Patent Application
20160180976
1. Field of Invention
The present invention relates to a method of synthesizing axial power distributions of a nuclear reactor core using a neural network circuit and an in-core protection system (ICOPS) using the same. More particularly, the present invention relates to a method of synthesizing axial power distributions of a nuclear reactor core using a neural network circuit and an ICOPS using the same, in which using the neural network circuit including an input layer, an output layer, and at least one hidden layer, each layer being configured with at least one node, each node of one layer being connected to nodes of the other layers, node-to-node connections being made with connection weights varied based on a learning result, optimum connection weights between the respective nodes constituting the neural network circuit are determined through learning based on various core design data applied to the design of a nuclear reactor core of a nuclear power plant, and axial power distributions of the nuclear reactor core are synthesized based on ex-core flux detector signals measured by ex-core neutron flux detectors during operation of a nuclear reactor, so that the initial time required to perform a start-up test of the nuclear reactor can be reduced since basic data for synthesizing axial power distributions need not be separately measured in the start-up test of the nuclear reactor contrary to a conventional ICOPS, thereby improving the economic efficiency of the nuclear power plant, and so that overall nuclear reactor core design data can be used rather than actual measurement data in the start-up test (i.e., at the beginning of a period of nuclear fuel), thereby more accurately replicating axial power distributions of the nuclear reactor core throughout the overall period of the nuclear fuel.
2. Description of the Prior Art
A core protection calculator system (CPCS) of a nuclear power plant is an essential nuclear reactor protection system for safely keeping a nuclear reactor from a nuclear fuel meltdown and a departure from nucleate boiling (DNB.) The CPCS is a system in which safety and reliability are absolutely required.
Accordingly, in order to safely keep the nuclear reactor, it is very important to monitor and check, in real time, a state of the nuclear reactor. Hence, it is requested to satisfy the strict conditions from a design process. Particularly, in order to monitor, in real time, axial power distributions of the nuclear reactor core, a plurality of ex-core neutron flux detectors provided along the circumference of the periphery of the nuclear reactor are respectively disposed at three levels (top, middle, and bottom portions) along the axial direction of the core, so that axial power distributions of the nuclear reactor core are synthesized based on ex-core flux detector signals at the three levels measured by the ex-core neutron flux detectors.
As such, a conventional in-core protection system (ICOPS), as disclosed in Korean Patent No. 10-0009517, entitled “METHOD & APPARATUS FOR MONITORING THE AXIAL POWER DISTRIBUTION WITHIN THE CORE OF A NUCLEAR REACTOR EXTERIOR OF THE REACTOR” (Westinghouse Electric Corporation), registered on Mar. 23, 1981, is configured to calculate core-periphery powers at three levels (top, middle, and bottom portions), using ex-core flux detector signals measured by ex-core neutron flux detectors at the periphery of a nuclear reactor, calculate average core-periphery powers at the three levels by reflecting rod shadowing factors (RSFs) based on the calculated core-periphery outputs, and then synthesize 20 axial power distributions using a cubic spline interpolation, based on the calculated average core periphery powers.
That is, in the conventional art disclosed in Korean Patent No. 10-0009517, a plurality of ex-core neutron flux detectors 130 provided along the circumference of the periphery of the nuclear reactor as shown in
Here, the ex-core neutron flux detectors 131, 132, and 133 disposed at the respective levels are spaced apart from the nuclear reactor core at a regular distance, to detect, as shown in
Here, PT, PM, and PB are core-periphery powers at top, middle, and bottom portions of the nuclear reactor core, respectively, LT, LM, and LB are ex-core flux detector signals detected by the ex-core neutron flux detectors disposed at the three levels, i.e., the top, middle, and bottom portions of the periphery of the nuclear reactor, respectively, and Aij is a constant which defines a relationship between the ex-core flux detector signals and the core-periphery powers.
As a result, the constants (Aij) of the SAM are required so as to obtain the core-periphery powers PT, PM, and PB. To this end, in the conventional art, the SAM is determined based on data acquired in a start-up test of the nuclear reactor (i.e., at the beginning of the nuclear fuel period), which is performed at the beginning of every plant operating period. In this case, the core-periphery powers PT, PM, and PB calculated based on the ex-core flux detector signals LT, LM, and LB are compared with the actual core-periphery powers measured by in-core neutron flux detectors (not shown) while the power of the nuclear reactor increases up to 30% to 80%, and the SAM is determined such that the differences between the calculated core-periphery powers and the actual core-periphery powers are minimized.
As such, core-periphery powers of the nuclear reactor core during one plant period are calculated using a SAM determined based on data acquired at the beginning of the period, and average core-periphery powers for the respective nodes are calculated through a correction process such as reflecting RSFs to the calculated core-periphery powers. Then, axial power distributions are synthesized based on the calculated average core-periphery powers for the respective nodes, so that axial power distributions having the same level as the actual core-periphery powers can be continuously synthesized in real time.
However, in the conventional art described above, the SAM was determined based on data acquired at the beginning of a period, and hence a change in power depending on changes in composition and state of nuclear fuel in the nuclear reactor core at the end of the period cannot be properly reflected. Therefore, an error in synthesizing axial power distributions would increase at the end of the period. Further, since the SAM should be newly determined at the beginning of every period, the time required to perform a start-up test of the nuclear reactor increases. For this reason, the efficiency of the nuclear power plant is lowered.
Accordingly, the present invention is conceived to solve the aforementioned problems in the prior art. An object of the present invention is to provide a method of synthesizing axial power distributions of a nuclear reactor core using a neural network circuit and an in-core protection system (ICOPS) using the same, in which using the neural network circuit including an input layer, an output layer, and at least one hidden layer, each layer being configured with at least one node, each node of one layer being connected to nodes of the other layers, node-to-node connections being made with connection weights varied based on a learning result, optimum connection weights between the respective nodes constituting the neural network circuit are determined through learning based on various core design data applied to the design of a nuclear reactor core of a nuclear power plant, and axial power distributions of the nuclear reactor core are synthesized based on ex-core flux detector signals measured by ex-core neutron flux detectors during operation of a nuclear reactor, so that the initial time required to perform a start-up test of the nuclear reactor can be reduced since basic data for synthesizing axial power distributions need not be separately measured in the start-up test of the nuclear reactor contrary to a conventional ICOPS, thereby improving the economic efficiency of the nuclear power plant, and so that overall nuclear reactor core design data can be used rather than actual measurement data in the start-up test (i.e., at the beginning of a period of nuclear fuel), thereby more accurately replicating axial power distributions of the nuclear reactor core throughout the overall period of the nuclear fuel.
According to an aspect of the present invention for achieving the objects, there is provided a method of synthesizing axial power distributions of a nuclear reactor core using a neural network circuit, which is applied to an ICOPS for controlling the operation of a nuclear reactor based on ex-core flux detector signals measured by ex-core neutron flux detectors, wherein the neural network circuit includes an input layer configured to receive ex-core flux detector signals measured by the ex-core neuron flux detectors; an output layer configured to output a core average power for each node calculated through the neural network circuit; and at least one hidden layer interposed between the input layer and the output layer to connect the two layers to each other, wherein each of the input, output, and hidden layers is configured with at least one node, each node of one layer being connected to nodes of the other layers, node-to-node connections being made with connection weights varied based on a learning result, so that optimum connection weights between the respective nodes constituting the neural network circuit are determined through repetitive learning based core design core design data applied to the design of the nuclear reactor core of a nuclear power plant.
The above and other objects, features and advantages of the present invention will become apparent from the following description of a preferred embodiment given in conjunction with the accompanying drawings, in which:
Hereinafter, exemplary embodiments of the present invention will be described in detail with reference to the accompanying drawings. Throughout the drawings, like reference numerals are used to designate like elements.
Referring to
In other words, a method of synthesizing axial power distributions of a nuclear reactor core using a neural network circuit and an ICOPS using the same according to the present invention have advantages in that using the neural network circuit including an input layer, an output layer, and at least one hidden layer, each layer being configured with at least one node, each node of one layer being connected to nodes of the other layers, node-to-node connections being made with connection weights varied based on a learning result, optimum connection weights between the respective nodes constituting the neural network circuit are determined through learning based on various core design data applied to the design of a nuclear reactor core of a nuclear power plant, and axial power distributions of the nuclear reactor core are synthesized based on ex-core flux detector signals measured by ex-core neutron flux detectors during operation of a nuclear reactor, so that the initial time required to perform a start-up test of the nuclear reactor can be reduced since basic data for synthesizing axial power distributions need not be separately measured in the start-up test of the nuclear reactor contrary to a conventional ICOPS, thereby improving the economic efficiency of the nuclear power plant, and so that overall nuclear reactor core design data can be used rather than actual measurement data in the start-up test (i.e., at the beginning of a period of nuclear fuel), thereby more accurately replicating axial power distributions of the nuclear reactor core throughout the overall period of the nuclear fuel.
Hereinafter, a method of synthesizing axial power distributions of a nuclear reactor core using a neural network circuit and an ICOPS using the same according to the present invention will be described in detail for each step based on the flowchart of
The ICOPS according to the present invention is configured such that a plurality of ex-core neutron flux detectors 130 (see
In this case, the ex-core neutron flux detectors 131, 132, and 133 disposed at the respective levels are spaced apart at from the nuclear reactor core a regular distance, to detect not only neutrons radiated from a corresponding level of the nuclear reactor core but also neutrons radiated from the other levels of the nuclear reactor core. Therefore, the calculated core-periphery power at the corresponding level is different from an actual core-periphery power at the corresponding level.
In order to solve this, in the present invention, using a neural network circuit configured to include an input layer, an output layer, and at least one hidden layer, each layer being configured with at least one node, each node of one layer being connected to nodes of the other layers, node-to-node connections being made with connection weights varied based on a learning result, core average powers for the respective nodes are calculated based on ex-core flux detector signals measured by the ex-core neutron flux detectors 131, 132, and 133, thereby synthesizing axial power distributions of the core.
As shown in
In this case, in order to synthesize axial power distributions through learning of the neural network, it is required to determine the number of nodes LDi, the number of nodes Hj, and the number of nodes PDk (S110). The numbers of the input and output layer nodes LDi, and PDk are naturally determined according to the number of ex-core neutron flux detectors and the number of core average power nodes to be sought so as to synthesize axial power distributions of the core. However, the number of hidden layer nodes Hj is determined through user's experiences and repetitive experiments. As the number of hidden layer nodes Hj increases, the difference between a core average power of the output layer and an actual core average power decreases. However, the processing speed decreases, and therefore, it is required to optimize the number of nodes Hj of the hidden layer.
That is, the input layer is a layer which receives, as input values, three ex-core flux detector signals measured by ex-core neutron flux detectors (D1, D2, and D3 of
The hidden layer is a layer which connects the hidden layer and the input layer to each other between the two layers, and at least one hidden layer may be added between the input layer and the output layer. In the present invention, one hidden layer is used. In the case of the hidden layer node Hj, it is appropriate as the result of repetitive experiments that the number of hidden layer nodes is set to 10 to 20. In this embodiment, the hidden layer is configured with 15 hidden layer nodes H1 to H15.
Here, the input layer and the hidden layer may be configured to additionally include one bias node B having a bias value when necessary. The numbers of the input, hidden, and output layer nodes LDi, Hj, and PDk are not limited to those proposed in this embodiment. It will be apparent that the numbers of the input, hidden, and output nodes LDi, Hj, and PDk may be properly selected and used according to the structure of the nuclear reactor or the processing speed of a neural network circuit system and the accuracy of a power value to be sought.
If the numbers of the input, hidden, and output layer nodes LDi, Hj, and PDk are determined, the neural network circuit is learned using various core design data (i.e., all data at the beginning, middle, and end of a period of loaded nuclear fuel) applied to the design of the nuclear reactor core of the nuclear power plant, thereby determining optimum connection weights between the respective nodes (S120).
In this case, a BP algorithm is used for learning of the neural network circuit. The BP algorithm, as shown in
First, arbitrary numbers randomly selected in an arbitrary section (in this embodiment, it is set to select arbitrary numbers in section [−2, 2]) are set to initial connection weights Wij and Wjk. A value of the hidden layer node Hj is calculated using, as input values of the input layer node LDi, the set initial connection weight Wij between the input layer and the hidden layer and an ex-core flux detector signal detected by the ex-core neutron flux detector, which is included in the design data. A value of the output layer node PDk is calculated based on the calculated value of the hidden layer node Hj and the initial connection weight Wjk between the hidden layer and the output layer.
The value of the output layer node PDk calculated as described above is compared with a true value for each node (here, an actual core average power based on a corresponding ex-core flux detector signal, which is included in the design data), thereby calculating an error.
Next, in order to update the respective connection weights Wij and Wjk such that the calculated error can be minimized, the calculated error is partially differentiated using the connection weight Wjk between the hidden layer and the output layer, thereby calculating a change ratio of the connection weight Wjk between the hidden layer and the output layer with respect to the error. Also, the error is partially differentiated using the connection weight Wij between the input layer and the hidden layer, thereby calculating a change ratio of the connection weight Wij between the input layer and the hidden layer with respect to the error.
Thereafter, the connection weight Wjk between the hidden layer and the output layer and the connection weight Wij between the input layer and the hidden layer are updated in the opposite direction of a change ratio having influence on the error, based on the respective calculated change ratios of the connection weights, and the above-described process is repeatedly performed on a set of various design data (i.e., ex-core flux detector signals and core average power data corresponding thereto) applied to the design of the nuclear reactor core, thereby calculating a performance index of a learning result value from a difference between a core average power value obtained from the neural network circuit and an actual core average power value shown in the design data. When the calculated performance index is equal to or smaller than a previously set measurement limit value, the BP algorithm is considered to converge, and the learning using the BP algorithm is finished, thereby optimizing the connection weights Wij and Wjk among the respective nodes LDi, Hj, and PDk.
Here, the hidden layer node and the output layer node except for the bias node and the input layer node have a differentiable active function (generally, a sigmoid or hyperbolic tangent function is frequently used) for the purpose of learning, and values of the hidden layer node Hj and the output layer node PDk are calculated by the following Equations 2 and 3. Accordingly, the performance index of the learning result value can be obtained from the following Equation 4.
Here, Hj is a value of a jth hidden layer node, n is the number of input layer nodes except for the bias node, Wi,j is a connection weight (weight value) between an ith input layer node and the jth hidden layer node, LDi is a value of the ith input layer node, B is the bias node, and a(x) is an active function of the hidden layer node.
Here, PDk is a value of a kth output layer node, n is the number of hidden layer nodes except for a bias node, Wj,k is a connection weight (weight value) between the jth hidden layer node and the kth output layer node, Hj is a value of the jth hidden layer node, B is the bias node, and a(x) is an active function of the output layer node.
Here, L and M are node numbers used in error calculation, where the calculation is being performed from Mth node to Lth node, oij is a calculation result value of the neural network circuit at a jth node at ith test case, tj is a true value at the jth node, and N is the number of test cases used in learning.
It should be noted that in the learning of the neural network circuit through the BP algorithm described above, the error between the true value and the result value calculated through the neural network circuit does not converge on a global minimum value but converges on a local minimum value according to the arbitrarily selected initial connection weight, and therefore, an optimum connection weight where an actual error is minimized may not be found.
In order to solve such a problem, in the present invention, an SA method is applied together with the BP algorithm in the learning of the neural network circuit for synthesizing axial power distributions, thereby more accurately synthesizing axial power distributions.
Here, the SA method, which is a probabilistic search algorithm which enables to search over the entire region of a solution space, is a technique technologically applying a process of finally stabilizing a metal into a crystal form having the minimum energy when the metal in a liquid state is cooled down through an annealing process. The SA method performs the global optimization by repeating a process of probabilistically determining a new solution from a current solution.
One of important features of the SA method is that it is possible to transfer the current solution to a solution having a cost function value inferior to the current solution. As shown in
The SA method described above is a general probabilistic meta algorithm with respect to a global optimization issue. The SA method is a method applied in various fields so as to derive an optimum solution in a process of deriving a convergence value. In this specification, detailed description of the SA method will be omitted.
Subsequently, if the optimum connection weights Wij and Wjk between the respective nodes are determined through the above-described process, core average powers for the respective nodes are calculated based on the ex-core flux detector signals measured by the ex-core neutron flux detectors D1, D2, and D3 during the operation of the nuclear reactor, using the neural network circuit (S130), and axial power distributions of the nuclear reactor core are synthesized based on the calculated core average powers for the respective nodes (S140).
As described above, according to the present invention, using a neural network circuit configured to include an input layer, an output layer, and at least one hidden layer, each layer being configured with at least one node, each node of one layer being connected to nodes of the other layers, node-to-node connections being made with connection weights varied based on a learning result, optimum connection weights between the respective nodes constituting the neural network circuit are determined through learning based on various core design data applied to the design of a nuclear reactor core of a nuclear power plant, and axial power distributions of the nuclear reactor core are synthesized based on ex-core flux detector signals measured by ex-core neutron flux detectors during operation of a nuclear reactor, so that the initial time required to perform a start-up test of the nuclear reactor can be reduced since basic data for synthesizing axial power distributions need not be separately measured in the start-up test of the nuclear reactor contrary to a conventional ICOPS, thereby improving the economic efficiency of the nuclear power plant, and so that overall nuclear reactor core design data can be used rather than actual measurement data in the start-up test (i.e., at the beginning of a period of nuclear fuel), thereby more accurately replicating axial power distributions of the nuclear reactor core throughout the overall period of the nuclear fuel.
Further, in the present invention, axial core average powers of the nuclear reactor core can be directly calculated through the neural network circuit, based on ex-core flux detector signals measured by three ex-core neutron flux detectors, so that it is possible to more simply synthesize axial power distributions of the nuclear reactor core based on the ex-core flux detector signal, without calculating separate core-periphery powers.
The scope of the present invention is not limited to the embodiment described and illustrated above but is defined by the appended claims. It will be apparent that those skilled in the art can make various modifications and changes thereto within the scope of the invention defined by the claims. Therefore, the true scope of the present invention should be defined by the technical spirit of the appended claims.
While illustrative embodiments have been illustrated and described, it will be appreciated that various changes can be made therein without departing from the spirit and scope of the invention.
| Number | Date | Country | Kind |
|---|---|---|---|
| 10-2014-0184557 | Dec 2014 | KR | national |
