KR20230090221A - Method and system for gmdh-based reactor core output prediction - Google Patents

Abstract

According to one embodiment, a method and a system thereof can predict an output distribution in an axial direction of a core by using a plurality of measurement devices in a furnace around a target nuclear fuel assembly without respect to whether the measurement devices are arranged in the furnace. In addition, when a control rod is not arranged, a processor selects a measurement signal in a furnace collected from one or more nuclear fuel assemblies and this is applied to a pre-learned GMDH-based core output prediction model to predict an output distribution for an axial direction of a core and when the control rod is arranged, another GMDH-based core output prediction model is replaced to predict an output distribution for the axial direction of the core.

Description

Method and system for predicting core output based on GMDH {METHOD AND SYSTEM FOR GMDH-BASED REACTOR CORE OUTPUT PREDICTION}

It relates to a method and system for predicting the output of a nuclear reactor core, and more particularly, a group method of data handling (GMDH) regardless of whether a processor is disposed of an in-core instrument (ICI) in a plurality of fuel assemblies. Power can be predicted using the base core power prediction model, and it is related to a method and system for predicting power using a different core power prediction model depending on whether control rods are disposed.

The power of the nuclear reactor core is the most important factor in the safety of the nuclear reactor, and it is strictly forbidden to increase the power beyond a certain power determined in the design process. If the output rises above the design output, it can cause damage to the nuclear fuel, and if the output rises beyond the cooling capacity of the coolant, the coolant in the reactor boils and bubbles can occur, which also damages the nuclear fuel and increases the pressure inside the reactor. This is because it can lead to very dangerous conditions.

In addition, even if the total output of the nuclear reactor is the same, even if the output of a specific position is locally increased according to the change in the power distribution, a similar risk exists, so it is very important to continuously monitor the change in the power distribution.

Since COLSS and CECOR computer programs use snapshot data of in-reactor measurement signals and a control rod position calculator, the real-time whole core power distribution cannot be predicted in a transient situation (control rod detachment or falling situation) where the real-time position of the control rod is not accurate. there is

The present invention has been made to solve the above problems, and it is possible to predict the power distribution of the whole core in real time even in the transient situation of the control rod, so that it can be used as a signal processing base technology for a cobalt-vanadium furnace instrument that generates an instantaneous furnace measurement signal. do.

However, the technical challenges are not limited to the above-described technical challenges, and other technical challenges may exist.

A core power prediction method performed by a processor according to an embodiment, comprising: collecting in-reactor measurement signals from one or more nuclear fuel assemblies in which an in-reactor instrument is located among a plurality of nuclear fuel assemblies; selecting one or more in-furnace measurement signals measured by an in-furnace instrument located in at least one of a target fuel assembly or a nuclear fuel assembly around the target fuel assembly from among the in-furnace measurement signals; and outputting a predicted power distribution in the axial direction of the core by applying the selected in-reactor measurement signals to a GMDH-based core power prediction model pre-learned for the target fuel assembly.

Selecting the one or more in-furnace instrumentation signals may include: determining a candidate in-furnace instrument based on a spatially proximate order of the one or more in-furnace instrument to the target fuel assembly; and selecting the one or more in-furnace measurement signals measured at the determined candidate in-furnace measurement instrument. can include

Determining the candidate in-reactor instruments may include determining the top four candidate in-reactor instruments that are spatially proximate to the target fuel assembly.

The outputting of the predicted power distribution may include: predicting, based on a first GMDH-based core power prediction model, for a nuclear fuel assembly lacking an in-reactor instrument; and predicting based on the second GMDH-based core power prediction model for the fuel assembly in which the in-reactor instrument is located; can include

Extracting an input value corresponding to a nuclear fuel assembly to which a GMDH-based core power prediction model to be trained is assigned or an in-reactor instrument located around the corresponding nuclear fuel assembly among input signals of a pre-generated training data set; and determining an output value by sampling an output signal of the previously generated training data set based on a predetermined sampling interval. may further include.

The step of generating the learning data set for each operating scenario of the nuclear reactor may be further included in the learning of the GMDH-based core power prediction model.

selecting, by the processor, coefficients of a polynomial using a pre-generated training data set; may further include.

The selecting of the coefficient may include determining an error between a value output by inputting an input signal from a training data set to the GMDH-based core power prediction model and an actual output signal value of the training data set for the GMDH-based core power prediction model. and selecting a coefficient by which the error is reduced based on the method.

Selecting the coefficient may include calculating the error based on a sum of squares of a difference between each predicted output value and an actual output value divided by an actual output value.

calculating a first coefficient of a first partial polynomial using the furnace instrument sample signal value; selecting a predetermined number of first coefficients from among the calculated first coefficients; and calculating and selecting a second coefficient of the second partial polynomial using the selected first coefficient.

The degree of the second partial polynomial may be higher than that of the first partial polynomial.

The first partial polynomial may be a quadratic expression.

The outputting of the predicted power distribution may include predicting the core power by using a GMDH-based core power prediction model having an increased order when the control rod is inserted.

and storing the GMDH-based core power prediction model for each nuclear fuel assembly.

A system for predicting nuclear reactor core power according to an embodiment, comprising: a nuclear reactor core; and electronics coupled to the reactor core; The nuclear reactor core includes: a plurality of nuclear fuel assemblies disposed in the nuclear reactor core; and an in-furnace instrument disposed within at least one fuel assembly of the plurality of fuel assemblies; The electronic device includes: a communication unit receiving an in-furnace measurement signal from the furnace instrument; a memory storing pre-learned GMDH-based core output prediction models individually for each of the plurality of fuel assemblies; and using a core power prediction model for a target fuel assembly among the core power prediction models, from one or more in-reactor measurement signals measured by an in-furnace instrument located in at least one of the target fuel assembly or a fuel assembly around the target fuel assembly. a processor predicting core power; can include

The reactor core may further include control rods inserted into the plurality of nuclear fuel assemblies.

When control rods are inserted into the plurality of fuel assemblies, the processor may replace a GMDH-based core output prediction model for each fuel assembly of the plurality of fuel assemblies into which the control rods are inserted.

When the control rods are inserted into a plurality of nuclear fuel assemblies, the processor may replace the model with a GMDH-based core output prediction model having a higher order than the default order.

The in-furnace meter may be a rhodium meter.

A computer readable recording medium storing one or more computer programs according to an embodiment may include instructions for performing a method.

1 shows an in-furnace instrument arrangement inside a pressurized water reactor.
2 shows an exemplary structure of a system for predicting nuclear reactor core power according to an embodiment.
3 is a schematic diagram of a cobalt-vanadium meter.
FIG. 4 shows a result of verifying the prediction of the axial power distribution for each nuclear fuel assembly having no control rods therein.
5 shows a result of verifying the prediction of the axial power distribution for each nuclear fuel assembly having a control rod therein.
6 is a flowchart of a method for predicting core power according to an embodiment.
7 is a flow diagram of a method for selecting one or more in-furnace measurement signals performed by a processor according to one embodiment.
8 is an exemplary diagram illustrating the arrangement of 177 nuclear fuel assemblies and 45 in-reactor instruments in the reactor core.
9 is an exemplary view of the arrangement of a target fuel assembly and a candidate in-reactor instrument selected to measure its in-reactor instrumentation signal.
10 is a flowchart of a method of outputting a predicted power distribution performed by a processor according to an embodiment.
11 is a schematic diagram showing a flow for estimating power in an axial direction in one nuclear fuel assembly.
12 is a flowchart of a method for learning a GMDH-based core power prediction model performed by a processor according to an embodiment.
13 is a multi-input-single-output GMDH algorithm example diagram.
14 is an exemplary diagram of an MIA method among multiple input-single output GMDH algorithms.
15 is a schematic diagram illustrating a flow for calculating coefficients used in a GMDH-based core power prediction model according to an embodiment.
16 illustrates a result of applying a GMDH-based core power prediction model to a cobalt-vanadium reactor instrument for each nuclear fuel assembly according to an embodiment.
17 is a graph of a result of applying a GMDH-based core output prediction model to a cobalt-vanadium reactor instrument of one nuclear fuel assembly according to an embodiment.

Specific structural or functional descriptions of the embodiments are disclosed for illustrative purposes only, and may be changed and implemented in various forms. Therefore, the form actually implemented is not limited only to the specific embodiments disclosed, and the scope of the present specification includes changes, equivalents, or substitutes included in the technical idea described in the embodiments.

Although terms such as first or second may be used to describe various components, such terms should only be construed for the purpose of distinguishing one component from another. For example, a first element may be termed a second element, and similarly, a second element may be termed a first element.

It should be understood that when an element is referred to as being “connected” to another element, it may be directly connected or connected to the other element, but other elements may exist in the middle.

Singular expressions include plural expressions unless the context clearly dictates otherwise. In this specification, terms such as "comprise" or "have" are intended to designate that the described feature, number, step, operation, component, part, or combination thereof exists, but one or more other features or numbers, It should be understood that the presence or addition of steps, operations, components, parts, or combinations thereof is not precluded.

Unless defined otherwise, all terms used herein, including technical or scientific terms, have the same meaning as commonly understood by one of ordinary skill in the art. Terms such as those defined in commonly used dictionaries should be interpreted as having a meaning consistent with the meaning in the context of the related art, and unless explicitly defined in this specification, it should not be interpreted in an ideal or excessively formal meaning. don't

Hereinafter, embodiments will be described in detail with reference to the accompanying drawings. In the description with reference to the accompanying drawings, the same reference numerals are given to the same components regardless of reference numerals, and overlapping descriptions thereof will be omitted.

1 shows an in-core instrument (ICI) arrangement inside a pressurized water reactor.

Referring to FIG. 1 , a plurality of nuclear fuel assemblies 110 may be located in the lower part 100 of the nuclear reactor. A plurality of nuclear fuel assemblies 110 may have an in-reactor instrument 120 disposed therein to monitor a change in the power distribution of the nuclear reactor core. An in-furnace meter may have five detectors 121 of equal length in the axial direction. Illustratively, the axial direction may indicate a direction (eg, a z-axis direction) perpendicular to a reference plane (eg, the ground).

Illustratively, the computer program may calculate the state in the reactor by receiving the measurement signal in the reactor. The computer programs may be, for example, COLSS (Core Operating Limit Supervisory System) and CECOR. In COLSS, as a core monitoring system, real-time measurement signals are provided within the reactor, and DNBR: Departure of Nucleate Boiling Ratio (DNBR), LPD: Linear Power Density (LPD), Licensed Power Level, and radial output Azimuthal tilt and axial shape index (ASI) can be calculated. In addition, COLSS can also monitor in-furnace conditions in real time. CECOR is not real-time, but it can predict the power distribution of the whole core by receiving the measurement signal in the furnace.

On the other hand, COLSS and CECOR's in-furnace measurement signal processing method can use the snapshot data (Snapshot file) of the furnace measurement signal from 45 in-furnace measurement instruments and the output penalty factor calculated by Control Element Assembly Calculator (CEAC). . COLSS and CECOR's in-reactor measurement signal processing method can estimate the average axial power distribution throughout the core through Fourier transform using snapshot data and output penalty factor. COLSS and CECOR's in-vessel measurement signal processing method can be used for core monitoring by calculating axial output deviation through Fourier transform.

2 shows an exemplary structure of a system for predicting nuclear reactor core power according to an embodiment.

Referring to FIG. 2 , the reactor core power prediction system 200 may include a reactor core 210 and an electronic device 220 . According to one embodiment, the reactor core 210 may include a plurality of fuel assemblies 211 and an in-reactor instrument 212 . However, it is not limited thereto, and the reactor core 210 may further include other components such as control rods 213. In addition, the electronic device 220 may include a communication unit 221, a memory 222, and a processor 223, but is not limited thereto, and the electronic device 220 may further include one or more other components. there is.

According to one embodiment, the nuclear reactor core 210 may operate in a state in which the control rods 213 are not inserted into the plurality of nuclear fuel assemblies 211 . A plurality of nuclear fuel assemblies 211 may be disposed within the reactor core 210 . The in-reactor instrument 212 may be disposed inside a fuel assembly of some of the plurality of fuel assemblies 211 . Exemplarily, in a pressurized water reactor in Korea, 45 in-reactor instruments in a radial direction out of a total of 177 nuclear fuel assemblies may be disposed inside the fuel assemblies.

Electronic device 220 may be physically and/or electrically coupled to in-furnace instrumentation 212 of reactor core 210 . The electronic device 220 may receive an in-furnace measurement signal measured by the in-furnace measuring instrument 212 through the communication unit 221 .

The processor 223 may predict the core power from the received in-furnace measurement signal using pre-learned group method of data handling (GMDH)-based core power prediction models stored in the memory 222 . The processor 223 may individually store GMDH-based core power prediction models for each of the plurality of fuel assemblies 211 in the memory 222 . The processor 223 may use a GMDH-based core power prediction model for a target fuel assembly among individually stored core power prediction models. Also, as described above, the in-reactor instrument 212 may not be disposed in all fuel assemblies, but may be disposed in some of the fuel assemblies. The processor 223 may predict the core power from one or more in-reactor measurement signals measured by an in-furnace instrument 212 located in at least one of the target fuel assembly or fuel assemblies adjacent to the target fuel assembly.

According to one embodiment, the control rod 213 may be inserted into the plurality of nuclear fuel assemblies 211 . The processor 223 may replace a GMDH-based core power prediction model for each fuel assembly of the plurality of fuel assemblies 211 into which the control rod 213 is inserted. The processor 223 may replace the GMDH-based core output prediction model of the plurality of nuclear fuel assemblies 211 into which the control rods 213 are inserted with a model having a higher order than the default order. If the GMDH-based core power prediction model is not changed when the control rods 213 are inserted into the plurality of fuel assemblies 211, the nonlinearity of the actual power distribution due to the insertion of the control rods 213 is difficult to predict, and the prediction Errors may occur in the results. As described above, the processor 223 may reduce a prediction error by selecting a GMDH-based core power prediction model having a higher order. Effects for this will be described later in FIG. 5 .

For reference, in this specification, an example in which the electronic device 220 performs both learning of the GMDH-based core power prediction model and prediction using the GMDH-based core power prediction model as a single device is mainly described, but is not limited thereto. For example, the electronic device 220 predicts core power for a target nuclear fuel assembly by using a first electronic device that learns a GMDH-based core power prediction model for each nuclear fuel assembly and the learned GMDH-based core power prediction model. It may be composed of hardware separated from each other, such as a second electronic device. Due to the separation of hardware, overload can be prevented and efficient function execution can be achieved in performing each function in separate electronic devices.

Illustratively, the furnace meter 212 may be a rhodium meter. However, it is not limited thereto, and the furnace meter 212 may be a cobalt meter, a vanadium meter, a platinum meter, or a cobalt-vanadium meter. The cobalt-vanadium meter will be described later in FIG. 3 below.

The in-furnace measurement signal may be an instrument reaction rate R(r) value. This instrument response rate can be calculated by Equation 1 (e.g. RAST-K code) below.

은 계측기 수밀도,

는 계측기 흡수핵단면적,

는 계측기 위치 중성자속을 나타낼 수 있다. 여기서, g는 다군 중성자 에너지그룹의 인덱스이며, RAST-K 코드는 2군 에너지 그룹을 사용하므로 g=1인 경우 고속중성자, g=2인 경우 열중성자를 나타낼 수 있다. 수학식 1의 도출 과정 및 수학식 1을 구현한 RAST-K코드를 이용한 상세 동작은 도 12에서 후술한다.In Equation 1 described above, r is a position variable of the furnace measurement signal and may be a value indicating one of the signals detected by the furnace measurement device. For example, when the number of signals detected by in-furnace measuring instruments is the number of furnace measuring instruments 45 X the number of detectors 5 = 225, r may be an integer equal to or greater than 1 and equal to or smaller than 225.

silver meter number density,

is the instrument absorber nuclear cross-section,

can represent the instrument position neutron flux. Here, g is an index of a multigroup neutron energy group, and since the RAST-K code uses a group 2 energy group, g = 1 can represent fast neutrons and g = 2 can represent thermal neutrons. The derivation process of Equation 1 and the detailed operation using the RAST-K code implementing Equation 1 will be described later with reference to FIG. 12 .

3 is a schematic diagram of a cobalt-vanadium meter.

Referring to FIG. 3 , the cobalt-vanadium meter 320 may have the same diameter and height as the rhodium meter 310 . The top and bottom of the rhodium meter 310 may be composed of a single rhodium (eg, Rh-103) material. Unlike the rhodium meter 310, the upper half 321 of the cobalt-vanadium meter 320 may be composed of cobalt-60 (Co-60) material and the lower half 322 of vanadium-51 (V-51) material. there is. Therefore, in the cobalt-vanadium measuring instrument 320, since the upper and lower instrument materials are different, the upper furnace measurement signal and the lower furnace measurement signal can be obtained separately. In the system including the cobalt-vanadium meter 320, an electronic device (eg, the electronic device 220 of FIG. 2 ) may separately measure and compare an upper measurement signal and a lower measurement signal to check.

FIG. 4 shows a result of verifying the prediction of the axial power distribution for each nuclear fuel assembly without the control rod 213 therein. 5 shows a result of verifying the prediction of the axial power distribution for each nuclear fuel assembly having a control rod therein.

Referring to FIG. 4 , squares indicate result values predicted through the GMDH-based core power prediction model, and triangles indicate values to be compared. The result used for verification may be, for example, a simulation result of full-power commercial operation of the Korean standard reactor. Simulation results of commercial operation may include an axial power distribution of a nuclear fuel assembly in a state in which the cycle burnup is about 200 days. In FIGS. 4 and 5 , a horizontal axis may represent an active height, and a vertical axis may represent axial power. Since the two distributions shown in the graphs shown in FIGS. 4 and 5 are similar, it may indicate that the predicted result value is similar to the actual comparison target value. At this time, the value to be compared is a value obtained by calculating the axial power distribution using the core design data using the RAST-K code, and a value divided by the volume considering the volume of the axial node may be used. RAST-K may be a kind of core analysis code.

Prediction based on the GMDH model according to an embodiment may exhibit high accuracy. Furthermore, the electronic device according to an embodiment may accurately predict the power distribution by using different GMDH-based core power prediction models regardless of whether or not the control rods 213 are present.

6 is a flowchart of a method for predicting core power according to an embodiment.

According to an embodiment, the following steps 610 to 630 may be performed by a system (eg, the reactor core 210 and the electronic device 220 in the system 200 of FIG. 2 ).

At step 610, in-reactor instruments within the reactor core may be located in only some of the plurality of fuel assemblies. An in-vessel instrument is located at each location to collect the in-vessel instrument signal of the fuel assembly.

In step 620, the processor of the electronic device may receive the in-furnace measurement signal from the communication unit. The processor may select one or more in-furnace measurement signals measured by an in-furnace instrument located in at least one of the target fuel assembly or fuel assemblies around the target fuel assembly from among the furnace measurement signals. Additional explanation on this will be described later with reference to FIGS. 7 to 9 .

At step 630, the memory may store a pretrained GMDH-based core power prediction model for the target fuel assembly. The processor of the electronic device may apply the selected in-furnace measurement signals to the GMDH-based core power prediction model stored in the memory. The processor of the electronic device may output a predicted power distribution in the axial direction of the core as a result of applying the in-furnace measurement signals to the GMDH-based core power prediction model. Additional explanation on this will be described later with reference to FIG. 10 .

7 is a flow diagram of a method for selecting one or more in-furnace measurement signals performed by a processor according to one embodiment. 8 is an exemplary diagram illustrating the arrangement of 177 nuclear fuel assemblies and 45 in-reactor instruments in the reactor core. 9 is an exemplary view in which a target nuclear fuel assembly and an in-furnace instrument measuring signals thereof are disposed.

Referring to FIG. 7 , in step 621 , selecting one or more in-furnace instrumentation signals may include determining candidate in-furnace instrumentation based on an order of spatial proximity of the one or more in-furnace instrumentation to the target fuel assembly. Referring to FIGS. 8 and 9 , determining candidate in-reactor instruments may include determining the top four candidate in-reactor instruments that are spatially proximate to the target fuel assembly.

Illustratively, when the fuel assembly No. 54 in the nuclear reactor core 800 in FIG. 8 is the target (810), the in-reactor instrument may not be disposed in the fuel assembly No. 54. The target may refer to a target nuclear fuel assembly for collecting in-reactor measurement signals. The processor may determine four in-furnace instruments that are spatially close together as shown in FIG. 9 . The processor may determine some in-reactor instruments (eg, in-reactor instruments numbered 12, 14, 15, and 19 in FIG. 8) as candidate in-reactor instruments (Near ICI) around target fuel assembly No. 54. In FIG. 8 , when fuel assembly No. 1 is the target (820), an in-reactor instrument may be disposed in the fuel assembly No. 1. The processor may determine in-reactor instruments No. 1, 3, 4, and 7 including the in-reactor instrument No. 1 disposed in the target fuel assembly No. 1 as the candidate in-reactor instrument (Near ICI).

At step 622, selecting one or more in-furnace measurement signals may include selecting one or more in-furnace measurement signals measured at the determined candidate in-furnace measurement signal. As mentioned above, one in-furnace meter may include five detectors. Since a total of four in-furnace instruments are selected as described above in step 621 for one target fuel assembly, the processor is able to collect a total of 20 signal values for the target fuel assembly. The processor may determine the 20 signal values as input values of the GMDH model described below.

10 is a flowchart of a method of outputting a predicted power distribution performed by a processor according to an embodiment.

Referring to FIG. 10 , in step 631 , outputting the predicted power distribution may include predicting based on the first GMDH-based core power prediction model for a fuel assembly lacking an in-reactor instrument. there is. In step 632 , outputting the predicted power distribution may include making a prediction based on the second GMDH-based core power prediction model for the fuel assembly in which the in-reactor instrumentation is located. That is, the processor may predict the power distribution of a plurality of nuclear fuel assemblies by using an individually set GMDH-based core power prediction model regardless of whether instrumentation is arranged in the furnace. A GMDH-based core power prediction model can also be built for fuel assemblies that do not include in-reactor instrumentation. As will be described later, the corresponding GMDH-based core power prediction model can be trained using in-reactor measurement signals from fuel assemblies including other in-reactor instruments around fuel assemblies that do not include in-reactor instruments. The core power prediction model based on GMDH may have an increased order when control rods are inserted.

11 is a schematic diagram showing a flow for estimating power in an axial direction in one nuclear fuel assembly.

As described above, the processor may input the in-reactor measurement signals 1110 (eg, an input value including 20 signal values) selected for the target fuel assembly to the GMDH-based core power prediction model. As input values are applied to the GMDH-based core power prediction model, the processor can generate a total of 24 result values through N layers. For convenience of description, 24 result values are expressed in a graph form, but are not limited thereto. The resulting values may be values representing a predicted power distribution. For example, the resulting values may be interpreted as values sampled from the predicted power distribution, or in other words, as quantized values from the predicted power distribution. The X axis of the graph may mean output intensity, and the Y axis may mean depth from a reference plane. In the form of a graph, result values can be visually checked, and thus result value analysis can be easily performed.

A series of operations shown in FIG. 11 may represent operations performed on one nuclear fuel assembly. The electronic device may predict a power distribution for a corresponding nuclear fuel assembly by applying a corresponding GMDH-based core power prediction model to each of the plurality of nuclear fuel assemblies. For example, a GMDH-based core power prediction model may be assigned to each of 177 nuclear fuel assemblies. The number of GMDH-based core power prediction models may be 177. As a result, the electronics can predict a total of 177 axial power distributions for the fuel assemblies.

12 is a flowchart of a method of learning a GMDH-based core power prediction model performed by a processor according to an embodiment.

Referring to FIG. 12 , in step 1210, the processor may extract an input value assigned to a GMDH-based core power prediction model, which is a learning target, from among input signals of a pre-generated training data set. The input value may be an input signal corresponding to an in-furnace measurement signal detected by an in-furnace instrument located in the periphery of the nuclear fuel assembly or the target nuclear fuel assembly. The input signal may be determined by RAST-K code. RAST-K may be a kind of core analysis code. For example, in this specification, RAST-K can be used as an algorithm capable of calculating in-furnace measurement signals to generate a training data set.

에서의 노내계측기의 반응률을 나타낼 수 있다.A method of deriving the aforementioned Equation 1 (eg, RAST-K code) will be described in detail below. As described above, Equation 1 is the position

The reaction rate of the in-furnace instrument can be expressed in

인 계측기 위치 중성자속은 수학식 2를 이용하여 계산될 수 있다.First of all, Equation 1

The phosphorus meter location neutron flux can be calculated using Equation 2.

는 전노심 2군 중성자속 분포로 STREAM에서 핵연료 집합체 및 반사체에 대한 격자해석 결과를 기반으로 2군 군정수가 생산될 수 있다. 전자 장치는 생산된 2군 군정수를 RAST-K에서 읽고, 2군 군정수에 대해 노달 계산을 수행함으로써 전노심 중성자속 분포를 계산할 수 있다. 전자 장치는 전노심 중성자속 분포에

를 곱함으로써 계측기 위치에서의 중성자속을 계산할 수 있다. 즉,

는 핵연료집합체 중앙의 안내관에 위치한 계측기 위치 2군 중성자속을 나타낼 수 있다.In the above Equation 2

is the whole-core group 2 neutron flux distribution, and group 2 group constants can be produced based on the grid analysis results for the fuel assembly and reflector in STREAM. The electronic device may calculate the whole core neutron flux distribution by reading the produced group 2 group constants from RAST-K and performing nodal calculation on the group 2 group constants. Electronic devices are applied to whole-core neutron flux distribution.

By multiplying by , the neutron flux at the instrument location can be calculated. in other words,

may represent the group 2 neutron flux at the location of the instrument located in the guide tube at the center of the fuel assembly.

은 계측기 수밀도로서 매 연소 스텝마다 하기 수학식3을 이용하여 갱신될 수 있다.In addition, Equation 1

is the number density of the instrument and can be updated at every combustion step using Equation 3 below.

와

는 각각 1군, 2군의 계측기 흡수핵단면적이고,

은 위치

, 시간

에서의 계측기 수밀도일 수 있다.In the above Equation 3

and

are the instrumental absorber nuclear cross-sections of groups 1 and 2, respectively,

silver location

, hour

may be the instrument number density at

The electronic device may calculate the output of the assembly with the instrument from the reaction rate of the nuclear instrument in the furnace calculated through the above formulas. The electronic device may calculate the transient by using the neutron value given from the transient calculation result. Details of RAST-K can be referenced in the following paper. ("Vanadium, rhodium, silver and cobalt self-powered neutron detector calculations by RAST-K v2.0", Farrokh Khoshahval, Minyong Park, Ho Cheol Shin, Peng Zhang, Deokjung Lee, January 2018, Annals of Nuclear Energy, see pages 644 to 659)

In step 1220, the processor may determine an output value by sampling the output signal of the pre-generated training data set based on a predetermined sampling interval. As described above, not only the input signal but also the output signal can be determined by the RAST-K code.

The training data set may be prepared in the form of a set including input values and output values for each operating scenario of the nuclear reactor using the RAST-K code. For example, the electronic device may generate training data consisting of a set of input values and output values using RAST-K codes based on a given scenario. The operation scenarios may include scenarios based on various operating environments, such as furnace type and expiration, output range, measurement signal noise, burnup step, control rod asymmetry probability, transient and normal operation selection, and control rod movement situation setting during transient operation. An operating scenario is a scenario specifying a state and/or state range of a core under an arbitrary operating environment, and input values and output values may vary for each operating scenario. The data amount of the learning data set according to the operating scenario may be adjusted by the user's selection.

The electronic device may automatically produce the training data set. Exemplarily, in response to a scenario specified by a user, the electronic device may set the thermal power of the entire core within a range corresponding to the specified scenario, and may sample input values and output values for each nuclear fuel assembly.

If the operation scenario of the learning data set is an output de-activation or load-following operation scenario, the electronic device may also sample the position of the control rod. The electronic device may randomly sample the position of the control rod, but is not limited thereto, and may sample the position of the control rod within a constraint described later. First, in the control rod position sampling process, the electronic device may set a power dependent insertion limit (PDIL) for the thermal output of the entire core. The control rod assembly may represent one assembly formed by a plurality of control rods. The electronic device may form a plurality of assemblies each including a plurality of control rods. The control rod group may represent a group including the plurality of control rod assemblies described above. The electronic device may differently determine insertion positions of the plurality of control rods of each group based on the thermal output according to the operating scenario. The current position of the control rod may be sampled within the threshold point PDIL.

In addition, the electronic device may additionally sample the position of one of the control rod assemblies based on the control rod asymmetry probability. The control rod asymmetry probability may indicate a probability that control rods are asymmetrically disposed and/or inserted in the reactor core. In other words, after disposing the control rod assemblies, the electronic device selects a nuclear fuel assembly based on the asymmetric probability, and presents an operating scenario in a situation in which control rod assemblies are additionally inserted into the selected fuel assembly (e.g., an asymmetric control rod situation). can create The electronic device may generate data (eg, a file to be input to a core analysis mode) according to an operation scenario in which control rods are asymmetric. The processor may calculate data according to the operating scenario using the core analysis code RAST-K. The processor may extract the in-reactor measurement signal and the power distribution of the fuel assembly from data according to the above-described operating scenario using RAST-K. Extracted in-reactor measurement signals and power distribution of nuclear fuel assemblies can be automatically stored in memory.

13 is a multi-input-single-output GMDH algorithm example diagram.

The training data set can be applied to a method based on the GMDH method to predict the core power. The GMDH method can be classified as one of the inductive algorithms for modeling structural features of multivariate data sets. The multi-input-single-output GMDH model can be modeled with a polynomial function such as Equation 4.

In Equation 4 above, f _i may represent a variable, a _i may represent a coefficient, and i may be an integer greater than or equal to 1 and less than or equal to m. m may be an integer greater than or equal to 1. Y is an estimated value of GMDH, and in the above invention, one value of the power distribution in the axial direction of the nuclear fuel assembly is received as an input of the instrument signal (x ₁ , x ₂ , ??, x _n ), and the GMDH on the right side is obtained. It may be a value predicted by calculating a polynomial.

In the learning algorithm of the GMDH method, the number of iterative synthesis times of partial polynomials may be determined according to the order of the learned polynomial function to be obtained. The number of iterations may also mean the number of layers. Referring to FIG. 13, in the learning algorithm of the GMDH method, there are f number of layers, and after f+1 iterative synthesis is performed, a final coefficient set may be selected.

The partial polynomial of the smallest unit is a second order polynomial, expressed as Equation 5.

In Equation 5 above, p(x) may represent a partial polynomial (eg, a second order polynomial). x ₁ and x ₂ may represent variables, and a ₀ , a ₁ , a _{2 ,} a ₃ , a ₄ , and a ₅ may represent coefficients. GMDH is unaffected by the structure of the training data set and can be used for learning directly without separate data processing.

Illustratively, in the present specification, X-data related to the variable x of GMDH may be set as an in-furnace measurement signal in order to predict an axial power distribution of a plurality of nuclear fuel assemblies. Y-data for the output value y of GMDH can be set as an axial output distribution. Data sets used herein may be classified into a training data set and a test data set. The electronic device may generate a polynomial based on the GMDH algorithm from a train data set. The electronic device may update the coefficient based on an error between a result of applying the polynomial to X-data and Y-data. The electronic device may calculate an error between a result of applying a polynomial to X-data and Y-data based on least square methods. The electronic device can complete the final polynomial by updating the coefficient while repeatedly reducing an error between the polynomial calculation result of X-data and Y-data in the test data set.

A final polynomial that has been learned may be generated for each nuclear fuel assembly. The electronic device may predict the power distribution as a result by applying the in-reactor measurement signal obtained in real time to the final polynomial for each nuclear fuel assembly. For example, the electronic device may generate output values corresponding to the power distribution by inputting an in-furnace measurement signal measured in real time as a variable of the final polynomial and applying a final polynomial having updated coefficients to the input furnace measurement signal. there is.

For reference, the main safety factors of the core monitoring system may include DNBR, LPD, ASI, and azimuthal tilt. The main safety factor of the core monitoring system can be derived through the power distribution. Accordingly, the electronic device may predict a power distribution using the GMDH-based core power prediction model and derive a safety factor from the predicted power distribution. The derived safety factor can be utilized in the core monitoring system.

14 is an exemplary diagram of an MIA method among multiple input-single output GMDH algorithms.

Referring to FIG. 14 , the processor may include selecting coefficients of a polynomial using a pre-generated training data set. In FIG. 14 , coefficients may be shown as nodes by way of example. The processor calculates the first full node 1410 by passing the input values x1, x2, x3, and x4 from the entire training data set 1400 through layer1. The processor selects a predetermined number of first selected nodes 1411 from among all the calculated nodes 1410 . After that, the processor calculates the second full node 1420 as the node 1410 passes through layer2. The processor selects a predetermined number of second selected nodes 1421 from among the calculated second total nodes 1420 . The processor may select a final node by performing a method of selecting a selected node by allowing all nodes calculated in each step to pass through the layer N times.

으로 나타낼 수 있다. 전자 장치는 MIA 방식에서 최소제곱법의 행렬계산식인 수학식6을 이용하여 계수를 연산할 수 있다.This GMDH-based core power prediction model can select coefficients as a multilayer iterational algorithm (MIA) method. In the MIA method, a partial polynomial may be defined as an illustrative second-order polynomial. If Equation 4 is expressed as a determinant,

can be expressed as The electronic device may calculate the coefficient using Equation 6, which is a matrix calculation equation of the least squares method in the MIA method.

는 출력 값(예: Nx1 차원의 데이터), X는 훈련 입력 벡터(예: Nx6 차원의 데이터), A는 계수 벡터(예: 6x1 차원의 데이터)일 수 있다. MIA 방식은 소규모 크기의 다수 레이어를 통해 각각 부분다항식의 계수 벡터를 독립적으로 구하므로 큰 데이터 입력에 대한 학습 계산을 수행할 수 있다. 즉, MIA 방식은 많은 시나리오가 있는 원자로 감시체계에 적합한 방식이다. GMDH 모델은 부분 다항식으로 2차 다항식을 사용하므로 다음 레이어로 이동할 때마다

차 다항식으로 확장될 수 있다. In the above Equation 6

may be an output value (eg, Nx1-dimensional data), X may be a training input vector (eg, Nx6-dimensional data), and A may be a coefficient vector (eg, 6x1-dimensional data). Since the MIA method independently obtains the coefficient vector of each partial polynomial through multiple layers of small size, learning calculation for large data input can be performed. That is, the MIA method is suitable for a nuclear reactor monitoring system with many scenarios. The GMDH model uses a second order polynomial as a partial polynomial, so each time you move to the next layer

It can be extended to quadratic polynomials.

As an example, coefficient update of the GMDH-based core power prediction model will be described in more detail with reference to FIG. 15 .

15 is a schematic diagram illustrating a flow for calculating coefficients used in a GMDH-based core power prediction model according to an embodiment.

If the training data set is 50000, the data set can be divided into a training data set and a test data set in a ratio of 9:1 (e.g., training data set-45000, test data set-5000).

The MIA GMDH-based core power prediction model may include a plurality of layers. Each layer may correspond to a partial polynomial. The processor may calculate the Z coefficient (1510, eg, the first coefficient) of the second-order partial polynomial using the sample signal value of the in-furnace instrument in the first layer. For reference, the letters Z and V representing each coefficient are arbitrarily selected, but are not limited thereto. The processor may select a predetermined number of upper values from the Z coefficients and extend some of the selected Z coefficients in the second layer. For example, the processor may calculate the V coefficient 1520 (eg, the second coefficient) of the 4th order partial polynomial by extending the upper value of the Z coefficient in the second layer. The processor may select a predetermined number of higher values from the V coefficient. The processor may repeat the aforementioned coefficient calculation process as many times as the number of times specified by the user. The number of times designated by the user may be appropriately set according to limitations of processing performance and memory of the electronic device and an error confirmed during verification.

Errors can also be used when selecting higher values of coefficients. The error can be calculated by Equation 7.

를 계산할 수 있다. 전술한 수학식 7에서,

는 학습 데이터 세트의 실제 출력 신호의 값을 나타낼 수 있다. 프로세서는

와

간의 오차(예: MSE 값)를 산출할 수 있다. 프로세서는 산출된 오차가 감소되도록 계수를 업데이트할 수 있다.

는 오차 계산 시 사용되는 테스트 데이터 세트의 데이터 수를 의미할 수 있다.The processor inputs an input signal from the training data set generated by the RAST-K method for the GMDH-based core power prediction model to the GMDH-based core power prediction model and outputs the output.

can be calculated. In the above Equation 7,

may represent the value of the actual output signal of the training data set. the processor is

and

Interval errors (e.g. MSE values) can be calculated. The processor may update the coefficients such that the calculated error is reduced.

may mean the number of data in the test data set used in calculating the error.

The error calculated by Equation 7 is a relative error, and unlike the absolute error of Equation 8 according to the comparative embodiment, it may have an effect of correcting the output value. An error of a small output value may be overestimated compared to an error of a large output value, and the electronic device according to an embodiment may calculate a more accurate value through a relative error.

The coefficients of the finally calculated polynomial may be stored in a text, ASCII, or binary format for each nuclear fuel assembly, but are not limited thereto. Such coefficient storage may be interpreted as storing and/or constructing a GMDH-based core power prediction model.

The GMDH model verification script can use the core state of any one case of the learned GMDH model or verification data produced when learning data is produced as input and reference. The GMDH model verification script can compare and verify the core state or verification data used as input and reference with the power distribution of the entire core reconstructed as the GMDH model. This result can evaluate the accuracy and uncertainty of the learned GMDH model, and the computational speed. Therefore, the GMDH model verification script can be used when evaluating the performance of the model. Illustratively, as shown in Table 1, the verification statistics according to the accuracy error range can be evaluated as the performance of the model.

error range 1 cycle
unrodded 1 cycle
rodded cycle 4
unrodded cycle 4
rodded < ±5% 95.925% 96.173% 97.138% 97.169% < ±3% 92.186% 93.563% 94.278% 95.070% < ±1% 73.157% 77.706% 77.104% 80.548% > ±15% 0.586% 0.417% 0.184 0.196%

16 illustrates a result of applying a GMDH-based core power prediction model to a cobalt furnace meter and/or a vanadium furnace meter for each nuclear fuel assembly according to an embodiment.

The cobalt furnace meter and/or the vanadium furnace meter may generate an immediate furnace meter signal. Since the cobalt in-furnace meter and/or the vanadium in-furnace meter is a low-combustible material, the life of the meter may also be increased.

Referring to FIG. 16, when a cobalt furnace instrument and/or a vanadium reactor instrument are used, the reference value for each nuclear fuel assembly, the value obtained by applying the GMDH-based core power prediction model to the cobalt reactor instrument, and the GMDH-based core power prediction Each value obtained by applying the model to the instrument in the vanadium furnace can be represented. If you check each value, you can see that it is the same value or there is only a slight difference.

17 is a graph of a result of applying a GMDH-based core power prediction model to a cobalt reactor and/or a vanadium furnace instrument of one nuclear fuel assembly according to an embodiment.

Referring to FIG. 17 , it is possible to visually confirm a result similar to the reference value by graphing values for each in-reactor instrument for each nuclear fuel assembly.

As a result, the electronic device according to an embodiment may predict a power distribution by applying a GMDH-based core power prediction model without separate data preprocessing, regardless of the type of in-furnace instrument.

The embodiments described above may be implemented as hardware components, software components, and/or a combination of hardware components and software components. For example, the devices, methods and components described in the embodiments may include, for example, a processor, a controller, an arithmetic logic unit (ALU), a digital signal processor, a microcomputer, a field programmable gate (FPGA). array), programmable logic units (PLUs), microprocessors, or any other device capable of executing and responding to instructions. The processing device may execute an operating system (OS) and software applications running on the operating system. A processing device may also access, store, manipulate, process, and generate data in response to execution of software. For convenience of understanding, there are cases in which one processing device is used, but those skilled in the art will understand that the processing device includes a plurality of processing elements and/or a plurality of types of processing elements. It can be seen that it can include. For example, a processing device may include a plurality of processors or a processor and a controller. Other processing configurations are also possible, such as parallel processors.

Software may include a computer program, code, instructions, or a combination of one or more of the foregoing, which configures a processing device to operate as desired or processes independently or collectively. You can command the device. Software and/or data may be any tangible machine, component, physical device, virtual equipment, computer storage medium or device, intended to be interpreted by or provide instructions or data to a processing device. , or may be permanently or temporarily embodied in a transmitted signal wave. Software may be distributed on networked computer systems and stored or executed in a distributed manner. Software and data may be stored on computer readable media.

The method according to the embodiment may be implemented in the form of program instructions that can be executed through various computer means and recorded on a computer readable medium. The computer readable medium may include program instructions, data files, data structures, etc. alone or in combination, and the program instructions recorded on the medium may be specially designed and configured for the embodiment or may be known and usable to those skilled in the art of computer software. may be Examples of computer-readable recording media include magnetic media such as hard disks, floppy disks and magnetic tapes, optical media such as CD-ROMs and DVDs, and magnetic media such as floptical disks. - includes hardware devices specially configured to store and execute program instructions, such as magneto-optical media, and ROM, RAM, flash memory, and the like. Examples of program instructions include high-level language codes that can be executed by a computer using an interpreter, as well as machine language codes such as those produced by a compiler.

The hardware device described above may be configured to operate as one or a plurality of software modules to perform the operations of the embodiments, and vice versa.

As described above, although the embodiments have been described with limited drawings, those skilled in the art can apply various technical modifications and variations based on this. For example, the described techniques may be performed in an order different from the method described, and/or the components of the described system, structure, device, circuit, etc. may be combined or combined in a different form than the method described, or other components may be used. Or even if it is replaced or substituted by equivalents, appropriate results can be achieved.

Therefore, other implementations, other embodiments, and equivalents of the claims are within the scope of the following claims.

Claims (20)

A core power prediction method performed by a processor,
collecting an in-reactor measurement signal from one or more nuclear fuel assemblies where an in-reactor instrument is located among a plurality of nuclear fuel assemblies;
selecting one or more in-furnace measurement signals measured by an in-furnace instrument located in at least one of a target fuel assembly or a nuclear fuel assembly around the target fuel assembly from among the in-furnace measurement signals; and
Outputting a predicted power distribution in the axial direction of the core by applying the selected in-reactor measurement signals to a pre-learned GMDH-based core power prediction model for the target fuel assembly:
Core power prediction method comprising a.
According to claim 1,
The step of selecting one or more in-furnace measurement signals,
determining a candidate in-reactor instrument based on an order of one or more in-reactor instruments that are spatially proximate to the target fuel assembly; and
selecting the one or more in-furnace measurement signals measured by the determined candidate in-furnace instrument;
Core output prediction method comprising a.
According to claim 2,
The step of determining the candidate in-furnace instrument,
determining the top four candidate in-reactor instruments that are spatially close to the target fuel assembly;
Core output prediction method comprising a.
According to claim 1,
In the step of outputting the predicted power distribution,
predicting based on a first GMDH-based core power prediction model for a nuclear fuel assembly lacking the in-reactor instrument; and
Predicting based on a second GMDH-based core power prediction model for a fuel assembly in which the in-reactor instrument is located.
Core power prediction method comprising a.
According to claim 1,
Extracting an input value corresponding to a nuclear fuel assembly to which a GMDH-based core power prediction model to be trained is assigned or an in-reactor instrument located around the corresponding nuclear fuel assembly among input signals of a pre-generated training data set; and
determining an output value by sampling an output signal of a previously generated training data set based on a predetermined sampling interval;
Core power prediction method further comprising.
According to claim 5,
Generating the learning data set for each nuclear reactor operation scenario in learning the GMDH-based core power prediction model;
Core power prediction method further comprising.
According to claim 1,
selecting, by the processor, coefficients of a polynomial using a pre-generated training data set;
Core power prediction method further comprising.
According to claim 7,
The step of selecting the coefficient is,
For the GMDH-based core power prediction model, a coefficient by which the error is reduced based on an error between a value output by inputting an input signal from a training data set to the GMDH-based core power prediction model and an actual output signal value of the training data set. Steps to select
Core power prediction method comprising a.
According to claim 8,
The step of selecting the coefficient is,
Calculating the error based on a sum of squares of the difference between each predicted output and the actual output value divided by the actual output value.
Core power prediction method comprising a.
According to claim 7,
calculating a first coefficient of a first partial polynomial using the furnace instrument sample signal value;
selecting a predetermined number of first coefficients from among the calculated first coefficients;
Calculating and selecting a second coefficient of a second partial polynomial using the selected first coefficient
Core power prediction method comprising a.
According to claim 10,
The degree of the second partial polynomial is higher than the degree of the first partial polynomial,
Core output prediction method.
According to claim 11,
The first partial polynomial is a quadratic expression,
Core output prediction method.
According to claim 1,
In the step of outputting the predicted power distribution,
Predicting core power using a GMDH-based core power prediction model having an increased order when control rods are inserted
Core power prediction method comprising a.
According to claim 1,
storing the GMDH-based core power prediction model for each nuclear fuel assembly;
Core power prediction method comprising a.
In the reactor core power prediction system,
nuclear reactor core; and
electronics coupled to the reactor core; including,
The reactor core,
a plurality of nuclear fuel assemblies disposed within the reactor core; and
an in-furnace instrument disposed inside at least one of the plurality of fuel assemblies; including,
The electronic device,
a communication unit for receiving an in-furnace measurement signal from the in-furnace measuring instrument;
a memory storing pre-trained GMDH-based core power prediction models individually for each of the plurality of fuel assemblies; and
Using a core power prediction model for a target fuel assembly among the GMDH-based core power prediction models, one or more in-reactor measurements measured by an in-reactor instrument located in at least one of the target fuel assembly or a fuel assembly around the target fuel assembly a processor predicting a core power from the signal;
Core power prediction system comprising a.
According to claim 15,
The reactor core further comprises a control rod inserted into the plurality of nuclear fuel assemblies.
According to claim 15,
the processor,
When a control rod is inserted into the plurality of nuclear fuel assemblies, a GMDH-based core power prediction model is replaced for each fuel assembly of the plurality of fuel assemblies into which the control rod is inserted.
Core power prediction system.
According to claim 17,
the processor,
When the control rods are inserted into the plurality of nuclear fuel assemblies, replacing with a GMDH-based core power prediction model of a higher order than the default order,
Core power prediction system.
According to claim 1,
The reactor core power prediction system is a rhodium meter.
A computer-readable recording medium storing one or more computer programs including instructions for performing the method of any one of claims 1 to 14.

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