifically, assume that the set reference value is 1/2 when ε n When the sum is more than or equal to 1/2, from the aspect of probability average, U and
only less than half of the probabilities satisfy the deviation to be within δ and the iteration can be terminated, let N be N-1. When epsilon n <1/2, the reconstruction function f may be used to improve performance by a probability greater than 50% n Further optimization is possible.
When epsilon n <1/2, f is calculated n Weight of function, for high ε n The recovery function of (2) requires a weight reduction for low epsilon n The function of (2), the weight needs to be increased. A typical weighting function is:
the present invention is not limited to a specific type of weighting function, and the function may be a linear function, an exponential function, a logarithmic function, or the like.
In order to further optimize the recovery function, in the resampling process, the sampling weight of the detector with poor performance should be increased and the sampling weight of the detector with good performance should be decreased in the recovery function, so that the detector with poor performance can be selected in the next iteration with higher probability. Intrinsic is meant to include two parts:
(1) the samples considered directly in the recovery function will have their spatial or temporal characteristics taken into account in an important way, so that the representation of the spatio-temporal region in the vicinity of the detector can be improved.
(2) The better performing samples, potentially from their own spatio-temporal regions or regions already characterized by other detectors or themselves, are also relatively flat in their transformation, which may be further down weighted in the following.
Wherein, the typical sampling weight for updating each detector is:
wherein alpha is n Is a function of the weight of the image,
is the updated weight of the kth detector sample in the given set of detector samples,
is the current weight of the kth detector sample in the given set of detector samples.
After the updating of the weights of the detector samples is completed, the steps S1-S5 are repeated according to the updated sampling weights until the reliability of the reconstruction function is greater than a preset reference value, and the iteration is stopped.
It should be noted that, when the detector weight is not considered, that is, a random equal probability sampling manner is adopted, and under the condition that the number of sample iterations is sufficient, the spatial effect of the detector can also be significantly captured, at this time:
and step S6, obtaining a final reconstruction function according to the reconstruction function of the past iteration.
Wherein, the step S6 specifically includes:
wherein f is the final reconstruction function, N is the number of iterations of the past, f n Is the reconstruction function for the nth iteration.
Correspondingly, when a feature is evaluated alone, it can be expressed as:
if the detector sampling weight is not changed:
in the process of obtaining the reconstruction function, the weight of the detector with larger error is gradually strengthened, and the weight of the detector with smaller error is reduced, so that the overall error is reduced globally.
Based on the first embodiment of the present invention, the second embodiment of the present invention provides a system for reconstructing a reactor space-time distribution model, the system comprising:
the acquisition module is used for sampling a given detector sample set for multiple times according to the weight of each detector sample to obtain a sampling detector sample set;
the space-time distribution function calculation module is used for using a reconstruction function for the sampling detector sample set to obtain a space-time distribution function of the sampling detector sample set;
a first calculation module, configured to calculate, by using the spatio-temporal distribution function, a calculation value of each detector sample in the given set of detector samples under the distribution;
the second calculation module is used for calculating the reliability of the reconstruction function according to the calculated value of each detector sample;
a reconstruction function optimization module, configured to update the weights of the detectors in the given sample set when the reliability is smaller than a preset reference value until the reliability of the reconstruction function is greater than the reference value;
and the reconstruction function calculation module is used for obtaining a final reconstruction function according to the reconstruction function of the past iteration.
For the working principle and the advantageous effects thereof, please refer to the description of the first embodiment of the present invention, which will not be described herein again.
While the invention has been described in connection with what is presently considered to be the most practical and preferred embodiment, it is to be understood that the invention is not to be limited to the disclosed embodiment, but on the contrary, is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims.
Claims (7)
1. A method for reconstructing a reactor space-time distribution model comprises the following steps:
step S1, sampling the given detector sample set for multiple times according to the weight of each detector sample in the given detector sample set to obtain a sampling detector sample set;
step S2, a reconstruction function is used for the sampling detector sample set to obtain a space-time distribution function of the sampling detector sample set;
step S3, calculating and obtaining a calculation value of each detector sample in the given detector sample set under the space-time distribution function by utilizing the space-time distribution function;
step S4, calculating the reliability of the reconstruction function according to the calculated value of each detector sample;
step S5, when the reliability is smaller than a preset reference value, updating the weight of each detector sample in the given detector sample set, and repeating the steps S1-S4 until the reliability of the reconstruction function is larger than the reference value;
step S6, obtaining a final reconstruction function according to the reconstruction function of the previous iteration;
the step S4 specifically includes:
step S41, calculating reliability of the calculated value of each detector sample in the given set of detector samples according to the calculated value of each detector sample:
wherein, sig k Is the reliability of the calculated value of the kth detector sample in a given set of detector samples, U k Is the value of the kth detector sample in a given set of detector samples,
δ being a given fitting error value for a computed value of the kth detector sample in the given set of detector samples;
step S42, calculating the reliability of the reconstruction function according to the reliability of the calculated value of each detector sample:
wherein epsilon n Is the reliability of the nth reconstruction function, p k The weight of the kth one of the given detector samples.
2. The method of claim 1, further comprising:
the given set of detector samples is acquired and the initial weight of each detector sample in the given set of detector samples is assumed to be equal.
3. The method according to claim 2, wherein the step S3 specifically includes: obtaining a calculated value for each detector sample in the given set of detector samples using:
wherein the content of the first and second substances,
for the calculated value of the kth detector sample in a given set of detector samples, Z (s, t) is the spatio-temporal distribution function, f 1 Is the fission reaction cross-section distribution of the kth probe.
4. The method according to claim 1, characterized in that said reconstruction function comprises in particular:
updating the current weight of each detector sample in the given set of detector samples according to the reliability of each detector sample in the given set of detector samples, and repeating steps S1-S4 according to the updated weight.
5. The method according to claim 4, wherein the updating the current weight of each detector sample according to the reliability of each detector sample specifically comprises:
wherein alpha is n Is a function of the weight of the image,
is the updated weight of the kth detector sample in the given set of detector samples,
is the current weight of the kth detector sample in the given set of detector samples.
6. The method of claim 5, wherein the final reconstruction function is calculated using the following equation:
wherein f is the final reconstruction function, N is the iteration times of the previous times, f n Is the reconstruction function for the nth iteration.
7. A system for reconstructing a reactor spatio-temporal distribution model, comprising:
the acquisition module is used for sampling a given detector sample set for multiple times according to the weight of each detector sample to obtain a sampling detector sample set;
the space-time distribution function calculation module is used for using a reconstruction function for the sampling detector sample set to obtain a space-time distribution function of the sampling detector sample set;
a first calculation module, configured to calculate, by using the spatio-temporal distribution function, a calculation value of each detector sample in the given set of detector samples under the distribution;
the second calculation module is used for calculating the reliability of the reconstruction function according to the calculated value of each detector sample; wherein the reliability of calculating the calculated value of each detector sample in the given set of detector samples from the calculated value of each detector sample is specifically:
wherein, sig k Is the reliability of the calculated value of the kth detector sample in a given set of detector samples, U k Is the value of the kth detector sample in a given set of detector samples,
δ being a given fitting error value for a computed value of the kth detector sample in the given set of detector samples;
calculating the reliability of the reconstruction function according to the reliability of the calculated value of each detector sample specifically comprises:
wherein epsilon n Is the reliability of the nth reconstruction function, p k A weight for a kth one of the given detector samples;
a reconstruction function optimization module, configured to update the weights of the detectors in the given sample set when the reliability is smaller than a preset reference value until the reliability of the reconstruction function is greater than the reference value;
and the reconstruction function calculation module is used for obtaining a final reconstruction function according to the reconstruction function of the past iteration.
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