Method and system for calculating uncertainty of natural circulation flow of integrated small reactor

Abstract

The invention provides a calculation method and system for uncertainty of natural circulation flow of an integrated small reactor. The calculation method comprises the following steps: determining the sampling frequency M of each round according to a physical quantity Xi of the natural circulation flow, and starting to carry out multi-round random sampling; calculating an indirect natural circulation flow yk, an estimated value y (k) and a standard deviation u (y (k)) corresponding to k rounds of random sampling according to the natural circulation flow physical quantity Xi, wherein the probability symmetry of the indirect natural circulation flow yk corresponding to the k rounds of random sampling comprises a space # imgabs0 #, and calculating a standard deviation parameter of the indirect natural circulation flow yk corresponding to the k rounds of random sampling; and determining a numerical tolerance delta, judging whether the standard deviation parameter meets a preset condition or not according to the numerical tolerance delta, if so, calculating a final standard deviation u (yk * M), and taking the final standard deviation u (yk * M) as the uncertainty of the natural circulation flow.

Description

Technical Field

[0001] The present application mainly relates to the field of nuclear power technology, and in particular to a method and system for calculating the uncertainty of the natural circulation flow of an integrated small reactor. Background Art

[0002] Due to the compact structure of the integrated small-scale reactor, it is impossible to directly arrange flow measurement instruments. The natural circulation flow in the reactor under the steady-state condition of startup heating is obtained through an indirect measurement method. Since the principle of the indirect measurement method is relatively complex and there are many factors affecting the uncertainty of the flow, the traditional partial derivative calculation method for calculating uncertainty requires many simplifications and it is difficult to accurately evaluate its uncertainty. Therefore, this field urgently needs a method that can automatically calculate the uncertainty of the natural circulation measurement flow in the reactor under the steady-state condition of startup heating. Summary of the invention

[0003] The technical problem to be solved by the present application is to provide a method and system for calculating the uncertainty of natural circulation flow, which can realize automatic calculation of the uncertainty of natural circulation flow in a nuclear reactor and improve the reliability and accuracy of the calculation of the uncertainty of natural circulation flow.

[0004] In order to solve the above technical problems, the present application provides a method for calculating the uncertainty of natural circulation flow, which is applicable to nuclear reactors. The calculation method comprises the following steps: i Determine the number of sampling times M for each round and start multiple rounds of random sampling; according to the natural circulation flow physical quantity X i Calculate the indirect natural circulation flow y corresponding to k rounds of random sampling k , where k is the total number of sampling rounds; calculate the indirect natural circulation flow y corresponding to the k rounds of random sampling k The valuation of (k) and standard deviation u(y (k) ), calculate the indirect natural circulation flow y corresponding to the k rounds of random sampling k The probability symmetric inclusion space Calculate the indirect natural circulation flow y corresponding to the k rounds of random sampling k ; determining a numerical tolerance δ, and judging whether the standard deviation parameter meets a preset condition according to the numerical tolerance δ, and if so, calculating k×M indirect natural circulation flow rates y in the multiple rounds of random sampling k The final average value y k×M And the final standard deviation u(y k×M ), and the final standard deviation u(y k×M ) as the natural circulation flow uncertainty.

[0005] Optionally, the calculation method further includes determining whether the current sampling number reaches the sampling number M during each round of random sampling, and if the determination result is no, continuing the current round of sampling, and if the determination result is yes, performing the next round of sampling.

[0006] Optionally, the multiple rounds of random sampling further include: i The sampling times M are determined by a preset inclusion probability p, wherein the preset inclusion probability p ranges from 80% to 99%.

[0007] Optionally, the indirect natural circulation flow y corresponding to the k rounds of random sampling is calculated k The valuation of (k) and standard deviation u(y (k) ) includes: in the process of k rounds of random sampling, in the natural circulation flow physical quantity X i Select M sample values ​​X from i,r , where i is the physical quantity X of the natural circulation flow i Input the serial number, i=1,…,N; r is the sampling serial number of each round of sampling, r=1,…,M; calculate the indirect natural circulation flow y corresponding to the rth random sampling in each round of random sampling r Calculate the indirect natural circulation flow y corresponding to the k rounds of random sampling according to the following formula: k The estimated value y (k) :

[0008]

[0009] The indirect natural circulation flow y corresponding to the k rounds of random sampling is calculated according to the following formula k The standard deviation u(y (k) )

[0010]

[0011] Optionally, the calculation method further comprises calculating the sampling number M by the following steps: assuming J to be a minimum positive integer greater than or equal to 100 / (1-p); the sampling number M=max(J,10 4 ).

[0012] Optionally, is the left endpoint of the probability symmetric inclusion space, is the right endpoint of the probability symmetric inclusion space, and the standard deviation parameter includes the indirect natural circulation flow y corresponding to the k rounds of random sampling k The standard deviation of the estimate y 、Standard deviation u(y (k) ) u(y), left endpoint The standard deviation of ylow and the right endpoint The standard deviation of yhigj .

[0013] Optionally, the preset condition includes the indirect natural circulation flow rate y k The standard deviation of the estimate s y , the standard deviation of the natural circulation flow u(y (k) ) u(y) , the left endpoint The standard deviation of ylow and the right endpoint The standard deviation of yhigh Any item of is less than and equal to the numerical tolerance δ.

[0014] Optionally, the indirect natural circulation flow y corresponding to k rounds of random sampling is calculated k The probability symmetric inclusion space Including: M indirect natural circulation flow y 　 Perform non-decreasing sorting to generate a non-decreasing sequence y of natural circulation flow (r) , where if (1-p)M / 2 is an integer, then r = (1-p)M / 2; if (1-p)M / 2 is not an integer, then r is the integer part of [(1-p)M / 2] + 1 / 2; select y (r) for Select y (r+pM) for That is, the probability symmetric inclusion space is

[0015] Optionally, the estimated value y of the indirect natural circulation flow rate of each round of random sampling is calculated (1) ,y (2) , …, y (k) Calculate the indirect natural circulation flow y corresponding to k rounds of random sampling by the following formula: k The valuation standard deviation s y

[0016]

[0017] Among them, y av is the indirect natural circulation flow y of the random sampling in round k k The average value of .

[0018] Optionally, the calculation method further comprises calculating the indirect natural circulation flow y of each round of random sampling k The standard deviation u(y (1) ), u(y (2) ),…,u(y(k) ); calculate y (1) ,y (2) , …, y (k) The corresponding standard deviation u(y (1) ), u(y (2) ),…,u(y (k) )’s average value u(y) av Calculate the indirect natural circulation flow y corresponding to k rounds of random sampling by the following formula: k The standard deviation of the standard deviation s u(y)

[0019]

[0020] Optionally, the calculation method further comprises: calculating the indirect natural circulation flow y of each round of random sampling k The left endpoint of Calculate y (1) ,y (2) , …, y (k) The corresponding left endpoint The average value (y low ) av Calculate the indirect natural circulation flow y corresponding to the k rounds of random sampling by the following formula: k The standard deviation s of the left endpoint ylow

[0021]

[0022] Optionally, the calculation method further comprises: calculating the indirect natural circulation flow y of each round of random sampling k The right endpoint of Calculate y (1) ,y (2) , …, y (k) The corresponding right endpoint The average value (y high ) av Calculate the indirect natural circulation flow y corresponding to k rounds of random sampling by the following formula: k The standard deviation s of the right endpoint yhigh

[0023]

[0024] Optionally, the calculation method further includes determining a numerical tolerance δ by the following formula:

[0025]

[0026] The value z is expressed as c×10 mIn the form of , c is an n-digit decimal integer, m is an integer, and n represents the number of valid digits of the value z.

[0027] Optionally, the natural circulation flow physical quantity X i It includes any one or more of the medium temperature measured at the inlet of the startup heating system injection reactor pressure vessel (RPV) pipe, the medium temperature measured at the outlet of the startup heating system discharge reactor pressure vessel (RPV) pipe, the loop mass flow measured at the outlet of the startup heating system loop circulation pump, the cross-sectional area of ​​each flow channel in the nuclear reactor and the resistance coefficient in the nuclear reactor.

[0028] To solve the above technical problems, the present application provides a natural circulation flow uncertainty calculation system, comprising: a memory for storing instructions executable by a processor; and a processor for executing the instructions to implement the above method.

[0029] In order to solve the above technical problem, the present application provides a computer-readable medium storing a computer program code, and the computer program code implements the above method when executed by a processor.

[0030] Compared with the prior art, the present application performs a large number of random samplings on the physical quantity of natural circulation flow through the uncertainty (estimated value and standard deviation) of the physical quantity of natural circulation flow and its probability distribution, and then calculates the corresponding indirect flow measurement value through the flow indirect measurement method. By sampling a large number of samples, the estimated value and standard deviation of the indirect flow measurement value can be obtained. By repeating the above steps, the uncertainty of the natural circulation flow in the nuclear reactor can be automatically calculated, thereby improving the reliability and accuracy of the uncertainty calculation of the natural circulation flow. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] The accompanying drawings are included to provide a further understanding of the present application. They are included and constitute a part of the present application. The accompanying drawings illustrate embodiments of the present application and together with the present specification serve to explain the principles of the present application. In the accompanying drawings:

[0032] Figure 1 It is a flow chart of a method for calculating uncertainty of natural circulation flow in one embodiment of the present application;

[0033] Figure 2 It is a module structure diagram of a natural circulation flow uncertainty calculation system in one embodiment of the present application. DETAILED DESCRIPTION

[0034] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the following is a brief introduction to the drawings required for the description of the embodiments. Obviously, the drawings described below are only some examples or embodiments of the present application. For ordinary technicians in this field, the present application can also be applied to other similar scenarios based on these drawings without creative work. Unless it is obvious from the language environment or otherwise explained, the same reference numerals in the figures represent the same structure or operation.

[0035] As shown in this application and claims, unless the context clearly indicates an exception, the words "a", "an", "an" and / or "the" do not refer to the singular and may also include the plural. Generally speaking, the terms "include" and "comprise" only indicate the inclusion of the steps and elements that have been clearly identified, and these steps and elements do not constitute an exclusive list. The method or device may also include other steps or elements.

[0036] Unless otherwise specifically stated, the relative arrangement, numerical expressions and numerical values ​​of the parts and steps set forth in these embodiments do not limit the scope of the present application. At the same time, it should be understood that, for ease of description, the sizes of the various parts shown in the accompanying drawings are not drawn according to the actual proportional relationship. The technology, method and equipment known to those of ordinary skill in the relevant field may not be discussed in detail, but in appropriate cases, the technology, method and equipment should be considered as a part of the authorization specification. In all examples shown and discussed here, any specific value should be interpreted as being merely exemplary, rather than as a limitation. Therefore, other examples of exemplary embodiments may have different values. It should be noted that similar reference numerals and letters represent similar items in the following drawings, so that once a certain item is defined in an accompanying drawing, it does not need to be further discussed in subsequent drawings.

[0037] This application refers to Figure 1 A calculation method 10 for the uncertainty of natural circulation flow (hereinafter referred to as "calculation method 10") is proposed, and calculation method 10 is applicable to nuclear reactors. Figure 1 As shown, a flowchart of the calculation method 10 is shown. The flowchart is used in this application to illustrate the operations performed by the system according to the embodiment of the present application. It should be understood that the previous or following operations are not necessarily performed in exact order. On the contrary, various steps can be processed in reverse order or simultaneously. At the same time, other operations may be added to these processes, or one or more operations may be removed from these processes. Specifically, the calculation method 10 includes steps S1 to S5. Now, in combination with Figure 1 Each step of the calculation method 10 is described in detail.

[0038] First, step S1 includes: iDetermine the number of sampling times M for each round and start multiple rounds of random sampling. Among them, multiple rounds of random sampling can be based on the physical quantity X of the natural circulation flow i The preset inclusion probability p determines the sampling number M, that is, J can be set to the smallest positive integer greater than or equal to 100 / (1-p), then the sampling number M = max(J,10 4 ). Exemplarily, the preset range of the inclusion probability p is 80% to 99%, and in this embodiment, 90% to 99% is preferred.

[0039] In this embodiment, the random sampling process depends on the natural circulation flow physical quantity X i The probability distribution of the natural circulation flow physical quantity X i The probability distribution of can be uniform distribution, normal distribution, etc., which can be determined based on available information such as engineering experience and historical data.

[0040] Furthermore, in step S1, the calculation method 10 further includes determining whether the current sampling number reaches the sampling number M during each round of random sampling, and if the determination result is no, continuing the current round of sampling, and if the determination result is yes, performing the next round of sampling. By determining the sampling number M during each round of random sampling, the sampling reliability and accuracy of the calculation method 10 can be improved, and the reliability and accuracy of the calculation method 10 can be further improved.

[0041] On the other hand, step S2 includes: i Calculate the indirect natural circulation flow y corresponding to k rounds of random sampling k , where k is the total number of sampling rounds. In this embodiment, the natural circulation flow physical quantity X i It includes any one or more of the medium temperature measured at the inlet of the reactor pressure vessel (RPV) pipe of the startup heating system, the medium temperature measured at the outlet of the RPV pipe of the startup heating system, the loop mass flow rate measured at the outlet of the loop circulation pump of the startup heating system, the cross-sectional area of ​​each flow channel in the nuclear reactor, and the resistance coefficient in the nuclear reactor. In other embodiments of the present application, the natural circulation physical quantity X i Other physical quantities may also be included depending on actual circumstances, and this application does not impose any limitation on this.

[0042] The physical quantity X of the natural circulation flow rate in step S2 i Solve for the indirect natural circulation flow y k The method can refer to the method disclosed in the patent text of "Method and system for determining natural circulation flow of nuclear reactor" with publication number CN118116629A, that is, through the conservation of momentum, conservation of energy and conservation of mass, a mathematical function relationship between the indirect natural circulation flow and the above-mentioned related factors can be established, and the corresponding indirect natural circulation flow can be calculated, which will not be elaborated here.

[0043] Further, step S3 includes calculating the indirect natural circulation flow y corresponding to k rounds of random sampling k The valuation of (k) and standard deviation u(y (k) , calculate the indirect natural circulation flow y corresponding to k rounds of random sampling k The probability symmetric inclusion space

[0044] Specifically, calculate the indirect natural circulation flow y corresponding to k rounds of random sampling k The valuation of (k) and standard deviation u(y (k) ) includes the following steps. First, in the process of k rounds of random sampling, the natural circulation flow physical quantity X i Select M sample values ​​X from ir , where i is the physical quantity X of the natural circulation flow i Input serial number, i=1,…,N; r is the sampling serial number of each round of sampling, r=1,…,M, M is the above sampling number M. Secondly, refer to the method disclosed in the patent document "Method and system for determining natural circulation flow of nuclear reactor" with publication number CN118116629A to calculate the indirect natural circulation flow y corresponding to the rth random sampling in each round of random sampling r .

[0045] The indirect natural circulation flow y corresponding to k rounds of random sampling can be calculated according to the following formula k The valuation of (k) :

[0046]

[0047] The indirect natural circulation flow y corresponding to the k-round random sampling is further calculated according to the following formula: k The standard deviation u(y (k) :

[0048]

[0049] Next, calculate the indirect natural circulation flow y corresponding to k rounds of random sampling k The probability symmetric inclusion space The specific calculation steps are as follows:

[0050] The indirect natural circulation flow y corresponding to each round of random sampling r Perform non-decreasing sorting to generate a non-decreasing sequence y of natural circulation flow (r), where if (1-p)M / 2 is an integer, then r = (1-p)M / 2, and if (1-p)M / 2 is not an integer, then r is the integer part of [(1-p)M / 2] + 1 / 2;

[0051] Select y (r) for Select y (r+pM) for That is, the probability symmetric inclusion space is is the left endpoint of the probability symmetric inclusion space, is the right endpoint of the probability symmetric inclusion space.

[0052] Get the above valuation y (k) 、Standard deviation u(y (k) ) and the probabilistic symmetric inclusion space Then, step S4 can be performed, which includes calculating the indirect natural circulation flow y corresponding to the k rounds of random sampling k The standard deviation parameter includes the indirect natural circulation flow y corresponding to the k rounds of random sampling k The standard deviation of the estimate s y 、Standard deviation u(y (k) ) u(y) , left endpoint The standard deviation of ylow and the right endpoint The standard deviation of yhigh Next, the method of solving each standard deviation parameter will be introduced in detail.

[0053] First, calculate the indirect natural circulation flow y corresponding to k rounds of random sampling k The valuation standard deviation s y include:

[0054] Calculate the estimated indirect natural circulation flow y for each round of random sampling (1) ,y (2) , …, y (k) ;

[0055] The indirect natural circulation flow y corresponding to k rounds of random sampling is calculated by the following formula k The standard deviation of the estimate s y

[0056]

[0057] Among them, y av is the indirect natural circulation flow y of k rounds of random sampling k The average value of y can be calculated by the following formula av :

[0058]

[0059] Next, calculate the indirect natural circulation flow y corresponding to k rounds of random sampling k The standard deviation of the standard deviation s u(y) include:

[0060] Calculate the indirect natural circulation flow y of each round of random sampling k The standard deviation u(y (1) ), u(y (2) ),…,u(y (k) );

[0061] Calculate y (1) ,y (2) , …, y (k) The corresponding standard deviation u(y (1) ), u(y (2) ),…,u(y (k) )’s average value u(y) av ;

[0062] The indirect natural circulation flow y corresponding to k rounds of random sampling is calculated by the following formula k The standard deviation of the standard deviation s u(y)

[0063]

[0064] Among them, u(y) av is the indirect natural circulation flow y of k rounds of random sampling k The average value of the standard value can be calculated by the following formula u(y) av :

[0065]

[0066] Furthermore, the indirect natural circulation flow y corresponding to the k rounds of random sampling is calculated k The standard deviation s of the left endpoint ylow include:

[0067] Calculate the indirect natural circulation flow y of each round of random sampling k The left endpoint of

[0068] Calculate y (1) ,y (2) , …, y (k) The corresponding left endpoint The average value (y low ) av ;

[0069] The indirect natural circulation flow y corresponding to k rounds of random sampling is calculated by the following formulak The standard deviation s of the left endpoint ylow

[0070]

[0071] Among them, (y low ) av is the indirect natural circulation flow y of k rounds of random sampling k The average value of the left endpoint of the probability symmetric space can be calculated by the following formula

[0072]

[0073] Finally, calculate the indirect natural circulation flow y corresponding to k rounds of random sampling k The standard deviation of the right endpoint s yhigh include:

[0074] Calculate the indirect natural circulation flow y of each round of random sampling k The right endpoint

[0075] Calculate y (1) ,y (2) , …, y (k) The corresponding right endpoint The average value (y high ) av ;

[0076] The indirect natural circulation flow y corresponding to k rounds of random sampling is calculated by the following formula k The standard deviation s of the right endpoint yhigh

[0077]

[0078] Among them, (y high ) av is the indirect natural circulation flow y of k rounds of random sampling k The average value of the right endpoint of the probability symmetric space can be calculated by the following formula

[0079]

[0080] In this embodiment, step S5 includes determining a numerical tolerance δ, and judging whether the standard deviation parameter meets a preset condition according to the numerical tolerance δ. If so, calculating k×M indirect natural circulation flow rates y in multiple rounds of random sampling k The final average value y k×M And the final standard deviation u(y k×M ), and the final standard deviation u(y k×M) as the natural circulation flow uncertainty.

[0081] Specifically, the numerical tolerance δ can be determined by the following formula:

[0082]

[0083] The value z is expressed as c×10 m In the form of, c is an n-digit decimal integer, m is an integer, and n represents the number of significant digits of the value z. For example, if the standard deviations of the first three rounds of sampling are 0.0351, 0.0352, and 0.0353, it can be considered that the number of significant digits is 2, that is, n = 2, z = 35*10 -3 , c = 35, m = -3, then the tolerance δ = 1 / 2*10 -3 =5*10 -4 .

[0084] Furthermore, the preconditions include the indirect natural circulation flow y k The standard deviation of the estimate s y , the standard deviation of natural circulation flow u(y (k) ) u(y) , left endpoint The standard deviation of ylow and the right endpoint The standard deviation of yhigh Any item of is less than or equal to the numerical tolerance δ. In this embodiment, if s y 、s u(y) 、s ylow 、s yhigh If any value in is greater than δ, it is necessary to calculate the standard deviation parameter of the k+1th round and continue to compare the standard deviation parameter with δ, and continue to iterate the calculation until the preset conditions are met. When the preset conditions are met, it means that the standard deviation of the statistical parameters (such as the estimation of the indirect natural circulation flow, the standard deviation, and the left and right endpoints of the probability symmetrical inclusion interval with a given probability of p) is less than the numerical tolerance, then it is determined that the various required results have reached statistical stability. At this time, the k×M indirect natural circulation flows y in multiple rounds of random sampling are calculated. k The final average value y k×M And the final standard deviation u(y k×M ), and the final standard deviation u(y k×M ) as the natural circulation flow uncertainty.

[0085] On the other hand, the present application also refers to Figure 2 A calculation system for the uncertainty of natural circulation flow is proposed20. Figure 2The natural circulation flow uncertainty calculation system 20 may include an internal communication bus 21, a processor 22, a read-only memory (ROM) 23, a random access memory (RAM) 24, and a communication port 25. When applied on a personal computer, the natural circulation flow uncertainty calculation system 20 may further include a hard disk 26.

[0086] The internal communication bus 21 can realize data communication between components of the natural circulation flow uncertainty calculation system 20. The processor 22 can make judgments and issue prompts. In some embodiments, the processor 22 can be composed of one or more processors. The communication port 25 can realize data communication between the natural circulation flow uncertainty calculation system 20 and the outside. In some embodiments, the natural circulation flow uncertainty calculation system 20 can send and receive information and data from the network through the communication port 22.

[0087] The natural circulation flow uncertainty calculation system 20 may also include different forms of program storage units and data storage units, such as a hard disk 26, a read-only memory (ROM) 23 and a random access memory (RAM) 24, which can store various data files used for computer processing and / or communication, and possible program instructions executed by the processor 22. The processor executes these instructions to implement the main part of the method. The results processed by the processor are transmitted to the user device through the communication port and displayed on the user interface.

[0088] The present application also provides a computer-readable medium storing computer program code, which, when executed by a processor, implements a method for calculating the uncertainty of natural circulation flow proposed in any embodiment of the present application, such as the above-mentioned calculation method 10.

[0089] The present application can calculate the uncertainty of the natural circulation flow in the reactor under the steady-state condition of startup heating according to the temperature at the inlet of the reactor pressure vessel (RPV) tube injected by the startup heating system, the temperature at the outlet of the reactor pressure vessel (RPV) tube discharged by the startup heating system, the injection flow of the startup heating system loop, the cross-sectional area of ​​each flow channel in the reactor, the resistance coefficient and other natural circulation flow physical quantities, thereby confirming the uncertainty level of the indirect measurement of the natural circulation flow. It avoids some simplifications made in the traditional partial derivative calculation method for calculating uncertainty. The calculation method of the uncertainty of the natural circulation flow provided by the present application can automatically determine the sample size to calculate the uncertainty of the indirect measurement flow. The calculation method provided by the present application is simple to implement, has a good degree of automation and reliability, and can optimize computing power and improve calculation accuracy when arranged in computer equipment. It can be more conveniently used to evaluate the uncertainty of the indirect measurement of the natural circulation flow, thereby providing a better solution for nuclear reactor design.

[0090] The basic concepts have been described above. Obviously, for those skilled in the art, the above application disclosure is only an example and does not constitute a limitation of the present application. Although not explicitly stated herein, those skilled in the art may make various modifications, improvements and amendments to the present application. Such modifications, improvements and amendments are suggested in the present application, so such modifications, improvements and amendments still belong to the spirit and scope of the exemplary embodiments of the present application.

[0091] At the same time, the present application uses specific words to describe the embodiments of the present application. For example, "one embodiment", "an embodiment", and / or "some embodiments" refer to a certain feature, structure or characteristic related to at least one embodiment of the present application. Therefore, it should be emphasized and noted that "one embodiment" or "an embodiment" or "an alternative embodiment" mentioned twice or more in different positions in this specification does not necessarily refer to the same embodiment. In addition, some features, structures or characteristics in one or more embodiments of the present application can be appropriately combined.

[0092] Some aspects of the present application may be performed entirely by hardware, entirely by software (including firmware, resident software, microcode, etc.), or by a combination of hardware and software. The above hardware or software may be referred to as "data blocks", "modules", "engines", "units", "components" or "systems". The processor may be one or more application specific integrated circuits (ASICs), digital signal processors (DSPs), digital signal processing devices (DAPDs), programmable logic devices (PLDs), field programmable gate arrays (FPGAs), processors, controllers, microcontrollers, microprocessors, or combinations thereof. In addition, various aspects of the present application may be expressed as computer products located in one or more computer-readable media, which include computer-readable program codes. For example, computer-readable media may include, but are not limited to, magnetic storage devices (e.g., hard disks, floppy disks, tapes ...), optical disks (e.g., compact disks CDs, digital versatile disks DVDs ...), smart cards, and flash memory devices (e.g., cards, sticks, key drives ...).

[0093] A computer-readable medium may include a propagated data signal containing computer program code, such as in baseband or as part of a carrier wave. The propagated signal may have a variety of manifestations, including electromagnetic, optical, etc., or a suitable combination. A computer-readable medium may be any computer-readable medium other than a computer-readable storage medium, which may be connected to an instruction execution system, device or apparatus to communicate, propagate or transmit a program for use. The program code on the computer-readable medium may be propagated via any suitable medium, including radio, cable, fiber optic cable, radio frequency signal, or similar medium, or any combination of the above mediums.

[0094] Similarly, it should be noted that in order to simplify the description of the disclosure of this application and thus help understand one or more application embodiments, in the above description of the embodiments of this application, multiple features are sometimes merged into one embodiment, figure or description thereof. However, this disclosure method does not mean that the features required by the object of this application are more than the features mentioned in the claims. In fact, the features of the embodiments are less than all the features of the single embodiment disclosed above.

[0095] In some embodiments, numbers describing the number of components and attributes are used. It should be understood that such numbers used in the description of the embodiments are modified by the modifiers "about", "approximately" or "substantially" in some examples. Unless otherwise specified, "about", "approximately" or "substantially" indicate 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 change according to the required features of individual embodiments. In some embodiments, the numerical parameters should take into account the specified significant digits and adopt the general method of retaining digits. Although the numerical domains and parameters used to confirm the breadth of their range in some embodiments of the present application are approximate values, in specific embodiments, the setting of such numerical values ​​is as accurate as possible within the feasible range.

[0096] Although the present application has been described with reference to the current specific embodiments, ordinary technicians in this technical field should recognize that the above embodiments are only used to illustrate the present application, and various equivalent changes or substitutions may be made without departing from the spirit of the present application. Therefore, as long as the changes and modifications to the above embodiments are within the essential spirit of the present application, they will fall within the scope of the claims of the present application.

Claims

1. A method for calculating the uncertainty of natural circulation flow, applicable to nuclear reactors, characterized in that: The calculation method comprises the following steps: According to the physical quantity X of natural circulation flow i Determine the number of sampling times M in each round and start multiple rounds of random sampling; According to the natural circulation flow physical quantity X i Calculate the indirect natural circulation flow y corresponding to k rounds of random sampling k , where k is the total number of sampling rounds; Calculate the indirect natural circulation flow y corresponding to the k rounds of random sampling k The valuation of (k) and standard deviation u(y (k) ), calculate the indirect natural circulation flow y corresponding to the k rounds of random sampling k The probability symmetric inclusion space in is the left endpoint of the probability symmetric inclusion space, is the right endpoint of the probability symmetric inclusion space; Calculate the indirect natural circulation flow y corresponding to the k rounds of random sampling k The standard deviation parameter of Determine the numerical tolerance δ, and judge whether the standard deviation parameter meets the preset condition according to the numerical tolerance δ. If so, calculate the k×M indirect natural circulation flow rates y in the multiple rounds of random sampling. k The final average value y k×M And the final standard deviation u(y k×M ), and the final standard deviation u(y k×M ) as the natural circulation flow uncertainty.

2. The calculation method according to claim 1, characterized in that: It also includes determining whether the current sampling number reaches the sampling number M during each round of random sampling, and if the determination result is no, continuing the current round of sampling, and if the determination result is yes, proceeding to the next round of sampling.

3. The calculation method according to claim 1, characterized in that: The multiple rounds of random sampling also include the following steps: i The sampling times M are determined by a preset inclusion probability p, wherein the preset inclusion probability p ranges from 80% to 99%.

4. The calculation method according to claim 3, characterized in that: Calculate the indirect natural circulation flow y corresponding to the k rounds of random sampling k The valuation of (k) and standard deviation u(y (k) )include: In the process of k rounds of random sampling, the natural circulation flow physical quantity X i Select M sample values ​​X from ir , where i is the physical quantity X of the natural circulation flow i Input serial number, i=1,…,N; r is the sampling serial number of each round of sampling, r=1,…,M; Calculate the indirect natural circulation flow y corresponding to the rth random sampling in each round of random sampling r ; The indirect natural circulation flow y corresponding to the k rounds of random sampling is calculated according to the following formula k The estimated value y (k) : The indirect natural circulation flow y corresponding to the k rounds of random sampling is calculated according to the following formula k The standard deviation u(y (k) ) 5. The calculation method according to claim 3, characterized in that: The method further includes calculating the sampling number M by the following steps: Let J be the smallest positive integer greater than or equal to 100 / (1-p); The sampling times M=max(J,10 4 ).

6. The calculation method according to claim 3, characterized in that: The standard deviation parameter includes the indirect natural circulation flow y corresponding to the k rounds of random sampling k Valuation (k) The standard deviation of y 、Standard deviation u(y (k) ) u(y) , the left endpoint The standard deviation of ylow and the right endpoint The standard deviation of yhigh .

7. The calculation method according to claim 6, characterized in that: The preset conditions include the indirect natural circulation flow rate y k The estimated value y (k) The standard deviation of y , the standard deviation of the natural circulation flow u(y (k) ) u(y) , the left endpoint The standard deviation of ylow and the right endpoint The standard deviation of yhigh Any item of is less than and equal to the numerical tolerance δ.

8. The calculation method according to claim 7, characterized in that: Calculate the indirect natural circulation flow y corresponding to k rounds of random sampling k The probability symmetric inclusion space include: The M indirect natural circulation flows y r Perform non-decreasing sorting to generate a non-decreasing sequence y of natural circulation flow (r) , where if (1-p)M / 2 is an integer, then r = (1-p)M / 2, and if (1-p)M / 2 is not an integer, then r is the integer part of [(1-p)M / 2] + 1 / 2; Select y (r) for Select y (r+pM) for That is, the probability symmetric inclusion space is 9. The calculation method according to claim 6, characterized in that: Calculate the indirect natural circulation flow y corresponding to the k rounds of random sampling k The standard deviation parameters include: Calculate the estimated value y of the indirect natural circulation flow of each round of random sampling (1) ,y (2) , …, y (k) ; The indirect natural circulation flow y corresponding to k rounds of random sampling is calculated by the following formula k The standard deviation of the estimate y Among them, y av is the indirect natural circulation flow y of the random sampling in round k k The average value of .

10. The calculation method according to claim 6, characterized in that: Calculate the indirect natural circulation flow y corresponding to the k rounds of random sampling k The standard deviation parameters include: Calculate the indirect natural circulation flow y of each round of random sampling k The standard deviation u(y (1) ), u(y (2) ),…,u(y (k) ), y (1) ,y (2) , …, y (k) the estimated value of the indirect natural circulation flow corresponding to each round of the random sampling; Calculate y (1) ,y (2) , …, y (k) The corresponding standard deviation u(y (1) ), u(y (2) ),…,u(y (k) )’s average value u(y) av ; The indirect natural circulation flow y corresponding to k rounds of random sampling is calculated by the following formula k The standard deviation of the standard deviation u(y) Among them, u(y) av is the indirect natural circulation flow y of the k rounds of random sampling k The mean and standard deviation.

11. The calculation method according to claim 6, characterized in that: Calculate the indirect natural circulation flow y corresponding to the k rounds of random sampling k The standard deviation parameters include: Calculate the indirect natural circulation flow y of each round of random sampling k The left endpoint of y (1) ,y (2) , …, y (k) the estimated value of the indirect natural circulation flow corresponding to each round of the random sampling; Calculate y (1) ,y (2) , …, y (k) The corresponding left endpoint The average value (y low ) av ; The indirect natural circulation flow y corresponding to the k rounds of random sampling is calculated by the following formula k The standard deviation s of the left endpoint ylow Among them, (y low ) av is the indirect natural circulation flow y of the random sampling in round k k The average of the left endpoints of the probability symmetric space.

12. The calculation method according to claim 6, characterized in that: Calculate the indirect natural circulation flow y corresponding to the k rounds of random sampling k The standard deviation parameters include: Calculate the indirect natural circulation flow y of each round of random sampling k The right endpoint y (1) ,y (2) , …, y (k) the estimated value of the indirect natural circulation flow corresponding to each round of the random sampling; Calculate y (1) ,y (2) , …, y (k) The corresponding right endpoint The average value (y hiigh ) av ; The indirect natural circulation flow y corresponding to the k rounds of random sampling is calculated by the following formula k The standard deviation s of the right endpoint yhigh Among them, (y hiigh ) av is the indirect natural circulation flow y of the random sampling in round k k The average of the right endpoints of the probability symmetric space.

13. The calculation method according to claim 1, characterized in that: It also includes determining the numerical tolerance δ by the following formula: Here, m is an integer.

14. The calculation method according to claim 1, characterized in that: The natural circulation flow physical quantity X i It includes any one or more of the medium temperature measured at the inlet of the startup heating system injection reactor pressure vessel (RPV) pipe, the medium temperature measured at the outlet of the startup heating system discharge reactor pressure vessel (RPV) pipe, the loop mass flow measured at the outlet of the startup heating system loop circulation pump, the cross-sectional area of ​​each flow channel in the nuclear reactor and the resistance coefficient in the nuclear reactor.

15. A natural circulation flow uncertainty calculation system, characterized in that: include: a memory for storing instructions executable by a processor; and a processor, configured to execute the instructions to implement the method according to any one of claims 1-14.

16. A computer readable medium storing computer program code, wherein the computer program code, when executed by a processor, implements the method according to any one of claims 1 to 14.

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