CN113868959A - Nuclear power plant accident failure probability calculation method based on combination of adaptive sampling and DET - Google Patents
Nuclear power plant accident failure probability calculation method based on combination of adaptive sampling and DET Download PDFInfo
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Abstract
The invention discloses a nuclear power plant accident failure probability calculation method based on the combination of adaptive sampling and DET, which comprises the following steps: s1, acquiring an initial state of the nuclear power plant; s2, constructing a DET simulation model; s3, inputting the uncertainty parameters into RELAP5 program coupling calculation; s4, introducing an objective function to divide the calculation result of the RELAP5 program into power plant state safety and power plant state danger; s5, training a classifier according to input uncertainty parameters and power plant state parameters by using a support vector machine method; s6, dividing an N-D grid aiming at a problem space formed by input parameters, and determining the position of a limit curved surface on the problem space; s7, calculating the failure space probability according to the problem space parameter probability distribution. The method has the advantages that all parameters influencing the state of the power plant are enveloped in the constructed problem space, and the DET branch is used as one dimension in the self-adaptive sampling problem space to accurately predict and calculate the output result.
Description
Technical Field
The invention relates to the technical field of safety analysis of nuclear power plants, in particular to a nuclear power plant accident failure probability calculation method based on combination of adaptive sampling and DET.
Background
The traditional nuclear power plant safety analysis method comprises a determinacy safety analysis method and a probability safety evaluation method; wherein, the security analysis method of the determinism generally adopts RELAP5 and other software; the probabilistic security evaluation method is based on a traditional event tree/fault tree method. The traditional single deterministic theory and probabilistic theory method has limitations on analyzing the dynamic characteristics of the nuclear power plant accidents, for example, the results of nuclear power plant case analysis conducted by the france power group show that the traditional analytical method is quite conservative in estimating the radioactive release frequency caused by the serious accident phenomenon of the nuclear power plant; therefore, in order to realize the explicit modeling of a possible complex interaction model among hardware/software/processes/human behaviors in the evolution process of a complex system, a dynamic event tree method is developed; and the main difference of the dynamic event tree method and the traditional analysis method is that the physical process of the nuclear power plant accident is driven by the dynamic simulation evolution result of the nuclear power plant system, so that the dependence on the experience of an analyst is reduced, and unnecessary conservative engineering judgment is reduced.
At present, a Discrete Dynamic Event Tree (DDET) is a method (hereinafter, except for special description, the DDET is abbreviated as DET) in which a dynamic event tree method is widely applied in practical engineering applications, the DET method generates a series of event sequences containing time dynamic changes according to effective branching rules thereof, and specifically determines a system evolution path by determining branching conditions, that is, when the conditions are satisfied, the complex system evolves on different branching paths, and further obtains a series of event sequence sets for generating a DET model; after the DET model is generated, all event sequences represented by branches can be subjected to simulation by using a deterministic theory security analysis method, namely deterministic theory analysis can be developed; through the dynamic coupling of the DET and the deterministic theory analysis software, the possibility of calculating the analysis result, namely the occurrence probability can be obtained besides the traditional deterministic theory analysis calculation result, and further risk-guidance-type decision support information is provided for the design, operation and management of the nuclear power plant.
Specifically, in complex systems such as nuclear power plants, uncertainty calculation is generally performed through a sampling algorithm, uncertain parameters are sampled through the sampling algorithm, and a series of simulation operations are performed on sampled data. In general, two problems arise:
firstly, in order to ensure the accuracy of an output result, an uncertain parameter set is required to be very large;
secondly, high-fidelity simulation software such as RELAP5 consumes time and has very high calculation cost.
Therefore, the space of possible uncertain parameter distribution, namely the problem space (each dimension corresponds to one uncertain parameter), can only be sampled very sparsely, and the influence of uncertainty on the system cannot be completely analyzed. The main idea behind the algorithm of latin hypercube sampling, etc., is to sample the problem space as uniformly as possible, but the problems listed above still exist. When using the sampling method for nuclear power plant safety analysis, there are also several problems:
parameter sets that really relate to security problems are partial subsets of the original uncertainty parameter sets;
secondly, the analysts are not interested in many areas of the problem space of the safety analysis, but are concerned mainly with the boundary areas of the safety and dangerous states.
Disclosure of Invention
The invention aims to solve the problems and provide a nuclear power plant accident failure probability calculation method based on the combination of adaptive sampling and DET, which is characterized in that all parameters influencing the power plant state are enveloped in a constructed problem space, the DET branch information is also used as one dimension in the adaptive sampling problem space, all possible problem spaces can be comprehensively enveloped, and the output result can be accurately predicted and calculated.
The technical scheme provided by the invention is a nuclear power plant accident failure probability calculation method based on the combination of adaptive sampling and DET, and the method comprises the following steps:
s1, acquiring an initial state of the nuclear power plant, namely performing self-adaptive sampling calculation on uncertain parameters of the state of the nuclear power plant to obtain initial state data of the nuclear power plant;
s2, constructing a DET simulation model, and constructing a discrete dynamic tree simulation model according to the response process of each system and component of the nuclear power plant along with time to obtain a DET branch time parameter;
s3, inputting the uncertainty parameters obtained in the step S1 and the step S2 into a RELAP5 program for coupling calculation to obtain the calculation output parameters of the nuclear power plant system in the corresponding problem space coordinates;
s4, introducing an objective function to divide the calculation result of the RELAP5 program into the state safety and the state danger of the power plant, and respectively representing by using a parameter "0" and a parameter "1";
s5, training a classifier according to the input uncertainty parameters and the power plant state parameters by using a support vector machine method;
s6, dividing an N-D grid according to the accumulated probability density of each parameter aiming at the problem space formed by the input parameters to represent N-dimensional data, and dividing each dimension into D equidistant areas; classifying the whole problem space by using a classifier, determining the position of a limit curved surface on the problem space by using a support vector machine method, and dividing the problem space into a success space and an invalid space, wherein the success space corresponds to the safety state of the nuclear power plant, and the invalid space corresponds to the dangerous state of the nuclear power plant;
s7, finding the point farthest from the limit surface position in the problem space, adding the data point into the training data set of the RELAP5 program in the step S3, starting iterative calculation from the step S3 until the position variation of the limit surface is smaller than the accepted error range, determining the position of the failure space, and calculating the probability of the failure space according to the uncertainty parameter probability distribution of the problem space.
According to the technical scheme, firstly, a common forward sampling method such as Monte Carlo sampling or Latin hypercube sampling is used in the process of acquiring training data by using the traditional self-adaptive sampling method, the uncertain change of the thermal parameters of the state of the power plant can be effectively reflected, and the influence on the input running time of components and a system in the power plant is difficult to reflect visually. Therefore, the DET method is coupled with the self-adaptive sampling method, the DET branch time is used as one-dimensional input data of the problem space, the changes of all uncertain parameters in the operation of the power plant can be comprehensively enveloped, and the safety boundary of the power plant after an accident occurs is comprehensively analyzed.
The self-adaptive sampling method is based on the traditional sampling calculation method such as Monte Carlo sampling and Latin hypercube sampling, guides the selection of next sampling data through the iteration of the existing sampling calculation result, can predict the state of unknown problem space based on sparse sampling, and specifically comprises the following 5 steps:
a. executing a set of initial simulation runs, namely training points; obtaining sampling data by using a classical sampling algorithm such as Monte Carlo and Latin hypercube sampling, and then obtaining a corresponding simulation result by using high-fidelity software;
b. establishing a surrogate model using the sampling results given in step a; support vector machine, regression-based or density-based algorithms are typically selected;
c. dividing grids aiming at the problem space to obtain an uncertainty parameter set enveloping the whole problem space;
d. b, predicting results of all data in the data set in the step c by using the substitution model established in the step b, dividing the results into a success space and a failure space, and determining a limit curved surface of a boundary of the divided spaces;
e. and d, allocating an importance parameter to each point selected in the step d, and selecting the point with the highest importance as the next sample to be added into the data set from the step a until the position of the limit surface is not changed drastically.
Further, the construction of the problem space of the adaptive sampling depends on uncertain parameters obtained by sampling, and in the safety analysis of the nuclear power plant, sampling data generally have two types, wherein one type is physical process parameters of the initial state of the power plant, such as power, temperature, pressure and the like, and is used for appointing the initial state of the power plant; one is a random state transition parameter, such as the plant or system runtime, to reflect changes in the plant runtime state. The random state transition parameters generally have an influence on the simulation output result of the nuclear power plant when the random state transition parameters change in a large range, and therefore the random state transition parameters are generally specified by using a discrete dynamic event tree method.
As shown in fig. 1, when simulating the state evolution process of a nuclear power plant, a Discrete Dynamic Event Tree (DDET) generates branches according to the state change of power plant equipment or a system after a certain time from an initial event, i.e., a root node, generates intermediate nodes, traverses all the branches, reaches a final node, ends the simulation, and judges whether the power plant state is safe or invalid according to the state of the final node.
Further, in step S1, the uncertainty parameter follows one of a uniform distribution, a normal distribution, and a chi-squared distribution.
Further, in step S2, the DET branch includes a demand-type DET branch and a run-type DET branch; the time parameter of the demand DET branch is the running time 0 of the nuclear power plantSAnd simulation end time; and the time parameter of the operation type DET branch is the operation time of the nuclear power plant.
Through the technical scheme, in the process of constructing the DET branch model, a demand type branch is generally divided according to whether the system or the component can successfully perform state transition or not, an operation type branch is divided according to the state transition duration of the system or the component, the operation type branch can directly use the operation time as one dimension of training input data, and the demand type branch corresponds to two states of the system or the component.
In order to realize the automatic coupling calculation of the demand-type DET branch and the RELAP5, the existing scheme is that a TRIP card of an input card file root.i file of the RELAP5 controls a system or a component in which state transition is to occur, and a logic TRIP card of permanent true or permanent false is used for controlling an original TRIP card to generate two branches of logic true or false. However, pure logic branches cannot be combined with the adaptive sampling method, and in order to realize the combination of demand type branches and adaptive sampling, the branch running time of the demand type unsuccessful state transition is considered to be 0s by converting the demand type branches into running type branches, and the branch running time of the successful state transition is the simulation running task time set by RELAP 5. And converting the logic data of the demand branch into time data, adding the time data to one dimension of the input space data, and combining with the self-adaptive sampling.
Specifically, the DET demand type branch has only two states of success and failure, which indicates whether a state transition of a responding system or component can occur successfully during an accident, and the operation type branch indicates the duration of the state of the responding system or component during the accident. According to the method, the time data of the DET branch is extracted to serve as one dimension of the problem space, the dimension of the problem space is expanded, and a more comprehensive uncertainty analysis range of the nuclear power plant is enveloped.
Further, in step S3, the uncertainty parameter is a training data set including the initial state data of the nuclear power plant and the DET branch time parameter.
Further, in step S3, replacing the RELAP5 program with uncertainty parameters conforming to the specified distribution into parameters of the specified position of the root.i. card file; the input root.i file is an input card file of the RELAP5 program, the Root represents any file name meeting the requirements of the RELAP5 program, and the i represents the file type.
Through the technical scheme, after the parameters needing to be sampled are determined, the root.i card of the RELAP5 is analyzed to be positioned at the position of the parameters needing to be sampled, and the parameters obtained by sampling replace the parameters at the position corresponding to the root.i card, so that the uncertainty simulation of the initial state of the power plant can be realized.
Further, in step S3, the TRIP card of the relax 5 program input file is modified by adding a generic auxiliary TRIP variable according to the DET simulation object state transition type so that the runtime of the DET branch corresponds to the TRIP card runtime.
The DET model needs to be established according to the actual accident progress of the power plant, and the response states of parts such as a safety system, a valve, a main pump and the like after the accident happens are the transition states of the DET branch. If the valve can be normally opened and the valve cannot be opened due to failure, the demand type branch of the valve can be correspondingly established, and the high-pressure safety injection system can operate for 1 hour (1h) or 2 hours (2h), namely the operation type branch of the high-pressure safety injection system can be correspondingly established.
Specifically, for the coupling of the demand-type DET branch with the RELAP5, there is a method of controlling a system or a component in which a state transition is to occur, by a TRIP card of the root.i. file of the input card of the RELAP5, such as the following 501 cards: 501 time 0 ge null 020.0 l, indicating that the state of the 501 card changed from "false" to "true" after 20s, the component or system controlled by the 501 card makes a state transition at 20s, indicating that a state transition is to be initiated.
In order to generate the DET branch after the 501 card is triggered, two auxiliary TRIP cards are used, the 598 card represents a permanent true state, the 599 card represents a permanent false state, when the 501 card is triggered, the normal branch is that the 501 card becomes true, the failure branch is that the 501 card and the 599 card are AND logic cards, and the permanent false state, namely the DET branch is divided into two branches of true and false after 20 s.
Two demand DET branches can be successfully generated as a logical branch on the 501 card, but explicit time data is needed for adaptive sampling to be added to the training data set for training the generation classifier, so the present invention determines the time information by translating the demand branch into run time. Still for the 501 card, the 502 card is generated to represent 0.0s after the 501 card is triggered, and the 502 card is triggered, namely the 502 card and the 501 card are triggered simultaneously.
502time 0ge timeof 501 0.0l
The 502 card is used for replacing a component or a system required by the 501 card for control, when the demand type branch is a normal branch, the sixth bit of the 502 card keeps 0.0, when the branch is invalid, the sixth bit of the 502 card is changed into simulation time, and at the moment, the 502 card is false after the 501 card is triggered until the simulation is finished. Through this transformation, the demand branch of the logic type is represented by time, so that the demand branch can be coupled with the adaptive sampling.
Further, in step S4, the objective function is a binary objective function C, such as formula C (y) C (F (p, h, t));
wherein y ═ F (p, h, t); y is the calculation output of the nuclear power plant system in the corresponding problem space coordinate, namely a small editing output parameter after the RELAP5 program simulation calculation; f is a RELAP5 simulation calculation model; p, h and t are uncertainty parameters; and comparing the output parameter y with a safety limit value, and if the output parameter y exceeds the safety limit value, considering the state of the power plant as dangerous and marking the state as 1, otherwise, considering the state of the power plant as safe and marking the state as 0.
By using the technical scheme, a large number of output parameters can be divided into two states by using the objective function, and the input space is reversely guided to be divided into a safe space and a failure space.
Further, in step S5, a classifier is established between the training data set of step S3 and the calculated output parameters of the nuclear power plant system in the corresponding problem space coordinates by using a support vector machine method; specifically, a support vector machine classification method is used in a sklern library of the python program, a Gaussian kernel function is determined, and after training data are input, a classification surface equation G can be fitted:
the support vector machine method is a classification method commonly used in machine learning, and the computational complexity depends on the number of support vectors, rather than the dimension of a sample space, and is suitable for classification computation of multi-dimensional parameters.
Further, in step S6, the problem space is divided into grids in equal steps for each dimension of the parameters, so that the cumulative probability of the grids is lower than the threshold of the assigned probability density, the distribution parameter values of the whole problem space are obtained, and all the parameters of the problem space are classified by using the classifier trained in step S5.
According to the technical scheme, the combination modes of the time parameters of the DET branch and the state parameters of the MC sampling are different, the MC sampling is used as the front end to ensure the complete envelope problem space, a DET branch model is linked in each sampling, and the corresponding parameters are combined into training data. Simulation processes of the power plant in different initial states and different running states are comprehensively enveloped through the combination of MC sampling and DET coupling data, data of the whole input space can be comprehensively and accurately obtained through gridding division of input space parameters, namely output data corresponding to an input problem space is comprehensively obtained, and a training data set is more complete;
further, the specific operation steps of the support vector machine are as follows:
s1, assuming a straight line corresponding to the output objective function response for each input parameter set:
s2, making the distance in the input parameter set be the assumed straight-line distance for accurate classification result
At a maximum wherein
A point which is closest to the assumed straight line is taken as a support vector;
s3, the states of all the parameter points in the whole input space are:
both sides are simultaneously divided by gamma to obtain
So to find
The maximum value can be converted into min
S4, calculating min
Values, using lagrange dual constructors:
are respectively paired
And b, obtaining the following result after partial derivation:
s5, based on the fact that the input parameters are too mixed and the straight lines are difficult to classify accurately, the dimension of the input parameter set is improved, accurate division is more convenient in a higher-dimensional space, but the too high dimension is too complex to calculate, and therefore a kernel function is introduced to simplify the calculation process, namely a Gaussian kernel function is used
S6, assume alpha1And alpha2Iterative calculation of the values to obtain the Lagrangian dual function value min
The invention has the beneficial effects that:
(1) firstly, a common forward sampling method such as Monte Carlo sampling or Latin hypercube sampling is used in the process of acquiring training data by the traditional self-adaptive sampling method, which can effectively reflect the uncertain change of thermal parameters of the state of a power plant, but the influence on the input running time of components and systems in the power plant is difficult to reflect visually. Therefore, the DET method is coupled with the self-adaptive sampling method, the DET branch time is used as one-dimensional input data of the problem space, the changes of all uncertain parameters in the operation of the power plant can be comprehensively enveloped, and the safety boundary of the power plant after an accident occurs is comprehensively analyzed.
(2) In the process of constructing the DET branch model, a demand type branch is generally divided according to whether the system or the component can successfully perform state transition or not, an operation type branch is divided according to the state transition duration of the system or the component, the operation type branch can directly take the operation time as one dimension of training input data, and the demand type branch corresponds to two states of the system or the component.
In order to realize the automatic coupling calculation of the demand-type DET branch and the RELAP5, the existing scheme is that a TRIP card of an input card file root.i file of the RELAP5 controls a system or a component in which state transition is to occur, and a logic TRIP card of permanent true or permanent false is used for controlling an original TRIP card to generate two branches of logic true or false. However, pure logic branches cannot be combined with the adaptive sampling method, and in order to realize the combination of demand type branches and adaptive sampling, the branch running time of the demand type unsuccessful state transition is considered to be 0s by converting the demand type branches into running type branches, and the branch running time of the successful state transition is the simulation running task time set by RELAP 5. And converting the logic data of the demand branch into time data, adding the time data to one dimension of the input space data, and combining with the self-adaptive sampling.
(3) The combination mode of the time parameter of the DET branch and the state parameter of the MC sampling is different, in order to ensure the complete envelope problem space, the MC sampling is used as the front end, a DET branch model is linked in each sampling, and the corresponding parameters are combined into training data. Through the combination of the MC sampling and the DET coupling data, the simulation process of the power plant in different initial states and different running states is comprehensively enveloped, and output data corresponding to an input problem space can be comprehensively obtained, so that a training data set is more complete.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and other drawings can be obtained by those skilled in the art without creative efforts.
FIG. 1 is a schematic structural diagram of a DET structure embodying the state evolution of a nuclear power plant according to the present invention;
FIG. 2 is a schematic diagram of a basic DET branching model embodying the present invention;
FIG. 3 is a schematic diagram of a DET branch model embodying causal relationships according to the present invention;
fig. 4 is a schematic structural diagram of a hybrid model of the MCDET embodying the present invention;
FIG. 5 is a diagram illustrating the classification effect of a support vector machine according to the present invention;
fig. 6 is a schematic diagram illustrating the effect of classifying the grid points according to the present invention;
fig. 7 is a schematic structural diagram of the present invention.
Detailed Description
The technical solutions of the present invention will be described clearly and completely with reference to the accompanying drawings, and it should be understood that the described embodiments are some, but not all embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In the description of the present invention, it should be noted that the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc., indicate orientations or positional relationships based on the orientations or positional relationships shown in the drawings, and are only for convenience of description and simplicity of description, but do not indicate or imply that the device or element being referred to must have a particular orientation, be constructed and operated in a particular orientation, and thus, should not be construed as limiting the present invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance.
In the description of the present invention, it should be noted that, unless otherwise explicitly specified or limited, the terms "mounted," "connected," and "connected" are to be construed broadly, e.g., as meaning either a fixed connection, a removable connection, or an integral connection; can be mechanically or electrically connected; they may be connected directly or indirectly through intervening media, or they may be interconnected between two elements. The specific meanings of the above terms in the present invention can be understood in specific cases to those skilled in the art.
The present invention will be further explained with reference to specific embodiments.
A nuclear power plant accident failure probability calculation method based on adaptive sampling and DET combined, as shown in fig. 7, includes the following steps:
s1, acquiring an initial state of the nuclear power plant, namely performing self-adaptive sampling calculation on uncertain parameters of the state of the nuclear power plant to obtain initial state data of the nuclear power plant;
s2, constructing a DET simulation model, and constructing a discrete dynamic tree simulation model according to the response process of each system and component of the nuclear power plant along with time to obtain a DET branch time parameter;
s3, inputting the uncertainty parameters obtained in the step S1 and the step S2 into a RELAP5 program for coupling calculation to obtain the calculation output parameters of the nuclear power plant system in the corresponding problem space coordinates;
s4, introducing an objective function to divide the calculation result of the RELAP5 program into the state safety and the state danger of the power plant, and using a parameter '0' and a parameter '1' to represent;
s5, training a classifier according to the input uncertainty parameters and the power plant state parameters by using a support vector machine method;
s6, dividing an N-D grid according to the accumulated probability density of each parameter aiming at a problem space formed by input parameters, classifying the whole problem space by using a classifier, determining the position of a limit curved surface by using a support vector machine method on the problem space, and dividing the problem space into a success space and a failure space;
s7, finding the point farthest from the limit surface position in the problem space, adding the data point into the training data set of the RELAP5 program in the step S3, starting iterative calculation from the step S3 until the position variation of the limit surface is smaller than the accepted error range, determining the failure space position, and calculating the failure space probability according to the problem space parameter probability distribution.
On the basis of the above scheme, the implementation process of step S1 is as follows: using RELAP5 as high-fidelity software for simulation calculation, performing MC sampling on n uncertain parameters of the power plant state, and performing u times of sampling on each MC sampling parameter to obtain an input data set X1{x11,x12,...x1u}，X2{x21,x22,...x2u}，...Xn{xn1,xn2,...xnu}。
Specifically, assume that two parameters, pressure p and water level h, are sampled 2 times, the pressure p obeying a uniform distribution U — (15.5, 16.5), and the water level h obeying a normal distribution N — (10.0, 5.0).
Sampling method in numpy library by python program:
n, 2, n, 2, n, 2, n;
normal distribution sampling parameters were obtained for normal (loc 10.0, scale 5.0, size 2).
The sampled data obtained for each parameter is P1,p2}，H{h1,h2Obtaining 2 groups of power plant initial state data { p ] by combining 2 times of MC sampling data1,h1}，{p2,h2}。
On the basis of the above scheme, the implementation process of step S2 is as follows:
as shown in fig. 1, a nuclear power plant system, equipment or personnel operation to be simulated is first used as a DET simulation object, and then the following analysis is performed according to the DET analysis method: each node in the graph represents a set of states of the object simulated by DETCombined nuclear power plant specific state SiWherein the root node represents the initial state S of the nuclear power plant during the dynamic coupling simulation of DET and RELAP50The middle node represents the combination of different states of a nuclear power plant system and equipment, and the end node represents a certain predefined absorption termination state of the nuclear power plant, such as the reactor core damage or the stable state of the nuclear power plant; the DET is dynamically coupled with RELAP5, starting from the root node, and the state of the DET simulation object is subjected to stochastic transition along with time change; when the preset branch rule is reached, the branch generated from the moment represents one state transition of the simulation object; and representing a state transition of the simulation object from the parent node to the child node;
when the DET simulation object state transition triggering condition is met, the DET simulation object state transition only has two states of state transition success and state transition failure, a parent node is corresponding to a new branch generated by a DET model and evolves into a success node and a failure node, wherein the upper node represents the success node, and the node coding mode is 'parent node name-1'; the lower node represents a transfer failure node, and the node coding mode is 'father node name-2'; the end node represents the termination of the DET coupling with the RELAP5, the node name is encoded in "parent node name-f", and the system evolution process from parent node to child node is calculated by 1 or more simulation steps of the RELAP5 program.
Specifically, the DET branch state is shown in FIG. 2, where the root node is the 1 st branch component and the runtime branch is t11And t12Two, the middle node is the 2 nd branch component, and the operation time branch is t21And t22Two, when there is no causal connection between two branch components, 4 root nodes are generated, and the corresponding data sets are: { t11，t21}，{t11，t22}，{t12，t21}，{t12，t22}
For causal branching components, as shown in FIG. 3, the operating time at component 1 is t12And in the process, the components 2 cannot be put into operation, 3 root nodes are formed, the operation time of the components 2 which cannot be put into operation is considered to be 0s, and the corresponding data set is as follows:{t11，t21}，{t11，t22}，{t12，0}
the method comprises the steps of constructing a DET branch model by using a response process of each system and component of a power plant along with time in an actual engineering process, adding time data generated by the DET branch into an input data set, and supposing that the DET branches v times at each time, obtaining the following input data set: x(n+1){t(n+1)1,t(n+1)2,...t(n+1)v}，...X(n+m){t(n+m)1,t(n+m)2,...t(n+m)v}
Specifically, the DET model shown in fig. 2 is used in the present invention, and the obtained data sets are: { t11，t21}，{t11，t22}，{t12，t21}，{t12，t22}。
On the basis of the scheme, the DET branches comprise a demand type DET branch and a running type DET branch; the time data generated by the DET branch of demand type includes 0STwo time points of simulation ending time; namely, the running time of the equipment or the system is divided into two time points of 0s and simulation ending time; the time data generated by the operation type DET branch is the operation time; i.e. specifying the running time of the device or system, e.g. divided into 1h, 2h, 3h, etc.
On the basis of the above scheme, the implementation process of step S3 is as follows:
the data obtained by the self-adaptive sampling method is combined according to the sampling times, the data obtained by sampling aiming at all uncertain parameters each time is used as a group of data sets, and the data sets are obtained by sampling for several times; each DET branch generates two or more time data, the time data of each DET branch is respectively added into each data set, the dimension of the generated data set is the number of sampling parameters plus the number of DET branches, and the number of the generated data set is the product of the number of sampling times and the number of DET root nodes.
Taking adaptive sampling as forward operation, determining the initial state of the nuclear power plant by using data of each adaptive sampling, namely the initial state of starting simulation calculation as RELAP 5; the DET model is used as the state change of the nuclear power plant after the simulation calculation is started, namely, each self-adaptive sampling is connected with one DET branch model;
specifically, the coupling mode of the adaptive sampling and RELAP5 is to obtain sampling parameters of specified distribution, and replace the sampling parameters conforming to the specified distribution with parameters of specified positions of a RELAP5 program input root.i card file; the input root.i file is an input card file of the RELAP5 program, the Root represents any file name meeting the requirements of the RELAP5 program, and the i represents the file type.
As shown in fig. 2, when DET is coupled with the RELAP5 program, calculations are performed between each node; different from the traditional event tree method, the time of node branching in DET is determined by the physical process simulated by RELAP5, namely according to the state transition type of the DET simulation object, the TRIP card of the input file of the RELAP5 program is modified by adding a general-purpose auxiliary TRIP variable, the TRIP card is used for controlling the DET branching component, the running time of the DET branching component corresponds to the running time of the TRIP card, namely, the DET branching model traversing the whole simulation process is constructed by generating branches according to the time of TRIP branching.
On the basis of the scheme, the adaptive sampling and the DET branch are integrated to obtain n + m-dimensional input data sets, the product of the sampling times of the adaptive sampling and the DET branch times is the number of the input data sets, and the input data sets are combined into a training data set; namely, the uncertainty parameter is a training data set containing the nuclear power plant initial state data and the DET branch time parameter:
{x11,x21,...xn1,t(n+1)1,...t(n+m)1},{x11,x21,...xn1,t(n+1)1,...t(n+m)2},..{x11,x21,...xn1,t(n+1)1,...t(n+m)v}
{x11,x21,...xn1,t(n+1)2,...t(n+m)1},{x11,x21,...xn1,t(n+1)2,...t(n+m)2},..{x11,x21,...xn1,t(n+1)2,...t(n+m)v}
...
{x11,x21,...xn1,t(n+1)v,...t(n+m)1},{x11,x21,...xn1,t(n+1)v,...t(n+m)2},..{x11,x21,...xn1,t(n+1)v,...t(n+m)v}
{x12,x22,...xn2,t(n+1)1,...t(n+m)1},{x12,x22,...xn2,t(n+1)1,...t(n+m)2},..{x12,x2,...xn2,t(n+1)1,...t(n+m)v}
{x12,x22,...xn2,t(n+1)2,...t(n+m)1},{x12,x22,...xn2,t(n+1)2,...t(n+m)2},..{x12,x22,...xn2,t(n+1)2,...t(n+m)v}
...
{x12,x22,...xn2,t(n+1)v,...t(n+m)1},{x12,x22,...xn2,t(n+1)v,...t(n+m)2},..{x12,x22,...xn2,t(n+1)v,...t(n+m)v}
{x1u,x21,...xnu,t(n+1)1,...t(n+m)1},{x1u,x2u,...xnu,t(n+1)1,...t(n+m)2},..{x1u,x2u,...xnu,t(n+1)1,...t(n+m)v}
{x1u,x2u,...xnu,t(n+1)2,...t(n+m)1},{x1u,x2u,...xnu,t(n+1)2,...t(n+m)2},..{x1u,x2u,...xnu,t(n+1)2,...t(n+m)v}
...
{x1u,x2u,...xnu,t(n+1)v,...t(n+m)1},{x1u,x2u,...xnu,t(n+1)v,...t(n+m)2},..{x1u,x2u,...xnu,t(n+1)v,...t(n+m)v}
specifically, the MCDET hybrid branch state generated by the combination of the above-mentioned hypothetical cases of step S1 and step S2 is shown in fig. 4, where a black node represents an initial state of the power plant and is determined by parameters sampled by the MC, subsequent gray nodes represent response states of systems and components in the power plant over time and are determined by the DET branch, a final white node represents a final state of the power plant after the operation is completed, a corresponding training data set includes changes of all dynamic parameters of the power plant from the beginning to the end of the operation, and the specific parameters of the data set are:
{p1,h1,t11,t21}，{p1,h1,t11,t22}，{p1,h1,t12,t21}，{p1,h1,t12,t22}
{p2,h2,t11,t21}，{p2,h2,t11,t22}，{p2,h2,t12,t21}，{p2,h2,t12,t22}
on the basis of the above scheme, in step S4, the obtained training data is input into the relax 5 simulation run, and the system state y of the training data set point is calculated as F (p, h, t), where:
y is the calculated output of the system in the corresponding problem space coordinate (i.e. corresponding to the input data set), i.e. the small edit output parameter after the RELAP5 simulation calculation;
f is a RELAP5 simulation calculation model;
p, h, t are the pressure, water level and time parameters to be input in the case.
On the basis of the scheme, the specific operation steps of the support vector machine are as follows:
s1, assuming a straight line corresponding to the output objective function response for each input parameter set:
s2, making the distance in the input parameter set be the assumed straight-line distance for accurate classification result
At a maximum wherein
A point which is closest to the assumed straight line is taken as a support vector;
s3, the states of all the parameter points in the whole input space are:
both sides are simultaneously divided by gamma to obtain
So to find
The maximum value can be converted into min
S4, calculating min
Values, using lagrange dual constructors:
are respectively paired
And b, obtaining the following result after partial derivation:
s5, based on the fact that the input parameters are too mixed and the straight lines are difficult to classify accurately, the dimension of the input parameter set is improved, accurate division is more convenient in a higher-dimensional space, but the too high dimension is too complex to calculate, and therefore a kernel function is introduced to simplify the calculation process, namely a Gaussian kernel function is used
S6, assume alpha1And alpha2Iterative calculation of the values to obtain the Lagrangian dual function value min
On the basis of the above assumed cases, in step S6, regarding pressure p, uniform distribution U — (15.5, 16.5), assuming that the probability density threshold is 0.1, and assuming that pressure 10 is divided equally, the data obtained after dividing the parameters by equal steps is (15.5, 15.6, 15.7.., 16.5), and the cumulative probability value of [15.5-15.6, 15.6-15.7.,. 16.4-16.5] is calculated to be [0.1, 0.1.. 0.1] not higher than the probability density threshold, and the division can be performed accordingly.
The water level h follows a normal distribution N (10.0, 5.0). Assuming that the upper and lower limits of the water level h are (5.0, 15.0), the data obtained by equally dividing the water level 10 is (5.0, 6.0, 7.0,. 15.0), and the cumulative probability values corresponding to [5.0-6.0, 6.0-7.0, 7.0-8.0,. 14.0-15.0] are calculated as [0.078, 0.091, 0.103, 0.112, 0.116, 0.112, 0.103, 0.091, 0.078]
And if the probability value is higher than 0.1, dividing the water level 11 into equal parts, and calculating the cumulative probability value again until all the cumulative probabilities are lower than 0.1 when the water level 12 is divided into equal parts, so as to obtain the parameter value of the water level parameter.
Specifically, the pressure and the water level may be two dimensions of the problem space, if a two-dimensional grid data set can be obtained by taking the two-dimensional parameters as an example, the classifier generated in step S5 can be used to predict whether each parameter point belongs to "safe" or "dangerous", the generated classification result is shown in fig. 6, the 2-dimensional coordinates in the drawing are respectively the water level h and the pressure p, the water level h coordinate parameter 12 is equally divided, the pressure p coordinate parameter 10 is equally divided, the middle black curve represents the classification curve obtained by the support vector machine method in step S5, the input space is divided into a safe space and a dangerous space, the circular points are in the safe space and represent the state safety, the triangular points are in the dangerous space and represent the state danger;
on the basis of the scheme, after the time parameter is added, the data of each grid point is determined on a higher-dimensional space, and then the same operation is carried out; each grid point can be used as input data of the support vector machine method again to determine a curve or a curved surface for dividing the input space, and the curved surface is called a limit curved surface; calculating the distance from each grid point to the limit surface in fig. 6, the more distant points have higher importance, adding the point farthest from the limit surface to the input data set, taking the above-mentioned assumed case as an example, obtaining a new grid point farthest from the limit surface generated in step S7, determined by pressure p, water level h and time t, inputting the data of the grid point again to the relax 5 program for calculation, obtaining a new output result, determining whether the output result is "safe" or "dangerous", adding training data to the new data point, obtaining a new limit surface position by using a support vector machine method, and repeating the steps until the position parameter of the limit surface does not change significantly.
The above-described embodiments are merely illustrative of one or more embodiments of the present invention, which are described in more detail and detail, but are not to be construed as limiting the scope of the invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the inventive concept, which falls within the scope of the present invention.
Claims (10)
1. A nuclear power plant accident failure probability calculation method based on combination of adaptive sampling and DET is characterized by comprising the following steps:
s1, acquiring an initial state of the nuclear power plant, namely performing self-adaptive sampling calculation on uncertain parameters of the state of the nuclear power plant to obtain initial state data of the nuclear power plant;
s2, constructing a DET simulation model, constructing a simulation model of a discrete dynamic tree according to the response process of each system and component of the nuclear power plant along with time, and obtaining DET branch time parameters;
s3, inputting the uncertainty parameters obtained in the step S1 and the step S2 into a RELAP5 program for coupling calculation to obtain the calculation output parameters of the nuclear power plant system in the corresponding problem space coordinates;
s4, introducing an objective function to divide the calculation result of the RELAP5 program into the state safety and the state danger of the power plant, and using a parameter '0' and a parameter '1' to represent;
s5, training a classifier according to the input uncertainty parameters and the power plant state parameters by using a support vector machine method;
s6, dividing an N-D grid according to the accumulated probability density of each parameter aiming at the problem space formed by the input parameters, wherein the N-D grid represents N-dimensional data, and each dimension is divided into D equidistant areas; classifying the whole problem space by using a classifier, determining the position of a limit curved surface on the problem space by using a support vector machine method, and dividing the problem space into a success space and an invalid space, wherein the success space corresponds to the safety state of the nuclear power plant, and the invalid space corresponds to the dangerous state of the nuclear power plant;
s7, finding the point farthest from the limit surface position in the problem space, adding the data point into the training data set of the RELAP5 program in the step S3, starting iterative calculation from the step S3 until the position variation of the limit surface is smaller than the accepted error range, determining the position of the failure space, and calculating the probability of the failure space according to the uncertainty parameter probability distribution of the problem space.
2. The nuclear power plant accident failure probability calculation method of claim 1, wherein in step S1, the uncertainty parameter follows one of a uniform distribution, a normal distribution, an exponential distribution, or other distribution.
3. The nuclear power plant accident failure probability calculation method according to claim 1, wherein in step S2, the DET branch includes a demand type DET branch and an operational type DET branch; the time parameter of the demand DET branch is the running time 0 of the nuclear power plantSAnd simulation end time; and the time parameter of the operation type DET branch is the operation time of the nuclear power plant.
4. The nuclear power plant accident failure probability calculation method according to claim 1, wherein in step S3, the uncertainty parameter is a training data set including the nuclear power plant initial state data and the DET branch time parameter.
5. The nuclear power plant accident failure probability calculation method according to claim 1, wherein in step S3, the uncertainty parameter conforming to the designated distribution is input to the parameter of the designated position of the root.i. card file in place of the RELAP5 program; the input root.i file is an input card file of the RELAP5 program, the Root represents any file name meeting the requirements of the RELAP5 program, and the i represents the file type.
6. The nuclear power plant accident failure probability calculation method according to claim 1, wherein in step S3, the TRIP card of the relax 5 program input file is modified by adding a general-purpose type auxiliary TRIP variable according to the DET simulation object state transition type so that the runtime of the DET branch corresponds to the TRIP card runtime.
7. The nuclear power plant accident failure probability calculation method according to claim 1, wherein, in step S4, the objective function is a binary objective function C, such as C (y) C (F (p, h, t));
wherein y ═ F (p, h, t); y is the calculation output of the nuclear power plant system in the corresponding problem space coordinate, namely a small editing output parameter after the RELAP5 program simulation calculation; f is a RELAP5 simulation calculation model; p, h and t are uncertainty parameters, p and h represent power plant state uncertainty parameters obtained by a sampling method, and t represents time uncertainty parameters determined by DET; comparing the output parameter y with a safety limit value, if the output parameter y exceeds the safety limit value, considering the state danger of the power plant, marking the state danger as '1', and at the moment, positioning the corresponding input parameter point in a failure space; otherwise, the state of the power plant is considered to be safe and marked as '0', and the corresponding input parameter point is located in the safe space.
8. The nuclear power plant accident failure probability calculation method of claim 4, wherein in step S5, a classifier is established for the training data set of step S3 and the calculation output parameters of the nuclear power plant system in the corresponding problem space coordinates by using a support vector machine method; specifically, a support vector machine classification method is used in a sklern library of the python program, a Gaussian kernel function is determined, and after training data are input, a classification surface equation G can be fitted:
9. the nuclear power plant accident failure probability calculation method of claim 1, wherein in step S6, the problem space is gridded with equal step length of each dimension parameter, the cumulative probability of the gridding is lower than the designated probability density threshold, the distribution parameter values of the whole problem space are obtained, and all the parameters of the problem space are classified by using the classifier trained in step S5.
10. The method for calculating the accident failure probability of the nuclear power plant according to claim 1 or 8, wherein the support vector machine method is a classification method commonly used in machine learning, and the specific operation steps are as follows:
s1, assuming a straight line corresponding to the output objective function response for each input parameter set:
s2, making the distance in the input parameter set be the assumed straight-line distance for accurate classification result
At a maximum wherein
A point which is closest to the assumed straight line is taken as a support vector;
s3, the states of all the parameter points in the whole input space are:
both sides are simultaneously divided by gamma to obtain
So to find
The maximum value can be converted into
S4, obtaining
Values, using lagrange dual constructors:
are respectively paired
And b, obtaining the following result after partial derivation:
s5, based on the fact that the input parameters are too mixed and the straight lines are difficult to classify accurately, the dimension of the input parameter set is improved, accurate division is more convenient in a higher-dimensional space, but the too high dimension is too complex to calculate, and therefore a kernel function is introduced to simplify the calculation process, namely a Gaussian kernel function is used
S6, assume alpha1And alpha2The value is iteratively calculated to obtain a Lagrangian dual function value, namely
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