CN114722646A - Method for optimizing three-dimensional measuring point arrangement of self-powered detector based on Kriging model - Google Patents

Method for optimizing three-dimensional measuring point arrangement of self-powered detector based on Kriging model Download PDF

Info

Publication number
CN114722646A
CN114722646A CN202210649975.1A CN202210649975A CN114722646A CN 114722646 A CN114722646 A CN 114722646A CN 202210649975 A CN202210649975 A CN 202210649975A CN 114722646 A CN114722646 A CN 114722646A
Authority
CN
China
Prior art keywords
measuring point
self
powered detector
point position
formula
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
CN202210649975.1A
Other languages
Chinese (zh)
Other versions
CN114722646B (en
Inventor
曹良志
周遥
贺清明
吴宏春
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Xian Jiaotong University
Original Assignee
Xian Jiaotong University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Xian Jiaotong University filed Critical Xian Jiaotong University
Priority to CN202210649975.1A priority Critical patent/CN114722646B/en
Publication of CN114722646A publication Critical patent/CN114722646A/en
Application granted granted Critical
Publication of CN114722646B publication Critical patent/CN114722646B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/18—Complex mathematical operations for evaluating statistical data, e.g. average values, frequency distributions, probability functions, regression analysis
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E30/00—Energy generation of nuclear origin
    • Y02E30/30—Nuclear fission reactors

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • General Physics & Mathematics (AREA)
  • Data Mining & Analysis (AREA)
  • General Engineering & Computer Science (AREA)
  • Pure & Applied Mathematics (AREA)
  • Mathematical Physics (AREA)
  • Computational Mathematics (AREA)
  • Mathematical Analysis (AREA)
  • Mathematical Optimization (AREA)
  • Algebra (AREA)
  • Probability & Statistics with Applications (AREA)
  • Operations Research (AREA)
  • Bioinformatics & Computational Biology (AREA)
  • Evolutionary Biology (AREA)
  • Databases & Information Systems (AREA)
  • Software Systems (AREA)
  • Bioinformatics & Cheminformatics (AREA)
  • Life Sciences & Earth Sciences (AREA)
  • Computer Hardware Design (AREA)
  • Evolutionary Computation (AREA)
  • Geometry (AREA)
  • Monitoring And Testing Of Nuclear Reactors (AREA)

Abstract

A method for optimizing the arrangement of three-dimensional measuring points of a self-powered detector based on a Kriging model is characterized in that the influence of a set of measuring point positions of the self-powered detector in a nuclear reactor monitoring system on the spatial estimation of non-measuring point positions is considered, the spatial covariance among specific positions of the monitoring system is calculated, and a weight function, a penalty factor and a Kriging variance of the non-measuring point positions are calculated according to the spatial covariance; based on the simulated annealing process, searching a minimum value taking the average Kriging variance of the position set of the non-measured points as a target function, and optimizing the arrangement scheme of the self-powered detector according to the minimum value; the measuring point arrangement optimization method can effectively reduce uncertainty of estimated parameters, has strong universality, is suitable for various nuclear reactor monitoring systems, can be used for evaluating the current measuring point arrangement scheme of the self-powered detector and recommending measuring point optimization design, and provides a new method for the core design of the self-powered detector.

Description

Method for optimizing three-dimensional measuring point arrangement of self-powered detector based on Kriging model
Technical Field
The invention relates to the field of nuclear reactor core design and reactor core neutron detectors, in particular to a method for optimizing the arrangement of three-dimensional measuring points of a self-powered detector based on a Kriging model.
Background
A set of operating parameters of a nuclear reactor core are important data concerning the safety and economy of a nuclear power plant. The power peak factor, deviation from the nucleate boiling factor and the like based on the reactor core power distribution directly influence the safety limit value of the nuclear power station; meanwhile, the power distribution condition determines the output capacity of the nuclear power station, and the most direct reference index is provided for the work of an operator. In a nuclear reactor, the core power distribution is reflected by the neutron flux density, and the magnitude of the neutron flux density, which is the most central parameter of a nuclear reactor system, also determines key indicators such as various nuclear reaction rates and effective multiplication factors.
In existing commercial pressurized water reactors, the neutron flux density distribution of the reactor core is measured based on neutron detectors inside or outside the reactor. For nuclear plant operators, the measured values of neutron detectors are the most direct and efficient reference data. However, practical reactor systems are large and complex, where the flux distributions are spatially and temporally variable, and the current requirements for fine and accurate nuclear safety also increase the difficulty of monitoring the nuclear reactor system. The number of neutron detectors used for core monitoring is limited by economic factors, mechanical constraints, and maintenance costs. Therefore, how to maximize the role of the in-core neutron detector under the condition of limited number, and most beneficial to the core reconstruction and on-line monitoring of neutron flux density is one of the important challenges of core design.
The traditional neutron detector arrangement optimization method is mainly based on the minimization of the reconstruction error of the state parameter. The method considers the influence of the arrangement schemes of different detectors on the reconstruction errors of reactor core parameters such as neutron flux density or power distribution level, selects an optimal design based on the minimization of the reconstruction errors, is limited by the acquisition of measured values, often needs high-precision simulation of a measuring process in the practice of a new reactor type, and has great difficulty and uncertainty; meanwhile, the method cannot ignore the influence of relative power coefficients of different measuring point positions and a detector checking coefficient, and the parameters are continuously changed when the reactor core runs.
The self-powered detector has the advantages of small volume, internal fixation, no need of an external power supply and the like, and is widely applied to the third-generation nuclear power technology. The AP1000 developed by American West House company and the European pressurized water reactor EPR jointly developed by two countries of Fade both adopt the design of a self-powered detector, the engineering experience of China in the field of self-powered detectors is relatively less, and the localization work of related technologies is also under development. Aiming at the characteristics of the self-powered detector, a more efficient measuring point arrangement optimization method suitable for the self-powered detector is needed to be invented.
Disclosure of Invention
In order to overcome the problems in the prior art, the invention aims to provide a method for optimizing the arrangement of three-dimensional measuring points of a self-powered detector based on a kriging model, aiming at the self-powered detector widely adopted by a third-generation nuclear power station, the influence of uncertainty of a measuring point position set on a non-measuring point position is considered under the condition of not carrying out prior direct measurement, and the optimization design of the arrangement of the three-dimensional measuring points of the self-powered detector is carried out by utilizing a spatial covariance function and the kriging model.
In order to achieve the above purpose, the invention adopts the following technical scheme:
a method for optimizing the arrangement of three-dimensional measuring points of a self-powered detector based on a Kriging model comprises the following steps:
step 1: establishing a radial and axial spatial position model of a nuclear reactor core, and establishing an initialized three-dimensional measuring point arrangement model of a self-powered detector;
step 2: calculating space covariance among measuring point positions by using a formula (1) according to the initialized three-dimensional measuring point arrangement model of the self-powered detector established in the step 1;
Figure 100002_DEST_PATH_IMAGE001
（1）
in the formula:
Figure 100002_DEST_PATH_IMAGE002
-a first stepiMeasuring point positions;
Figure 100002_DEST_PATH_IMAGE003
-a first stepjMeasuring point positions;
Figure 100002_DEST_PATH_IMAGE004
-measuring point position
Figure 397877DEST_PATH_IMAGE002
And
Figure 100002_DEST_PATH_IMAGE005
spatial covariance of the cells;
Figure 100002_DEST_PATH_IMAGE006
-the standard deviation of the random variable that the monitoring system needs to estimate;
Figure 100002_DEST_PATH_IMAGE007
-measuring points
Figure 338151DEST_PATH_IMAGE002
And measuring point
Figure 64798DEST_PATH_IMAGE005
The distance of (d);
Figure 100002_DEST_PATH_IMAGE008
-a characteristic length;
and step 3: according to the nuclear reactor core radial and axial spatial position models established in the step 1 and the initialized self-powered detector three-dimensional measuring point arrangement model, classifying the spatial positions in the nuclear reactor core radial and axial spatial position models into a measuring point position set and a non-measuring point position set, calculating the spatial covariance between the measuring point position and the non-measuring point position by using a formula (2), and solving a linear equation set formula (3) to obtain a weight function and a penalty factor corresponding to the non-measuring point;
Figure 100002_DEST_PATH_IMAGE009
（2）
in the formula:
Figure 100002_DEST_PATH_IMAGE010
-a first stepkPositions of non-measuring points;
Figure 100002_DEST_PATH_IMAGE011
-measuring point position
Figure 100002_DEST_PATH_IMAGE012
And the position of the NAND measuring point
Figure 100002_DEST_PATH_IMAGE013
Spatial covariance of the cells;
Figure 100002_DEST_PATH_IMAGE014
-measuring points
Figure 100002_DEST_PATH_IMAGE015
NAND measuring point
Figure 576201DEST_PATH_IMAGE013
The distance of (d);
Figure 100002_DEST_PATH_IMAGE016
（3）
in the formula:
Figure 100002_DEST_PATH_IMAGE017
-a certain non-measured point position;
Figure 100002_DEST_PATH_IMAGE018
-measuring point position
Figure 755509DEST_PATH_IMAGE012
And with
Figure 100002_DEST_PATH_IMAGE019
Spatial covariance of the cells;
Figure 100002_DEST_PATH_IMAGE020
-measuring point position
Figure 968316DEST_PATH_IMAGE012
And a certain non-measuring point position
Figure 100002_DEST_PATH_IMAGE021
Spatial covariance of each other;
Figure 100002_DEST_PATH_IMAGE022
-number of measurement points from powered detector;
Figure 100002_DEST_PATH_IMAGE023
-NAND measuring point
Figure 100002_DEST_PATH_IMAGE024
To a corresponding secondjA weight function;
Figure 100002_DEST_PATH_IMAGE025
-NAND measuring point
Figure 487153DEST_PATH_IMAGE024
Corresponding penalty factors;
and 4, step 4: calculating the kriging variance of the non-measured point position by using a formula (4) according to the space covariance between the measured point position and the non-measured point position obtained in the step (3), and a weight function and a penalty factor corresponding to the non-measured point position;
Figure 100002_DEST_PATH_IMAGE026
（4）
in the formula:
Figure 100002_DEST_PATH_IMAGE027
a certain non-measuring point
Figure 100002_DEST_PATH_IMAGE028
Kriging variance of (c);
Figure 100002_DEST_PATH_IMAGE029
-NAND measuring point
Figure 100002_DEST_PATH_IMAGE030
To a corresponding secondiA weight function;
Figure 100002_DEST_PATH_IMAGE031
-measuring point position
Figure 100002_DEST_PATH_IMAGE032
And a certain non-measuring point
Figure 570122DEST_PATH_IMAGE030
Spatial covariance of the cells;
and 5: calculating the average Kriging variance value of all the non-measuring point position sets by using a formula (5) according to the non-measuring point position sets classified in the step (3) and the Kriging variance values of the non-measuring point positions obtained in the step (4);
Figure 100002_DEST_PATH_IMAGE033
（5）
in the formula:
Figure 100002_DEST_PATH_IMAGE034
-the number of non-measured points in the nuclear reactor monitoring system;
Figure 100002_DEST_PATH_IMAGE035
-a set of non-measured point locations within the nuclear reactor monitoring system;
Figure 100002_DEST_PATH_IMAGE036
-set of non-measured point positions
Figure 705569DEST_PATH_IMAGE035
Average kriging variance of (c);
Figure 100002_DEST_PATH_IMAGE037
-a first stepkPositions of non-measuring points;
Figure 100002_DEST_PATH_IMAGE038
-a first step ofkA non-measuring point
Figure DEST_PATH_IMAGE039
Kriging variance of (c);
step 6: and (3) disturbing the initialized three-dimensional measuring point arrangement model of the self-powered detector established in the step 1, and searching the minimum value of the Kriging variance average value calculated in the step 5 and the corresponding three-dimensional measuring point arrangement model of the self-powered detector by adopting a simulated annealing algorithm, namely, serving as the optimized three-dimensional measuring point arrangement of the self-powered detector.
And (3) expressing the radial and axial spatial position model of the nuclear reactor core in the step 1 by using spatial position coordinates.
The initialized three-dimensional measuring point arrangement model of the self-powered detector in the step 1 is represented by space position coordinates.
Compared with the prior art, the invention has the following outstanding advantages:
1. in the method, the influence of uncertainty of a measuring point position of an energy detector on a non-measuring point position is considered based on the principle of minimum Kriging variance, and early measurement values or measurement simulation values of parameters such as reactor core power distribution or neutron flux distribution are not needed;
2. in the method, the calculation result is not influenced by the fluctuation characteristics of the reactor core state parameters, and the monitoring system has good stability; meanwhile, the modeling is convenient, the modeling is not related to the design of a specific reactor core, the universality is strong, and the method is suitable for various nuclear reactor monitoring systems;
3. in the method, as the three-dimensional measuring point arrangement optimization searching mode of the self-powered detector suitable for the Kriging model is adopted, the calculation efficiency is higher, and the calculation cost is lower than that of the traditional state parameter reconstruction error minimum method.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
FIG. 2 is a diagram of an AP1000 reactor core assembly layout.
FIG. 3 is a self-powered detector measuring point layout design obtained by the AP1000 heap type calculation according to the invention.
Fig. 4 shows a self-powered probe station arrangement for AP1000 reactor engineering applications.
Detailed Description
The invention is described in further detail below with reference to the following figures and detailed description:
the method mainly comprises the steps of modeling a reactor core space grid, solving the average Kriging variance of non-measured point positions and optimizing the measured point arrangement, and comprises the following specific steps:
step 1: establishing a radial and axial spatial position model of a nuclear reactor core (taking American West House company AP1000 introduced by three-door nuclear power as an example, the arrangement of core components is shown in figure 2), and establishing an initialized three-dimensional measuring point arrangement model of a self-powered detector;
step 2: calculating space covariance among measuring point positions by using a formula (1) according to the initialized three-dimensional measuring point arrangement model of the self-powered detector established in the step 1;
Figure DEST_PATH_IMAGE040
（1）
in the formula:
Figure DEST_PATH_IMAGE041
-a first stepiMeasuring point positions;
Figure DEST_PATH_IMAGE042
-a first stepjMeasuring point positions;
Figure DEST_PATH_IMAGE043
-measuring point position
Figure DEST_PATH_IMAGE044
And
Figure 941640DEST_PATH_IMAGE042
spatial covariance of the cells;
Figure DEST_PATH_IMAGE045
the standard deviation of the random variable that the monitoring system needs to estimate,S1.0 can be taken;
Figure DEST_PATH_IMAGE046
-measuring points
Figure 102932DEST_PATH_IMAGE044
And measuring point
Figure 140159DEST_PATH_IMAGE042
The distance of (d);
Figure DEST_PATH_IMAGE047
-the length of the feature is such that,Lcan be 1.5-8.0, the finer the grid model isLThe smaller the value is;
and 3, step 3: according to the nuclear reactor core radial and axial spatial position model established in the step 1 and the initialized self-powered detector three-dimensional measuring point arrangement model, classifying the spatial positions in the nuclear reactor core radial and axial spatial position model into a measuring point position set and a non-measuring point position set, calculating the spatial covariance between the measuring point position and the non-measuring point position by using a formula (2), and solving a linear equation set formula (3) to obtain a weight function and a penalty factor corresponding to the non-measuring point;
Figure DEST_PATH_IMAGE048
（2）
in the formula:
Figure DEST_PATH_IMAGE049
-a first stepkPositions of non-measuring points;
Figure DEST_PATH_IMAGE050
-measuring point position
Figure DEST_PATH_IMAGE051
And the position of the NAND measuring point
Figure DEST_PATH_IMAGE052
Spatial covariance of the cells;
Figure DEST_PATH_IMAGE053
-measuring points
Figure 435005DEST_PATH_IMAGE051
NAND measuring point
Figure DEST_PATH_IMAGE054
The distance of (a);
Figure DEST_PATH_IMAGE055
（3）
in the formula:
Figure DEST_PATH_IMAGE056
-a certain notMeasuring point positions;
Figure DEST_PATH_IMAGE057
-measuring point position
Figure DEST_PATH_IMAGE058
And with
Figure DEST_PATH_IMAGE059
Spatial covariance of the cells;
Figure DEST_PATH_IMAGE060
-measuring point position
Figure 192876DEST_PATH_IMAGE058
And a certain non-measuring point position
Figure DEST_PATH_IMAGE061
Spatial covariance of the cells;
Figure DEST_PATH_IMAGE062
the number of measuring points of the self-powered detector can be obtained by a measuring point arrangement model;
Figure DEST_PATH_IMAGE063
-NAND measuring point
Figure DEST_PATH_IMAGE064
To correspond to the firstjA weight function;
Figure DEST_PATH_IMAGE065
-NAND measuring point
Figure 951885DEST_PATH_IMAGE064
Corresponding penalty factors;
and 4, step 4: calculating the kriging variance of the non-measured point position by using a formula (4) according to the space covariance between the measured point position and the non-measured point position obtained in the step (3), and a weight function and a penalty factor corresponding to the non-measured point position;
Figure DEST_PATH_IMAGE066
（4）
in the formula:
Figure DEST_PATH_IMAGE067
a certain non-measuring point
Figure DEST_PATH_IMAGE068
Kriging variance of (c);
Figure DEST_PATH_IMAGE069
-NAND measuring point
Figure 298028DEST_PATH_IMAGE068
To a corresponding secondiA weight function;
Figure DEST_PATH_IMAGE070
-measuring point position
Figure DEST_PATH_IMAGE071
And a certain non-measuring point
Figure DEST_PATH_IMAGE072
Spatial covariance of each other;
and 5: calculating the average Kriging variance value of all the non-measuring point position sets by using a formula (5) according to the non-measuring point position sets classified in the step (3) and the Kriging variance values of the non-measuring point positions obtained in the step (4);
Figure DEST_PATH_IMAGE073
（5）
in the formula:
Figure DEST_PATH_IMAGE074
the number of non-measuring points in the nuclear reactor monitoring system can be obtained by a reactor core space grid model and a measuring point arrangement model;
Figure DEST_PATH_IMAGE075
-a set of non-measured point locations within the nuclear reactor monitoring system;
Figure DEST_PATH_IMAGE076
-set of non-measured point positions
Figure 814591DEST_PATH_IMAGE075
Average kriging variance of (c);
Figure DEST_PATH_IMAGE077
-a first stepkPositions of non-measuring points;
Figure DEST_PATH_IMAGE078
-a first stepkOne non-measuring point
Figure DEST_PATH_IMAGE079
Kriging variance of (c);
step 6: and (3) disturbing the initialized three-dimensional measuring point arrangement model of the self-powered detector established in the step (1), searching the minimum value of the kriging variance average value obtained by calculation in the step (5) and the corresponding three-dimensional measuring point arrangement model of the self-powered detector by adopting a simulated annealing algorithm, namely, using the minimum value as the optimized three-dimensional measuring point arrangement of the self-powered detector, disturbing different numbers of measuring point arrangement variables in a staged mode in the searching process, and increasing the local disturbance inspection function of stage searching results.
In the invention, the initial selection of the arrangement scheme of the self-powered detector in the step 1 is arbitrary, and the method has no specific selectivity on the initial scheme of the self-powered detector and is not limited by human factors and practical experience.
Steps 2-4The standard deviation of the random variables to be estimated by the monitoring system in the formula (1), the formula (2) and the formula (4)SThe uncertainty of the measured value of the self-powered detector can be regarded as a function of the accuracy of the measuring tool and the actual measuring process, the value does not influence the optimization result of the three-dimensional measuring point arrangement of the self-powered detector, and the subsequent calculation is facilitatedSThe value is 1.0.
The calculation of the weight function matrix and the penalty factor in the formula (3) can adopt various linear equation system solving methods, such as an LU decomposition method, a Jacobian iteration method, a QR decomposition method and the like, and the selection of the linear equation system solving method is not limited by the invention.
And 6, when the minimum value process of the average value of the Kriging variance is solved, selecting a near implicit enumeration method based on a simulated annealing process mainly to ensure the stability of the optimization process. The relevant influence parameters comprise initial temperature, heat balance times, temperature management functions and the disturbance number of measuring point arrangement variables in different search stages, and the specific selection of the parameters is not particularly limited by the invention.
To verify the effectiveness of the present invention, FIG. 3 shows a self-powered probe arrangement calculated using the present invention and suitable for the AP1000 stack type shown in FIG. 2. Compared with the self-powered detector measuring point arrangement scheme in the current AP1000 nuclear power generating unit engineering practice shown in FIG. 4, the self-powered detector measuring point arrangement optimization scheme based on the Kriging model has high overall fitting degree and is reasonable and reliable.
By utilizing the self-powered detector arrangement scheme with optimized design, the estimation uncertainty of the positions of non-measuring points can be obviously reduced, and the monitoring and control of various parameters of the reactor core can be better realized. The method can provide an effective method for designing a measuring point arrangement scheme of a self-powered detector in the third-generation nuclear power technology, has reliable stability and higher efficiency, and can be applied to actual engineering calculation.

Claims (3)

1. A method for optimizing the arrangement of three-dimensional measuring points of a self-powered detector based on a Kriging model is characterized by comprising the following steps of: the method comprises the following steps:
step 1: establishing a radial and axial spatial position model of a nuclear reactor core, and establishing an initialized three-dimensional measuring point arrangement model of a self-powered detector;
and 2, step: calculating space covariance among measuring point positions by using a formula (1) according to the initialized three-dimensional measuring point arrangement model of the self-powered detector established in the step (1);
Figure DEST_PATH_IMAGE001
（1）
in the formula:
Figure DEST_PATH_IMAGE002
-a first stepiMeasuring point positions;
Figure DEST_PATH_IMAGE003
-a first stepjMeasuring point positions;
Figure DEST_PATH_IMAGE004
-measuring point position
Figure 874890DEST_PATH_IMAGE002
And
Figure 57609DEST_PATH_IMAGE003
spatial covariance of the cells;
Figure DEST_PATH_IMAGE005
-the standard deviation of the random variable that the monitoring system needs to estimate;
Figure DEST_PATH_IMAGE006
-measuring points
Figure 777959DEST_PATH_IMAGE002
And measuring point
Figure 376431DEST_PATH_IMAGE003
The distance of (d);
Figure DEST_PATH_IMAGE007
-a characteristic length;
and step 3: according to the nuclear reactor core radial and axial spatial position models established in the step 1 and the initialized self-powered detector three-dimensional measuring point arrangement model, classifying the spatial positions in the nuclear reactor core radial and axial spatial position models into a measuring point position set and a non-measuring point position set, calculating the spatial covariance between the measuring point position and the non-measuring point position by using a formula (2), and solving a linear equation set formula (3) to obtain a weight function and a penalty factor corresponding to the non-measuring point position;
Figure DEST_PATH_IMAGE008
（2）
in the formula:
Figure DEST_PATH_IMAGE009
-a first stepkPositions of non-measuring points;
Figure DEST_PATH_IMAGE010
-measuring point position
Figure DEST_PATH_IMAGE011
And the position of the NAND measuring point
Figure DEST_PATH_IMAGE012
Spatial covariance of the cells;
Figure DEST_PATH_IMAGE013
-measuring points
Figure 66169DEST_PATH_IMAGE011
NAND measuring point
Figure 154211DEST_PATH_IMAGE012
The distance of (d);
Figure DEST_PATH_IMAGE014
（3）
in the formula:
Figure DEST_PATH_IMAGE015
-a certain non-measured point position;
Figure DEST_PATH_IMAGE016
-measuring point position
Figure DEST_PATH_IMAGE017
And
Figure DEST_PATH_IMAGE018
spatial covariance of the cells;
Figure DEST_PATH_IMAGE019
-measuring point position
Figure 968714DEST_PATH_IMAGE017
And a certain non-measuring point position
Figure DEST_PATH_IMAGE020
Spatial covariance of the cells;
Figure DEST_PATH_IMAGE021
-from a powered detectorMeasuring point quantity;
Figure DEST_PATH_IMAGE022
-NAND measuring point
Figure DEST_PATH_IMAGE023
To a corresponding secondjA weight function;
Figure DEST_PATH_IMAGE024
-NAND measuring point
Figure 839718DEST_PATH_IMAGE023
Corresponding penalty factors;
and 4, step 4: calculating the kriging variance of the non-measured point position by using a formula (4) according to the space covariance between the measured point position and the non-measured point position obtained in the step (3), and a weight function and a penalty factor corresponding to the non-measured point position;
Figure DEST_PATH_IMAGE025
（4）
in the formula:
Figure DEST_PATH_IMAGE026
a certain non-measuring point
Figure 177771DEST_PATH_IMAGE023
Kriging variance of (a);
Figure DEST_PATH_IMAGE027
-NAND measuring point
Figure 639977DEST_PATH_IMAGE023
To a corresponding secondiA weight function;
Figure DEST_PATH_IMAGE028
-measuring point position
Figure DEST_PATH_IMAGE029
And a certain non-measuring point
Figure DEST_PATH_IMAGE030
Spatial covariance of the cells;
and 5: calculating the average Kriging variance value of all the non-measuring point position sets by using a formula (5) according to the non-measuring point position sets classified in the step (3) and the Kriging variance values of the non-measuring point positions obtained in the step (4);
Figure DEST_PATH_IMAGE031
（5）
in the formula:
Figure DEST_PATH_IMAGE032
-the number of unmeasured points in the nuclear reactor monitoring system;
Figure DEST_PATH_IMAGE033
-a set of non-measured point locations within the nuclear reactor monitoring system;
Figure DEST_PATH_IMAGE034
-set of non-measured point positions
Figure DEST_PATH_IMAGE035
Average kriging variance of (c);
Figure DEST_PATH_IMAGE036
-a first stepkPositions of non-measuring points;
Figure DEST_PATH_IMAGE037
-a first stepkA non-measuring point
Figure DEST_PATH_IMAGE038
Kriging variance of (a);
step 6: and (3) disturbing the initialized three-dimensional measuring point arrangement model of the self-powered detector established in the step (1), and searching the minimum value of the kriging variance average value obtained by calculation in the step (5) and the corresponding three-dimensional measuring point arrangement model of the self-powered detector by adopting a simulated annealing algorithm, namely, the three-dimensional measuring point arrangement model of the self-powered detector is used as optimized three-dimensional measuring point arrangement of the self-powered detector.
2. The method for optimizing the arrangement of the three-dimensional measuring points of the self-powered detector based on the Kriging model as claimed in claim 1, wherein: and (3) expressing the radial and axial spatial position model of the nuclear reactor core in the step 1 by using spatial position coordinates.
3. The method for optimizing the arrangement of the three-dimensional measuring points of the self-powered detector based on the Kriging model as claimed in claim 1, wherein: the initialized three-dimensional measuring point arrangement model of the self-powered detector in the step 1 is represented by space position coordinates.
CN202210649975.1A 2022-06-10 2022-06-10 Method for optimizing three-dimensional measuring point arrangement of self-powered detector based on Kriging model Active CN114722646B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202210649975.1A CN114722646B (en) 2022-06-10 2022-06-10 Method for optimizing three-dimensional measuring point arrangement of self-powered detector based on Kriging model

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202210649975.1A CN114722646B (en) 2022-06-10 2022-06-10 Method for optimizing three-dimensional measuring point arrangement of self-powered detector based on Kriging model

Publications (2)

Publication Number Publication Date
CN114722646A true CN114722646A (en) 2022-07-08
CN114722646B CN114722646B (en) 2022-08-26

Family

ID=82232863

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202210649975.1A Active CN114722646B (en) 2022-06-10 2022-06-10 Method for optimizing three-dimensional measuring point arrangement of self-powered detector based on Kriging model

Country Status (1)

Country Link
CN (1) CN114722646B (en)

Citations (11)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPH0587977A (en) * 1991-09-27 1993-04-09 Toshiba Corp Method for arranging neutron detector
GB201522288D0 (en) * 2015-11-12 2016-02-03 China Nuclear Power Engineering Co Ltd And China Guangdong Nuclear Power Holding Corp Method, server and system for surveilling core state of nuclear power plant
CN105550784A (en) * 2016-01-20 2016-05-04 中科宇图科技股份有限公司 Distribution point optimizing method of air quality monitoring station
CN106714336A (en) * 2016-10-25 2017-05-24 南京邮电大学 Wireless sensor network temperature monitoring method based on improved Kriging algorithm
CN108899102A (en) * 2018-07-06 2018-11-27 中国核动力研究设计院 The method for arranging of the fixed self-power neutron detector general for presurized water reactor
CN110765618A (en) * 2019-10-28 2020-02-07 西安交通大学 Method for calculating response current of self-powered neutron detector in pressurized water reactor
CN111581803A (en) * 2020-04-30 2020-08-25 北京航空航天大学 Krigin proxy model algorithm for global ionosphere electron content
CN112395808A (en) * 2020-11-18 2021-02-23 南京林业大学 Biomass remote sensing mapping method combining random forest and collaborative kriging
CN112577671A (en) * 2020-11-27 2021-03-30 武汉工程大学 Well lid monitoring method and system by using Kriging method
CN113435073A (en) * 2021-03-15 2021-09-24 国网冀北电力有限公司张家口供电公司 GIS bus shell temperature measuring point arrangement optimization method
CN114140706A (en) * 2021-11-25 2022-03-04 乌鲁木齐海关技术中心 Novel method for positioning multiple radioactive sources by unmanned aerial vehicle aerial survey for large-scale cargo yard

Patent Citations (11)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPH0587977A (en) * 1991-09-27 1993-04-09 Toshiba Corp Method for arranging neutron detector
GB201522288D0 (en) * 2015-11-12 2016-02-03 China Nuclear Power Engineering Co Ltd And China Guangdong Nuclear Power Holding Corp Method, server and system for surveilling core state of nuclear power plant
CN105550784A (en) * 2016-01-20 2016-05-04 中科宇图科技股份有限公司 Distribution point optimizing method of air quality monitoring station
CN106714336A (en) * 2016-10-25 2017-05-24 南京邮电大学 Wireless sensor network temperature monitoring method based on improved Kriging algorithm
CN108899102A (en) * 2018-07-06 2018-11-27 中国核动力研究设计院 The method for arranging of the fixed self-power neutron detector general for presurized water reactor
CN110765618A (en) * 2019-10-28 2020-02-07 西安交通大学 Method for calculating response current of self-powered neutron detector in pressurized water reactor
CN111581803A (en) * 2020-04-30 2020-08-25 北京航空航天大学 Krigin proxy model algorithm for global ionosphere electron content
CN112395808A (en) * 2020-11-18 2021-02-23 南京林业大学 Biomass remote sensing mapping method combining random forest and collaborative kriging
CN112577671A (en) * 2020-11-27 2021-03-30 武汉工程大学 Well lid monitoring method and system by using Kriging method
CN113435073A (en) * 2021-03-15 2021-09-24 国网冀北电力有限公司张家口供电公司 GIS bus shell temperature measuring point arrangement optimization method
CN114140706A (en) * 2021-11-25 2022-03-04 乌鲁木齐海关技术中心 Novel method for positioning multiple radioactive sources by unmanned aerial vehicle aerial survey for large-scale cargo yard

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
YAODONGSANG: "Development and verification of a simulation toolkit for Self-Powered Neutron Detector", 《ANNALS OF NUCLEAR ENERGY》 *
李茁等: "基于谐波展开法的压水堆堆芯功率分布在线监测", 《核动力工程》 *
陈贝贝等: "基于遥感的桂林空气监测点位优化布设研究", 《地理空间信息》 *

Also Published As

Publication number Publication date
CN114722646B (en) 2022-08-26

Similar Documents

Publication Publication Date Title
CN107066745B (en) Method for obtaining three-dimensional neutron flux density distribution in fast neutron reactor core transient process
Daeubler et al. High-fidelity coupled Monte Carlo neutron transport and thermal-hydraulic simulations using Serpent 2/SUBCHANFLOW
CN111446014B (en) Subcritical rod carving method using source range detector signal as signal source
JP5357389B2 (en) How to determine the margin to the operational limit for reactor operation
CN110457802B (en) Precision optimization implementation method for SFCOMPO fuel consumption experiment benchmark question check simulation
CN113409975B (en) Reactor core power distribution monitoring method and system based on model order reduction and data assimilation
CN113076684B (en) Intelligent calculation method for transient parameters in rod adjusting process of nuclear reactor core
CN113421669B (en) Reactor core power distribution online reconstruction method and system based on local nonlinear correction
CN110765618A (en) Method for calculating response current of self-powered neutron detector in pressurized water reactor
CN114722646B (en) Method for optimizing three-dimensional measuring point arrangement of self-powered detector based on Kriging model
Lee et al. Prediction of DNBR using fuzzy support vector regression and uncertainty analysis
Li et al. Proper orthogonal decomposition based online power-distribution reconstruction method
Daeubler et al. Development of a high-fidelity Monte Carlo thermal-hydraulics coupled code system Serpent/SUBCHANFLOW–first results
Willermoz et al. HORUS3D code package development and validation for the JHR modelling
Hassan et al. Simulation of BEAVRS benchmark at hot zero power using MCNP6
EP4174875B1 (en) Computer implemented method for simulating an operation of a reactor core
Tuyle et al. Linearized transient analysis of nuclear steam generators
Gairola et al. RELAP5-3D Simulation of PG-27 Test at the HTTF Facility
Zhou et al. Layout Optimization of Self-Powered Neutron Detector for HPR1000
EP4174875A1 (en) Computer implemented method for simulating an operation of a reactor core
CN118053604A (en) Control rod position detection method and device and electronic equipment
Corak Improvements on Power Calibration and Core Monitoring at the Penn State Breazeale Reactor
Qian et al. Inverse method study based on Characteristic Statistic Algorithm (CSA) with application in estimating core states parameters
Webb et al. Comparison of CECOR algorithm to Lagrange multiplier method to estimate reactor power distributions
Ivanov et al. Using the OECD/NRC pressurized water reactor main steam line break benchmark to study current numerical and computational issues of coupled calculations

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant