A multi-objective optimization method and system for nuclear power system sensor deployment

Abstract

The application discloses a kind of multi-objective optimization method and system for nuclear power system sensor layout, comprising: based on directed graph theory, by analyzing fault propagation path and the correlation matrix of sensor and fault is established by the correlation of fault and sensor, and correlation matrix is improved based on actual industrial process;Establish the reliability model of sensor arrangement number and position;Based on the correlation matrix of sensor and fault, form the multi-objective optimization model of sensor optimal arrangement;Improved NSGA-II algorithm is constructed, and multi-objective optimization model is solved based on NSGA-II algorithm;Realize sensor selection and arrangement multi-objective optimization;The formed sensor selection and arrangement multi-objective optimization method is verified in nuclear power system deaerating system simulation model.The application establishes the quantitative relationship between fault diagnosis efficiency and sensor arrangement number and position, improves the fault diagnosis capability to the operating state of nuclear power equipment, and guarantees the safe operation of nuclear power station.

Description

Technical Field

[0001] This invention relates to nuclear power systems, and in particular to a multi-objective optimization method and system for sensor deployment in nuclear power systems. Background Technology

[0002] Safety and reliability are indispensable prerequisites for ensuring the sustainable development of the nuclear power industry, and sensors are key equipment for characterizing the operating status of nuclear power plants. In the engineering practice of nuclear power plants, the number of sensors that can be deployed is clearly constrained by practical conditions such as space layout, cost budget, and equipment compatibility. Based on the above considerations, the placement of sensors must follow strict positioning criteria. The core objective is to achieve accurate mapping and feature extraction of the system's operating status through the scientific selection of key monitoring points, ensuring that the monitoring data can truly reflect the dynamic operating characteristics of the system. However, as a typical multivariate strongly coupled system, the nuclear power system contains process variables with high dimensionality and strong correlation characteristics, which makes determining the optimal number of sensors and selecting the optimal placement locations a significant technical challenge. Therefore, in the context of the deep application of nuclear power plant simulation technology and the gradual construction of intelligent operation and maintenance systems, the systematic optimization of the number and placement of sensors is not only a technical path to improve the core effectiveness of fault diagnosis systems, but also a key preliminary work to support the accuracy of nuclear power system status perception and intelligent operation and maintenance decision-making, which has important theoretical value and practical guiding significance.

[0003] The directed graph-based multi-objective optimization method for sensor deployment, as an innovative technical solution with outstanding application prospects in the field of sensor optimization, can provide strong support for fault diagnosis and safety monitoring of critical systems in nuclear power plants. The main drawbacks of existing technologies can be summarized as follows:

[0004] 1. Traditional methods often involve complex or abstract system models, making it difficult for engineers to quickly understand and grasp the actual structure and relationships of the system.

[0005] 2. The reasoning process of traditional methods may be like a "black box," with the basis and path to the conclusion not being clear enough, making it difficult to convince people and to be effectively verified;

[0006] 3. When dealing with large and complex systems like nuclear power plants, which have many components and are tightly coupled, traditional methods encounter bottlenecks in computational efficiency, analytical accuracy, or implementation feasibility, and lack scalability. Summary of the Invention

[0007] Purpose of the invention: The purpose of this invention is to provide a multi-objective optimization method and system for sensor deployment in nuclear power systems. Based on directed graph theory, it proposes a sensor optimization layout scheme for nuclear power equipment fault diagnosis tasks, establishes a quantitative relationship between fault diagnosis efficiency and the number and location of sensors, improves the fault diagnosis capability of nuclear power equipment operating status, and ensures the safe operation of nuclear power plants.

[0008] Technical solution: The method described in this invention includes the following steps:

[0009] Based on directed graph theory, a correlation matrix between sensors and faults is established by analyzing fault propagation paths and the correlation between faults and sensors, and the correlation matrix is ​​improved based on actual industrial processes.

[0010] Establish a reliability model for the number and location of sensors, including models of the number of sensors and fault diagnosis capability, and models of sensor location and fault diagnosis capability. The construction of the model of the number of sensors and fault diagnosis capability includes: establishing a probabilistic statistical model of sensor failure and inability to diagnose system faults, calculating the probability of sensor failure and the probability that the failure cannot be detected by the entire sensor system. Based on information entropy theory and Bayesian model, construct a model of sensor location and fault diagnosis capability.

[0011] A multi-objective optimization model for optimal sensor placement is formed based on the correlation matrix between sensors and faults. The objective functions include: minimizing the cost of sensor placement under the sensor configuration scheme, minimizing the undetectable rate of system faults, and maximizing the ability of the sensor system to obtain fault information under the sensor configuration scheme. The constraints include: setting an upper limit on the number of sensors at each measuring point and requiring at least one corresponding sensor to be placed for each fault in the system.

[0012] The NSGA algorithm is improved by introducing a fast non-dominated sorting operator, using a crowding comparison operator to maintain the diversity and uniformity of the solution set, and passing on superior individuals from the evolutionary process to the next generation through an elite retention strategy, resulting in the improved NSGA-II algorithm. The NSGA-II algorithm is then used to solve a multi-objective optimization model, achieving multi-objective optimization of sensor selection and placement.

[0013] The resulting multi-objective optimization method for sensor selection and placement was validated in a simulation model of a nuclear power system's deoxygenation system.

[0014] Furthermore, the correlation matrix between sensors and faults Represented as:

[0015] ;

[0016] in, When the fault occurs The sensors are arranged in the... The fault results detected at each location This indicates the number of sensors at a given location. Indicates the total number of positions; The expression is: ; To characterize the coefficients that represent the influence of the sensor's measurement environment, The internal detection coefficient of the sensor;

[0017] Improved correlation matrix The expression is:

[0018] ;

[0019] in, .

[0020] Furthermore, the probabilistic statistical model for the inability to diagnose system faults due to sensor failure is expressed as follows:

[0021] ;

[0022] in, For time; Let be a random variable, representing the time interval. The number of times the internal sensor system failed; In the time interval The number of times the internal sensor system fails is equal to The probability of; This indicates the number of times the sensor system fails within a calibration cycle. These are characteristic coefficients related to sensor stability; the probability of sensor failure. Represented as:

[0023] ;

[0024] in, In the time interval The probability that the internal sensor will not fail;

[0025] Due to malfunction The probability of an event occurring that cannot be detected by the entire sensor system. Should meet:

[0026] ;

[0027] in, Defined as fault The probability of occurrence can be obtained through experience; for The number of redundant sensors deployed at the location. for Characteristic coefficients related to the stability of position sensors.

[0028] Furthermore, the modeling methods for sensor location and fault diagnosis capabilities include:

[0029] According to Bayes' theorem, if a fault occurs in the system... If the event is the source of the fault, then the description of the fault is a fault. Posterior probability of occurrence:

[0030] ;

[0031] in, For fault The posterior probability of occurrence, This represents the total number of fault types.

[0032] Construction Fault Self-information The mathematical expression is:

[0033] ;

[0034] Fault probability of occurrence The smaller the value, the more likely it is to cause a malfunction. Posterior probability of occurrence The smaller, The larger the value; if the fault source is definite, then the fault... The self-information is 0; according to the conditional probability formula, after deploying sensors... Then, construct a fault. Conditional self-information The mathematical expression is:

[0035] ;

[0036] in, For sensors Fault detected The probability of occurrence, which is a probability distribution model;

[0037] Based on Bayes' theorem, by constructing faults Sensor when it occurs Probability distribution model capable of diagnosing faults Then for The result is as follows:

[0038] ;

[0039] probability distribution model Further expressed as:

[0040] ;

[0041] in, for Characteristic coefficients related to the stability of position sensors To determine the fault without considering sensor information The probability of occurrence;

[0042] Changes in the information entropy of the system for fault diagnosis before and after sensor deployment Represented as:

[0043] ;

[0044] Therefore, by analyzing the changes in information entropy, a quantitative analysis model was established to determine the impact of sensor placement on the fault diagnosis capability of the entire sensor system.

[0045] Furthermore, under the sensor configuration scheme, the cost of deploying the sensors... Represented as:

[0046] ;

[0047] in, For the cost of a single sensor, In order to be in The number of sensors deployed at the location, , The location number representing the sensor placement point;

[0048] System fault undetectability rate The expression is:

[0049] ;

[0050] in, Indicates a fault The probability of something occurring that cannot be detected by the entire sensor system. Indicates a fault The probability of occurrence;

[0051] Under the sensor configuration scheme, the correlation model between faults and measuring points Represented as:

[0052] ;

[0053] in, Indicates in The ability of the sensor system to obtain fault information. The larger the value, the higher the efficiency of the sensor system in fault diagnosis. This represents the change in information entropy of the system during fault diagnosis. Indicates the first The configuration status of each location. This indicates the total number of locations where sensors can be installed. This indicates the total number of fault types that need to be diagnosed.

[0054] Furthermore, the multi-objective optimization model for optimal sensor placement is expressed as follows:

[0055] ;

[0056] in, This indicates the cost of deploying the sensors. In order to be in The number of sensors deployed at the location, , The location number representing the sensor placement point. For the cost of a single sensor, This indicates the rate at which system faults are undetectable. Indicates a fault The probability of something occurring that cannot be detected by the entire sensor system. Indicates a fault The probability of occurrence Indicates in The ability of the sensor system to obtain fault information. Represents the fault-measuring point mutual information matrix. For the decision variable vector, This represents the upper limit on the number of sensors at a specific location. It is a set of positive integers. Indicates the first The sensor for the first Sensitivity to various faults.

[0057] Furthermore, the multi-objective optimization model is solved based on the NSGA-II algorithm, including:

[0058] First, the system generates an initial population randomly and performs an initial fast non-dominated sort to determine individual rank, then initializes the number of generations. In each iteration, the population sequentially undergoes selection, crossover, and mutation operators to produce offspring, and the parent and offspring populations are merged to maintain the genetic stability of superior genes. Next, the algorithm performs another fast non-dominated sort on the merged population and introduces a crowding calculation mechanism to evaluate the distribution density of individuals in the solution space, thereby selecting the individuals with the best overall performance to form the new generation of parent population. This iterative process continues until the number of generations reaches a preset termination limit, at which point the algorithm stops and outputs the optimized Pareto solution set.

[0059] The system corresponding to the method described in this invention includes:

[0060] The correlation matrix improvement unit is used to establish a correlation matrix between sensors and faults based on directed graph theory by analyzing fault propagation paths and the correlation between faults and sensors, and to improve the correlation matrix based on actual industrial processes.

[0061] The reliability model building unit is used to establish reliability models for the number and location of sensors, including models of the number of sensors and fault diagnosis capability, and models of sensor location and fault diagnosis capability. The construction of the model of the number of sensors and fault diagnosis capability includes: establishing a probabilistic statistical model of sensor failure and inability to diagnose system faults, calculating the probability of sensor failure and the probability that the failure cannot be detected by the entire sensor system; and constructing a model of sensor location and fault diagnosis capability based on information entropy theory and Bayesian model.

[0062] The multi-objective optimization model construction unit is used to form a multi-objective optimization model for optimal sensor placement based on the correlation matrix between sensors and faults. The objective functions include: minimizing the cost of sensor placement under the sensor configuration scheme, minimizing the undetectable rate of system faults, and maximizing the ability of the sensor system to obtain fault information under the sensor configuration scheme. The constraints include: setting an upper limit on the number of sensors at each measuring point and requiring at least one corresponding sensor to be placed for each fault in the system.

[0063] The model solving unit is used to improve the NSGA algorithm, including: introducing a fast non-dominated sorting operator, using a crowding comparison operator to maintain the diversity and uniformity of the solution set, and using an elite retention strategy to pass on superior individuals in the evolutionary process to the next generation, resulting in the improved NSGA-II algorithm. The NSGA-II algorithm is then used to solve multi-objective optimization models, realizing multi-objective optimization of sensor selection and placement.

[0064] The verification unit is used to verify the developed multi-objective optimization method for sensor selection and placement in a simulation model of a nuclear power system deoxygenation system.

[0065] A non-volatile storage medium for storing and executing the method, for storing a computer program, wherein the computer program implements the method when executed by a processor.

[0066] A computer program product for storing and executing the method includes a computer program / instructions that, when executed by a processor, implement the method.

[0067] Beneficial effects: Compared with the prior art, the significant technical effects of the present invention are: (1) Based on the representation form of directed graph, a correlation matrix between sensor and fault is established through directed graph, and improved by combining the multi-dimensional and strongly coupled causal relationship in actual industrial process. The improved correlation matrix is ​​more readable in engineering; (2) A reliability model based on multi-objective optimization of the number and location of sensor arrangement is proposed. This model is more comprehensive than the previous model and clearly reveals the dynamic propagation path and hierarchical evolution law of a specific fault from the initial triggering source to the subsequent affected nodes in an intuitive and rigorous way; (3) An improved NSGA-II algorithm is proposed to solve the reliability model established in (2). This algorithm has lower complexity, higher accuracy and faster solution speed than the traditional algorithm. Attached Figure Description

[0068] Figure 1 This is a flowchart of the multi-objective optimization method described in this invention;

[0069] Figure 2 This is a schematic diagram of a 6-node undirected graph model;

[0070] Figure 3 This is a schematic diagram of a 6-node directed graph model;

[0071] Figure 4 This is a schematic diagram of a fast non-dominated sorting algorithm for a bi-objective optimization problem.

[0072] Figure 5 This is a flowchart of the NSGA-II algorithm;

[0073] Figure 6 This is a model diagram of the deaerator system for verifying the method;

[0074] Figure 7 This is a schematic diagram of the Pareto solution set of a multi-objective model during the multi-objective iterative process of sensor deployment under standard conditions;

[0075] Figure 8 This is a schematic diagram illustrating the relationship between the extreme values ​​of the number of sensors and the iteration process during multi-target sensor deployment under standard conditions.

[0076] Figure 9This is a schematic diagram showing the arrangement of the number of sensors at different locations during a multi-target iteration process under standard conditions.

[0077] Figure 10 This is a schematic diagram illustrating the relationship between sensor deployment cost and detection unreliability under standard conditions;

[0078] Figure 11 This is a diagram illustrating the relationship between sensor deployment cost and fault correlation under standard conditions;

[0079] Figure 12 This is a schematic diagram illustrating the correlation between sensor detection unreliability and faults under standard conditions;

[0080] Figure 13 This is a schematic diagram of the Pareto solution set of a multi-objective model under standard conditions with multiple sensors.

[0081] Figure 14 This is a schematic diagram illustrating the relationship between the extreme values ​​of the number of multiple sensors and iterative changes under a standard multi-sensor arrangement.

[0082] Figure 15 This is a schematic diagram showing the arrangement of the number of sensors in different locations under standard multi-sensor layout conditions. Detailed Implementation

[0083] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0084] like Figure 1 As shown, the method of the present invention includes the following steps:

[0085] First, based on directed graph theory, a correlation matrix between sensors and faults is established and improved by analyzing fault propagation paths and the correlation between faults and sensors. Then, based on information entropy theory and Bayesian models, a reliability model for the number and location of sensors is constructed, forming a multi-objective optimization model for optimal sensor placement, which is solved using the NSGA-II algorithm. Finally, the results of the multi-objective optimization of sensor selection and placement are validated in a simulation model of a nuclear power system's deoxygenation system.

[0086] (1) Based on directed graph theory, the correlation matrix between sensors and faults is established by analyzing the fault propagation path and the correlation between faults and sensors, and then improved.

[0087] The mathematical description of the directed graph model of the sensor system used in nuclear power heat exchange systems can be expressed as:

[0088] (1)

[0089] in, For the directed graph model of the sensor system, it is a triplet structure; This represents the functional relationships within a directed graph. These are edge attribute functions used to describe the characteristics of each directed edge; It is a directed graph. Defined as:

[0090] (2)

[0091] in, It is the set of nodes in a directed graph. Represents system variables; It is the set of cause nodes in a directed graph. Indicates the cause node; It is a set of directed edges. Indicates from system variables to system variables Relationship, and For set Elements within a directed graph. Functional relationships within the directed graph. It can be represented as:

[0092] (3)

[0093] Here, -1 and +1 represent the symbols for directed edges.

[0094] In addition, edge attribute functions It can be defined as:

[0095] (4)

[0096] in, This represents the state of a variable node; similar definitions exist:

[0097] (5)

[0098] in, The state of the cause node. At any given moment, the set of instantaneous state values ​​of all nodes in a directed graph model is called the instantaneous sample. A comparison of a 6-node undirected graph and a directed graph is shown below. Figure 2 and Figure 3 As shown.

[0099] In a directed graph model, the three symbols represent three different states of the process system. The different signals "+1", "0", and "-1" represent the limit range above the normal state, the normal state, and the limit range below the normal state, respectively. The positive values ​​of the directed edges... This indicates that the cause node and the result node change in the same direction, while negative values... This indicates that the direction of change is reversed. The cause node is defined as the root node of the anomaly, representing whether a system failure has occurred. If the state of the cause node is "0", it means that the process is in a normal state.

[0100] Typically, directed graphs can be represented using an adjacency matrix. Let the adjacency matrix of a directed graph be... ,in Represents the number of nodes, matrix elements for:

[0101] (6)

[0102] Establish adjacency matrix Afterwards, the reachable matrix It can be defined as:

[0103] (7)

[0104] In the formula, For directed graphs The length of the longest connected path.

[0105] also, reachability matrix The element in the table represents a global node. When an anomaly occurs, for global nodes The resulting final state effect takes the value of +1, -1, or 0, and is represented as .

[0106] To eliminate redundant dimensions of unmeasurable intermediate variables, a low-dimensional space targeting the diagnostic objective is constructed. Perform node set mapping extraction, assuming the system has a node set mapping extraction... The location sensor has a global node index of 1. The correlation matrix between sensors and faults elements in It can be defined as:

[0107] (8)

[0108] According to the above definition, This indicates a global node. When an anomaly occurs, at a certain location The impact of individual sensors. (By elements) The correlation matrix between the sensor and the fault (Hereinafter referred to as the correlation matrix) can be defined as:

[0109] (9)

[0110] Wherein, the first in the matrix row vector This represents the time when the fault occurs. The result detected by the first sensor can be regarded as the sensor characteristic after a certain fault occurs. And the result of the second sensor... column vector It represents a certain position. The fault results detected by the sensors deployed at the location can be regarded as the measuring points. The sensor's ability to detect faults. And any... Line number Column elements This represents the time when the fault occurred. The sensors are arranged in the... The fault results detected at each location This indicates the number of sensors at a given location. This indicates the total number of positions.

[0111] The above content transforms the qualitative relationship between system fault states and sensor reading changes into a graphical relationship, and proposes a correlation matrix. The following section will improve the correlation matrix based on actual industrial processes.

[0112] In actual industrial processes, the changes in process variables caused by faults not only include differences in readings but also directional information, such as increases or decreases in readings. Therefore, the correlation matrix between sensors and faults... The qualitative information represented by Boolean values ​​is not rich enough, and information about the direction of the fault's impact will be lost, making it impossible to effectively isolate the fault in some cases.

[0113] In reality, whether the true state of a variable at a measurement point can be effectively detected by the sensor can be considered a probabilistic problem. The sensor's ability to detect faults is not only related to external environmental factors but also significantly influenced by the sensor's own sensitivity and reliability. Based on this, a sensor... For the fault The detection capability model of a sensor: The mathematical model of a sensor's fault detection capability needs to consider both internal sensor factors and the external measurement environment. Its mathematical expression can be expressed as:

[0114] (10)

[0115] in, It is a continuous variable representing the sensor's fault detection capability. , , ; To characterize the coefficients that represent the influence of the sensor's measurement environment, The value can be determined based on relevant empirical formulas. For ease of calculation, let... ; The internal detection coefficient of the sensor can be defined as:

[0116] (11)

[0117] in, Indicates sensor Detection Fault sensitivity; Indicates sensor Its own signal-to-noise ratio; Indicates sensor Detection The detection time; This indicates the duration for which the sensor can continuously detect a fault. Indicates a fault Continue until the sensor The required duration was detected. Improved correlation matrix. The elements within can be represented as:

[0118] (12)

[0119] Improved correlation matrix It can be represented in matrix form as follows:

[0120] (13)

[0121] The improved correlation matrix between nuclear power system sensors and faults has been transformed from a simple Boolean matrix into a probability matrix that truly reflects the sensor's fault detection capability. This matrix can contain more effective information, and by incorporating the sensor's fault detection capability into the optimization layout model, the accuracy of the optimization results is greatly improved.

[0122] (2) Establish a reliability model for the number and location of sensors, including a model of the number of sensors and fault diagnosis capability, and a model of the location of sensors and fault diagnosis capability.

[0123] The modeling methods for the relationship between the number of sensors and fault diagnosis capability include:

[0124] Sensor failure is a significant factor affecting sensor diagnostic capabilities. Digital sensors are susceptible to electromagnetic interference (EMI) and radio frequency interference (RFI) during measurement, which can prevent them from accurately updating key field parameters in real time. External electromagnetic interference can cause a small probability of sensor software, controller, or communication failures, leading to sensor measurement failure. Furthermore, random errors inevitably occur in the process parameters of sensor measurements; we can assume that these random errors follow a probability statistical distribution. Additionally, each measuring instrument needs to be calibrated within a unit period. Therefore, we can assume that sensor failure and inability to diagnose equipment faults within a calibration period is a low-probability event. The time it takes for an instrument to reliably measure the system follows an exponential probability distribution, and the probability of instrument failure is independent of operating time. Therefore, the statistical model for the probability of sensor failure and inability to diagnose system faults within a calibration period can be expressed as:

[0125] (14)

[0126] in, For time; Let be a random variable, representing the time interval. The number of times the internal sensor system failed; In the time interval The number of times the internal sensor system fails is equal to The probability of; This indicates the number of times the sensor system fails within a calibration cycle. These are characteristic coefficients related to sensor stability. In other words, if the sensor operates normally during the two calibration periods, it means the sensor has not failed. Therefore, the probability of sensor failure is... It can be represented as:

[0127] (15)

[0128] in, In the time interval The probability that the internal sensor will not fail.

[0129] Due to malfunction The probability of an event occurring that cannot be detected by the entire sensor system. Should meet:

[0130] (16)

[0131] in, Defined as fault The probability of occurrence can be obtained through experience; for The number of redundant sensors deployed at the location. for Characteristic coefficients related to the stability of position sensors.

[0132] Methods for establishing models of sensor location and fault diagnosis capabilities include:

[0133] According to Bayes' theorem, if a fault occurs in the system... If an event is the source of a fault, then it can be described as a fault. The posterior probability of occurrence can be expressed by the following formula:

[0134] (17)

[0135] in, For fault The posterior probability of occurrence, This represents the total number of fault types.

[0136] Fault detection capabilities can be characterized using the law of mutual information in information theory. In information theory, information entropy, as a core concept, is used to measure the uncertainty of an event. When a macroscopic event has multiple possible microscopic realizations, the specific microscopic state that the event ultimately presents is uncertain to the observer; this uncertainty is quantified as information entropy. Information and information entropy exhibit a binary opposition in their essential attributes. The essential function of information is to eliminate the uncertainty of events; therefore, the process of reducing information entropy essentially corresponds to the process by which the observer acquires information.

[0137] The impact of sensor placement on the system's fault diagnosis capability is mainly considered in the following two cases: When no sensors are placed in the system, the system's fault diagnosis follows statistical laws, as shown in formula (17). Since the system fault cannot be diagnosed through process data at this time, it can only be judged through posterior probability. The process data is in a highly disordered state, and the information entropy of the fault diagnosis system is the largest at this time. When the system has reasonable sensor placement, all faults in the system can be isolated and diagnosed by the sensor system. That is, the data obtained by the sensors is in a highly ordered state, and the information entropy is the smallest.

[0138] The definition of self-information in information theory can be used to construct faults. Self-information The mathematical expression is:

[0139] (18)

[0140] Fault probability of occurrence The smaller the value, the more likely it is to cause a malfunction. Posterior probability of occurrence The smaller, The larger the fault, the greater the potential for damage. If the fault source is definite, then the fault... The self-information is 0. According to the conditional probability formula, after deploying sensors... Then, a fault can be constructed. Conditional self-information The mathematical expression is:

[0141] (19)

[0142] in, For sensors Fault detected The probability of occurrence is represented by a probability distribution model.

[0143] After sensors were installed at the measuring points, the fault information changed. Compared to when no sensors were installed, the fault information changed after the sensors were installed. Fault under the arrangement conditions The probability distribution will change, therefore a probability distribution model is established. It's quite difficult. However, based on Bayes' theorem, by constructing faults... Sensor when it occurs Probability distribution model capable of diagnosing faults Then it can be used for The result is as follows:

[0144] (20)

[0145] Thus, a probability distribution model is established. The key is to construct a probability distribution model. Probability distribution model The following properties must be satisfied: First, the probability distribution model The range of the product must be between 0 and 1, which is a basic requirement of probability models; secondly, the probability model must satisfy the condition that the sum of the products is 1, which is a basic requirement of Bayes' theorem; then, the probability distribution model... The range of values ​​satisfies The monotonically decreasing property is added because the sensor information entropy decreases with the increase of the number of sensors; finally, the construction of the probability distribution model needs to be consistent with the statistical law of sensor performance degradation to ensure that the model has physical meaning. Therefore, the probability distribution model... This can be further expressed as:

[0146] (twenty one)

[0147] in, for Characteristic coefficients related to the stability of position sensors To determine the fault without considering sensor information The probability of occurrence.

[0148] Changes in the information entropy of the system for fault diagnosis before and after sensor deployment It can be represented as:

[0149] (twenty two)

[0150] Therefore, by analyzing the changes in information entropy, a quantitative analysis model was established to determine the impact of sensor placement on the fault diagnosis capability of the entire sensor system.

[0151] (3) Establish a multi-objective optimization model for optimal sensor placement;

[0152] In conjunction with the principles of minimizing cost, maximizing diagnostic accuracy, and optimizing diagnostic efficiency when deploying sensors, a multi-objective optimization model was established. The first step considers cost, which can be determined by the sensor configuration scheme, calculated by multiplying the cost of a single sensor by the number of sensors in the deployment scheme. The second step considers the accuracy of sensor diagnosis, defining the undetectable fault rate; the lowest undetectable rate indicates the highest sensor accuracy. The final step considers the diagnostic efficiency of the sensors, first by combining the improved correlation matrix from step (1). elements Multiply by the mutual information coefficient The change in information entropy of the system for fault diagnosis in step (2). Matrix representation was used, and finally, a correlation model between faults and measurement points was derived. A higher correlation indicates higher diagnostic efficiency. The specific mathematical descriptions of the relevant steps are as follows:

[0153] The sensor configuration model can be defined as:

[0154] (twenty three)

[0155] in, For sensor configuration schemes, In order to be in The number of sensors deployed at the location, , here This represents the location number of the sensor placement point.

[0156] exist Cost of deploying sensors under configuration for:

[0157] (twenty four)

[0158] in, Cost of a single sensor.

[0159] Fault detection rate is defined as the rate at which a system fault occurs. The probability of being detected by the sensor at that time. To ensure timely diagnosis of faults, a system fault undetectability rate is defined. , which is the ratio of the number of faults that the fault diagnosis system failed to detect correctly to the total number of faults. Its mathematical expression is:

[0160] (25)

[0161] The fault detection rate can be expressed as: As can be seen, the system fault undetectability rate is... It can be regarded as a sensor The harmonic mean of the probabilities that all possible faults cannot be monitored. The fault detection rate of a sensor system can also be seen as the reliability of fault diagnosis in a sensor system.

[0162] Formula (26) describes the measurement point After placing sensors at the location, it can detect faults. The increased information content of the diagnosis will be expressed as the change in the information entropy of the system for fault diagnosis in formula (22). The matrix composed of elements This is called the fault-measurement point mutual information matrix. It can be represented as:

[0163] (26)

[0164] element It can be represented as:

[0165] (27)

[0166] In the formula, For the improved correlation matrix The elements in For mutual information coefficients.

[0167] The mutual information between system faults and measurement points quantitatively describes the degree of correlation between faults and sensors. Under the same sensor deployment, a stronger correlation between each sensor and more faults indicates that the sensor can simultaneously diagnose multiple different types of faults, and thus, the higher the sensor's diagnostic efficiency. Therefore, the efficiency of sensor system fault diagnosis can be quantitatively represented by the system's mutual information. (The last sentence appears to be incomplete and possibly refers to a different context.) In this case, the correlation model between the fault and the measuring point It can be represented as:

[0168] (28)

[0169] in, Indicates in The ability of the sensor system to obtain fault information. The larger the value, the higher the efficiency of the sensor system in fault diagnosis. This represents the change in information entropy of the system during fault diagnosis. Indicates the first The configuration status of each location. This indicates the total number of locations where sensors can be installed. This indicates the total number of fault types that need to be diagnosed.

[0170] In actual sensor deployment, redundant arrangements are often required for certain critical measurement points. However, due to limitations in structure, manufacturing processes, and other factors, the number of sensors cannot be increased indefinitely; each measurement point has an upper limit on the number of sensors. Therefore:

[0171] (29)

[0172] in, This represents the upper limit of the number of sensors at a specific location, and is generally a positive integer. It is a set of positive integers.

[0173] Fault detectability refers to the ability to detect faults. When this occurs, at least one corresponding sensor can detect the fault. To ensure that every fault in the system is detected... If all occurrences can be detected, then at least one sensor corresponding to that fault must be deployed:

[0174] (30)

[0175] Based on the above analysis, the sensor optimization layout problem studied in this invention can be described as follows: Selecting certain measuring points from the set of measuring points according to certain optimization criteria, and arranging a certain number of sensors, while satisfying the above constraints, to achieve the overall optimality of each objective. Essentially, it is a nonlinear integer programming problem under multiple objectives and constraints. The multi-objective optimization model for optimal sensor layout is established as follows:

[0176] (31)

[0177] in, This is a vector of decision variables.

[0178] To obtain the Pareto solution set for the multi-objective optimization problem, the following assumptions are made. First, each sensor operates independently, and the failure of any sensor will not affect other sensors. Second, the probability of multiple sensors failing simultaneously is extremely small; therefore, this chapter only considers the case of a single sensor failure. Third, the maximum number of sensors at a specific location should be limited. To simplify the model solution, the placement of different sensors is restricted to having the same upper limit on the number of sensors.

[0179] (4) Construct an improved NSGA-II algorithm to solve the multi-objective optimization model;

[0180] Multi-objective optimization is a common problem in various fields. Intelligent evolutionary algorithms, with their advantages of low complexity and high solution efficiency, excel in solving multi-objective optimization problems. Based on the non-dominated sorting genetic algorithm (NSGA), this invention proposes an improved algorithm (NSGA-II). As a representative method of intelligent evolutionary algorithms, NSGA-II upgrades the NSGA algorithm through three improvements:

[0181] Firstly, a fast non-dominated sorting operator is introduced, which significantly reduces the solution complexity while helping to preserve high-quality individuals in the population during the evolutionary process. Specifically, in the operation, individuals within the population are first compared pairwise to determine their dominance relationships. Non-dominated individuals (those with no other individuals in the population that can dominate them) are selected and classified as first-level individuals and stored in F1. Subsequently, the dominance sets of individuals in F1 are used to... For each target, repeat the above filtering process, and the resulting non-dominated individuals will be categorized into the second level and stored in F2. Continue this cycle, progressively classifying and archiving the individuals within the dominance set of newly acquired non-dominated individuals, until all individuals have been categorized.

[0182] Secondly, by using the crowding comparison operator to maintain the diversity and uniformity of the solution set, the operation is as follows: by calculating the average distance of the neighboring points on both sides of all individuals after hierarchical stratification along each objective function, the density of surrounding individuals is estimated, which helps to enhance population diversity and solution set uniformity; for example... Figure 4 In bi-objective optimization, the crowding distance of an intermediate individual is an estimate of the perimeter of the cuboid formed by its neighboring individuals i+1 and i-1 as vertices. The crowding distance and crowding degree comparison operator overcomes the defect of manually specifying the shared radius. As a standard for comparing individuals after hierarchical stratification, it enables individuals within the feasible region to be more evenly distributed across the entire Pareto front, ensuring population diversity and distribution.

[0183] Third, by using the elite preservation strategy, superior individuals from the evolutionary process are passed on to the next generation, which effectively improves the quality of the population and increases the probability of finding the optimal solution. Specifically, during the algorithm iteration process, elite individuals from the previous generation are directly introduced into the next generation, avoiding the loss of superior genes, thereby accelerating the convergence speed of the algorithm and improving the quality of the solution.

[0184] The main calculation steps of NSGA-II are as follows: Figure 5 As shown in the diagram, Gen represents the initial generation, and limit represents the preset iteration termination limit. The algorithm steps are as follows: First, the system generates an initial population randomly and performs an initial fast non-dominated sort to determine the individual rank, then initializes the number of generations. In each iteration, the population sequentially undergoes selection, crossover, and mutation operators to produce offspring, and the parent and offspring populations are merged to maintain the genetic stability of superior genes. Next, the algorithm performs another fast non-dominated sort on the merged population and introduces a crowding calculation mechanism to evaluate the distribution density of individuals in the solution space, thereby selecting the individuals with the best overall performance to form the new generation of parent population. This iterative process continues until the number of generations reaches the preset termination limit, at which point the algorithm stops and outputs the optimized Pareto solution set.

[0185] In multi-objective optimization scenarios, due to the competition among multiple objective functions, there is no solution that simultaneously satisfies all objectives optimally. Decision-makers face significant challenges in selecting the best solution based on objective circumstances and practical preferences. Multi-objective decision analysis can largely alleviate this pressure. It can conduct reasonable and scientific evaluations and select the best solution for two or more conflicting objective functions based on multiple criteria. The Top-Approximation-Ideal-Solution Ranking (TOPSIS) method is a highly effective decision-making method. This method scientifically ranks solutions by evaluating their comprehensive distance from the ideal optimal solution and the ideal worst solution; the closer a solution is to the ideal optimal solution and the farther it is from the ideal worst solution, the better.

[0186] Because evaluation indicators differ significantly in magnitude and unit, to ensure the scientific rigor and effectiveness of multi-objective decision analysis, the original solution data needs to be standardized before analysis, mapping all data to the [0,1] interval. This chapter employs a positive transformation of the original matrix, converting all original indicators into extremely large indicators (larger indicator values ​​are better). Assume the problem to be evaluated includes... Each evaluation object and For each evaluation indicator, the standardized matrix is... It can be represented as:

[0187] (32)

[0188] in, The original decision matrix, For the first The evaluation object is in the first Values ​​on each evaluation indicator;

[0189] For the normalized matrix Each element in ,satisfy:

[0190] (33)

[0191] Ideal optimal vector And the worst ideal vector By standardizing the matrix The maximum and minimum values ​​of each indicator are collected and combined, as defined below:

[0192] (34)

[0193] Entropy weighting is an objective method for determining the weight of an indicator based on the differences in the degree of orderliness of the information it contains. The weight determination depends solely on the dispersion of the data itself. Specifically, the greater the dispersion of an indicator, the greater its entropy value, indicating that the indicator data provides more information, and correspondingly, the greater its weight in the evaluation. This method also requires normalization of the original matrix during calculation. This section uses the simplest and most commonly used method to calculate the entropy weight. The first item under the indicator The proportion of each option:

[0194] (35)

[0195] in, For the first The first item under the indicator The proportion of each option This represents the total number of schemes;

[0196] The entropy values ​​of each indicator can be expressed as:

[0197] (36)

[0198] in As an indicator Total number

[0199] index The entropy weight can be expressed as:

[0200] (37)

[0201] in For the first The weighting coefficient of each indicator.

[0202] Based on the weighting coefficients determined by the entropy weighting method, the distance between each feasible solution and the ideal optimal and ideal worst solutions can be calculated using Euler's formula (Euclidean distance formula). Then the... Euclidean distance between feasible solutions and the ideal optimal solution The Euclidean distance between the sum and the worst-case solution of the ideal They can be represented as:

[0203] (38)

[0204] in, For the first The ideal optimal value of each evaluation indicator for The ideal worst value of each evaluation indicator;

[0205] Get the first The comprehensive distance between each evaluated object and the ideal optimal solution and the worst solution is the evaluation criterion. In the formula... The value of is between [0, 1]. The larger the value, the closer it is to the optimal solution.

[0206] (39)

[0207] (5) Calculation and verification results;

[0208] The above steps proposed and improved the correlation matrix, and proposed a reliability model for the number and location of sensors. Subsequently, a multi-objective optimization model for optimal sensor placement was derived using the correlation matrix and the reliability model. In step (4), an improved NSGA-II algorithm was proposed, forming a closed-loop logic of model building and solution algorithm. In this step, the method for forming the content of steps (1)-(4) will be verified.

[0209] The selected object for verification is a typical heat exchanger-deaerator in nuclear power plants, and its system model schematic diagram is shown below. Figure 6 As shown, the heated steam from the high-pressure cylinder enters the deaerator system, where it is cooled into liquid water by the low-temperature condensate from the upstream heater and the condensate feedwater from the condenser. The oxygen carried in the liquid water is removed by the high temperature, and finally it enters the steam generator. Figure 6 The symbol meanings of parameter nodes and component nodes are shown in Table 1.

[0210] Table 1

[0211]

[0212] The multi-objective problem of sensor placement and selection can be solved using the NSGA-II algorithm. The initial parameters of NSGA-II are set as follows: population size of 200; maximum number of generations of 500; crossover probability of 0.9; and mutation probability between 0.1 and 0.4. To facilitate understanding of the relationship between sensor characteristics and placement schemes, the unit price of each sensor is set to 1, and the probability of sensor failure within any calibration period is set to 0.3. Under standard conditions, the multi-objective calculation results for sensor placement are as follows: Figures 7 to 15As shown.

[0213] Multi-objective calculations for sensor placement under standard conditions show a high correlation between the total cost of sensor placement and the relevance and reliability of fault diagnosis. For example... Figure 7 As shown, among all sensor arrangement schemes, the maximum number of sensors reached 55 at the initial stage of iteration, which was the maximum number of sensors allowed in the arrangement scheme. As the number of iterations increased, the arrangement schemes approached the Pareto solution set, and the maximum number of sensors in the arrangement schemes decreased and stabilized at 45.

[0214] As the number of sensors increases, the unreliability of sensor placement scheme fault diagnosis shows a clear inflection point, exhibiting a trend of first linear decline followed by stable fluctuations, such as... Figure 10 As shown, when the number of sensors is less than 20, the unreliability of fault diagnosis decreases by an order of magnitude for each additional sensor; however, when the number of sensors is greater than 20, unlimited increases in sensor redundancy do not significantly improve the system's fault diagnosis capability. The reliability and correlation of fault diagnosis are consistent; increasing the sensor arrangement and number helps improve the reliability of fault diagnosis, such as... Figure 12 As shown.

[0215] The multi-target sensor placement model can eliminate two invalid measurement point locations out of 11 possible placement locations. For example... Figure 14 As shown, in all schemes, the median and mean number of sensor placements at locations 8 and 9 are close to 0, indicating that these two measurement points are not useful for fault diagnosis. The proposed multi-objective optimization model for sensor placement can eliminate invalid measurement points and improve the effectiveness of sensor placement.

[0216] Each solution in the Pareto solution set can be viewed as a sensor placement scheme, containing specific locations and numbers of sensors. The application of evolutionary algorithms leads to the continuous nature of discrete variables, thus requiring re-discretization of the variables in the Pareto solution set. A rounding discretization method is used to convert continuous decision variables into integer values, ensuring feasible solutions are obtained in the discrete domain. Repeated schemes are proposed, and the Pareto solution set is sorted according to the number of sensors deployed. The final result is as follows: Figure 15 As shown, with the increase in the number of sensors, the sensor fault diagnosis performance indicators (reliability curve and correlation curve) oscillate upwards, which means that the sensor placement also affects the diagnostic performance. When the number of sensors is limited, the placement can be optimized to improve fault diagnosis performance. Schemes 29 to 45 show that the fault diagnosis correlation is significantly affected by the number of sensors, the sensor placement cost remains stable, and the reliability of fault diagnosis has reached its maximum.

[0217] Table 2 Pareto Solution Set for Sensor Deployment

[0218]

[0219] The Pareto solution set of the sensor multi-objective model obtained by the NSGA-II algorithm was evaluated and ranked using the TOPSIS method. The optimal sensor placement scheme was selected from the Pareto solution set based on its approximation distance to the optimal solution. The top 10 sensor placement schemes, ranked by comprehensive distance, are shown in Table 1. The results show that the optimal number of sensors is around 20, consistent with the NSGA-II calculation results. The top-ranked scheme covers all effective measurement points, indicating that under the same number of sensors, increasing the diversity of sensor placement helps improve the reliability of fault diagnosis. In the second-ranked scheme, sensors are placed at positions 2, 5, 7, and 11, reaching the upper limit of sensor placement, indicating that when sensor placement is limited, effective fault diagnosis can be achieved by improving the measurement reliability of important locations. Rounding the Pareto solution set shows that as the total cost of sensor deployment increases, the ability to detect errors and differentiate faults significantly improves. These results demonstrate that operations and maintenance personnel can select the most suitable sensor deployment scheme based on the measurement environment and the requirements of fault diagnosis and detection.

Claims

1. A multi-objective optimization method for sensor deployment in nuclear power systems, characterized in that, Includes the following steps: Based on directed graph theory, a correlation matrix between sensors and faults is established by analyzing fault propagation paths and the correlation between faults and sensors, and the correlation matrix is ​​improved based on actual industrial processes. Establish a reliability model for the number and location of sensors, including a model of the relationship between the number of sensors and fault diagnosis capability, and a model of the relationship between the location of sensors and fault diagnosis capability. The model construction of the sensor quantity and fault diagnosis capability includes: establishing a probabilistic statistical model of sensor failure that cannot diagnose system faults, calculating the probability of sensor failure and the probability that the sensor system cannot detect the failure due to the failure; and constructing a model of sensor location and fault diagnosis capability based on information entropy theory and Bayesian model. A multi-objective optimization model for optimal sensor placement is formed based on the correlation matrix between sensors and faults. The objective functions include: minimizing the cost of sensor placement under the sensor configuration scheme, minimizing the undetectable rate of system faults, and maximizing the ability of the sensor system to obtain fault information under the sensor configuration scheme. The constraints include: setting an upper limit on the number of sensors at each measuring point and requiring at least one corresponding sensor to be placed for each fault in the system. The NSGA algorithm is improved by introducing a fast non-dominated sorting operator, using a crowding comparison operator to maintain the diversity and uniformity of the solution set, and passing on superior individuals from the evolutionary process to the next generation through an elite retention strategy, resulting in the improved NSGA-II algorithm. The NSGA-II algorithm is then used to solve a multi-objective optimization model, achieving multi-objective optimization of sensor selection and placement. The resulting multi-objective optimization method for sensor selection and placement was validated in a simulation model of a nuclear power system's deoxygenation system.

2. The method according to claim 1, characterized in that, Correlation matrix between sensors and faults Represented as: ； in, When the fault occurs The sensors are arranged in the... The fault results detected at each location This indicates the number of sensors at a given location. Indicates the total number of positions; The expression is: ; To characterize the coefficients that represent the influence of the sensor's measurement environment, The internal detection coefficient of the sensor; Improved correlation matrix The expression is: ； in, .

3. The method according to claim 1, characterized in that, The probabilistic statistical model for the inability to diagnose system faults due to sensor failure is expressed as follows: ； in, For time; Let be a random variable, representing the time interval. The number of times the internal sensor system failed; In the time interval The number of times the internal sensor system fails is equal to The probability of; This indicates the number of times the sensor system fails within a calibration cycle. These are characteristic coefficients related to sensor stability; the probability of sensor failure. Represented as: ； in, In the time interval The probability that the internal sensor will not fail; Due to malfunction The probability of an event occurring that cannot be detected by the entire sensor system. Should meet: ； in, Defined as fault The probability of occurrence can be obtained through experience; for The number of redundant sensors deployed at the location. for Characteristic coefficients related to the stability of position sensors.

4. The method according to claim 1, characterized in that, Methods for establishing models of sensor location and fault diagnosis capabilities include: According to Bayes' theorem, if a fault occurs in the system... If the event is the source of the fault, then the description of the fault is a fault. Posterior probability of occurrence: ； in, For fault The posterior probability of occurrence, This represents the total number of fault types. Construction Fault Self-information The mathematical expression is: ； Fault probability of occurrence The smaller the value, the more likely it is to cause a malfunction. Posterior probability of occurrence The smaller, The larger the value; if the fault source is definite, then the fault... The self-information is 0; according to the conditional probability formula, after deploying sensors... Then, construct a fault. Conditional self-information The mathematical expression is: ； in, For sensors Fault detected The probability of occurrence, which is a probability distribution model; Based on Bayes' theorem, by constructing faults Sensor when it occurs Probability distribution model capable of diagnosing faults Then for The result is as follows: ； probability distribution model Further expressed as: ； in, for Characteristic coefficients related to the stability of position sensors To determine the fault without considering sensor information The probability of occurrence; Changes in the information entropy of the system for fault diagnosis before and after sensor deployment Represented as: ； Therefore, by analyzing the changes in information entropy, a quantitative analysis model was established to determine the impact of sensor placement on the fault diagnosis capability of the entire sensor system.

5. The method according to claim 1, characterized in that, Under the sensor configuration scheme, the cost of deploying the sensors Represented as: ； in, For the cost of a single sensor, In order to be in The number of sensors deployed at the location, , The location number representing the sensor placement point; System fault undetectability rate The expression is: ； in, Indicates a fault The probability of something occurring that cannot be detected by the entire sensor system. Indicates a fault The probability of occurrence; Under the sensor configuration scheme, the correlation model between faults and measuring points Represented as: ； in, Indicates in The ability of the sensor system to obtain fault information. The larger the value, the higher the efficiency of the sensor system in fault diagnosis. This represents the change in information entropy of the system during fault diagnosis. Indicates the first The configuration status of each location. This indicates the total number of locations where sensors can be installed. This indicates the total number of fault types that need to be diagnosed.

6. The method according to claim 1, characterized in that, The multi-objective optimization model for optimal sensor placement is expressed as follows: ； in, This indicates the cost of deploying the sensors. In order to be in The number of sensors deployed at the location, , The location number representing the sensor placement point. For the cost of a single sensor, This indicates the rate at which system faults are undetectable. Indicates a fault The probability of something occurring that cannot be detected by the entire sensor system. Indicates a fault The probability of occurrence Indicates in The ability of the sensor system to obtain fault information. Represents the fault-measuring point mutual information matrix. For the decision variable vector, This represents the upper limit on the number of sensors at a specific location. It is a set of positive integers. Indicates the first The sensor for the first Sensitivity to various faults.

7. The method according to claim 1, characterized in that, Solving multi-objective optimization models based on the NSGA-II algorithm includes: First, the system generates an initial population randomly and performs an initial fast non-dominated sort to determine individual rank, then initializes the number of generations. In each iteration, the population sequentially undergoes selection, crossover, and mutation operators to produce offspring, and the parent and offspring populations are merged to maintain the genetic stability of superior genes. Next, the algorithm performs another fast non-dominated sort on the merged population and introduces a crowding calculation mechanism to evaluate the distribution density of individuals in the solution space, thereby selecting the individuals with the best overall performance to form the new generation of parent population. This iterative process continues until the number of generations reaches a preset termination limit, at which point the algorithm stops and outputs the optimized Pareto solution set.

8. A multi-objective optimization system for sensor deployment in nuclear power systems, characterized in that, include: The correlation matrix improvement unit is used to establish a correlation matrix between sensors and faults based on directed graph theory by analyzing fault propagation paths and the correlation between faults and sensors, and to improve the correlation matrix based on actual industrial processes. The reliability model building unit is used to establish a reliability model for the number and location of sensors, including a model of the number of sensors and fault diagnosis capability, and a model of the location of sensors and fault diagnosis capability. The model construction of the sensor quantity and fault diagnosis capability includes: establishing a probabilistic statistical model of sensor failure that cannot diagnose system faults, calculating the probability of sensor failure and the probability that the sensor system cannot detect the failure due to the failure; and constructing a model of sensor location and fault diagnosis capability based on information entropy theory and Bayesian model. The multi-objective optimization model construction unit is used to form a multi-objective optimization model for optimal sensor placement based on the correlation matrix between sensors and faults. The objective functions include: minimizing the cost of sensor placement under the sensor configuration scheme, minimizing the undetectable rate of system faults, and maximizing the ability of the sensor system to obtain fault information under the sensor configuration scheme. The constraints include: setting an upper limit on the number of sensors at each measuring point and requiring at least one corresponding sensor to be placed for each fault in the system. The model solving unit is used to improve the NSGA algorithm, including: introducing a fast non-dominated sorting operator, using a crowding comparison operator to maintain the diversity and uniformity of the solution set, and using an elite retention strategy to pass on superior individuals in the evolutionary process to the next generation, resulting in the improved NSGA-II algorithm. The NSGA-II algorithm is then used to solve multi-objective optimization models, realizing multi-objective optimization of sensor selection and placement. The verification unit is used to verify the developed multi-objective optimization method for sensor selection and placement in a simulation model of a nuclear power system deoxygenation system.

9. A non-volatile storage medium, characterized in that, Used to store a computer program, wherein the computer program, when executed by a processor, implements the method as described in any one of claims 1-7.

10. A computer program product comprising a computer program / instructions, characterized in that, When the computer program / instructions are executed by the processor, they implement the method described in any one of claims 1-7.

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