A time-varying reliability analysis system and method for space reactor core structure

Abstract

The present invention proposes a time-varying reliability analysis system and method for a core structure. The system uses interval variables to describe static uncertainty parameters such as the outer diameter of fuel rods, the total length of fuel rods, fuel density, and neutron absorption content. It also uses interval process models to represent time-varying uncertainty parameters for dynamic loads and material degradation. The system then obtains the stress responses corresponding to the static and time-varying uncertainty parameters. The system then determines the maximum stress response of the core structure uncertainty parameter that meets design requirements, and determines whether the core structure is in a safe state by determining whether the actual stress response value is less than the maximum stress response value corresponding to the uncertainty parameter. The system uses interval variable models to describe static uncertainty parameters such as geometric dimensions, and uses interval process models to characterize dynamic uncertainty parameters such as dynamic loads and material degradation, thereby avoiding model inaccuracies caused by traditional methods that assume that structural parameters and external loads are deterministic.

Description

Technical Field

[0001] The present invention relates to the technical field of reliability analysis of space reactor core structures, and mainly to a system and method for analyzing the time-varying reliability of a space reactor core structure. Background Art

[0002] Currently, environmentally unaffected, long-life space reactor power systems have become a key option for deep space exploration. The core structure is a crucial component of a space nuclear reactor. During space missions, the reactor core may be subject to significant dynamic loads during spacecraft acceleration and deceleration. Limited by volume and mass, the associated equipment and systems cannot achieve the same redundancy and diversity as terrestrial facilities. Therefore, efforts must be made to improve the reliability of space reactors under various emergencies, ensuring that the reactor system possesses exceptional safety characteristics.

[0003] At the same time, static uncertainties such as fuel rod outer diameter, total fuel rod length, fuel density, and neutron absorption content, as well as dynamic uncertainties such as material properties and external dynamic loads, inevitably exist during reactor design, manufacturing, and service, significantly impacting reactor safety. Accurate uncertainty measurement and analysis of static and dynamic parameters is crucial for core reliability design. Therefore, these characteristics and current status quo necessitate that these uncertainties be fully considered during the conceptual design of space reactors to improve operational reliability and ensure continued mission performance in the event of an emergency. Therefore, a system and method for time-varying reliability analysis of space reactor core structures is crucial. Summary of the Invention

[0004] The present invention proposes a time-varying reliability analysis system for a core structure, which includes an uncertainty parameter description module, a response solution module, and a reliability analysis module;

[0005] The uncertainty parameter description module uses interval variables to describe the static uncertainty parameters of fuel rod outer diameter, fuel rod total length, fuel density, and neutron absorption content; and uses interval process models to describe the time-varying uncertainty parameters of dynamic load and material performance degradation;

[0006] The response solving unit is used to obtain the stress response corresponding to the static uncertainty parameter and the time-varying uncertainty parameter;

[0007] The reliability analysis module determines the maximum core structure uncertainty parameter stress response that meets the design requirements, and determines whether the core structure is in a safe state by determining whether the actual stress response value is less than the maximum stress response value corresponding to the uncertainty parameter;

[0008] The interval variable of the static uncertainty parameter is expressed as:

[0009]

[0010] Among them, Y I represents an interval variable for a static uncertainty parameter, represent the interval variables of the static uncertainty parameters corresponding to the outer diameter of the fuel rod, the total length of the fuel rod, the fuel density, and the neutron absorption content;

[0011] The interval process of the time-varying uncertainty parameter is expressed as:

[0012]

[0013] Among them, X I (t) represents the interval process of time-varying uncertainty parameter, An interval process representing the time-varying uncertainty parameter of a dynamic load, The interval process of the time-varying uncertainty parameter representing the degradation of material properties, t represents the time variable;

[0014] The function required for solving the reliability index of the reliability analysis module is:

[0015] W(t)=e0-e(X I (t),Y I ,t)

[0016] Among them, e0 represents the stress allowable value of the core components to meet the function, e(X I (t),Y I ,t) represents the response function of the uncertainty parameters in the core structure.

[0017] Furthermore, the dynamic uncertainty parameter is the process parameter X in the i-th interval I i (t), i = 1, 2, is expressed as follows by the truncated interval KL expansion method:

[0018]

[0019] Where, represents the characteristic function vector, represents the time-varying uncertainty parameter median function, represents an uncorrelated interval vector, whose joint uncertainty domain is:

[0020]

[0021] in, represents θ i The joint uncertainty domain of

[0022] The function required to solve the reliability index of the reliability analysis module is converted into:

[0023] W(Q,t)=e0-e′(Q,t)

[0024] In the formula, e′() can be expressed by e(). Transformation is obtained;

[0025] The joint uncertainty domain of Q is:

[0026]

[0027] Among them, Ω Q represents the joint uncertainty domain of Q.

[0028] Furthermore, the performance function W(Q, t) is always greater than 0, that is:

[0029]

[0030] The condition in the formula is equivalent to the minimum value of W(Q,t) within the service period [0,T] being greater than 0, that is:

[0031]

[0032] make Then:

[0033] F(Q)>0

[0034] The time-varying reliability analysis problem of the core structure is converted into a non-probabilistic time-invariant reliability analysis problem of the performance function F(Q).

[0035] Furthermore, the functional function F(Q) is a function of the interval variable vector Q, and the value range of F(Q) is also within an interval, and its upper boundary F U (Q) and the lower boundary F L (Q) can be obtained by solving two optimization problems:

[0036]

[0037] The non-probabilistic structural reliability index η is defined as:

[0038]

[0039] Among them, F m (Q) is the midpoint [F U (Q)+F L (Q)] / 2,F r (Q) is the radius [F U (Q)-F L (Q)] / 2;

[0040] When -1.5<η<-1, the upper boundary of the stress value response F U (Q) is less than 0, that is, all possible values ​​of the function are less than 0, indicating that the core structure is unreliable during service, so the core structure needs to be inspected and improved; when η is in the interval [-1,1], the possible values ​​of the function greater than 0 increase with the increase of η, indicating that the reliability of the core structure is increasing, so it can be inspected according to specific requirements; when 1<η<1.5, the lower boundary F of the stress value response is L (Q) is greater than 0, that is, all possible values ​​of the performance function are greater than 0, indicating that the core structure is completely reliable during service and the core structure does not need further inspection and improvement.

[0041] Furthermore, the reliability analysis module uses a feedforward neural network to establish an extreme value prediction model of the performance function within the design reference period. To approximately replace the original model F(Q) for solving the reliability index;

[0042] The non-probabilistic reliability index η is obtained by solving the analytical expression of F(Q).

[0043] A time-varying reliability analysis method for a core structure is also provided, characterized in that the time-varying reliability analysis method comprises the following steps:

[0044] Step 1: Obtain interval variables to describe the static uncertainty parameters of the fuel rod outer diameter, total fuel rod length, fuel density, and neutron absorption content; and obtain the time-varying uncertainty parameters of the interval process model to describe the dynamic load and material performance degradation;

[0045] Step 2: Establish a mapping relationship between the stress response corresponding to the static uncertainty parameters and the time-varying uncertainty parameters;

[0046] Step 3: Determine the minimum accuracy of the core structure that meets the design requirements, that is, determine the maximum core structure uncertainty parameter stress response that meets the design requirements;

[0047] Step 4: Whether the stress response of the static uncertainty parameter and the dynamic uncertainty parameter is less than the maximum stress response that meets the design requirements is used as a criterion for judging whether the core structure is in a safe state;

[0048] Step 5: Perform time-invariant reliability analysis to obtain the time-varying reliability index of the core structure during service.

[0049] Furthermore, in step 4, a structure function is established:

[0050] W(t)=e0-e(X I (t),Y I,t)

[0051] Among them, e0 represents the stress allowable value of the core components to meet the function, e(X I (t),Y I ,t) represents the response function of the uncertainty parameters in the core structure, X I (t) represents the interval process of time-varying uncertainty parameter, Y I represents the interval variable of the static uncertainty parameter, and t represents the time variable.

[0052] Furthermore, in step 5, the following steps are also included:

[0053] Step 51: Through KL expansion and corresponding transformation, the structure function can also be expressed as W(Q,t)=e0-e′(Q,t), The core structure of a space reactor is in a safe and reliable state during its service life, which means that within a given design service life [0, T], the performance function W(Q, t) is always greater than 0. By focusing only on whether the minimum value of the difference between the allowable value of the stress response of the uncertainty parameter in the time domain and the actual response is greater than 0, that is, Convert time-varying reliability analysis into time-invariant reliability analysis;

[0054] Step 52: performing a time-invariant reliability analysis to obtain a time-varying reliability index η of the core structure during service;

[0055] Step 53: In the process of calculating the structural reliability index, a feedforward neural network is used to establish an extreme value prediction model of the performance function within the design reference period. To approximately replace the original model F(Q) for solving the reliability index;

[0056] Step 54: Use a feedforward neural network as the global proxy model of the dynamic system. A feedforward neural network consists of three types of layers, including input layer, hidden layer and output layer. The calculation process is expressed as Rectified linear unit (ReLU) is used as the activation function for training fuzzy neural networks, and the MSE between the actual training labels and the predicted output is used as the loss function;

[0057] Step 55: Obtain input sample set Q by sampling s , obtain the extreme value response F through an efficient global optimization algorithm s ,Using the training samples, an extreme value prediction model FNN is established.

[0058] Compared with the existing technology, the advantages of the present invention are:

[0059] The present invention adopts an interval variable model to describe static uncertainty parameters such as geometric dimensions, and an interval process model to characterize dynamic uncertainty parameters such as dynamic loads and material performance degradation. This allows the fluctuation of related parameters and the correlation of parameters at different times to be taken into account in reliability analysis, avoiding the model inaccuracy problem caused by the traditional method assuming that structural parameters and external loads are deterministic.

[0060] The estimation method of the present invention does not require a large number of experimental samples and uses an accurate probability distribution function with upper and lower boundaries instead of uncertainty parameters to describe its fluctuation range. The interval process model can handle dynamic or time-varying uncertainties.

[0061] The present invention solves the problem of reliability detection of core structures where it is difficult to obtain sample data; at the same time, the time-varying reliability index of the core structure during service can also be used as a reference index for improving static uncertainty parameters such as the outer diameter of the core structure's fuel rods, the total length of the fuel rods, the fuel density, the neutron absorption content, and dynamic uncertainty parameters such as material properties and external dynamic loads. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 This is a schematic diagram of the modules of the time-varying reliability analysis system for the core structure in service;

[0063] Figure 2 It is a schematic diagram of the core structure;

[0064] Figure 3 This is a diagram of the training process of a feedforward neural network;

[0065] Figure 4 It is a schematic diagram of the solution process of reliability index;

[0066] Figure 5 It is a flow chart of the time-varying reliability analysis method for the core structure in service. DETAILED DESCRIPTION

[0067] The technical solutions of the present invention are described in more detail below with reference to the accompanying drawings. The present invention includes but is not limited to the following embodiments.

[0068] like Figure 1 As shown, an embodiment of the present application provides a time-varying reliability analysis system for a core structure, the system comprising an uncertainty parameter description module, a response solution module, and a reliability analysis module, wherein:

[0069] like Figure 2As shown in the figure, the uncertainty parameter description module uses interval variables to describe static uncertainty parameters of the core structure, such as the outer diameter of the fuel rod, the total length of the fuel rod, the fuel density, and the neutron absorption content; and uses the interval process model to deal with time-varying uncertainty parameters such as dynamic loads and material performance degradation. That is, the dynamic loads and material performance degradation are expressed as interval processes, and the time-varying uncertainty parameters are characterized by their median function, radius function, and correlation coefficient function or covariance function.

[0070] The static uncertainty parameters of fuel rod outer diameter, fuel rod total length, fuel density, and neutron absorption content are treated as interval variables. Where n1 is the type of static uncertainty parameter. In this embodiment, it includes four types: fuel rod outer diameter, fuel rod total length, fuel density, and neutron absorption content. n1 = 4. The external dynamic load and material performance degradation of the core structure are treated as interval processes. For the external dynamic loads and material performance degradation of the core structure at any time Where i is the type of time-varying uncertainty parameter. In this embodiment, it includes two types: external dynamic load and material performance degradation. External dynamic load or material performance degradation is an interval variable X(t i ). The time-varying uncertainty of the uncertainty parameter is described by the interval process, and the load and material performance degradation X(t i ) All possible values ​​belong to the interval X I (t i )=[X l (t i ),X U (t i )], that is, X(t i )∈X I (t i )=[X L (t i ),X U (t i )]. At the same time, based on engineering experience, the basic characteristic parameters used to characterize the interval process are given. The upper and lower boundary functions of the time-varying uncertainty parameters are X U (t) and X L (t), on this basis, the time-varying uncertainty parameter median function X can be obtained m (t) and the radius function X r (t);

[0071]

[0072] Based on engineering samples, the time-varying uncertainty parameters are i With t j The correlation coefficient function at time is:

[0073]

[0074] The response solving unit is used to solve the stress response of the core structure corresponding to static uncertainty parameters such as the outer diameter of the fuel rod, the total length of the fuel rod, the fuel density, the neutron absorption content, and dynamic uncertainty parameters such as material properties and external dynamic loads during the service process. That is, when a certain parameter size is given, the response solving unit can give a corresponding stress response value.

[0075] The reliability analysis module determines whether the core structure is in a safe state by judging whether the difference between the stress response limit value of the core component uncertainty parameter obtained by the response solution unit and the actual stress response is greater than 0. Using the idea of ​​the extreme value method, the time-varying reliability analysis is converted into a time-invariant reliability analysis by only focusing on whether the minimum value of the difference between the allowable stress response value and the actual stress response in the time domain is greater than 0.

[0076] Define the function W(t) required to solve the reliability index, assuming that the response function of the core structure to the uncertainty parameter is e(X I (t),Y I ,t), then the core structure function is:

[0077] W(t)=e0-e(X I (t),Y I ,t) (4)

[0078] Wherein, e0 represents the allowable stress value of the core components to meet the function, is the dynamic uncertainty parameter of dynamic load and material performance degradation represented by interval process vector, The static uncertainty parameters such as fuel rod outer diameter, fuel rod total length, fuel density, and neutron absorption content are represented by n1-dimensional interval variable vectors, and t represents the time variable.

[0079] For the i-th interval process parameter X I i (t), i = 1, 2, is expressed as follows by the truncated interval KL expansion method:

[0080]

[0081] Where, represents the characteristic function vector, represents an uncorrelated interval vector, whose joint uncertainty domain is:

[0082]

[0083] Substituting formula (5) into formula (4) yields:

[0084] W(t)=e0-e′(θ1,θ2,Y I ,t) (7)

[0085] In the formula, e′() can be obtained by transforming e(). Let The above formula can be simplified as follows:

[0086] W(Q,t)=e0-e′(Q,t) (8)

[0087] Where, the joint uncertainty domain of Q is:

[0088]

[0089] Since any component in Q is an interval variable, W(Q,t) is an interval with upper and lower bounds given a time parameter t.

[0090] The core structure of a space reactor is in a safe and reliable state, which means that within a given design service period [0, T], the performance function W(Q, t) is always greater than 0, that is:

[0091]

[0092] It can be seen from the above formula that when the value of the space reactor core structure function function is greater than zero at any time during the design service cycle, the space reactor core structure is in a safe state during the design service cycle. Using the idea of ​​the extreme value method, the condition in the above formula is equivalent to the minimum value of W(Q,t) within the service cycle [0,T] being greater than 0, that is:

[0093]

[0094] make Then the above formula is:

[0095] F(Q)>0 (12)

[0096] Through the above extreme value analysis, we transform the core structure time-varying reliability analysis problem into a non-probabilistic time-invariant reliability analysis problem with a performance function F(Q).

[0097] Since the newly constructed functional function F(Q) is a function of the interval variable vector Q, the value range of F(Q) is also within an interval, and its upper boundary F U (Q) and the lower boundary F L (Q) can be obtained by solving two optimization problems:

[0098]

[0099] The non-probabilistic structural reliability index η is defined as:

[0100]

[0101] Where, F m (Q) is the midpoint [F U (Q)+F L (Q)] / 2,F r (Q) is the radius [F U (Q)-F L (Q)] / 2.

[0102] According to the definition of reliability index, when -1.5<η<-1, the upper boundary F of stress value response is U (Q) is less than 0, that is, all possible values ​​of the function are less than 0, indicating that the core structure is unreliable during service. Therefore, the core structure needs to be inspected and improved. When η is in the interval [-1,1], the possible values ​​of the function greater than 0 increase with the increase of η, indicating that the reliability of the core structure is increasing. Therefore, it can be inspected according to specific requirements. When 1<η<1.5, the lower boundary F of the stress value response is L (Q) is greater than 0, that is, all possible values ​​of the performance function are greater than 0, indicating that the core structure is completely reliable during service and the core structure does not need further inspection and improvement.

[0103] From formula (15), we can see that the non-probabilistic reliability index η requires the function The lower boundary F L (Q) and the upper boundary F U (Q), and the analytical expression of the function F(Q) is difficult to obtain, so the interval F I The lower bound F of (Q) L (Q) and the upper boundary F U Therefore, in order to reduce the computational cost and the difficulty of solving the problem, this paper uses a feedforward neural network to establish an extreme value prediction model of the performance function within the design benchmark period in the process of calculating the structural reliability index. To approximate the original model F(Q) and obtain the proxy model Upper boundary of and the lower boundary Used to solve the reliability index. The solution of structural reliability index mainly consists of three consecutive steps: obtaining the time extreme value response of the functional function, establishing and updating the extreme value prediction model based on the feedforward neural network model, and calculating the reliability index. The solution process of the reliability index is as follows: Figure 4 shown.

[0104] A feedforward neural network (FNN) is used as the global proxy model for the dynamic system. A feedforward neural network consists of three types of layers: input layer, hidden layer, and output layer. Each hidden layer contains a set of independent neurons. Each neuron is fully connected to all neurons in the previous layer. Assuming that neuron m′ is connected to p neurons in the previous layer, the calculation process can be expressed as:

[0105]

[0106] Where, f act represents the activation function, w i and b i Represent the weight and bias of the i-th neuron respectively. We use the rectified linear unit (ReLU) to avoid gradient vanishing as the activation function for training the fuzzy neural network. The MSE between the actual training label and the predicted output is used as the loss function, which is minimized during the network training process.

[0107] As attached Figure 3-4 As shown in the figure, a global agent model is proposed, which constructs a feedforward neural network (FNN) based on multi-input and one-dimensional output, where the input sample set Q s is the interval vector Q, and the output is the extreme response F s First, the input sample set is obtained by sampling, and the extreme value response F is obtained by the efficient global optimization algorithm (EGO). s , using the training samples, a feedforward neural network (FNN) extreme value prediction model is established. The feedforward neural network training process is shown in the attached Figure 3 shown.

[0108] As attached Figure 5 As shown, this embodiment also provides a time-varying reliability analysis method for a core structure, and the specific steps are as follows:

[0109] Step 1: Considering the uncertainty of static uncertainty parameters such as fuel rod outer diameter, total fuel rod length, fuel density, and neutron absorption content during the service life of the core structure, as well as the uncertainty of dynamic uncertainty parameters such as material properties and external dynamic loads, an interval process model is established based on samples or engineering experience to describe the time-varying uncertainty of the service life of the core structure;

[0110] In this embodiment, the static uncertainty parameters such as fuel rod outer diameter, fuel rod total length, fuel density, neutron absorption content are processed as interval variables. According to samples or engineering experience, the external dynamic loads on the core structure and the material performance degradation are treated as interval processes. To describe the time-varying uncertainty of the uncertainty parameters of the core structure during service. Determine the median function, radius function, and autocorrelation coefficient function;

[0111] Step 2: Establish a response solution unit. By establishing a mapping relationship between input and response, it is ensured that for each input sample, a corresponding response sample can be obtained. That is, a mapping relationship is established between static uncertainty parameters such as the outer diameter of the fuel rod, the total length of the fuel rod, the fuel density, and the neutron absorption content of the core structure during service, as well as dynamic uncertainty parameters such as material properties and external dynamic loads, and the stress response generated by the core structure during service. This allows the corresponding stress response of the core structure to be calculated for different uncertainty parameter samples. Establish a response solution unit. By establishing static uncertainty parameters such as the outer diameter of the fuel rod, the total length of the fuel rod, the fuel density, and the neutron absorption content of the core structure during service, a mapping relationship is established between dynamic uncertainty parameters such as material properties and external dynamic loads and the stress response generated by the core structure during service. and dynamic uncertainty parameters of dynamic loads and material performance degradation Input and response e(X I (t),Y I ,t) to ensure that for each input sample, its corresponding stress response sample can be obtained, that is, to establish a mapping relationship between the uncertainty parameters of the core structure during service and the stress response of the core structure during service, so that for different uncertainty parameter samples, their corresponding core structure stress response values ​​can be calculated;

[0112] Step 3: Determine the minimum accuracy of the core structure that meets the design requirements, that is, determine the maximum stress response that meets the design requirements. By using a large number of samples of static uncertainty parameters such as fuel rod outer diameter, total fuel rod length, fuel density, and neutron absorption content, as well as dynamic uncertainty parameters such as material properties and external dynamic loads, the corresponding stress response of the core structure is calculated, and the stress response allowance e0 of the core structure uncertainty parameters is found.

[0113] Step 4: Whether the actual stress response is less than the maximum response e0 that meets the design requirements is used as the criterion for judging whether the core structure is in a safe state. The core structure is judged to be in a safe state only if the response at all times during the service process does not exceed the design allowable value. If there is a moment during the service process when the response of the core structure exceeds the design allowable value, the core structure is judged to be in a failed state. Establish a structural function function W(t) = e0-e(X I (t),Y I ,t).

[0114] Step 5: Perform time-invariant reliability analysis to obtain the time-varying reliability index of the core structure during service.

[0115] The specific steps include:

[0116] Step 51: Through KL expansion and corresponding transformation, the structural performance function can also be expressed as W(Q,t)=e0-e′(Q,t). The core structure of the space reactor is in a safe and reliable state during the service period, which means that within the given design service period [0,T], the performance function W(Q,t) is always greater than 0. Therefore, by only focusing on whether the minimum value of the difference between the allowable value of the stress response of the uncertainty parameter in the time domain and the actual response is greater than 0, that is, Instead of focusing on whether the difference between the allowed value of the response and the actual response at all moments in the time domain is greater than 0 to transform the time-varying reliability analysis into a time-invariant reliability analysis;

[0117] Step 52: Based on step 4, a time-invariant reliability analysis is performed to obtain a time-varying reliability index η of the core structure during service.

[0118] Step 53: To obtain the non-probabilistic reliability index η, it is necessary to obtain the analytical expression of the function F(Q), and the interval F I The lower bound F of (Q) L (Q) and the upper boundary F U Therefore, in the process of calculating the structural reliability index, this paper uses a feedforward neural network to establish an extreme value prediction model of the performance function within the design reference period. To approximately replace the original model F(Q) for solving the reliability index.

[0119] Step 54: Use a feedforward neural network as the global proxy model of the dynamic system. A feedforward neural network consists of three types of layers, including input layer, hidden layer and output layer. The calculation process is expressed as The rectified linear unit (ReLU) is used as the activation function for training the fuzzy neural network. The MSE between the actual training labels and the predicted output is used as the loss function.

[0120] Step 55: First, obtain the input sample set Q by sampling s , the extreme response F is obtained by the efficient global optimization algorithm (EGO) s ,Using the training samples, an extreme value prediction model FNN is established.

[0121] For the utility function W(Q,t), given any realization value Q of the interval variable Q * , the performance function is expressed as W(Q * ,t), the functional function is actually a single variable function W(t) only about time t, so the realization value Q of any interval variable * The minimum value of the functional function corresponding to the realization value in the continuous grinding cycle can be obtained That is the time extreme value response F s, this extreme response can be solved using EGO.

[0122] Neural network input sample set Q s is the interval variable Q, and the output is the extreme value prediction model The extreme value prediction model is the response approximation of the limit state function F(Q). The upper and lower bounds of F(Q) are used to solve the reliability index η.

[0123] It is obvious to those skilled in the art that the present invention is not limited to the details of the above exemplary embodiments, and that the present invention can be implemented in other specific forms without departing from the spirit or essential features of the present invention. Therefore, no matter from which point of view, the embodiments should be regarded as exemplary and non-restrictive, and the scope of the present invention is defined by the appended claims rather than the above description, and it is intended that all changes that fall within the meaning and scope of the equivalent elements of the claims are included in the present invention. Although the principles of the present invention are described in detail above in conjunction with the preferred embodiments of the present invention, it should be understood by those skilled in the art that the above embodiments are merely explanations of illustrative implementations of the present invention and are not intended to limit the scope of the present invention. The details in the embodiments do not constitute a limitation on the scope of the present invention. Without departing from the spirit and scope of the present invention, any obvious changes such as equivalent transformations, simple replacements, etc. based on the technical solution of the present invention fall within the scope of protection of the present invention.

Claims

1. A time-varying reliability analysis system for a core structure, characterized in that: The time-varying reliability analysis system includes an uncertainty parameter description module, a response solution module and a reliability analysis module; The uncertainty parameter description module uses interval variables to describe the static uncertainty parameters of fuel rod outer diameter, fuel rod total length, fuel density, and neutron absorption content; and uses interval process models to describe the time-varying uncertainty parameters of dynamic load and material performance degradation; The response solving module is used to obtain the stress response corresponding to the static uncertainty parameter and the time-varying uncertainty parameter; The reliability analysis module determines the maximum core structure uncertainty parameter stress response that meets the design requirements, and determines whether the core structure is in a safe state by determining whether the actual stress response value is less than the maximum stress response value corresponding to the uncertainty parameter; The interval process of the time-varying uncertainty parameter is expressed as: Among them, X I (t) represents the interval process of time-varying uncertainty parameter, An interval process representing the time-varying uncertainty parameter of a dynamic load, The interval process of the time-varying uncertainty parameter representing the degradation of material properties, t represents the time variable; The function required for solving the reliability index of the reliability analysis module is: W(t)=e0-e(X I (t),Y I ,t) Where, e0 represents the stress allowable value of the core components to meet their functions, e(X I (t),Y I ,t) represents the response function of the uncertainty parameters in the core structure, Y I interval variables representing static uncertainty parameters; The time-varying uncertainty parameter is the process parameter X in the i-th interval I i (t), i = 1, 2, is expressed as follows by the truncated interval KL expansion method: Where, represents the characteristic function vector, represents the time-varying uncertainty parameter median function, represents an uncorrelated interval vector, whose joint uncertainty domain is: in, represents θ i The joint uncertainty domain of The function required to solve the reliability index of the reliability analysis module is converted into: W(Q,t)=e0-e′(Q,t) In the formula, e′() can be expressed by e(). Transformation is obtained; The joint uncertainty domain of Q is: Among them, Ω Q represents the joint uncertainty domain of Q.

2. The time-varying reliability analysis system according to claim 1, characterized in that: The functional function W(Q,t) is always greater than 0, that is: The condition in the formula is equivalent to the minimum value of W(Q,t) within the service period [0,T] being greater than 0, that is: make Then: F(Q)>0 The time-varying reliability analysis problem of the core structure is converted into a non-probabilistic time-invariant reliability analysis problem of the performance function F(Q).

3. The time-varying reliability analysis system according to claim 2, characterized in that: The functional function F(Q) is a function of the interval variable vector Q. The value range of F(Q) is also within an interval, and its upper boundary F U (Q) and the lower boundary F L (Q) can be obtained by solving two optimization problems: The non-probabilistic structural reliability index η is defined as: Among them, F m (Q) is the midpoint [F U (Q)+F L (Q)] / 2,F r (Q) is the radius [F U (Q)-F L (Q)] / 2; When -1.5<η<-1, the upper boundary of the stress value response F U (Q) is less than 0, that is, all possible values ​​of the function are less than 0, indicating that the core structure is unreliable during service, so the core structure needs to be inspected and improved; when η is in the interval [-1,1], the possible values ​​of the function greater than 0 increase with the increase of η, indicating that the reliability of the core structure is increasing, so it can be inspected according to specific requirements; when 1<η<1.5, the lower boundary F of the stress value response is L (Q) is greater than 0, that is, all possible values ​​of the performance function are greater than 0, indicating that the core structure is completely reliable during service and the core structure does not need further inspection and improvement.

4. The time-varying reliability analysis system according to claim 3, characterized in that: The reliability analysis module uses a feedforward neural network to establish an extreme value prediction model of the performance function within the design reference period To approximately replace the original model F(Q) for solving the reliability index; By solving the The non-probabilistic reliability index η is obtained by using an analytical expression of .

5. The time-varying reliability analysis system according to claim 1, characterized in that: The interval variable of the static uncertainty parameter is expressed as: Among them, Y I represents an interval variable for a static uncertainty parameter, They represent the interval variables of the static uncertainty parameters corresponding to the outer diameter of the fuel rod, the total length of the fuel rod, the fuel density, and the neutron absorption content.

6. A time-varying reliability analysis method for a core structure applied to any time-varying reliability analysis system according to any one of claims 1 to 5, characterized in that: The time-varying reliability analysis method comprises the following steps: Step 1: Obtain interval variables to describe the static uncertainty parameters of the fuel rod outer diameter, total fuel rod length, fuel density, and neutron absorption content; and obtain the time-varying uncertainty parameters of the interval process model to describe the dynamic load and material performance degradation; Step 2: Establish a mapping relationship between the stress response corresponding to the static uncertainty parameters and the time-varying uncertainty parameters; Step 3: Determine the minimum accuracy of the core structure that meets the design requirements, that is, determine the maximum core structure uncertainty parameter stress response that meets the design requirements; Step 4: Whether the stress response of the static uncertainty parameter and the time-varying uncertainty parameter is less than the maximum stress response that meets the design requirements is used as a criterion for judging whether the core structure is in a safe state; Step 5: Perform time-invariant reliability analysis to obtain the time-varying reliability index of the core structure during service.

7. The time-varying reliability analysis method according to claim 6, characterized in that: In step 4, create a structure function: W(t)=e0-e(X I (t),Y I ,t) Where, e0 represents the stress allowable value of the core components to meet their functions, e(X I (t),Y I ,t) represents the response function of the uncertainty parameters in the core structure, X I (t) represents the interval process of time-varying uncertainty parameter, Y I represents the interval variable of the static uncertainty parameter, and t represents the time variable.

8. The time-varying reliability analysis method according to claim 7, characterized in that: In step 5, the following steps are also included: Step 51: Through KL expansion and corresponding transformation, the structure function can also be expressed as W(Q,t)=e0-e′(Q,t), The core structure of a space reactor is in a safe and reliable state during its service life, which means that within a given design service life [0, T], the performance function W(Q, t) is always greater than 0. By focusing only on whether the minimum value of the difference between the allowable value of the stress response of the uncertainty parameter in the time domain and the actual response is greater than 0, that is, Convert time-varying reliability analysis into time-invariant reliability analysis; Step 52: performing a time-invariant reliability analysis to obtain a time-varying reliability index η of the core structure during service; Step 53: In the process of calculating the structural reliability index, a feedforward neural network is used to establish an extreme value prediction model of the performance function within the design reference period. To approximately replace the original model F(Q) for solving the reliability index; Step 54: Use a feedforward neural network as the global proxy model of the dynamic system. A feedforward neural network consists of three types of layers, including input layer, hidden layer and output layer. The calculation process is expressed as The rectified linear unit (ReLU) is used as the activation function for training the fuzzy neural network, and the MSE between the actual training label and the predicted output is used as the loss function. Step 55: Obtain input sample set Q by sampling s , obtain the extreme value response F through an efficient global optimization algorithm s ,Using the training samples, an extreme value prediction model FNN is established.

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