Battery module thermal runaway key node identification method based on graph theory and multi-criterion decision

Abstract

The invention relates to a battery module thermal runaway key node identification method based on a graph theory and a multi-criterion decision. The method comprises the following steps: S1) constructing a weighted thermal network model of a battery module; s2) calculating a multi-centrality index of each node in the network; s3) constructing a decision matrix based on the centrality indexes of all nodes; s4) normalizing the decision matrix and determining an index weight; and S5) calculating comprehensive scores of the nodes by adopting a TOPSIS method, sorting the comprehensive scores, and outputting a thermal runaway protection priority list. Under the condition that the space structure and thermal connection parameters of the battery module are known, the method can accurately and quickly identify the key monomer in the thermal runaway spreading process, and provides a decision basis for precise thermal safety protection of the battery module and optimized layout of sensors.

Description

Technical Field

[0001] This invention belongs to the field of battery safety management and fault diagnosis technology, specifically involving a method for identifying key nodes of thermal runaway in battery modules based on graph theory and multi-criteria decision-making. Background Technology

[0002] Lithium-ion batteries are widely used in electric vehicles, energy storage power stations, and other fields due to their high energy density and long cycle life. As the core energy unit, the thermal safety of the battery module is the primary guarantee for the safe operation of the system. Thermal runaway is the most serious safety failure in a battery system, often triggered by a single cell and spreading throughout the module via thermal propagation, ultimately leading to catastrophic consequences. Therefore, accurately identifying key cells within the module that are prone to triggering chain reactions before thermal runaway occurs, and focusing on protecting or monitoring them, is an effective strategy to break the thermal propagation chain and improve the overall safety of the battery system.

[0003] However, current research and management strategies for battery thermal runaway propagation mostly focus on post-event monitoring and early warning or material-level improvements, such as optimizing the cooling performance of the thermal management system or using thermal insulation materials to slow down the propagation rate. While these methods have some effect, they lack pre-event analysis of the thermal runaway network structure and precise location of key points. Traditional methods struggle to quantify the criticality of each cell in the thermal network from a system topology perspective, failing to scientifically answer the core question of "which cell should be prioritized for protection among many battery cells." This leads to blind spots in safety design, inefficient allocation of protective resources, and difficulty in achieving optimal safety protection performance. Therefore, establishing a key node identification method that integrates thermal runaway network characteristics with multi-dimensional evaluation indicators has significant engineering application value for achieving precise and proactive thermal safety management of battery modules. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention proposes a method for identifying critical nodes in battery module thermal runaway based on graph theory and multi-criteria decision-making. By introducing complex network theory and multi-attribute decision-making algorithms, a scientific and quantitative model for identifying and ranking critical nodes is constructed, improving the accuracy and foresight of battery module thermal runaway protection. Furthermore, this method is applicable to different battery module configurations, such as cylindrical and prismatic battery modules, and can quickly assess the priority of thermal runaway risks for individual cells within the module. This method is easy to implement using computer programming, requiring only basic information such as the spatial structure of the battery module and the thermal resistance parameters between individual cells to accurately and quickly output a thermal runaway protection priority list, providing crucial decision-making basis for targeted enhancement of thermal management and optimization of sensor layout and other safety strategies.

[0005] A method for identifying key nodes of thermal runaway in battery modules based on graph theory and multi-criteria decision-making, characterized by the following steps:

[0006] Step S1: Construct a network model of the battery module, in which individual battery cells are used as nodes, thermal connections between individual battery cells are used as edges, and thermal resistance parameters of thermal connections are used as edge weights, thereby abstracting the physical battery module into a weighted network.

[0007] Step S2: Calculate multiple graph theory centrality indices for each node in the weighted network, wherein the centrality indices include degree centrality, proximity centrality, and betweenness centrality;

[0008] Step S3: Construct a decision matrix based on the multiple graph theory centrality indices of all nodes;

[0009] Step S4: Normalize the decision matrix and determine the weights of each centrality index;

[0010] Step S5: Based on the weighted normalized decision matrix, use TOPSIS (Approximation of Ideal Solution Ranking Method) to calculate the comprehensive score of each node, and sort all nodes according to the comprehensive score to output a thermal runaway protection priority list.

[0011] Preferably,

[0012] 1.1 In step S1, the weight w of the edge ij Calculate using the following formula:

[0013]

[0014] In the formula: w ij - The weight of the edge between battery i and battery j;

[0015] R ij - Thermal resistance between battery i and battery j, K / W;

[0016] d ij - The distance between battery i and battery j, in meters;

[0017] k -- equivalent thermal conductivity of the main material along the path, W / (m·K);

[0018] A ij -Effective heat transfer area between battery i and battery j, m 2 .

[0019] 1.2 In step S1, battery i and battery j are adjacent batteries, which can be classified as horizontally adjacent, vertically adjacent, or diagonally adjacent.

[0020] 1.3 In step S2, the degree centrality C wd(i) The formula for calculating weighted degree centrality is as follows:

[0021]

[0022] In the formula: N(i) - the set of adjacent battery nodes of battery i.

[0023] 1.4 In step S2, proximity centrality C c(i) The calculation formula is as follows:

[0024]

[0025] Where: n - the total number of network nodes, i.e., the number of battery cells;

[0026] d(i,k) - the weight of the shortest path from battery i to battery k.

[0027] 1.5. In step S2, betweenness centrality C b(i) The calculation formula is as follows:

[0028]

[0029] In the formula: σ st - The number of shortest paths from battery s to battery t;

[0030] σ st (i) - The number of shortest paths from battery s to battery t that pass through battery i.

[0031] 1.6 In step S3, the formula for the decision matrix X is as follows:

[0032]

[0033] The rows represent the number of battery nodes, with a total of n batteries; the columns represent graph centrality indices.

[0034] 1.7 In step S4, the decision matrix X is normalized to construct the normalized decision matrix R. The construction method is as follows:

[0035] R = [r] lm (6)

[0036]

[0037] In the formula: x lm - The elements in the l-th row and m-th column of the decision matrix X, where l∈(1,n) and m∈(1,2,3);

[0038] r lm - The element in the l-th row and m-th column of the normalized decision matrix R.

[0039] 1.8 In step S4, the weights of each centrality indicator are determined, and the objective weights of each centrality indicator are calculated using the entropy weight method. The specific steps are as follows:

[0040] 1) Calculate the characteristic proportion P lm The specific formula is as follows:

[0041]

[0042] 2) Calculate the information entropy e m The specific formula is as follows:

[0043]

[0044] In the formula: q - coefficient,

[0045] 3) Calculate the coefficient of difference g m The specific formula is as follows:

[0046] g m =1-e m (10)

[0047] 4) Calculate the objective weight w m The specific formula is as follows:

[0048]

[0049] 1.9 In step S5, the TOPSIS (Topology-Sorting Method for Approximating Ideal Solutions) is used to calculate the comprehensive score of each node, specifically including:

[0050] 1) Construct the weighted normalization matrix V, with the following formula:

[0051] V = [v lm ] = [w m ·r lm (12)

[0052] 2) Determine the positive ideal solution matrix V+ and the negative ideal solution matrix V-, where the elements in the positive (negative) ideal solution matrix are the maximum (minimum) values ​​of each centrality index;

[0053] 3) Calculate the first distance D from each node to the positive ideal solution. l+ and the second distance D to the negative ideal solution. l- The specific formula is as follows:

[0054]

[0055] 4) Calculate the relative closeness C l And according to C l The calculation results are sorted in descending order for all battery nodes to obtain the final critical node protection priority ranking, with a relative proximity C. l The calculation formula is as follows:

[0056]

[0057] The beneficial effects of this invention are as follows:

[0058] 1) A scientific identification framework integrating complex network theory and multi-criteria decision-making is proposed, applicable not only to standard battery modules but also to honeycomb battery modules. This method abstracts the physical battery module into a weighted thermal network and comprehensively considers the centrality of nodes in multiple dimensions such as connectivity, propagation efficiency, and control capability. This enables the systematic and quantitative identification of key nodes in thermal runaway, significantly improving the scientific nature and accuracy of battery thermal safety management strategies and overcoming the limitations of traditional methods that rely on post-event monitoring or global uniform protection.

[0059] 2) In the network model construction, thermal resistance is used as the weight of the edges in the graph. The scientific basis of this method is as follows: First, thermal resistance is an inherent physical quantity in heat transfer that characterizes the ability of a medium to impede heat flow. Its definition directly determines the heat flow rate, and thus the time for adjacent propagation of thermal runaway, which gives the weights a clear physical meaning. Second, this model transforms the physical problem into finding the propagation path with the minimum cumulative thermal resistance in graph theory, ensuring a high degree of consistency between the model and the physical process. Finally, thermal resistance can be calculated from specific physical parameters, making this method not only an analysis tool, but also a predictive and optimization tool that can be used for the thermal safety design of battery modules.

[0060] 3) A multi-indicator fusion decision-making mechanism was introduced to enhance the robustness and reliability of the evaluation results. By using multiple graph theory indicators such as comprehensive degree centrality, proximity centrality, and betweenness centrality, and employing objective weighting and the TOPSIS ranking method, the evaluation bias that may be caused by a single indicator is avoided. This allows for a more comprehensive and profound revelation of the true criticality of a single entity in the thermal propagation network, ensuring the accuracy and persuasiveness of the identification results.

[0061] 4) This method has good versatility and ease of engineering use, and is easy to integrate into battery management systems (BMS) or thermal runaway early warning platforms. Its input parameters (such as module structure and thermal resistance) are easy to obtain, the calculation process has clear logic, and it can be easily automated through programming software, which greatly improves the analysis efficiency. It provides a powerful tool for realizing forward-looking protection against thermal runaway and optimized allocation of safety resources in actual battery products, and has important engineering application value. Attached Figure Description

[0062] Figure 1 A flowchart of a method for identifying key nodes of thermal runaway in battery modules based on graph theory and multi-criteria decision-making;

[0063] Figure 2 This is a layout diagram of a 2×3 battery module;

[0064] Figure 3 This is a network model diagram of a 2×3 battery module.

[0065] Explanation of main component symbols

[0066] 1. Battery; 2. Node; 3. Edge.

[0067] The above description of the main component symbols, together with the accompanying drawings and specific embodiments, provides a more detailed explanation of the present invention. Detailed Implementation

[0068] The specific embodiments of the present invention are further described below with reference to the accompanying drawings. It should be emphasized that the following description is merely exemplary and is not intended to limit the scope of the present invention or its application.

[0069] A method for identifying key nodes of thermal runaway in battery modules based on graph theory and multi-criteria decision-making, the flowchart of which is shown below. Figure 1 As shown:

[0070] Step S1: Construct a weighted network model

[0071] A network model of the battery module is constructed, where individual battery cells are nodes, thermal connections between battery cells are edges, and the thermal resistance parameter of the thermal connection is used as the edge weight, w. ij Calculate using the following formula:

[0072]

[0073] In the formula: w ij - The weight of the edge between battery i and battery j;

[0074] R ij - Thermal resistance between battery i and battery j, K / W;

[0075] d ij - The distance between battery i and battery j, in meters;

[0076] Equivalent thermal conductivity of the main material along the k-path, W / (m·K);

[0077] A ij -Effective heat transfer area between battery i and battery j, m 2 ;

[0078] Battery i and battery j are adjacent batteries, which can be classified as horizontally adjacent, vertically adjacent, or diagonally adjacent.

[0079] Step S2: Calculate the multicentrism index

[0080] Calculate multiple graph-theoretic centrality indices for each node in the weighted network, where the centrality indices include degree centrality, proximity centrality, and betweenness centrality, wherein degree centrality C... wd(i) For weighted degree centrality, the calculation formula is as follows:

[0081]

[0082] In the formula: N(i) - the set of adjacent battery nodes of battery i;

[0083] Proximity centrality C c(i) The calculation formula is as follows:

[0084]

[0085] Where: n - the total number of network nodes, i.e., the number of battery cells;

[0086] d(i, k) - the weight of the shortest path from battery i to battery k;

[0087] Betweenness centrality C b(i) The calculation formula is as follows:

[0088]

[0089] In the formula: σ st - The number of shortest paths from battery S to battery t;

[0090] σ st (i) - The number of shortest paths from battery s to battery t that pass through battery i.

[0091] Step S3: Construct the decision matrix

[0092] Based on the multiple graph theory centrality indices of all nodes, a decision matrix is ​​constructed, where the formula for the decision matrix X is as follows:

[0093]

[0094] The rows represent the number of battery nodes, with a total of n batteries; the columns represent graph centrality indices.

[0095] Step S4: Determine the weights of the centrality metric

[0096] The decision matrix is ​​normalized to construct a normalized decision matrix R. The construction method is as follows:

[0097] R = [r] lm (6)

[0098]

[0099] In the formula: x lm- The elements in the l-th row and m-th column of the decision matrix X, where l∈(1,n) and m∈(1,2,3);

[0100] r lm - The element in the l-th row and m-th column of the normalized decision matrix R.

[0101] The objective weights of each centrality index are calculated using the entropy weight method. The specific steps are as follows:

[0102] 1) Calculate the characteristic proportion P lm The specific formula is as follows:

[0103]

[0104] 2) Calculate the information entropy e m The specific formula is as follows:

[0105]

[0106] In the formula: q - coefficient,

[0107] 3) Calculate the coefficient of difference g m The specific formula is as follows:

[0108] g m =1-e m (10)

[0109] 4) Calculate the objective weight w m The specific formula is as follows:

[0110]

[0111] Step S5: Output thermal runaway protection priority list

[0112] Based on the weighted normalized decision matrix, the TOPSIS (Topology for Ideal Solutions) method is used to calculate the comprehensive score of each node, specifically including:

[0113] 1) Construct the weighted normalization matrix V, with the following formula:

[0114] V = [vlm] = [wm·rlm](12)

[0115] 2) Determine the positive ideal solution matrix V+ and the negative ideal solution matrix V-, where the elements in the positive (negative) ideal solution matrix are the maximum (minimum) values ​​of each centrality index;

[0116] 3) Calculate the first distance D from each node to the positive ideal solution. l+ and the second distance D to the negative ideal solution. l- The specific formula is as follows:

[0117]

[0118] 4) Calculate the relative closeness C l And according to C l The calculation results are sorted in descending order for all battery nodes to obtain the final critical node protection priority ranking, with a relative proximity C. l The calculation formula is as follows:

[0119]

[0120] All nodes are sorted according to the comprehensive score, and a thermal runaway protection priority list is output.

[0121] Example:

[0122] Taking a module with 6 battery cells arranged in 2 rows and 3 columns as an example, the horizontal, vertical, and diagonal spacing between all battery cells is the same. The specific numbering and arrangement are as follows: Figure 2 As shown.

[0123] For the aforementioned battery module, the steps of a method for identifying key nodes of thermal runaway in a battery module based on graph theory and multi-criteria decision-making in this embodiment are briefly described as follows:

[0124] Step S1: Construct the network model of the battery module, specifically as follows: Figure 3 As shown, the edge weights (inter-cell thermal resistance) of the network model are simplified for this example only. It is assumed that the edge weights of the horizontal and vertical edges are 1; according to the edge weight calculation formula, the edge weight of the diagonal edge is...

[0125] Step S2: Calculate multiple graph centrality indices for each node in the weighted network, as follows:

[0126] 1) Degree centrality:

[0127] According to the degree centrality calculation formula, the degree centrality of each node in the embodiment is as follows:

[0128]

[0129]

[0130] 2) Proximity centrality:

[0131] As shown in the proximity centrality calculation formula, the proximity centrality of each node in the embodiment is as follows:

[0132]

[0133] 3) Betweenness centrality:

[0134] As can be seen from the betweenness centrality calculation formula, the betweenness centrality of each node in the embodiment is as follows:

[0135] C b(1) =0 (28)

[0136]

[0137] C b(3) =0 (30)

[0138] C b(4) =0 (31)

[0139]

[0140] C b(6) =0 (33)

[0141] Step S3: Based on the multiple graph theory centrality indices of all nodes, construct the decision matrix X, as follows:

[0142]

[0143] Step S4: Normalize the decision matrix. According to the vector normalization method, the normalized decision matrix R is as follows:

[0144]

[0145] Then, based on the normalized decision matrix R, the objective weights of each centrality index are calculated using the entropy weight method, and the results are as follows:

[0146] 1) Degree centrality weight:

[0147] w1 = 0.025 (36)

[0148] 2) Proximity centrality weights:

[0149] w2 = 0.009 (37)

[0150] 3) Betweenness centrality weight:

[0151] w3 = 0.965 (38)

[0152] Step S5: Based on the weighted normalization matrix construction method, establish the weighted normalized decision matrix V, as shown below:

[0153]

[0154] Based on the weighted normalized decision matrix V, the positive ideal solution V+ and the negative ideal solution V- are determined, as shown below:

[0155] V +=[0.013 0.004 0.682] (40)

[0156] V - =[0.008 0.003 0.000] (41)

[0157] Next, calculate the distance from each node to the positive and negative ideal solutions, as follows:

[0158]

[0159] Finally, based on the relative closeness C i The formula for solving the overall score of each node is as follows:

[0160]

[0161]

[0162] Based on the comprehensive score of each node, the thermal runaway protection priority of the battery module in the embodiment is as follows: 1) Battery 2 and Battery 5 are the core hubs of the network and the critical path for heat propagation; 2) Battery 1, 3, 4 and 6 are the edge nodes of the network and have a lower priority than Battery 2 and Battery 5.

[0163] As can be seen from the implementation steps and results of the method for identifying key nodes of thermal runaway in battery modules based on graph theory and multi-criteria decision-making described in this invention, this method achieves rapid and accurate identification of key nodes under different module configurations, thermal connections, and thermal runaway risk scenarios by constructing a weighted thermal network of the battery module and a multi-index fusion decision model. Based on known battery module spatial structure and thermal resistance parameters, this invention can efficiently and reliably output a priority list of thermal runaway risks for individual battery cells. This method can be implemented using computer programming languages; users only need to input the module structure and thermal connection parameters to automatically complete the identification and sorting of key nodes, significantly improving the efficiency and accuracy of thermal safety management, which is precisely the core objective that this invention aims to achieve.

[0164] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for identifying key nodes of thermal runaway in battery modules based on graph theory and multi-criteria decision-making, characterized in that, Includes the following steps: Step S1: Construct a network model of the battery module, in which individual battery cells are used as nodes, thermal connections between individual battery cells are used as edges, and thermal resistance parameters of thermal connections are used as edge weights, thereby abstracting the physical battery module into a weighted network. Step S2: Calculate multiple graph theory centrality indices for each node in the weighted network, including degree centrality, proximity centrality, and betweenness centrality; Step S3: Construct a decision matrix based on the multiple graph theory centrality indices of all nodes; Step S4: Normalize the decision matrix and determine the weights of each centrality index; Step S5: Based on the weighted normalized decision matrix, use TOPSIS (Approximation of Ideal Solution Ranking Method) to calculate the comprehensive score of each node, and sort all nodes according to the comprehensive score to output a thermal runaway protection priority list.

2. The method for identifying key nodes of thermal runaway in battery modules based on graph theory and multi-criteria decision-making as described in claim 1, characterized in that, In step S1, the weight w of the edge ij Calculate using the following formula: In the formula: w ij - The weight of the edge between battery i and battery j; R ij - Thermal resistance between battery i and battery j, K / W; d ij - The distance between battery i and battery j, in meters; k --- Equivalent thermal conductivity of the main material along the path, W / (m·K); A ij -Effective heat transfer area between battery i and battery j, m 2 .

3. The edge weight w according to claim 2 ij Its characteristics are, Battery i and battery j are adjacent batteries, which can be classified as horizontally adjacent, vertically adjacent, or diagonally adjacent.

4. The method for identifying key nodes of thermal runaway in battery modules based on graph theory and multi-criteria decision-making as described in claim 1, characterized in that, In step S2, the degree centrality C wd(i) The formula for calculating weighted degree centrality is as follows: In the formula: N(i) - the set of adjacent battery nodes of battery i.

5. The method for identifying key nodes of thermal runaway in battery modules based on graph theory and multi-criteria decision-making as described in claim 1, characterized in that, In step S2, the proximity centrality C c(i) The calculation formula is as follows: Where: n - the total number of network nodes, i.e., the number of battery cells; d(i,k) - the weight of the shortest path from battery i to battery k.

6. The method for identifying key nodes of thermal runaway in battery modules based on graph theory and multi-criteria decision-making as described in claim 1, characterized in that, In step S2, the betweenness centrality C b(i) The calculation formula is as follows: In the formula: σ st - The number of shortest paths from battery s to battery t; σ st (i) - The number of shortest paths from battery s to battery t that pass through battery i.

7. The method for identifying key nodes of thermal runaway in battery modules based on graph theory and multi-criteria decision-making as described in claim 1, characterized in that, In step S3, the formula for the decision matrix X is as follows: The rows represent the number of battery nodes, with a total of n batteries; the columns represent graph centrality indices.

8. The method for identifying key nodes of thermal runaway in battery modules based on graph theory and multi-criteria decision-making as described in claim 1, characterized in that, In step S4, the decision matrix X is normalized to construct a normalized decision matrix R. The construction method is as follows: R＝[r lm ] (6) In the formula: r lm - The elements in the l-th row and m-th column of the normalized decision matrix R, where l∈(1,n) and m∈(1,2,3); x lm - The element in the l-th row and m-th column of the decision matrix X.

9. The method for identifying key nodes of thermal runaway in battery modules based on graph theory and multi-criteria decision-making as described in claim 1, characterized in that, In step S4, the objective weights of each centrality index are calculated using the entropy weight method, based on the determined weights of each centrality index. The specific steps are as follows: 1) Calculate the characteristic proportion P lm The specific formula is as follows: 2) Calculate the information entropy e m The specific formula is as follows: In the formula: q - coefficient, 3) Calculate the coefficient of difference g m The specific formula is as follows: g m =1-e m (10) 4) Calculate the objective weight w m The specific formula is as follows:

10. The method for identifying key nodes of thermal runaway in battery modules based on graph theory and multi-criteria decision-making according to claim 1, characterized in that, In step S5, the calculation of the comprehensive score for each node using TOPSIS (Topology for Approximating Ideal Solutions) specifically includes: 1) Construct the weighted normalization matrix V, with the following formula: V=[v lm ]=[w m ·r lm ] (12) 2) Determine the positive ideal solution matrix V+ and the negative ideal solution matrix V-, where the elements in the positive (negative) ideal solution matrix are the maximum (minimum) values ​​of each centrality index; 3) Calculate the first distance D from each node to the positive ideal solution. l+ and the second distance D to the negative ideal solution. l- The specific formula is as follows: 4) Calculate the relative closeness C l And according to C l The calculation results are sorted in descending order for all battery nodes to obtain the final critical node protection priority ranking, with a relative proximity C. l The calculation formula is as follows:

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