Method for establishing chf relationship based on artificial intelligence
By simulating CHF experiments on reactor fuel assemblies and using a symbolic regression model, a CHF relationship that conforms to physical laws was constructed and screened out, solving the problem of inaccurate CHF prediction in existing technologies and realizing a simple and interpretable CHF prediction method.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- SHANGHAI NUCLEAR ENGINEERING RESEARCH & DESIGN INSTITUTE CO LTD
- Filing Date
- 2026-02-24
- Publication Date
- 2026-05-15
AI Technical Summary
Existing technologies struggle to establish a critical heat flux (CHF) relationship that can both uncover complex nonlinear patterns between data and output a concise, explicit, and physically consistent formula, especially lacking accurate CHF prediction methods in nuclear reactors.
CHF (Chicken-Fluid Content) experiments were conducted on simulated reactor fuel assemblies to construct a CHF database. Multiple candidate CHF relationships were established using a symbolic regression model, and the target CHF relationship was selected through physical behavior verification to ensure that it is concise, explicit, and physically interpretable.
A method for accurately predicting CHF in nuclear reactors has been developed, outputting an explicit mathematical expression with physical interpretability, applicable to nuclear engineering procedures, and improving prediction accuracy and physical plausibility.
Smart Images
Figure CN121706434B_ABST
Abstract
Description
Technical Field
[0001] This application mainly relates to the field of nuclear reactor technology, and in particular to a method for establishing CHF relations based on artificial intelligence. Background Technology
[0002] Critical heat flux (CHF) is of great significance in nuclear engineering, especially in light water reactor systems. CHF is one of the key parameters in reactor thermal-hydraulic analysis, and establishing an accurate formula for predicting CHF is a core task in the development, optimization, and safety analysis of new fuel assemblies.
[0003] Currently, methods for establishing CHF (Chemical, Chemical, and Fault) relationships include mechanistic modeling, empirical formula fitting, lookup table methods, and data-driven AI prediction methods. However, mechanistic modeling relies on fundamental theories of thermodynamics and fluid mechanics. Due to the complex geometry and flow heat transfer phenomena of rod bundle channels, especially the geometric and multi-physics coupling phenomena in irregularly shaped reactors, existing theories struggle to accurately describe these complex mechanisms. Empirical formula fitting methods depend on pre-defined formula structures, thus their prediction accuracy is affected by human factors and they struggle to uncover complex nonlinear relationships between data. Lookup table methods rely on large amounts of experimental data, and their applicability is limited by experimental conditions and data coverage. Furthermore, their accuracy and stability decrease significantly when experimental data is scarce. Data-driven AI prediction methods are essentially black-box models, unable to output explicit mathematical expressions, lacking physical interpretability, and these large models are difficult to port to existing nuclear engineering system programs.
[0004] Therefore, there is an urgent need in this field for a method to establish CHF relations that can both uncover the complex nonlinear patterns between data and establish simple, explicit mathematical relations that conform to physical laws. Summary of the Invention
[0005] The technical problem to be solved by this application is to provide a method for establishing CHF relations based on artificial intelligence, which can use artificial intelligence technology to mine complex patterns between data and further establish CHF relations that are concise, explicit and physically interpretable.
[0006] To address the aforementioned technical problems, this application provides a method for establishing CHF relationships based on artificial intelligence, comprising: step S1, conducting CHF tests using CHF test specimens simulating reactor fuel assemblies to obtain CHF test data; step S2, constructing a CHF database based on the CHF test data, the CHF database including a first parameter set and actual CHF values corresponding to the first parameter set; step S3, constructing a mathematical correlation between the first parameter set and the actual CHF values; step S4, processing the first parameter set according to the thermal-hydraulic mechanism to obtain a second parameter set, the second parameter set including a dimensionless ratio combination of the first parameter set, and a dimensionless combination of the operating parameters of the heat exchange medium in the reactor fuel assembly and the first parameter set; step S5, establishing multiple candidate CHF relationships using a symbolic regression model, the grammatical element set of the symbolic regression model including the second parameter set and the mathematical correlation; and step S6, selecting a target CHF relationship from the multiple candidate CHF relationships, wherein the target CHF relationship satisfies: the calculated loss function value is less than a first preset threshold and the physical trend is consistent with the CHF test data.
[0007] In one embodiment of this application, the CHF test specimen has the same geometry as the reactor fuel assembly, wherein the geometry includes grid pitch, channel size, fuel rod arrangement and rod diameter.
[0008] In one embodiment of this application, the step of constructing a CHF database based on the CHF test data includes: processing the CHF test data using a subchannel program to extract local thermo-hydraulic parameters within the flow channel of the CHF test specimen; constructing an initial first parameter set based on the local thermo-hydraulic parameters and the geometry of the CHF test specimen, wherein the initial first parameter set includes parameters that affect CHF; calculating the correlation between the parameters in the initial first parameter set and the actual CHF value, deleting parameters in the initial first parameter set whose correlation is less than a second preset threshold to obtain the first parameter set; and establishing the CHF database based on the first parameter set and the actual CHF value corresponding to the first parameter set.
[0009] In one embodiment of this application, the first parameter group includes geometric parameters, flow parameters, and thermodynamic parameters. The geometric parameters include the length, diameter, and spacing between the simulated fuel rods. The flow parameters include the local mass flow rate and local gas content. The thermodynamic parameters include pressure and inlet enthalpy.
[0010] In one embodiment of this application, the step of constructing a mathematical correlation between the first parameter set and the actual CHF value includes: constructing the mathematical correlation based on physical laws and mathematical regression analysis, wherein the actual CHF value and the local gas content show a linear correlation trend in the mathematical correlation.
[0011] In one embodiment of this application, the second parameter set includes the ratio of the length to the diameter of the simulated fuel rod, the ratio of the diameter to the spacing between the simulated fuel rods, the Reynolds number characterizing the flow characteristics, and the Weber number characterizing the interface characteristics of the two-phase flow.
[0012] In one embodiment of this application, the step of establishing multiple candidate CHF relations using a symbolic regression model includes: setting the set of grammatical elements, wherein the set of operators of the set of grammatical elements includes the mathematical correlation and basic mathematical operators, and the terminal set includes at least some parameters in the first parameter set and the second parameter set; setting the structural constraints of the symbolic regression model; inputting the second parameter set, at least some parameters in the first parameter set, and the actual CHF values corresponding to the first parameter set into the symbolic regression model; and generating multiple candidate CHF relations with the optimization objective of minimizing prediction error and formula complexity.
[0013] In one embodiment of this application, the step of selecting a target CHF relation from the plurality of candidate CHF relations includes: performing physical behavior verification on the plurality of candidate CHF relations, eliminating the candidate CHF relations that fail the physical behavior verification, and retaining the candidate CHF relations that pass the physical behavior verification, wherein the physical behavior verification includes determining whether the mathematical validity, physical dimension consistency, generalization rationality, and physical monotonicity of the plurality of candidate CHF relations conform to physical laws.
[0014] In one embodiment of this application, the target CHF relation is the candidate CHF relation with the smallest loss function value.
[0015] In one embodiment of this application, the method further includes: an evaluation step of the target CHF relation, wherein the evaluation step includes: calculating the DNBR limit using a subchannel program and the target CHF relation, determining whether the DNBR limit satisfies the condition of being higher than the safety limit under 95 / 95 conditions; if not, returning to step S5 and adjusting the parameters of the symbolic regression model.
[0016] Compared with the prior art, this application has the following advantages:
[0017] (1) By using artificial intelligence technology to mine the complex patterns between data, and generating a variety of candidate CHF relational expressions based on CHF experimental data, the candidate CHF relational expressions are concise, explicit and physically interpretable;
[0018] (2) Compared with traditional artificial intelligence methods, this application can output explicit mathematical expressions and has physical interpretability, so that nuclear engineering programs can directly use the output mathematical expressions to predict CHF without having to port the huge model to the nuclear engineering program.
[0019] (3) Compared with traditional empirical expression fitting methods, this application does not require a fixed formula structure and can uncover complex patterns between data. Attached Figure Description
[0020] The accompanying drawings are included to provide a further understanding of this application; they are incorporated into and constitute a part of this application. The drawings illustrate embodiments of this application and, together with this specification, serve to explain the principles of this application. In the drawings:
[0021] Figure 1 This is a flowchart illustrating a method for establishing CHF relationships based on artificial intelligence in one embodiment of this application;
[0022] Figure 2 This is a schematic diagram of the process of constructing a CHF database in one embodiment of this application;
[0023] Figure 3 This is a flowchart illustrating a method for establishing candidate CHF relationships using a symbolic regression model in one embodiment of this application.
[0024] Figure 4 This is a schematic diagram of the structure of an electronic device according to an embodiment of this application. Detailed Implementation
[0025] To more clearly illustrate the technical solutions of the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are merely some examples or embodiments of this application. For those skilled in the art, these drawings can be applied to other similar scenarios without creative effort. Unless obvious from the context or otherwise specified, the same reference numerals in the drawings represent the same structures or operations.
[0026] As indicated in this application and claims, unless the context clearly indicates otherwise, the words "a," "an," "an," and / or "the" are not specifically singular and may include plural forms. Generally speaking, the terms "comprising" and "including" only indicate the inclusion of explicitly identified steps and elements, which do not constitute an exclusive list, and the method or apparatus may also include other steps or elements.
[0027] Unless otherwise specifically stated, the relative arrangement, numerical expressions, and values of the components and steps described in these embodiments do not limit the scope of this application. It should also be understood that, for ease of description, the dimensions of the various parts shown in the drawings are not drawn to actual scale. Techniques, methods, and devices known to those skilled in the art may not be discussed in detail, but where appropriate, such techniques, methods, and devices should be considered part of the specification. In all examples shown and discussed herein, any specific values should be interpreted as merely exemplary and not as limitations. Therefore, other examples of exemplary embodiments may have different values. It should be noted that similar reference numerals and letters in the following drawings denote similar items; therefore, once an item is defined in one drawing, it need not be further discussed in subsequent drawings.
[0028] Furthermore, it should be noted that the use of terms such as "first" and "second" to define components is merely for the purpose of distinguishing the corresponding components. Unless otherwise stated, these terms have no special meaning and therefore should not be construed as limiting the scope of protection of this application. In addition, although the terminology used in this application is selected from commonly known and used terms, some terms mentioned in this application's specification may have been chosen by the applicant according to his or her judgment, and their detailed meanings are explained in the relevant sections of this description. Moreover, this application should be understood not only through the actual terms used, but also through the meaning implied by each term.
[0029] Flowcharts are used in this application to illustrate the operations performed by the system according to embodiments of this application. It should be understood that the preceding or following operations are not necessarily performed in exact order. Instead, various steps can be processed in reverse order or simultaneously. Furthermore, other operations may be added to these processes, or one or more steps may be removed from these processes.
[0030] The following specific examples illustrate the method for establishing CHF relationships based on artificial intelligence in this application.
[0031] refer to Figure 1 The flowchart shown in one embodiment illustrates a method for establishing CHF relations based on artificial intelligence. The method for establishing CHF relations includes... Figure 1Steps S1 to S6 are described in detail below.
[0032] In step S1, CHF tests are conducted using CHF test specimens that simulate reactor fuel assemblies to obtain CHF test data.
[0033] Specifically, CHF test specimens simulating reactor fuel assemblies typically refer to specialized CHF test specimens designed in scale or full-size configurations based on the geometry and material properties of reactor fuel assemblies to simulate their actual operating conditions. Under laboratory conditions, CHF test specimens can simulate the flow and heat transfer processes of the heat exchange medium within the reactor fuel assembly under real operating conditions to determine the CHF value. For example, CHF test specimens include components such as simulated fuel rods (e.g., using heating rods instead of fuel rods), positioning grids, and flow channel shells, simulating the actual operating conditions in the reactor core by controlling the test conditions. However, it can be understood that any CHF test specimen capable of simulating the actual operating conditions of a reactor fuel assembly is a CHF test specimen simulating a reactor fuel assembly.
[0034] In some embodiments, the CHF test specimen has the same geometry as the reactor fuel assembly, including grid pitch, channel dimensions, fuel rod arrangement, and rod diameter, to simulate the actual operating conditions of the reactor fuel assembly. For example, the CHF test specimen has the same grid pitch, channel dimensions, simulated fuel rod arrangement, and rod diameter as the reactor fuel assembly.
[0035] In this step, CHF tests are conducted under various test conditions to obtain corresponding CHF test data under different test conditions. As an example, CHF test conditions include combinations of different pressures, temperatures, and flow rates, with pressure ranges from 5.8 MPa to 16.87 MPa, temperature ranges from 54.2℃ to 298.3℃, and flow rate ranges from 200 kg / m³. 2 ·s~1300kg / m 2 CHF tests were conducted under different combinations, for example, at a pressure of 6 MPa, a temperature of 56 °C, and a flow rate of 200 kg / m³. 2 CHF tests were conducted under the test conditions of ·s, and the CHF test data measured under this combination were recorded.
[0036] In step S2, a CHF database is constructed based on the CHF test data. The CHF database includes a first parameter group and the actual CHF values corresponding to the first parameter group.
[0037] As an example, such as Figure 2 As shown, the steps for constructing a CHF database based on CHF experimental data include: Figure 2Steps S21 to S24 are described in detail below.
[0038] In step S21, a subchannel program is used to process the CHF test data and extract the local thermo-hydraulic parameters within the flow channels of the CHF test specimen. Specifically, based on the CHF test data obtained in step S1, the thermo-hydraulic parameters at the burnout (BO) point are calculated using the subchannel program. For example, the subchannel program includes mass, energy, and momentum integral balance equations to jointly simulate the flow and heat transfer process of the heat exchange medium inside the CHF test specimen. The mass integral balance equation is:
[0039]
[0040] In the formula, For fluid density, To control the area, Let be the fluid surface area. It is a velocity vector. It is the unit vector of the surface outward normal.
[0041] The energy integral balance equation is:
[0042]
[0043] In the formula, For fluid density, To control the area, Let be the fluid surface area. It is a velocity vector. The surface outward normal unit vector, For enthalpy, For heat flux density, Internal heat source per unit mass.
[0044] The momentum integral equilibrium equation is:
[0045]
[0046] In the formula, For fluid density, In order to control the area, Let be the fluid surface area. It is a velocity vector. The surface outward normal unit vector, It is the acceleration due to gravity. For pressure, The surface area of the solid wall. It is the viscous stress tensor.
[0047] Solving the aforementioned integral balance equations of mass, energy, and momentum yields the thermo-hydraulic parameters at the burn-out point. For example, the thermo-hydraulic parameters at the burn-out point include pressure, enthalpy, and the velocity vector of the heat exchange medium.
[0048] In some embodiments, local thermal-hydraulic parameters include pressure, inlet enthalpy, local gas content of the heat exchange medium, and local mass flow rate.
[0049] In step S22, an initial first parameter set is constructed based on the local thermal-hydraulic parameters and the geometry of the CHF test specimen. The initial first parameter set includes parameters that affect CHF.
[0050] In a nuclear reactor, thermohydraulic parameters represent the flow and thermodynamic state of the system during operation, while geometry provides the physical space and boundary conditions for flow and heat transfer processes. Both together influence the reactor's thermal safety. The initial first parameter set includes parameters that affect CHF (Chemical Heat Failure). Therefore, combining local thermohydraulic parameters and the geometry of the CHF test specimen as the initial first parameter set fully considers various parameters that may affect the CHF value. For example, the initial first parameter set includes geometric parameters, flow parameters, and thermodynamic parameters. Geometric parameters include the length, diameter, and spacing between simulated fuel rods; flow parameters include local mass flow rate and local gas holdup; and thermodynamic parameters include pressure and inlet enthalpy.
[0051] In step S23, the correlation between the parameters in the initial first parameter group and the actual CHF value is calculated, and parameters in the initial first parameter group whose correlation is less than the second preset threshold are deleted to obtain the first parameter group.
[0052] Specifically, if the correlation between a parameter in the initial first parameter group and the actual CHF value is not less than the second preset threshold, then that parameter may be a factor influencing the CHF value; if the correlation between a parameter in the initial first parameter group and the actual CHF value is less than the second preset threshold, then that parameter may be noise affecting the CHF value. Therefore, by calculating the correlation and deleting parameters in the initial first parameter group whose correlation is less than the threshold, a first parameter group consisting of the remaining parameters in the initial first parameter group is obtained, thereby selecting the first parameter group for subsequent establishment of the CHF relationship. The second preset threshold is based on the statistical significance level of the correlation between the initial first parameter group and the actual CHF value, and the weighting of the parameters in the initial first parameter group on the actual CHF value; for example, the second preset threshold is set to 0.05.
[0053] In some embodiments, the correlation coefficient between each parameter in the initial first parameter group and the actual CHF value is calculated to perform a correlation test. This correlation coefficient represents the correlation between each parameter and the CHF value; a larger correlation coefficient indicates a higher correlation between the parameter and the CHF value.
[0054] For example, calculate the Pearson correlation coefficient between each parameter in the initial first parameter group and the actual CHF value. The calculation formula is as follows:
[0055]
[0056] In the formula, For one of the parameters in the initial first parameter group, This is the actual CHF value. This is the standard deviation of the parameter. The standard deviation of the CHF value. The covariance between this parameter and the actual CHF value. This is the correlation coefficient between this parameter and the actual value of CHF.
[0057] In some embodiments, the first parameter set includes geometric parameters, flow parameters, and thermodynamic parameters, wherein the geometric parameters include the length of the simulated fuel rod (denoted as ). ), the diameter of the simulated fuel rod (denoted as ), ), simulated fuel rod spacing (denoted as ), ), flow parameters include local mass flow rate (denoted as ), ) and local gas content (denoted as Thermodynamic parameters include pressure (denoted as ), ) and entrance enthalpy (denoted as ).
[0058] In step S24, a CHF database is established based on the first parameter group and the actual CHF values corresponding to the first parameter group.
[0059] In practical implementation, local thermal-hydraulic parameters are obtained by processing the CHF test results through the aforementioned step S21. Under the constraints of each set of local thermal-hydraulic parameters and the geometry of the CHF test specimen used in the test, there is a unique corresponding actual CHF value. Subsequently, each parameter in the first parameter group selected in steps S22 and S23 is used as a field of the data record and associated with the corresponding actual CHF value, thereby forming a structured CHF database. For example, as shown in Table 1, the CHF database can be designed to include "sample ID", "rod length", etc. "Bar diameter" "Bar spacing" "Local mass flow rate" ","pressure ”, “entrance enthalpy The system includes fields such as "CHF actual value" and supports functions such as querying and updating data. The "sample ID" is a unique identifier for each data entry.
[0060] Table 1: Field table of an exemplary CHF database.
[0061]
[0062] It is understandable that the CHF database provides real experimental data, establishes a correspondence between the first parameter set and the actual CHF values, and can support data calls for subsequent steps (such as establishing the second parameter set, model training, and relational fitting) to improve the accuracy and efficiency of establishing CHF relations.
[0063] Continue to refer to Figure 1 In step S3, a mathematical correlation is established between the first parameter set and the actual CHF value.
[0064] In this step, by constructing the mathematical correlation between the parameters in the first parameter group and the actual CHF value, a preset relational operator that conforms to physical laws and data patterns can be provided for subsequent steps (including step S5), thereby improving the convergence efficiency and physical rationality of establishing the relation.
[0065] In some embodiments, step S3 includes: constructing a mathematical correlation based on physical laws and mathematical regression analysis, wherein the actual CHF value shows a linear correlation with the local gas content. As the gas content increases, the proportion of gas phase in the fluid increases, causing the liquid film that was originally cooled against the wall to continuously thin due to violent evaporation and airflow shearing, or making it easier for bubbles on the wall to coalesce into a film due to the decreased mainstream condensation capacity; this makes it increasingly difficult to replenish the liquid required to maintain nucleate boiling. At this point, only a lower heat flux density is needed to "deplete" or "isolate" the last layer of liquid phase on the wall, thereby triggering heat transfer deterioration, and thus reducing CHF. It can be understood that, in addition to constructing a mathematical correlation based on physical laws in the above example, a mathematical correlation can also be constructed by using mathematical regression analysis to determine the mathematical variation (or mathematical statistical law) between the parameters in the first parameter group and the actual CHF value.
[0066] In step S4, the first parameter group is processed according to the thermal-hydraulic mechanism to obtain the second parameter group. The second parameter group includes the dimensionless ratio combination of the first parameter group and the dimensionless combination of the operating parameters of the heat exchange medium in the reactor fuel assembly with the first parameter group.
[0067] Specifically, firstly, based on the mechanism of thermal hydraulics, the parameters in the first parameter group are combined in the form of dimensionless ratios, and the combination is used as one of the parameters in the second parameter group. For example, the first parameter group includes the length of the simulated fuel rod (expressed as...). ) and bar diameter (expressed as The length and diameter of the simulated fuel rods are combined in the form of dimensionless ratios to obtain the length-to-diameter ratio combination (expressed as...). This combination is used as the parameter in the second parameter group.
[0068] Next, based on the thermo-hydraulic mechanism, the operating parameters of the heat exchange medium are combined with the first parameter set in a dimensionless form, and this combination is used as one of the parameters in the second parameter set. For example, the operating parameters of the heat exchange medium and the first parameter set include the length of the simulated fuel rod (denoted as...). ), the velocity scalar of the heat exchange medium (expressed as) ), fluid density (expressed as ) and dynamic viscosity (expressed as The Reynolds number (expressed as ) is obtained by combining the rod length, fluid density, dynamic viscosity, and surface tension coefficient in a dimensionless form. This combination will be used as the parameter in the second parameter group.
[0069] It should be noted that not all parameters in the first parameter group can be combined according to the thermo-hydraulic mechanism. Therefore, in actual processing, not all parameters in the first parameter group are combined in dimensionless form and used as parameters in the second parameter group. In some embodiments, the parameters in the second parameter group are obtained by combining some parameters from the first parameter group.
[0070] In some embodiments, the operating parameters of the heat exchange medium include the physical properties of the heat exchange medium, such as the fluid density, dynamic viscosity, and surface tension coefficient of the heat exchange medium.
[0071] The second set of parameters obtained in this step can provide the parameters needed to establish the CHF relationship for the model in subsequent steps (such as the symbolic regression model in step S5), thereby better reflecting the characteristics of the flow field development.
[0072] In some embodiments, the second parameter set includes the ratio of the simulated fuel rod length to its diameter (expressed as...). The ratio of the diameter of the simulated fuel rods to the spacing between the rods (expressed as...) ), and the Reynolds number (denoted as ), which characterizes the flow properties. ) and the Weber number (denoted as ) which characterizes the interfacial properties of two-phase flow. ), where the Reynolds number is expressed as:
[0073]
[0074] In the formula, The fluid density of the heat exchange medium. For the velocity scalar of the heat exchange medium, To simulate the length of fuel rods, The dynamic viscosity of the heat exchange medium;
[0075] The Weber number is represented as:
[0076]
[0077] In the formula, The fluid density of the heat exchange medium. For the velocity scalar of the heat exchange medium, To simulate the length of fuel rods, is the surface tension coefficient of the heat exchange medium.
[0078] In step S5, a symbolic regression model is used to establish multiple candidate CHF relations. The grammatical element set of the symbolic regression model includes the second parameter set and mathematical correlation relations.
[0079] In specific implementation, such as Figure 3 As shown, the method for establishing multiple candidate CHF relationships using a symbolic regression model includes the following steps.
[0080] In step S31, a set of grammar elements is defined, wherein the set of operators in the grammar element set includes mathematical correlations and basic mathematical operators, and the terminal set includes at least some parameters from the first parameter set and the second parameter set. In the symbolic regression model, the set of grammar elements refers to the set of functions and terminals provided to the symbolic regression model for searching and combining, used to construct and evolve candidate CHF relations, wherein basic mathematical operators include addition, subtraction, multiplication, division, exponentiation, logarithm, etc. In some embodiments, since the parameters in the second parameter set obtained in step S4 are combinations of some parameters from the first parameter set, the terminal set includes the uncombined parameters from the first parameter set and the second parameter set.
[0081] In step S32, structural constraints are set for the symbolic regression model. Specifically, structural constraints are set for the candidate CHF relations constructed by the symbolic regression model. For example, the maximum depth of the candidate CHF expressions is limited to 6 layers to prevent the generated candidate CHF relations from becoming too complex and overfitting.
[0082] In step S33, the second parameter set, at least some parameters from the first parameter set, and the actual CHF values corresponding to the first parameter set are input into the symbolic regression model. As an example, the second parameter set includes the ratio of the simulated fuel rod length to its diameter, the ratio of the simulated fuel rod diameter to its spacing, the Reynolds number, and the Weber number. The uncombined parameters in the first parameter set include pressure and inlet enthalpy. Based on the CHF database constructed in step S2, each set of the aforementioned parameters has a corresponding actual CHF value. Each set of the aforementioned parameters and the corresponding actual CHF value are input into the symbolic regression model, and iterative evolution is performed through genetic operations such as population initialization, tournament selection, mutation, and recombination. During the evolution process, a Pareto optimization strategy is used for optimization.
[0083] In step S34, multiple candidate CHF relational expressions are generated with the optimization objective of minimizing prediction error and formula complexity. Specifically, a loss function is set based on the prediction error and formula complexity. During the optimization process based on this loss function, the prediction error and formula complexity are minimized. The prediction error refers to the error between the actual CHF value and the CHF prediction value obtained from the relational expression constructed by the model. The formula complexity refers to the structural complexity of the relational expression constructed by the model. In some embodiments, the prediction error is the mean squared error (MSE), whose formula is:
[0084]
[0085] In the formula, The total amount of data input in step S33. This is the actual CHF value. This is the predicted value for CHF.
[0086] The number of nodes in the population tree structure (i.e., a relational data structure representation) is used as a quantification of formula complexity. The formula for the loss function is:
[0087]
[0088] In the formula, For loss, Mean square error, For the formula complexity, This is the regularization coefficient. In practice, the regularization coefficient can be set according to the actual situation.
[0089] Based on the aforementioned loss function and Pareto optimization strategy, a series of candidate CHF relations located at the Pareto front are constructed.
[0090] It should be noted that symbolic regression models are not the focus of this application. Their model architecture and implementation methods can refer to relevant technologies, such as using a symbolic regression framework based on genetic programming (such as PySR) to implement symbolic regression models, which will not be elaborated here.
[0091] Back Figure 1 In step S6, a target CHF relation is selected from multiple candidate CHF relation formulas. The target CHF relation formula satisfies the following conditions: the calculated loss function value is less than a first preset threshold, and the physical trend is consistent with the CHF experimental data. In specific implementation, the loss function includes both prediction error and formula complexity. The regularization coefficient and the first preset threshold of the loss function are set according to the actual situation. Candidate CHF relation formulas whose calculated loss function values are less than the first preset threshold are all target CHF relation formulas. That is, there can be multiple target relation formulas. Preferably, in some embodiments, the candidate CHF relation formula with the smallest loss function value is selected as the target CHF relation formula.
[0092] In some embodiments, the step of selecting the target CHF relation from multiple candidate CHF relations includes: performing physical behavior verification on multiple candidate CHF relations, eliminating candidate CHF relations that fail the physical behavior verification, and retaining candidate CHF relations that pass the physical behavior verification, wherein the physical behavior verification includes determining whether the mathematical validity, physical dimension consistency, generalization rationality, and physical monotonicity of multiple candidate CHF relations conform to physical laws.
[0093] In practical implementation, the following steps are taken: First, the mathematical validity of the candidate CHF relation is determined by whether it is defined throughout the range of values for each variable, avoiding mathematical errors such as division by zero, square root of negative numbers, or non-positive logarithms. Second, the physical dimensional consistency of the candidate CHF relation is assessed by checking whether the physical units of the left and right sides of the relation and each variable match, and whether the input of the transcendental function is dimensionless. Third, the generalization rationality of the candidate CHF relation is determined by whether it yields results consistent with physical common sense, such as non-negative energy or speed not exceeding the speed of light, in limits or extrapolations outside the training data (i.e., at least some parameters in the second and first parameter sets and their corresponding actual CHF values). Fourth, the physical monotonicity of the candidate CHF relation is assessed by checking whether the variable relationship described by the candidate CHF relation conforms to the increasing or decreasing trends of existing physical laws. Finally, the target CHF relation should be verified through physical behavior, meaning it possesses mathematical validity, physical dimensional consistency, generalization rationality, and physical monotonicity consistent with physical laws.
[0094] As another embodiment of the method for establishing CHF relation based on artificial intelligence in this application, in addition to steps S1 to S6 as described above, it also includes an evaluation step of the target CHF relation, wherein the evaluation step includes the following steps.
[0095] First, the deviated nucleus boiling ratio (DNBR) is calculated using a subchannel procedure and the target CHF relationship. The calculation results are then subjected to statistical tests, including outlier tests, normality tests, and miscibility tests. The DNBR limit is calculated, and it is determined whether the DNBR limit meets the 95 / 95 condition of being higher than the safety limit. Specifically, meeting the 95 / 95 condition of being higher than the safety limit means that, at a 95% confidence level, there is at least a 95% probability that the calculated DNBR limit is higher than the safety limit. In some embodiments, the safety limit is defined based on the actual conditions of the reactor.
[0096] Subsequently, if the DNBR limit calculated using the subchannel procedure and the target CHF relationship does not meet the 95 / 95 condition and exceeds the safety limit, then return to step S5 and adjust the parameters of the symbolic regression model. In practice, the parameters of the symbolic regression model are adjusted by adjusting the structural constraints and / or adjusting the weights of prediction error and formula complexity in the loss function.
[0097] Finally, a target CHF relationship was obtained that satisfies the requirement that the DNBR limit is higher than the safety limit under the 95 / 95 condition, which can be used for reactor thermal design.
[0098] Some methods and steps in this application (such as steps S5, S6, and the evaluation step of the target CHF relation) can be achieved by, for example... Figure 4 The electronic device 400 shown is performing this action.
[0099] according to Figure 4 The electronic device 400 may include an internal communication bus 401, a processor 402, a read-only memory (ROM) 403, a random access memory (RAM) 404, and a communication port 405. When used in a personal computer, the electronic device may also include a hard disk 406.
[0100] The internal communication bus 401 enables data communication between components of the electronic device 400. The processor 402 can perform judgments and issue prompts. In some embodiments, the processor 402 may consist of one or more processors. The communication port 405 enables data communication between the electronic device 400 and external devices. In some embodiments, the electronic device 400 can send and receive information and data from a network through the communication port 405.
[0101] Electronic device 400 may also include different forms of program storage units and data storage units, such as hard disk 406, read-only memory (ROM) 403, and random access memory (RAM) 404, capable of storing various data files used for computer processing and / or communication, as well as possible program instructions executed by processor 402. The processor executes these instructions to implement the main parts of some of the methods and steps described above. The results of processor processing are transmitted to user equipment via a communication port and displayed on a user interface.
[0102] In some embodiments, some methods and steps of this application may also form a computer-readable medium storing computer program code, which, when executed by a processor, implements some of the methods and steps described above.
[0103] In addition, some of the methods and steps of this application can also form a computer program product, including computer program code, which, when executed by one or more processors, can implement some of the methods and steps described above.
[0104] The basic concepts have been described above. Obviously, for those skilled in the art, the above disclosure is merely illustrative and does not constitute a limitation of this application. Although not explicitly stated herein, those skilled in the art may make various modifications, improvements, and corrections to this application. Such modifications, improvements, and corrections are suggested in this application, and therefore remain within the spirit and scope of the exemplary embodiments of this application.
[0105] Furthermore, this application uses specific terms to describe embodiments of the application. For example, "an embodiment," "one embodiment," and / or "some embodiments" refer to a particular feature, structure, or characteristic related to at least one embodiment of the application. Therefore, it should be emphasized and noted that "an embodiment," "one embodiment," or "an alternative embodiment" mentioned twice or more in different locations in this specification do not necessarily refer to the same embodiment. In addition, certain features, structures, or characteristics in one or more embodiments of the application can be appropriately combined.
[0106] Similarly, it should be noted that, in order to simplify the description of the present application and thus aid in the understanding of one or more embodiments, the foregoing description of the embodiments of the present application sometimes combines multiple features into a single embodiment, drawing, or description thereof. However, this disclosure method does not imply that the subject matter of the present application requires more features than those mentioned in the claims. In fact, the embodiments contain fewer features than all the features of the single embodiments disclosed above.
[0107] In some embodiments, numbers describing the quantity of components and attributes are used. It should be understood that such numbers used in the description of embodiments are modified in some examples with the terms "approximately," "approximately," or "generally." Unless otherwise stated, "approximately," "approximately," or "generally" indicates that the numbers are allowed to vary by ±20%. Accordingly, in some embodiments, the numerical parameters used in the specification and claims are approximate values, which may be changed depending on the characteristics required by individual embodiments. In some embodiments, numerical parameters should take into account specified significant digits and employ a general method of digit reservation. Although the numerical ranges and parameters used to confirm their breadth of scope in some embodiments of this application are approximate values, in specific embodiments, such values are set as precisely as feasible.
[0108] Although this application has been described with reference to specific embodiments, those skilled in the art should recognize that the above embodiments are only used to illustrate this application, and various equivalent changes or substitutions can be made without departing from the spirit of this application. Therefore, any changes or modifications to the above embodiments within the essential spirit of this application will fall within the scope of the claims of this application.
Claims
1. A method for establishing CHF relations based on artificial intelligence, characterized in that, include: Step S1: Conduct CHF tests using CHF test specimens of simulated reactor fuel assemblies to obtain CHF test data; Step S2: Construct a CHF database based on the CHF test data. The CHF database includes a first parameter group and actual CHF values corresponding to the first parameter group. Step S3: Construct a mathematical correlation between the first parameter set and the actual CHF value; Step S4: Process the first parameter group according to the thermal-hydraulic mechanism to obtain the second parameter group. The second parameter group includes a dimensionless ratio combination of the first parameter group and a dimensionless combination of the operating parameters of the heat exchange medium in the reactor fuel assembly with the first parameter group. Step S5: Establish multiple candidate CHF relations using a symbolic regression model. The syntactic element set of the symbolic regression model includes the second parameter set and the mathematical correlation. The step of establishing multiple candidate CHF relations using a symbolic regression model includes: Define the set of syntax elements, wherein the set of operators of the set of syntax elements includes the mathematical relations and basic mathematical operators, and the terminal set includes at least some parameters in the first parameter set and the second parameter set; Set the structural constraints for the symbolic regression model; The second parameter group, at least some parameters in the first parameter group, and the actual CHF value corresponding to the first parameter group are input into the symbolic regression model; With the optimization objective of minimizing prediction error and formula complexity, multiple candidate CHF relations are generated; and Step S6: Select a target CHF relation from the multiple candidate CHF relation formulas, wherein the target CHF relation formula satisfies the following conditions: the calculated loss function value is less than a first preset threshold and the physical trend is consistent with the CHF experimental data.
2. The method for establishing CHF relations based on artificial intelligence as described in claim 1, characterized in that, The CHF test specimen has the same geometry as the reactor fuel assembly, wherein the geometry includes grid pitch, channel size, fuel rod arrangement and rod diameter.
3. The method for establishing CHF relations based on artificial intelligence as described in claim 1, characterized in that, The steps for constructing a CHF database based on the CHF test data include: The CHF test data are processed using a sub-channel program to extract local thermo-hydraulic parameters within the flow channel of the CHF test specimen; Based on the local thermal-hydraulic parameters and the geometry of the CHF test specimen, an initial first parameter set is constructed, wherein the initial first parameter set includes parameters that affect CHF; Calculate the correlation between the parameters in the initial first parameter group and the actual CHF value, and delete the parameters in the initial first parameter group whose correlation is less than a second preset threshold to obtain the first parameter group; The CHF database is established based on the first parameter group and the actual CHF values corresponding to the first parameter group.
4. The method for establishing CHF relations based on artificial intelligence as described in claim 1, characterized in that, The first parameter group includes geometric parameters, flow parameters, and thermodynamic parameters. The geometric parameters include the length, diameter, and spacing between the simulated fuel rods. The flow parameters include the local mass flow rate and local gas content. The thermodynamic parameters include pressure and inlet enthalpy.
5. The method for establishing CHF relations based on artificial intelligence as described in claim 4, characterized in that, The step of constructing a mathematical correlation between the first parameter set and the actual CHF value includes: constructing the mathematical correlation based on physical laws and mathematical regression analysis, wherein the actual CHF value and the local gas content show a linear correlation trend in the mathematical correlation.
6. The method for establishing CHF relations based on artificial intelligence as described in claim 1, characterized in that, The second set of parameters includes the ratio of the length to the diameter of the simulated fuel rod, the ratio of the diameter to the spacing between the simulated fuel rods, the Reynolds number characterizing the flow characteristics, and the Weber number characterizing the interface characteristics of the two-phase flow.
7. The method for establishing CHF relations based on artificial intelligence as described in claim 1, characterized in that, The step of selecting the target CHF relation from the plurality of candidate CHF relations includes: performing physical behavior verification on the plurality of candidate CHF relations, eliminating candidate CHF relations that fail the physical behavior verification, and retaining candidate CHF relations that pass the physical behavior verification, wherein the physical behavior verification includes determining whether the mathematical validity, physical dimension consistency, generalization rationality and physical monotonicity of the plurality of candidate CHF relations conform to physical laws.
8. The method for establishing CHF relations based on artificial intelligence as described in claim 1, characterized in that, The target CHF relation is the candidate CHF relation with the smallest loss function value.
9. The method for establishing CHF relations based on artificial intelligence as described in claim 1, characterized in that, Also includes: The evaluation steps for the target CHF relation include: calculating the DNBR limit using a subchannel program and the target CHF relation; determining whether the DNBR limit is higher than the safety limit under the 95 / 95 condition; if not, returning to step S5 and adjusting the parameters of the symbolic regression model.