A multi-state system multi-source inaccurate information correction method

Abstract

The application discloses a multi-state system multi-source inaccurate information correction method, comprising the following steps: step 1, constructing a reliability function of the system, building an evidence network model and a conditional belief quality table; step 2, collecting multi-source inaccurate information provided by experts on the reliability evaluation of the multi-state system at different moments in the whole life cycle of the multi-state system; step 3, constructing a reliability consensus reaching model according to the multi-source inaccurate information provided by the experts to correct the multi-source inaccurate information; by solving the model, the multi-source inaccurate information reaching a specified consensus threshold is obtained under the premise of fully respecting the original opinions of the experts; and step 4, calculating the reliability function of the system and outputting the reliability evaluation result reaching the consensus. The application can identify and effectively correct the multi-source inaccurate information collected from the multi-state system, and maximally resolves the conflicts, so that the reliability information at different levels is effectively fused.

Description

Technical Field

[0001] This invention belongs to the field of reliability technology, specifically relating to a method for correcting multi-source inaccurate information in a multi-state system. Background Technology

[0002] As modern engineering systems become increasingly large-scale, precise, information-based, and complex, they inevitably experience shortened lifespans, increased failure frequencies, and severe losses due to failures. Complex systems, during service, frequently suffer from safety accidents due to reliability issues, often resulting in incalculable losses. Therefore, it is urgent to conduct reliability assessment research on complex systems to improve reliable operating time and reduce failure risks. For complex systems, reliability assessment based on expert opinions overcomes the difficulties caused by small samples and limited data. Due to incomplete subjective knowledge, expert assessments are often imprecise, leading to cognitive uncertainty. Furthermore, experts may offer different types of opinions due to their different fields of expertise. Additionally, expert information may originate from different physical levels of the system. Information satisfying these three criteria is called multi-source imprecise information (MSII). In practical engineering, expert assessments are often difficult to represent with precise values ​​or probabilities, while multi-source imprecise information can effectively reflect some typical characteristics of expert opinions. Therefore, in recent years, methods for reliability assessment of multi-state systems using multi-source imprecise information have attracted considerable attention from scholars both domestically and internationally.

[0003] However, due to differences in expert knowledge backgrounds and the influence of information inaccuracy, multi-source inaccurate information may conflict to some extent. In such cases, it is impossible to directly fuse multi-source inaccurate information, leading to the failure of system reliability assessment. Therefore, how to identify opinions that conflict significantly with other expert opinions, and how to determine the direction and extent of opinion correction, ultimately ensuring that different experts hold a more consistent opinion on the system reliability range, is a crucial aspect of system reliability analysis based on expert opinions. In conclusion, there is an urgent need for a method for correcting multi-source inaccurate information in multi-state systems that can handle conflicting opinions from different experts, in order to fuse different expert opinions to obtain a more consistent reliability range. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method for correcting multi-source imprecise information in a multi-state system that can handle reliable opinions from multiple levels of conflict among different experts, quantify the degree of consensus among multiple sources of imprecise information, construct a system reliability consensus model to correct conflicting multiple sources of imprecise information, and make the corrected multiple sources of imprecise information meet a certain degree of consensus.

[0005] The objective of this invention is achieved through the following technical solution: a method for correcting multi-source inaccurate information in a multi-state system, comprising the following steps:

[0006] Step 1: Based on the state probability distribution of the components in the nuclear reactor control rod drive mechanism and the transfer function of the system, construct the reliability function of the system; based on the subordinate relationship between the components and the system, build the evidence network model of the nuclear reactor control rod drive mechanism, and construct the conditional belief quality table corresponding to each node.

[0007] Step 2: Collect multi-source inaccurate information provided by experts for the reliability assessment of the multi-state system at different points in the entire life cycle of the multi-state system;

[0008] Step 3: Based on the multi-source inaccurate information provided by experts, construct a reliability consensus model to correct the multi-source inaccurate information; by solving this model, obtain the multi-source inaccurate information that reaches the specified consensus threshold while fully respecting the original opinions of experts.

[0009] Step 4: Integrate the corrected multi-source inaccurate information, calculate the system's reliability function, and output the consensus-based reliability assessment results.

[0010] The beneficial effects of this invention are as follows: This invention proposes a method for correcting multi-source imprecise information in multi-state systems, which can handle reliability opinions from multiple levels of conflict among different experts, quantify the degree of consensus among multi-source imprecise information, construct a system reliability consensus model to correct conflicting multi-source imprecise information, so that the corrected multi-source imprecise information meets a certain degree of consensus, thereby realizing the reliability assessment of multi-state systems under conflicting opinions. Attached Figure Description

[0011] Figure 1 This is a flowchart illustrating the multi-source inaccurate information correction method for multi-state systems according to the present invention.

[0012] Figure 2 This is a structural diagram of the nuclear reactor control rod drive mechanism used in this embodiment;

[0013] Figure 3 This is the evidence network model used in this embodiment;

[0014] Figure 4 This is the correction result for multi-source inaccurate information in this embodiment. Detailed Implementation

[0015] The technical solution of the present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0016] like Figure 1As shown, the present invention provides a method for correcting multi-source inaccurate information in a multi-state system, comprising the following steps:

[0017] Step 1: Based on the state probability distribution of the components in the nuclear reactor control rod drive mechanism and the transfer function of the system, construct the reliability function of the system; based on the subordinate relationship between the components and the system, build the evidence network model of the nuclear reactor control rod drive mechanism, and construct the conditional belief quality table corresponding to each node.

[0018] This embodiment uses a nuclear reactor control rod drive mechanism (CRDM) consisting of five types of components: drive rod (DR), moving claw (MG), moving link (MLR), holding claw (SG), and holding link (SLR). Figure 2 As shown. The system mainly consists of subsystems. Maintaining the organization and subsystems Composition of mobile mechanisms and subsystems The subsystem consists of two retaining links and two sets of retaining claws. It consists of two moving links and two sets of moving claws. The holding links and moving links have low stress intensity and are two-state components. The holding claws, moving claws, and drive rods are three-state components; these components can operate in normal operation, complete failure, and derating states. Therefore, the entire nuclear reactor control rod drive mechanism has three states: complete failure state 1, normal operation state 3, and derating operation state 2. When the mechanism is in state 2 or 3, the system meets reliability requirements. Specifically, the subsystem... It consists of two parallel branches, with its state representing the highest performance state of the two branches. Each branch consists of a holding link and a holding chuck connected in series, with its state representing the lowest performance state of the link and chuck. For the subsystem... It is also based on a similar principle, subsystem Subsystem The control rod and drive rod DR are connected in series to form the entire control rod drive system. The lowest performance state among the three functional mechanisms represents the system's performance state. Therefore, the reliability function of the nuclear reactor control rod drive mechanism is specifically expressed as:

[0019] (1)

[0020] , , , , , , , and These represent the positions of retaining link 1, retaining link 2, moving link 1, moving link 2, retaining pawl 1, retaining pawl 2, moving pawl 1, moving pawl 2, and the drive rod, respectively. The probability of each state is modeled as a homogeneous Markov model, and the state probability distribution of each component is obtained. This is obtained by solving the Kolmogorov differential equation, specifically expressed as:

[0021] (2)

[0022] Indicates the first Each component is composed of State transition State transition strength, Indicates the first Components The number of states, l=1,2,…,9, represent the holding link 1, holding link 2, moving link 1, moving link 2, holding pawl 1, holding pawl 2, moving pawl 1, moving pawl 2, and drive rod, respectively.

[0023] Based on the aforementioned hierarchical relationships between components and the system, an evidence network model of the nuclear reactor control rod drive mechanism is constructed, such as... Figure 3 As shown. Figure 3 There are two logical connection methods between components and the system in the evidence network: "AND" and "OR". The conditional belief quality table of "AND" gate is shown in Table 1, and the conditional belief quality table of "OR" gate is shown in Table 2.

[0024] Table 1

[0025]

[0026] Table 2

[0027]

[0028] Step 2: Collect multi-source inaccurate information provided by experts for the reliability assessment of the multi-state system at different points in the entire life cycle of the multi-state system.

[0029] This embodiment collects information from three experts who assessed the system's reliability at different levels at different points in the nuclear reactor control rod drive mechanism's operating cycle. The state probabilities of components, subsystems, and the system as assessed by experts are expressed as follows: The first expert provided all the components of the system. The annual state probability interval information, provided by Expert 2, includes two subsystems and the drive rod. The expert 3 provides the state probability interval information for the entire system in the year. The state probability interval information for the year is shown in Table 3, with specific imprecise information.

[0030] Table 3

[0031]

[0032] Step 3: Based on the multi-source imprecise information provided by the three experts, construct a reliability consensus model to correct the multi-source imprecise information; by solving this model, obtain the multi-source imprecise information that reaches the specified consensus threshold while fully respecting the original opinions of the experts.

[0033] Multi-source imprecise information is represented in the form of intervals, denoted as , , , and These represent components, subsystems, and systems, respectively. , These are the lower and upper bounds of the multi-source imprecise information, respectively; the objective function of the consensus model is the total correction amount of all imprecise information, and the calculation method is shown in formula (3); the objective function contains 5 constraints, as shown in formulas (4) to (8);

[0034] (3)

[0035]

[0036] (4)

[0037] (5)

[0038] (6)

[0039] (7)

[0040] (8)

[0041] and Each inaccurate piece of information represents a part. Subsystem And the correction amount of system S, This represents the correction amount for multi-source inaccurate information; in this embodiment, , , , , , , , and These represent the positions evaluated by the first expert for retaining link 1, retaining link 2, moving link 1, moving link 2, retaining pawl 1, retaining pawl 2, moving pawl 1, moving pawl 2, and the drive lever. The correction amount for the state probability. , and These represent the second expert's views on the subsystem. Subsystem and the drive lever evaluation is located in The correction amount for the state probability. This indicates that the third expert has a positive view of the system. The assessment is located at The correction amount for the state probability. Indicates the number of parts. Indicates the number of subsystems. Indicates the first Subsystem The number of states, system representation The number of states; and These represent the upper and lower bounds of the corrected multi-source inaccuracy information, respectively. Indicates the corrected number of The individual opinion quality function under 100 expert opinions, where I represents the total number of experts. ~ The state probability of a corrected component, subsystem, or system is a function of the total transfer intensity of the component's degradation process; This indicates the use of evidence networks to assess the first... The system's reliability function is derived by reasoning based on inaccurate information provided by experts. It is a fusion operator used to combine The individual opinions of several experts are combined to form the collective opinion. This represents the corrected quality function of group opinions; express The degree of consensus among the experts' opinions. This indicates the predetermined consensus threshold.

[0042] By solving the model of formula (3), multi-source imprecise information that reaches the specified consensus threshold while fully respecting the original opinions of experts is obtained; the specific operation process is as follows:

[0043] Step 31: Represent the collected multi-source imprecise information at different levels at any given time as a distribution of prior belief quality for components, subsystems, or the system, specifically as follows:

[0044] (9)

[0045] Indicates that a component, subsystem, or system is in The mass function of the state Represents the empty set. This refers to the number of focal elements in the identification framework, representing the number of possible states of a component, subsystem, or system. In this embodiment, the prior belief quality distribution of the component, subsystem, or system is represented as follows:

[0046]

[0047]

[0048] Therefore, it can be seen that in this embodiment It can be 2 or 3;

[0049] According to the system's evidence network model ( Figure 3 The conditional belief quality tables (Table 1 and Table 2) of the reactor and its nodes are used to infer the a priori belief quality distribution into the belief quality distribution of the nuclear reactor control rod drive mechanism using equation (10), specifically expressed as follows:

[0050] (10)

[0051] Represents child nodes in the evidence network The parent node; Represents a node The conditional belief quality table reflects the dependency relationship between the node and its parent node. Represents a node The belief quality distribution of the parent node; Table 4 shows the belief quality distribution of the nuclear reactor control rod drive mechanism under the opinions of three experts.

[0052] Table 4

[0053]

[0054] Based on the correspondence between the system's belief quality distribution and the system's reliability function, the system's reliability interval is obtained, specifically expressed as:

[0055] (11)

[0056] and These represent the opinions of the i-th expert, respectively. Upper and lower bounds of the system reliability function at time t; The belief function represents the system state. The likelihood function representing the system state; It is the focal element in any state (2-state or 3-state) of the belief mass distribution of the nuclear reactor control rod drive mechanism that satisfies the system reliability requirements. The set of states that do not meet the reliability requirements of the nuclear reactor control rod drive mechanism (state 1); if you are interested in the reliability of the system at a certain time during the operation of the system, then construct an optimization model to solve the reliability function of the system at any time; the objective function is the upper and lower bounds of the system reliability function at any time, and its calculation method is shown in equation (12). The objective function includes four constraints from equation (13) to (16);

[0057] (12)

[0058]

[0059] (13)

[0060] (14)

[0061] (15)

[0062] (16)

[0063] The vector representing the transfer intensity of the degradation process of all components of the nuclear reactor control rod drive mechanism is specifically represented as: ; The state probability of a component, subsystem, or system is a function of the total transfer intensity of the component's degradation process. The system reliability function also represents the transfer strength of all components and time. The function;

[0064] Taking the assessment opinion provided by the first expert as an example, in order to evaluate the reliability of the nuclear reactor control rod drive mechanism throughout its entire life cycle, the upper and lower bounds of the system reliability function at any time are used as the optimization objective, the upper and lower bounds of the reliability under the first expert's opinion at t=10 years are used as the constraints, and the total transfer strength of the components is used as the optimization variable. The following optimization model is constructed to solve the reliability function of the system at any time:

[0065] (17)

[0066] The constraints for optimizing the model are:

[0067] (18)

[0068] (19)

[0069] (20)

[0070] (twenty one)

[0071] Equation (18) indicates that the state probability of a component is a function of the total transfer intensity of its degradation process;

[0072] By constructing the individual opinion quality function of the system using the reliability function at any time point, an identification framework is established. , This indicates that the system is working. This indicates a system failure; therefore, the first The individual opinion quality function of each expert is specifically expressed as:

[0073] (twenty two)

[0074] In a closed world, the following conditions are usually met. That is, the mass of the system when the state is in an empty set is zero at any time; and They represent the first The belief value that the system is in a working or failed state based on the expert evaluation opinions. This indicates the magnitude of cognitive uncertainty. Three experts... The individual opinion quality function for each year is shown in Table 5.

[0075] Table 5

[0076]

[0077] Step 32: Use the ordered weighted average operator to calculate the individual opinion quality function obtained in Step 31. The fusion is expressed as a group opinion quality function, specifically as follows:

[0078] (twenty three)

[0079] (twenty four)

[0080] (25)

[0081] Describe the quality function of group opinions at any given time. Each term in the vector represents a quality function of an individual opinion from an expert. This represents the reliability fusion weight vector for each expert, where, and Three experts The group opinion quality function for that year is shown in Table 5.

[0082] Step 33: This embodiment specifies the entire life cycle of the nuclear reactor control rod drive mechanism. In 2018, using the individual and group opinion quality functions obtained in steps 31 and 32, the group consensus level and average group consensus level of each individual opinion were calculated to identify multi-source imprecise information with low consensus levels, specifically represented as follows:

[0083] (26)

[0084] (27)

[0085] and They represent the first The opinions of the experts The degree of group consensus at any given moment and in Average level of group consensus over a given period; The dimension is The matrix, whose elements are calculated from the Jaccard coefficients, is specifically represented as:

[0086]

[0087] The opinions of the three experts in this embodiment are... Average level of group consensus over a period of time , and They are represented as follows:

[0088]

[0089]

[0090]

[0091] This allows for the identification of multi-source, imprecise information with low consensus levels.

[0092] Step 34: Based on the degree of consensus among the multi-source imprecise information obtained in Step 33, determine whether the degree of consensus is greater than or equal to the prescribed consensus threshold. Requirements; This embodiment specifies the consensus threshold. ;

[0093] If the requirements are not met, the multi-source inaccurate information is corrected, and then the process returns to step 31; since each piece of inaccurate information is represented as an interval, it is denoted as... Therefore, it is necessary to correct both its upper and lower bounds. The specific method is as follows:

[0094] (28)

[0095] (29)

[0096] If the requirements are met, proceed to step 4 to output the consensus-reaching multi-source inaccurate information and the system's reliability function.

[0097] Step 4: After repeated corrections of conflicting multi-source imprecise information, multi-source imprecise information that meets the consensus threshold is obtained. The corrected multi-source imprecise information is then fused, the system reliability function is calculated, and the reliability assessment result of the consensus is output. In this embodiment, the reliability intervals and fusion results under each expert opinion after correction are as follows: Figure 4 As shown.

[0098] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A method for correcting multi-source inaccurate information in a multi-state system, characterized in that, Includes the following steps: Step 1: Based on the state probability distribution of the components in the nuclear reactor control rod drive mechanism and the transfer function of the system, construct the reliability function of the system; based on the subordinate relationship between the components and the system, build the evidence network model of the nuclear reactor control rod drive mechanism, and construct the conditional belief quality table corresponding to each node. Step 2: Collect multi-source inaccurate information provided by experts for the reliability assessment of the multi-state system at different points in the entire life cycle of the multi-state system; Step 3: Based on the multi-source inaccurate information provided by experts, construct a reliability consensus model to correct the multi-source inaccurate information; by solving the reliability consensus model, obtain the multi-source inaccurate information that reaches the specified consensus threshold while fully respecting the original opinions of experts; the objective function of the reliability consensus model is the total correction amount of all inaccurate information. By solving the objective function of the reliability consensus model, obtain the multi-source inaccurate information that reaches the specified consensus threshold while fully respecting the original opinions of experts; the specific operation process is as follows: Step 31: Represent the collected multi-source imprecise information at different levels at any given time as a prior belief quality distribution of components, subsystems, or the system; transform the prior belief quality distribution into the system's belief quality distribution using an evidence network model; solve for the system's reliability interval based on the correspondence between the system's belief quality distribution and the system's reliability function; construct the system's individual opinion quality function using the system's reliability function at any given time. Step 32: Use the ordered weighted average operator to merge the individual opinion quality functions obtained in Step 31 into a group opinion quality function; Step 33: Using the individual opinion and group opinion quality functions obtained in Step 31 and Step 32, calculate the group consensus degree and average group consensus degree for each individual opinion, and identify multi-source imprecise information with low consensus degree; Step 34: Based on the average group consensus level among the multi-source imprecise information obtained in Step 33, determine whether the average group consensus level is greater than or equal to the specified consensus threshold requirement; if the requirement is not met, correct the multi-source imprecise information and then return to Step 31; if the requirement is met, execute Step 4 and output the multi-source imprecise information that has reached consensus and the reliability function of the system. Step 4: Integrate the corrected multi-source inaccurate information, calculate the system's reliability function, and output the consensus-based reliability assessment results.

2. The method for correcting multi-source inaccurate information in a multi-state system according to claim 1, characterized in that, In step 1, the component degradation process is modeled as a homogeneous Markov model, and the component's state probability distribution is... This is obtained by solving the Kolmogorov differential equation, specifically expressed as: （1）； Indicates the first Each component is composed of State transition State transition strength, Indicates the first Components The number of states.

3. The method for correcting multi-source inaccurate information in a multi-state system according to claim 2, characterized in that, The multi-source inaccurate information in step 3 is represented in interval form, denoted as . , , , and These represent components, subsystems, and systems, respectively. , These are the lower and upper bounds of the multi-source imprecise information, respectively; the objective function of the reliability consensus model is the total correction amount of all imprecise information, and the calculation method is shown in formula (2); the objective function contains 5 constraints, as shown in formulas (3) to (7); （2）； （3）； （4）； （5）； （6）； （7）； and Each inaccurate piece of information represents a part. Subsystem And the correction amount of system S, This represents the correction amount for inaccurate information from multiple sources; Indicates the number of parts. Indicates the number of subsystems. Indicates the first Subsystem The number of states, system representation The number of states; and These represent the upper and lower bounds of the corrected multi-source inaccuracy information, respectively. Indicates the corrected number The individual opinion quality function under 100 expert opinions, where I represents the total number of experts. ~ The state probability of a corrected component, subsystem, or system is a function of the total transfer intensity of the component's degradation process; This indicates the use of evidence networks to assess the first... The system's reliability function is derived by reasoning based on inaccurate information provided by experts. It is a fusion operator used to combine The individual opinions of several experts are combined to form the collective opinion. This represents the corrected quality function of group opinions; express The degree of consensus among the experts' opinions. This represents the predetermined consensus threshold; By solving the model of formula (2), we obtain multi-source imprecise information that reaches the specified consensus threshold while fully respecting the original opinions of experts; the specific operation process is as follows: Step 31: Represent the collected multi-source imprecise information at different levels at any given time as a distribution of prior belief quality for components, subsystems, or the system, specifically as follows: （8）； Indicates that a component, subsystem, or system is in The mass function of the state To represent the empty set, It is the number of focal elements in the identification framework, representing the number of possible states of a component, subsystem, or system. The prior belief quality distribution is transformed into the system's belief quality distribution using an evidence network model, specifically represented as follows: （9）； Represents child nodes in the evidence network The parent node; Represents a node The conditional belief quality table reflects the dependency relationship between the node and its parent node. Represents a node The belief quality distribution of the parent node; based on the correspondence between the system's belief quality distribution and the system's reliability function, the system's reliability interval is obtained, specifically expressed as: （10）； and These represent the opinions of the i-th expert, respectively. Lower and upper bounds of the system reliability function at time t; The belief function represents the system state. The likelihood function representing the system state; It is the focal element in any state of the belief mass distribution of the nuclear reactor control rod drive mechanism that satisfies the system reliability requirements. This represents the set of states that do not meet the reliability requirements of the nuclear reactor control rod drive mechanism; if we are interested in the reliability of the system at a certain time during operation, we construct an optimization model to solve the reliability function of the system at any time; the objective function is the upper and lower bounds of the system reliability function at any time, and its calculation method is shown in equation (11). The objective function includes four constraints from equation (12) to (15). （11）； （12）； （13）； （14）； （15）； A vector representing the transfer intensity of the degradation process of all components of the nuclear reactor control rod drive mechanism. The state probability of a component, subsystem, or system is a function of the total transfer intensity of the component's degradation process. The system reliability function also represents the transfer strength of all components and time. The function; using the reliability function of the system at any time point to construct the individual opinion quality function of the system, and establishing an identification framework. , This indicates that the system is working. This indicates a system failure; therefore, the first The individual opinion quality function of each expert is specifically expressed as: （16）； In a closed world, the conditions are met. That is, the mass of the system when the state is in an empty set is zero at any time; and They represent the first The belief value that the system is in a working or failed state based on the expert evaluation opinions. Indicates the magnitude of cognitive uncertainty; Step 32: Use the ordered weighted average operator to calculate the individual opinion quality function obtained in Step 31. The fusion is expressed as a group opinion quality function, specifically as follows: （17）； （18）； （19）； Describe the quality function of group opinions at any given time. Each term in the vector represents a quality function of an individual opinion from an expert. This represents the reliability fusion weight vector for each expert, where, and ; Step 33: Using the individual and group opinion quality functions obtained in Steps 31 and 32, calculate the group consensus level and average group consensus level for each individual opinion, and identify multi-source imprecise information with low consensus levels, specifically represented as follows: （20）； （21）； and They represent the first The opinions of the experts The degree of group consensus at any given moment and in Average level of group consensus over a given period; The dimension is The matrix, whose elements are calculated from the Jaccard coefficients, is specifically represented as: ； Step 34: Based on the average group consensus level among the multi-source imprecise information obtained in Step 33, determine whether the average group consensus level is greater than or equal to the prescribed consensus threshold. Require; If the requirements are not met, the multi-source inaccurate information is corrected, and then the process returns to step 31; since each piece of inaccurate information is represented as an interval, it is denoted as... Therefore, it is necessary to correct both its upper and lower bounds. The specific method is as follows: （22）； （23）； If the requirements are met, proceed to step 4 to output the consensus-reaching multi-source inaccurate information and the system's reliability function.

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