A temperature sensor optimization arrangement method for solid oxide fuel cell thermal fault monitoring

Abstract

The present application belongs to the technical field of solid oxide fuel cell operation state detection, and particularly relates to a temperature sensor optimization arrangement method for solid oxide fuel cell thermal fault monitoring, comprising: obtaining a two-dimensional temperature field of a solid oxide fuel cell under a fault-free working condition; discretizing a planar region of the solid oxide fuel cell into multiple candidate nodes and constructing a weighted thermal network model; sequentially taking each candidate node as a potential fault source node, calculating the heat generated by the fault source node at each candidate node based on a preset fault heat at the fault source node and a preset fault influence radius, so as to solve the response temperature rise of each candidate node under the corresponding fault condition; and optimizing the nodes with the weighted sum of the fault source node detectability of the selected m candidate nodes, the average temperature rise response strength of all fault source nodes, and the fault distinguishability of different fault source nodes as the target. The present application can improve the coverage and reliability of thermal fault detection.

Description

Technical Field

[0001] This invention belongs to the technical field of solid oxide fuel cell operating status detection, and more specifically, relates to an optimized arrangement method for temperature sensors for monitoring thermal faults in solid oxide fuel cells. Background Technology

[0002] Solid oxide fuel cells (SOCs) are a type of highly efficient electrochemical energy conversion device, possessing advantages such as high energy conversion efficiency, strong fuel adaptability, and suitability for distributed power generation. However, SOCs typically operate under high-temperature conditions, which can easily lead to uneven temperature distribution, localized heat accumulation, and large temperature gradients during operation. This can result in thermal stress concentration, electrode or electrolyte material degradation, seal failure, and localized thermal faults. Therefore, reliable temperature monitoring and thermal fault monitoring of SOCs are of great significance.

[0003] Existing technologies already include solutions for fault detection and location in solid oxide fuel cells. For example, Chinese patent application CN108615917A discloses a fault detection system and method for a solid oxide fuel cell system, which determines the fault point of the fuel cell stack based on the error in the stack outlet temperature by combining a physical model with the fault detection system. Chinese patent CN114243063B discloses a fault location and diagnosis method for a solid oxide fuel cell system, which uses a long short-term memory neural network model combined with experimental data to establish a performance prediction model for the solid oxide fuel cell system, and performs fault judgment and location based on the prediction error. Furthermore, Chinese patent CN112421081B discloses a sensor fault detection method applicable to multi-stack fuel cell systems, which achieves sensor fault detection and isolation through a local fault detection estimator, a fault isolation estimator, and an adaptive threshold.

[0004] The aforementioned existing technologies can achieve fault detection (including location) or fault diagnosis of solid oxide fuel cell systems to a certain extent, but their focus is mainly on system operating status identification, model prediction error analysis, or sensor fault judgment, without fully addressing the determination of the optimal arrangement of sensors under the condition of a limited number of temperature sensors.

[0005] In practical battery stacks, the placement of temperature sensors is limited by factors such as high-temperature environment, installation space, insulation requirements, sealing structure, wiring complexity, and sensor cost, making it difficult to obtain a complete temperature field through a large number of densely arranged sensors. Existing empirical placement methods, geometrically based placement methods, or placement methods based on a single sensitivity index tend to concentrate a limited number of sensors in localized high-temperature or high-response areas, resulting in monitoring blind spots in boundary regions, weak-response regions, or potential thermal fault areas. In particular, for cross-flow solid oxide fuel cells, air and fuel flow in different directions, resulting in significant spatial non-uniformity of the planar temperature field, and the propagation patterns of localized thermal faults within the cell plane are also quite complex.

[0006] Therefore, there is an urgent need for a method to optimize the arrangement of a limited number of temperature sensors in order to improve the coverage and reliability of thermal fault detection in solid oxide fuel cells, thereby improving the accuracy of fault diagnosis. Summary of the Invention

[0007] In view of the above-mentioned defects or improvement needs of the existing technology, the present invention provides a method for optimizing the arrangement of temperature sensors for monitoring thermal faults in solid oxide fuel cells. The purpose is to improve the coverage and reliability of thermal fault detection in solid oxide fuel cells, thereby improving the accuracy of fault diagnosis.

[0008] To achieve the above objectives, according to one aspect of the present invention, a method for optimizing the arrangement of temperature sensors for thermal fault monitoring in solid oxide fuel cells is provided, comprising: A two-dimensional temperature field under fault-free operating conditions of a solid oxide fuel cell is obtained. The planar region of the solid oxide fuel cell is discretized into multiple candidate nodes. Each candidate node is used to characterize the local thermal state of the corresponding local region and serves as a candidate installation location for a temperature sensor. A weighted thermal network model is constructed: candidate nodes are used as network nodes, and the equivalent thermal coupling relationship between adjacent candidate nodes is used as network edges. The temperature at each node is determined based on the two-dimensional temperature field to determine the equivalent thermal coupling strength between adjacent candidate nodes. The edge weights between adjacent nodes are determined based on the distance between adjacent nodes and the equivalent thermal coupling strength. Each candidate node is sequentially considered as a potential fault source node. Based on the preset fault heat and fault influence radius at the fault source node, the heat generated at each candidate node is calculated. Based on this heat, the known battery inlet temperature, outlet temperature, and edge weights between adjacent nodes, the fault temperature at all candidate nodes under the current fault is recursively calculated according to the geometric adjacency relationship and steady-state thermal balance relationship. The difference between this fault temperature and the temperature determined by the two-dimensional temperature field is used to obtain the response temperature rise of each candidate node under each fault source node. From all candidate nodes, select m nodes as sensor deployment nodes. The goal is to optimize the m candidate nodes by maximizing the fault source node detectability rate, the average temperature rise response intensity of all fault source nodes, and the fault distinguishability of different fault source nodes. The fault source node detectability rate, average temperature rise response intensity, and fault distinguishability are all calculated based on the response temperature rise of the m candidate nodes.

[0009] Furthermore, the edge weights are: ; In the formula, Based on the fundamental thermal coupling coefficient, based on adjacent candidate nodes i and j The equivalent thermal coupling strength between them is preset; Adjacent candidate nodes i and j Spatial distance between them; Alternatively, the edge weights are:

[0010] in, This is the preset temperature gradient correction factor. and These represent the highest and lowest temperatures among the candidate node temperatures in the two-dimensional temperature field. Indicates candidate nodes i Temperature in a two-dimensional temperature field.

[0011] Furthermore, when the first k When a candidate node is considered as a fault source node, the heat generated at each candidate node... Represented as:

[0012] in, For the first k The spatial coordinates of each fault source node This is the preset fault impact radius centered on the node location. This refers to the fault heat at the fault source node; and The effective fault strength of the fault source node is characterized collaboratively. The fault heat at the fault source node The value can be preset, or determined by calculation in the following ways:

[0013] in, The preset reference calorie content. The preset fault weighting coefficient for the high-temperature zone. For the first k The temperature of each fault source node in a two-dimensional temperature field.

[0014] Furthermore, the first k When the candidate node experiences a thermal failure, the first i Temperature rise of each candidate node's response R k,i for:

[0015] in, Indicates the first k When the candidate node experiences a thermal failure, the first i Fault temperature of each candidate node Indicates the first i The temperature of each candidate node in the two-dimensional temperature field; The following steady-state thermal equilibrium relationship is used for calculation. :

[0016] In the formula, In order to be with the first i The set of nodes adjacent to each candidate node, Q i Let be the equivalent heat source term for the i-th candidate node. , This represents the known intensity of a uniform basic heat source. This represents the known background heat source intensity in the high-temperature region. The radius of influence of the known high-temperature background region; (x h ,y h (x) represents the spatial coordinates of the center of the high-temperature background region. i ,y i ) is the first i Spatial coordinates of the candidate nodes; Indicates the first k When the candidate node experiences a thermal failure, the first i The heat generated at each candidate node. Candidate nodes i and candidate nodes j The edge weight between them, H air H fuel and H env,i These are the air side, fuel side, and candidate nodes, respectively. i The equivalent heat transfer coefficient on the environmental side, T air,i T fuel,i and T amb These are the equivalent air temperature, equivalent fuel temperature, and ambient temperature, respectively. Indicates when the first k When a local thermal failure occurs at the candidate node, it is related to the first...i The node adjacent to the first j The temperature of each node under this fault condition.

[0017] Furthermore, the detectability rate of the fault source nodes among the currently selected m candidate nodes is calculated as follows: Let S be the group of the currently selected m candidate nodes. The detectability rate Coverage(S) of the fault source nodes in S is calculated as follows: ; In the formula, This indicates that among the currently selected m candidate nodes, the one that is the [number]th [node]... k Maximum response temperature rise under each fault source node; The preset sensor detection threshold; if Determine the first k The fault source node can be detected, that is, the current S covers the fault source node. k There are 1 fault source node; n is the total number of candidate nodes; The currently selected value is calculated using the following formula. m The average temperature rise response intensity AvgResponse(S) of each candidate node to all fault source nodes: ; The currently selected value is calculated in the following way. m Fault distinguishability of candidate nodes for different fault source nodes: set up R a ( S )and R b ( S ) are respectively the first a The and the first b Each fault source node is m The response vector formed by the fault responses on candidate nodes is given by the fault distinguishability D(S): .

[0018] Furthermore, the comprehensive evaluation objective function J(S) for the m candidate nodes is:

[0019] in, , , For weighting coefficients, AvgResponse norm (S) represents the normalized average temperature rise response intensity, and D norm (S) represents the normalized fault distinguishability; In the formula, R best This represents the theoretically optimal average temperature rise response. ; In the formula, D all This represents the average fault response vector distance when all candidate nodes are used as sensor deployment nodes. The response temperature rise of each candidate node under each fault source node constitutes a fault response vector. Used to perform dimensional correction on the distinguishability under different numbers of sensors.

[0020] Furthermore, a fault propagation-guided genetic optimization algorithm is used to obtain the optimal set of sensor nodes, implemented as follows: In each iteration, a comprehensive evaluation objective function is calculated for each candidate sensor placement node in the population; the objective function value is used to guide the selection and crossover operations to obtain a new set of candidate sensor placement nodes, i.e., a new population. For any new population, if the maximum temperature rise response of a fault source node in the current sensor deployment node set is lower than a preset detection threshold, then the fault source node is determined to be an undetectable fault source node. All undetectable fault source nodes together constitute the coverage gap of the new population. When a coverage gap exists, coverage gap-guided mutation is performed: the fault source node with the smallest maximum temperature rise response is selected from all undetectable fault source nodes as the priority compensation object; from candidate nodes outside the current sensor deployment node set, under the constraint of spatial dispersion, the node with a temperature rise response higher than the maximum response temperature of the current sensor deployment node set is selected as the node to be added; a low-contribution sensor deployment node is selected from the current sensor deployment node set as the node to be replaced; wherein, the low-contribution sensor deployment node is determined comprehensively based on the detectability rate of the fault source node, the average temperature rise response intensity, and / or the magnitude of its influence on the comprehensive evaluation objective function; the low-contribution sensor deployment node is replaced with the node to be added to obtain the mutated candidate sensor deployment node set, i.e., the mutated population; if there is no coverage gap, random mutation or spatial dispersion-guided mutation is performed. After mutation, the set of candidate sensor placement nodes whose comprehensive evaluation objective function values ​​meet the preset requirements are retained through the elite retention strategy, and the population set update of the current iteration is completed. Once the maximum number of iterations is reached or the termination condition is met, the iteration is completed, and an optimal population is selected from the final population set.

[0021] Furthermore, after obtaining the optimal population, the genetic optimization algorithm further includes: performing cover-priority local repair on the population, implemented as follows: For each sensor placement node in the population, replace it one by one with candidate nodes outside the set. Determine whether the detectability rate of fault source nodes and the value of the comprehensive evaluation objective function of the replaced set are improved. If they are improved, accept the replacement. Continue until it is impossible to further improve the detectability rate of fault source nodes or the value of the comprehensive evaluation objective function through single node replacement. Finally, output the optimal set of sensor placement nodes.

[0022] Furthermore, the population initialization method before the iteration is as follows: Calculate the fault propagation impact of each fault source node. Where n is the total number of candidate nodes. I k Used to characterize the k The overall temperature rise effect on all candidate nodes when a fault source node experiences a thermal failure; R k,i Indicates the first k When the candidate node experiences a thermal failure, the first i Temperature rise of each candidate node's response R k,i ; ; Calculate the sensor observation contribution of each candidate node. , of which O i Used to characterize the i The overall observation capability of each candidate node for all potential fault source nodes; Calculate the weighted degree centrality of each candidate node. ,in, Used to characterize the local thermal connectivity strength of the i-th candidate node in the weighted thermal network model. Indicates adjacent candidate nodes i and j The boundary rights between them In order to be with the first i The set of nodes adjacent to each candidate node; Based on the impact of fault propagation I k Identify potential fault sources, select candidate sensor placement nodes that have a high contribution to the sensing observation of each potential fault source, and distribute multiple nodes in the same set of sensor placement nodes according to the weighted degree centrality to obtain the initial population.

[0023] In another aspect, the present invention provides a computer-readable storage medium comprising a stored computer program, wherein the computer program, when executed by a processor, controls the device in which the storage medium is located to perform the steps of the method described above.

[0024] In summary, compared with the prior art, the technical solutions conceived by this invention have the following main advantages: 1. This invention addresses the problem in existing solid oxide fuel cell (SOCF) thermal fault monitoring where the number of temperature sensors is limited by factors such as installation space, high-temperature environment, insulation sealing, and wiring complexity, making it difficult to obtain a complete temperature field through dense temperature measurement. It provides an optimized arrangement method for temperature sensors in SOCF thermal fault monitoring to improve the coverage, response effectiveness, and fault source distinguishability of thermal fault monitoring with a limited number of temperature sensors. First, this invention constructs a weighted thermal network model of the SOCF plane, where the initial edge weights between adjacent nodes are determined based on the distance between adjacent nodes and the equivalent thermal coupling strength, providing a reliable model basis for temperature sensor arrangement. Furthermore, this invention sets local thermal fault sources, sequentially treating each candidate node as a potential fault source node. Based on the preset fault heat and preset fault influence radius at the fault source node, the heat generated by the fault source node at each candidate node is calculated to solve for the response temperature rise of each candidate node under each fault source node. This quantitatively describes the impact of different fault source nodes on the temperature rise of each candidate sensor node, avoiding reliance solely on empirical locations, geometric center locations, or single sensitivity indicators for sensor arrangement, and improving the monitoring capability of thermal faults in high-risk and boundary areas. Finally, the method of this invention comprehensively considers fault coverage, average response intensity, and fault distinguishability during sensor layout optimization. This reduces monitoring blind spots and improves fault detection coverage, fault source differentiation ability, and optimization result stability under a limited number of temperature sensors. Simultaneously, it reduces the number of sensors, wiring complexity, and installation difficulty in high-temperature environments. Therefore, the method of this invention can improve the coverage and reliability of thermal fault detection in solid oxide fuel cells under a limited number of temperature sensors, thereby improving the accuracy of fault diagnosis.

[0025] 2. The present invention further proposes to modify the initial edge weights between adjacent candidate nodes based on the temperature difference between adjacent candidate nodes in the two-dimensional temperature field, so that the modified weighted thermal network model reflects the local temperature non-uniformity, thereby more accurately reflecting the heat propagation characteristics in the plane of solid oxide fuel cells, and providing a reliable model basis for the arrangement of temperature sensors.

[0026] 3. After setting up local thermal fault sources, this invention also introduces fault weights for high-temperature zones, based on the fault heat at the fault source node. Calculate the first k When a candidate node is considered a fault source node, the heat generated by each candidate node is significant. This will further enhance the monitoring capabilities for thermal faults in high-risk and boundary areas.

[0027] 4. Furthermore, this invention comprehensively considers fault coverage, average response intensity, and fault distinguishability during the sensor layout optimization process, and uses a fault propagation-guided optimization algorithm to output a sensor layout scheme. This further reduces monitoring blind spots, improves fault detection coverage, fault source distinguishability, and optimization result stability under a limited number of temperature sensors, while reducing the number of sensors, wiring complexity, and installation difficulty in high-temperature environments. Attached Figure Description

[0028] Figure 1 A flowchart illustrating a method for optimizing the arrangement of temperature sensors for monitoring thermal faults in solid oxide fuel cells, provided in an embodiment of the present invention. Figure 2 This is a schematic diagram of the crossflow plane discretization of a solid oxide fuel cell provided in an embodiment of the present invention; Figure 3 The flowchart of the fault propagation guidance optimization algorithm provided in the embodiments of the present invention is shown below; Figure 4 This is a schematic diagram showing the optimized arrangement of temperature sensors provided in an embodiment of the present invention. Detailed Implementation

[0029] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0030] Existing methods for fault detection or diagnosis of solid oxide fuel cells (SOFCs) primarily focus on system operating status identification, model prediction error analysis, or fault type determination. However, in actual fuel cell stack thermal monitoring, the number and installation location of temperature sensors are limited by factors such as high-temperature environment, spatial structure, insulation sealing, and wiring complexity. This makes it difficult to obtain a complete temperature field through densely arranged temperature sensors, thus affecting the accuracy of fault detection or diagnosis. Therefore, this invention focuses on illustrating a sensor optimization arrangement method based on the planar temperature field and local thermal fault propagation characteristics of solid oxide fuel cells under the condition of a limited number of temperature sensors.

[0031] Example 1 An optimized arrangement method for temperature sensors in solid oxide fuel cell thermal fault monitoring, such as... Figure 1 As shown, it includes: A two-dimensional temperature field under fault-free operating conditions of a solid oxide fuel cell is obtained. The planar region of the solid oxide fuel cell is discretized into multiple candidate nodes. Each candidate node is used to characterize the local thermal state of the corresponding local region and serves as a candidate installation location for a temperature sensor. A weighted thermal network model is constructed: candidate nodes are used as network nodes, and the equivalent thermal coupling relationship between adjacent candidate nodes is used as network edges. The temperature at each node is determined based on the two-dimensional temperature field to determine the equivalent thermal coupling strength between adjacent candidate nodes. The edge weights between adjacent nodes are determined based on the distance between adjacent nodes and the equivalent thermal coupling strength. Each candidate node is sequentially considered as a potential fault source node. Based on the preset fault heat and fault influence radius at the fault source node, the heat generated at each candidate node is calculated. Based on this heat, the known battery inlet temperature, outlet temperature, and edge weights between adjacent nodes, the fault temperature at all candidate nodes under the current fault is recursively calculated according to the geometric adjacency relationship and steady-state thermal balance relationship. The difference between this fault temperature and the temperature determined by the two-dimensional temperature field is used to obtain the response temperature rise of each candidate node under each fault source node. From all candidate nodes, select m nodes as sensor deployment nodes. The goal is to optimize the m candidate nodes by maximizing the fault source node detectability rate, the average temperature rise response intensity of all fault source nodes, and the fault distinguishability of different fault source nodes. The fault source node detectability rate, average temperature rise response intensity, and fault distinguishability are all calculated based on the response temperature rise of the m candidate nodes.

[0032] In this embodiment, the two-dimensional temperature field under fault-free operating conditions can be obtained through multiphysics simulation, experimental measurement, empirical models, or online state estimation methods. While acquiring the two-dimensional temperature field under fault-free operating conditions, battery operating parameters can be simultaneously acquired for subsequent calculation of the response temperature rise. These operating parameters include one or more of the following: battery planar geometry, airflow direction, fuel flow direction, inlet temperature, ambient temperature, heat transfer parameters, and basic heat source parameters.

[0033] The temperature at each node can be determined based on a two-dimensional temperature field. This can be represented by the th... i The temperature of each candidate node is Let the total number of candidate nodes be n, and the th... i The spatial coordinates of the candidate nodes are (x... i ,y i Candidate nodes can be regular mesh nodes, irregular mesh nodes, simulation interpolation nodes, experimental measurement points, or sensor locations that the structure allows for installation.

[0034] As a preferred implementation method, the above-mentioned edge weights are determined as follows: In the formula, Based on the fundamental thermal coupling coefficient, based on adjacent candidate nodes i and j The equivalent thermal coupling strength between them is preset; Adjacent candidate nodes i and j The spatial distance between nodes. The number of edges at each node can be determined by geometric adjacency.

[0035] As a preferred implementation, the edge weights described above can also be adjusted based on the temperature difference between adjacent candidate nodes in the two-dimensional temperature field. Temperature gradient correction is performed to ensure that the corrected weighted thermal network model reflects local temperature non-uniformity; the corrected edge weights... Represented as:

[0036] in, This is the preset temperature gradient correction factor. and These represent the highest and lowest temperatures among the candidate node temperatures in the two-dimensional temperature field. Indicates candidate nodes i Temperature in a two-dimensional temperature field.

[0037] As a preferred embodiment, when the first k When a candidate node is considered as a fault source node, the heat generated at each candidate node... Represented as:

[0038] in, For the first k The spatial coordinates of each fault source node This is the preset fault impact radius centered on the node location. The fault heat at the fault source node has a preset value. and The effective fault strength of the fault source node is mainly determined by the battery itself.

[0039] To assign appropriate risk weights to faults in high-temperature regions, the risk level of the fault source node in the two-dimensional temperature field is used as the basis for risk assessment. Corrections were made. After correction, the fault heat at the fault source node was [reduced / reduced / reduced]. Calculate using the following method:

[0040] in, The preset reference calorie content. The preset fault weighting coefficient for the high-temperature zone. For the first k The temperature of each fault source node in a two-dimensional temperature field.

[0041] As a preferred embodiment, the first k When the candidate node experiences a thermal failure, the first i Temperature rise of each candidate node's response R k,i for:

[0042] in, Indicates the first k When the candidate node experiences a thermal failure, the first i Fault temperature of each candidate node Indicates the first i The temperature of each candidate node in the two-dimensional temperature field; The calculation method is as follows: When the k-th candidate node is identified as the fault source node, the local thermal fault source is superimposed onto the basic steady-state thermal balance equation, and the temperature field under the fault condition is re-solved. For the k-th... i For candidate nodes, the steady-state thermal equilibrium relationship under fault conditions can be expressed as:

[0043] The equivalent gas temperatures of air and fuel can be given along their respective flow directions as follows:

[0044]

[0045] Among them, T air,in and T fuel,in These are the air inlet temperature and the fuel inlet temperature, respectively. and These represent the temperature changes of air and fuel along the flow direction, respectively (x i ,y i ) is the first i The spatial coordinates of the candidate nodes, L x and L y These represent the lengths of the battery's planar region in the x and y directions, respectively.

[0046] The equivalent heat source term can be composed of a uniform basic heat source and a background high-temperature region, and is represented as:

[0047] Among them, Q gen To ensure uniform basic heat source intensity, Q h As the background heat source intensity in the high-temperature region, (xh ,y h () represents the spatial coordinates of the center of the high-temperature region in the background. The radius of influence of the high-temperature region in the background.

[0048] Solving the steady-state thermal balance equations under the above fault conditions simultaneously for all candidate nodes yields the fault temperature field corresponding to the k-th fault source node:

[0049] Alternatively, when the k-th candidate node is identified as the fault source node, the local thermal fault source is superimposed onto the basic steady-state thermal equilibrium equation, and the temperature field under the fault condition is resolved. For the i-th candidate node, the steady-state thermal equilibrium relationship under the fault condition can be expressed as:

[0050] in, Let K be the fault temperature field vector corresponding to the k-th fault source node. The local thermal fault source vector has the following element as its i-th element:

[0051] The elements of matrix A can be represented as:

[0052]

[0053] The i-th element of vector b can be represented as:

[0054] Therefore, we can conclude that:

[0055] It should be noted that, For a matrix, It is a single value.

[0056] Constructing the fault response matrix: For each fault source node, calculate the response temperature rise of each candidate node under the corresponding fault condition. The response temperature rise of each candidate node under each fault source node constitutes a fault response vector. The fault response vectors corresponding to all fault source nodes constitute the fault response matrix, represented as:

[0057] In this matrix, each row corresponds to a fault source node, and each column corresponds to a candidate node.

[0058] As a preferred implementation method, the detectability rate of the fault source nodes of the currently selected m candidate nodes is calculated as follows: Let S be the group of the currently selected m candidate nodes. The detectability rate Coverage(S) of the fault source nodes in S is calculated as follows: ; In the formula, This indicates that among the currently selected m candidate nodes, the one that is the [number]th [node]... k Maximum response temperature rise under each fault source node; The preset sensor detection threshold; if Determine the first k The fault source node can be detected, that is, the current S covers the fault source node. k There are 1 fault source node; n is the total number of candidate nodes; The currently selected value is calculated using the following formula. m The average temperature rise response intensity AvgResponse(S) of each candidate node to all fault source nodes: ; The currently selected value is calculated in the following way. m Fault distinguishability of candidate nodes for different fault source nodes: set up R a ( S )and R b ( S ) are respectively the first a The and the first b Each fault source node is m The response vector formed by the fault responses on candidate nodes is given by the fault distinguishability D(S): .

[0059] Furthermore, as a preferred option, the comprehensive evaluation objective function J(S) for the m candidate nodes is:

[0060] in, , , For weighting coefficients, AvgResponse norm (S) represents the normalized average temperature rise response intensity, and D norm (S) represents the normalized fault distinguishability; In the formula, R best This represents the theoretically optimal average response. ; In the formula, D allThis represents the average fault response vector distance when all candidate nodes are used as sensor deployment nodes. The response temperature rise of each candidate node under each fault source node constitutes a fault response vector. Used to perform dimensional correction on the distinguishability under different numbers of sensors.

[0061] In other words, the method in this embodiment optimizes sensor placement based on the aforementioned sensor placement evaluation metrics (detectability of fault source nodes, average temperature rise response intensity, and fault distinguishability). With the number of sensors *m* as a constraint, and fault coverage, average response intensity, and fault distinguishability as optimization objectives, *m* sensor installation nodes are selected from all candidate nodes, and an optimized temperature sensor placement scheme is output. The optimization objective is expressed as:

[0062] Among them, S The optimized sensor arrangement set.

[0063] As a preferred implementation, a fault propagation-guided genetic optimization algorithm is used to obtain the optimal set of sensor nodes. The fault propagation-guided optimization algorithm includes fault propagation-guided initialization, coverage gap-guided mutation, and coverage-priority local repair.

[0064] Among them, fault propagation guidance initialization is used to determine the degree of fault impact. The initial sensor set is generated by considering the contribution of sensor observations and spatial dispersion; coverage gap-guided variation is used to identify fault source nodes that are not effectively covered, and candidate nodes with high response to uncovered fault source nodes are selected to replace low-contribution sensor nodes; coverage-priority local repair is used to replace nodes one-to-one with the optimization results, and further improve the comprehensive evaluation index on the basis of prioritizing the improvement of fault coverage.

[0065] The optimized layout scheme for temperature sensors includes one or more of the following: the number of sensors, the number of sensor nodes, the spatial coordinates of the sensors, the corresponding fault coverage, the average response intensity, the fault distinguishability, and the comprehensive evaluation value.

[0066] To better illustrate the specific implementation of the present invention, the following implementation examples are given.

[0067] An optimized arrangement method for thermal fault sensors in solid oxide fuel cells based on regular grid discretization.

[0068] like Figure 2As shown, the planar region of a cross-flow solid oxide fuel cell is taken as the object. The airflow direction of the solid oxide fuel cell is along the x-direction, and the fuel flow direction is along the y-direction. The planar region of the cell is used to characterize the two-dimensional thermal state distribution region to be monitored in the cell stack. The planar region of the cell is discretized into regular grid nodes, each node representing the local thermal state at the corresponding location and serving as a candidate temperature sensor installation location. In a specific example, the planar region of the cell is discretized into a 7×7 regular grid, resulting in 49 candidate nodes; the node numbers can be determined sequentially from bottom to top and from left to right, or according to the node spatial coordinates or the engineering installation order.

[0069] The method for optimizing the arrangement of thermal fault sensors in solid oxide fuel cells includes the following steps: obtaining the two-dimensional temperature field and operating parameters of the solid oxide fuel cell under fault-free conditions; discretizing the battery planar region into multiple candidate nodes; constructing a weighted thermal network model; correcting the edge weights according to the temperature gradient; setting local thermal fault sources and correcting the fault intensity; constructing a fault response matrix; constructing sensor arrangement evaluation indicators; optimizing the sensor arrangement and outputting the results.

[0070] In this example, the two-dimensional temperature field can be obtained by multiphysics simulation, and the simulated temperature data is interpolated to 49 candidate nodes to obtain the temperature value of each candidate node.

[0071] A weighted thermal network is constructed using candidate nodes as network nodes and the equivalent thermal coupling relationship between adjacent candidate nodes as network edges. The initial edge weights between nodes are determined based on the distance between them, and then corrected according to the aforementioned temperature gradient edge weight correction method, based on the fundamental temperature difference between adjacent candidate nodes, to obtain the corrected edge weights. This allows the modified weighted heat network to simultaneously reflect geometric adjacency relationships and local temperature nonuniformity.

[0072] Forty-nine candidate nodes are sequentially designated as potential fault source nodes. Local thermal fault sources are set at their corresponding locations, and the effective influence intensity of the local thermal fault sources on each node is adjusted according to the temperature level of the fault source node, following the aforementioned high-temperature zone fault intensity correction method. For each fault source node, the response temperature rise of each candidate node under fault conditions is calculated, and a fault response matrix is ​​constructed accordingly. The elements in the fault response matrix are represented as follows:

[0073] Among them, R k,i This represents the temperature rise of the i-th candidate node when a local thermal fault occurs at the k-th fault source node. After traversing all candidate fault source nodes, a 49×49 fault response matrix is ​​obtained. Each row of this fault response matrix corresponds to a fault source node, and each column corresponds to a candidate sensing node.

[0074] Based on the fault response matrix and the modified weighted heat network, network metrics can be further calculated to explain fault propagation characteristics and guide the initialization of optimization algorithms.

[0075] The fault propagation impact I of the k-th fault source node k Represented as:

[0076] Where n is the total number of candidate nodes, I k Used to characterize the overall temperature rise effect on all candidate nodes when the k-th fault source node experiences a thermal failure.

[0077] No. i The sensor observation contribution of each candidate node O i Represented as:

[0078] in, O i Used to characterize the i The overall observation capability of each candidate node for all potential fault source nodes.

[0079] No. i Weighted degree centrality of candidate nodes Represented as:

[0080] in, Used to characterize the local thermal connectivity strength of the i-th candidate node in the modified weighted thermal network.

[0081] The aforementioned fault propagation impact, sensor observation contribution, and weighted degree centrality can serve as the basis for ranking candidate nodes and generating the initial sensor set (m nodes).

[0082] Spatial dispersion is evaluated based on the spatial distance between candidate nodes to avoid multiple sensors being concentrated in a local area, and is expressed as:

[0083] in, Let m be the selected set of sensor nodes, and m be the number of selected sensors. For sensor nodes s a With sensor nodes s b The spatial distance between them.

[0084] Based on the fault response matrix, any candidate sensor deployment node set is evaluated. For the k-th fault source node, the maximum temperature rise response of the selected sensor deployment node set is expressed as:

[0085] Therefore, the detectability rate Coverage(S) of the fault source nodes of the current sensor deployment node set, the average temperature rise response intensity AvgResponse(S) for all fault source nodes, and the fault distinguishability D(S) for different fault source nodes are calculated. Then, AvgResponse(S) and D(S) are normalized.

[0086] Based on the above indicators, a comprehensive evaluation objective function for the sensor set S is constructed.

[0087] like Figure 3 As shown, in the sensor optimization deployment stage, a fault propagation-guided optimization algorithm is used to output the optimal sensor set. The optimization algorithm takes the fault response matrix R, the number of sensors m, the detection threshold θ, the population size P, and the maximum number of iterations G as inputs. First, based on the fault propagation influence I... k Contribution of sensor observation O i The initial sensor ensemble population is generated based on the spatial dispersion Disp(S). Specifically, it is based on the fault propagation impact degree I. k Identify potential fault sources, prioritize candidate sensor nodes with strong observation capabilities of potential fault sources, and combine the spatial distance between candidate nodes to distribute multiple sensors in the same sensor set as widely as possible, thereby avoiding too many sensors concentrated in a local area in the initial scheme.

[0088] In each iteration, a comprehensive evaluation objective function is calculated for each candidate sensor set in the population, and the evaluation results are used to guide selection and crossover operations to obtain a new candidate sensor set. For any candidate sensor set, the fault response matrix is ​​used to determine whether each potential fault source node can be effectively detected. If the maximum temperature rise response of a fault source node in the current sensor set is lower than a preset detection threshold, the fault source node is determined to be an uncovered fault source node; all uncovered fault source nodes together constitute the coverage gap of the current sensor set.

[0089] When a coverage gap exists, a coverage gap-guided mutation is performed. Specifically, firstly, the fault source node with the weakest current response or the most difficult to detect (the uncovered fault source node corresponding to the smallest maximum response) is selected from the uncovered fault source nodes as the priority compensation target. Then, among the candidate nodes outside the current sensor set, under the constraint of spatial dispersion, the node with a temperature rise response that is higher than the maximum response temperature rise under the current sensor set is selected as the node to be added. The spatial dispersion constraint is introduced to consider the spatial distance between the selected node and the existing nodes in the current sensor set, so as to avoid excessive clustering of the new node with existing sensors. Subsequently, a low-contribution sensor node is selected from the current sensor set as the node to be replaced. The low-contribution sensor node can be determined comprehensively based on its influence on fault coverage, average response intensity, and / or on the comprehensive evaluation objective function. For example, the sensor placement node with the least impact on the comprehensive evaluation objective function after deletion is selected. Finally, the low-contribution sensor node is replaced with the node to be added, resulting in the mutated sensor set.

[0090] By guiding mutations through the aforementioned coverage gaps, the algorithm can perform targeted corrections to fault source nodes in the current deployment scheme that have not yet been effectively detected. This allows newly added sensor nodes to prioritize compensating for monitoring blind spots, rather than relying solely on random mutations for searching, thereby improving the fault coverage rate and optimizing search efficiency of the sensor deployment scheme.

[0091] If the current candidate sensor set does not contain any uncovered fault source nodes, it means that the set has met the fault coverage requirements. At this time, random mutation or spatially dispersed guided mutation can be performed to maintain population diversity and further improve the average response strength and fault distinguishability.

[0092] After mutation, an elite retention strategy is used to preserve the set of candidate sensors with higher comprehensive evaluation objective function, thereby achieving population renewal.

[0093] Once the maximum number of iterations is reached or the termination condition is met, the iteration is complete. An optimal population is selected from the final population set. Further optimization involves performing coverage-priority local repair on each current optimal sensor set. Coverage-priority local repair involves attempting to replace each node in the current sensor deployment node set with a candidate node from outside the set, judging whether the fault coverage rate and the overall evaluation objective function improve after the replacement. If they improve, the replacement is accepted, until no further improvement in fault coverage rate or the overall evaluation objective function can be achieved through single-node replacement. Finally, the optimal sensor set is output.

[0094] In a specific example, 8 temperature sensors are selected from 49 candidate nodes, i.e., m=8; the detection threshold is set to 3K; and the weights of fault coverage, normalized average response intensity, and normalized fault distinguishability in the comprehensive evaluation objective function are 0.4, 0.3, and 0.3, respectively. After optimization by the fault propagation-guided optimization algorithm, the optimal sensor set is obtained:

[0095] like Figure 4 As shown, solid black nodes represent selected temperature sensor nodes, and hollow white nodes represent candidate nodes. Figure 4 As can be seen, the selected sensor nodes are distributed across multiple locations at the boundaries and within the battery plane area, rather than concentrated in a single local area, which helps to improve the coverage and distinguishability of thermal faults at different locations. In this embodiment, the sensor arrangement scheme can achieve effective coverage of candidate fault source nodes with a limited number of temperature sensors, achieving a fault coverage rate of 1.000 and a comprehensive target value of 0.826.

[0096] Furthermore, in other embodiments, candidate temperature sensor nodes are not limited to regular grid nodes. They can also be determined as irregular candidate nodes based on the actual structure of the solid oxide fuel cell stack, the location of temperature sensing holes, the flow channel arrangement, the manifold structure, the sealed area, the insulating area, or the possible installation location of the sensor. For irregular candidate nodes, the node adjacency relationship can be determined based on the actual spatial coordinates of the node, distance threshold, nearest neighbor relationship, finite element mesh connection relationship, or actual heat conduction path. Then, a weighted thermal network, fault response matrix, and sensor arrangement evaluation index are constructed according to the above method, thereby outputting an optimized temperature sensor arrangement scheme.

[0097] Example 2 This application also relates to a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method described above.

[0098] Specifically, the memory may include high-speed random access memory, as well as non-volatile memory, such as hard disks, RAM, plug-in hard disks, smart media cards (SMC), secure digital (SD) cards, flash cards, at least one disk storage device, flash memory device, or other volatile solid-state storage devices.

[0099] The relevant technical solutions are the same as above, and will not be repeated here.

[0100] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for optimizing the arrangement of temperature sensors for thermal fault monitoring in solid oxide fuel cells, characterized in that, include: Obtain the two-dimensional temperature field of a solid oxide fuel cell under fault-free operating conditions; The planar region of a solid oxide fuel cell is discretized into multiple candidate nodes. Each candidate node is used to characterize the local thermal state of the corresponding local region and serves as a candidate installation location for a temperature sensor. A weighted thermal network model is constructed: candidate nodes are used as network nodes, and the equivalent thermal coupling relationship between adjacent candidate nodes is used as network edges. The temperature at each node is determined based on a two-dimensional temperature field to determine the equivalent thermal coupling strength between adjacent candidate nodes. The edge weights between adjacent nodes are determined based on the distance between adjacent nodes and the equivalent thermal coupling strength. Each candidate node is sequentially used as a potential fault source node to construct different faults. For each fault, the heat generated at each candidate node is calculated based on the preset fault heat and fault influence radius at the fault source node. Based on this heat and the known battery inlet temperature, outlet temperature, and edge weight between adjacent nodes, the fault temperature at all candidate nodes under the current fault is recursively calculated according to the geometric adjacency relationship and steady-state thermal balance relationship. The difference between this fault temperature and the temperature determined by the two-dimensional temperature field is used to obtain the response temperature rise of each candidate node under each fault. From all candidate nodes, select m nodes as sensor deployment nodes. The goal is to optimize the m candidate nodes by maximizing the fault source node detectability rate, the average temperature rise response intensity of all fault source nodes, and the fault distinguishability of different fault source nodes. The fault source node detectability rate, average temperature rise response intensity, and fault distinguishability are all calculated based on the response temperature rise of the m candidate nodes.

2. The temperature sensor optimization arrangement method as described in claim 1, characterized in that, The edge weights are: ; In the formula, Based on the fundamental thermal coupling coefficient, and based on adjacent candidate nodes i and j The equivalent thermal coupling strength between them is preset; Adjacent candidate nodes i and j Spatial distance between them; Alternatively, the edge weights are: in, This is the preset temperature gradient correction factor. and These represent the highest and lowest temperatures among the candidate node temperatures in the two-dimensional temperature field. Indicates candidate nodes i Temperature in a two-dimensional temperature field.

3. The temperature sensor optimization arrangement method as described in claim 1, characterized in that, When the k When a candidate node is considered as a fault source node, the heat generated at each candidate node... Represented as: in, For the first k Spatial coordinates of each fault source node This is the preset fault impact radius centered on the node location. This refers to the heat generated at the fault source node. and The effective fault strength of the fault source node is characterized collaboratively. Let be the spatial coordinates of any candidate node; The fault heat at the fault source node The value can be preset, or determined by calculation in the following ways: in, The preset reference calorie content. The preset fault weighting coefficient for the high-temperature zone. For the first k The temperature of each fault source node in a two-dimensional temperature field; and These represent the highest and lowest temperatures among the candidate node temperatures in the two-dimensional temperature field.

4. The temperature sensor optimization arrangement method as described in claim 1, characterized in that, No. k When the candidate node experiences a thermal failure, the first i Temperature rise of each candidate node's response R k,i for: in, Indicates the first k When the candidate node experiences a thermal failure, the first i Fault temperature of each candidate node Indicates the first i The temperature of each candidate node in the two-dimensional temperature field; The following steady-state thermal equilibrium relationship is used for calculation. : In the formula, In order to be with the first i The set of nodes adjacent to each candidate node, Q i Let be the equivalent heat source term for the i-th candidate node. , This represents the known intensity of a uniform basic heat source. This represents the known background high-temperature region heat source intensity. The radius of influence of the known high-temperature background region; (x h ,y h (x) represents the spatial coordinates of the center of the high-temperature background region. i ,y i ) is the first i The spatial coordinates of the candidate nodes; Indicates the first k When the candidate node experiences a thermal failure, the first i The heat generated at each candidate node. Candidate nodes i and candidate nodes j The edge weight between them, H air H fuel and H env,i These are the air side, fuel side, and candidate nodes, respectively. i The equivalent heat transfer coefficient on the environmental side, T air,i T fuel,i and T amb These are the equivalent air temperature, equivalent fuel temperature, and ambient temperature, respectively. Indicates when the first k When a local thermal failure occurs at the candidate node, it is related to the first... i The node adjacent to the first j The temperature of each node under this fault condition.

5. The temperature sensor optimization arrangement method as described in claim 1, characterized in that, The detectability rate of the fault source nodes of the currently selected m candidate nodes is calculated as follows: Let S be the group of the currently selected m candidate nodes. The detectability rate Coverage(S) of the fault source nodes in S is calculated as follows: ； In the formula, This indicates that among the currently selected m candidate nodes, the one that is the [number]th [node]... k Maximum response temperature rise under each fault source node; The preset sensor detection threshold; if Determine the first k The fault source node can be detected, that is, the current S covers the fault source node. k There are 1 fault source node; n is the total number of candidate nodes; The currently selected value is calculated using the following formula. m The average temperature rise response intensity AvgResponse(S) of each candidate node to all fault source nodes: ； The currently selected value is calculated in the following way. m Fault distinguishability of candidate nodes for different fault source nodes: set up R a ( S )and R b ( S ) are respectively the first a The and the first b Each fault source node is m The response vector formed by the fault responses on candidate nodes is given by the fault distinguishability D(S): 。 6. The temperature sensor optimization arrangement method as described in claim 5, characterized in that, The comprehensive evaluation objective function J(S) for m candidate nodes is: in, , , For weighting coefficients, AvgResponse norm (S) represents the normalized average temperature rise response intensity, and D norm (S) represents the normalized fault distinguishability; In the formula, R best This represents the theoretically optimal average temperature rise response. ; In the formula, D all This represents the average fault response vector distance when all candidate nodes are used as sensor deployment nodes. The response temperature rise of each candidate node under each fault source node constitutes a fault response vector. Used to perform dimensional correction on the distinguishability under different numbers of sensors.

7. The temperature sensor optimization arrangement method as described in claim 1, characterized in that, A fault propagation-guided genetic optimization algorithm is used to obtain m candidate nodes, i.e., the optimal set of sensor nodes. The implementation method is as follows: In each iteration, a comprehensive evaluation objective function is calculated for each candidate sensor placement node in the population; the objective function value is used to guide the selection and crossover operations to obtain a new set of candidate sensor placement nodes, i.e., a new population. For any new population, if the maximum temperature rise response of a fault source node under the current sensor deployment node set is lower than the preset detection threshold, then the fault source node is determined to be an undetectable fault source node; all undetectable fault source nodes together constitute the coverage gap of the new population. When a coverage gap exists, coverage gap-guided mutation is performed: The fault source node with the smallest maximum temperature rise response from all undetectable fault source nodes is selected as the priority compensation target; from candidate nodes outside the current sensor deployment node set, under the constraint of spatial dispersion, a node with a temperature rise response higher than the maximum response temperature rise of the current sensor deployment node set is selected as the node to be added; a low-contribution sensor deployment node is selected from the current sensor deployment node set as the node to be replaced; wherein, the low-contribution sensor deployment node is determined comprehensively based on the detectability rate of the fault source node, the average temperature rise response intensity, and / or the magnitude of its influence on the comprehensive evaluation objective function; the low-contribution sensor deployment node is replaced with the node to be added, resulting in the mutated candidate sensor deployment node set, i.e., the mutated population; if no coverage gap exists, random mutation or spatial dispersion-guided mutation is performed. After mutation, the set of candidate sensor placement nodes whose comprehensive evaluation objective function values ​​meet the preset requirements is retained through the elite retention strategy, and the population set update of the current iteration is completed. Once the maximum number of iterations is reached or the termination condition is met, the iteration is completed, and an optimal population is selected from the final population set.

8. The temperature sensor optimization arrangement method as described in claim 7, characterized in that, After obtaining the optimal population, the genetic optimization algorithm further includes: performing cover-priority local repair on the population, implemented as follows: For each sensor placement node in the population, replace it one by one with candidate nodes outside the set. Determine whether the detectability rate of fault source nodes and the value of the comprehensive evaluation objective function of the replaced set are improved. If they are improved, accept the replacement. Continue until it is impossible to further improve the detectability rate of fault source nodes or the value of the comprehensive evaluation objective function through single node replacement. Finally, output the optimal set of sensor placement nodes.

9. The temperature sensor optimization arrangement method as described in claim 7, characterized in that, The population initialization method before iteration is as follows: Calculate the fault propagation impact of each fault source node. Where n is the total number of candidate nodes. I k Used to characterize the k The overall temperature rise effect on all candidate nodes when a fault source node experiences a thermal failure; R k,i Indicates the first k When the candidate node experiences a thermal failure, the first i Temperature rise of each candidate node's response R k,i ; ; Calculate the sensor observation contribution of each candidate node. , of which O i Used to characterize the i The overall observation capability of each candidate node for all potential fault source nodes; Calculate the weighted degree centrality of each candidate node. ,in, Used to characterize the local thermal connectivity strength of the i-th candidate node in the weighted thermal network model. Indicates adjacent candidate nodes i and j The boundary rights between them In order to be with the first i The set of nodes adjacent to each candidate node; Based on the impact of fault propagation I k Identify potential fault sources, select candidate sensor placement nodes that have a high contribution to the sensing observation of each potential fault source, and distribute multiple nodes in the same set of sensor placement nodes according to the weighted degree centrality to obtain the initial population.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium includes a stored computer program, wherein the computer program, when executed by a processor, controls the device on which the storage medium is located to perform the steps of the method as described in any one of claims 1 to 9.

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