Improved FMEA method and analysis and evaluation system considering failure mode interrelation and subjective factors

Abstract

The application provides an improved FMEA method and analysis and evaluation system considering failure mode interrelation and subjective factors, and the method comprises the following steps: obtaining scoring results of potential failure modes of a system to be analyzed; determining subjective weights of risk factors S, O and D based on a triangular fuzzy analytic hierarchy process, determining objective weights of the risk factors S, O and D based on a standard deviation method and trapezoidal fuzzy numbers, and obtaining comprehensive weights w of the risk factors S, O and D by using a comprehensive weighting method according to the subjective weights and the objective weights j ; determining a comprehensive ranking value R p corresponding to each potential failure mode according to a TODIM method improved based on an entropy weight method, and ranking the potential failure modes according to the comprehensive ranking value R p ; and clustering and analyzing the potential failure modes by using a dichotomous K-means clustering method according to W-RPN and the comprehensive ranking value R p , and formulating corresponding prevention and response measures for each potential failure mode.

Description

Technical Field

[0001] This invention relates to the field of reliability and risk analysis methods, specifically to an improved FMEA method and analysis and evaluation system that considers the interrelationship of failure modes and subjective factors. Background Technology

[0002] Failure Mode and Effects Analysis (FMEA) was first proposed by the U.S. Department of Aeronautics in 1963. With the increasing demand for product quality improvement, FMEA has been widely used due to its ability to effectively identify potential failure modes to minimize or even avoid potential problems. It has demonstrated unique advantages in industries such as automotive and medical equipment, becoming one of the five major quality control tools in the field of quality management. However, traditional FMEA methods still have some shortcomings, such as not considering the relative importance of risk factors and the questionable formula for calculating risk priority coefficients. These deficiencies have made it highly controversial in academia, making research on this topic of great practical value.

[0003] Improving FMEA models has always been a hot topic. Currently, the most research focuses on improving traditional FMEA models using aggregation functions and failure mode ranking methods for FMEA evaluation information. Researchers have proposed hundreds of specific methods, one common approach being the use of fuzzy multi-criteria decision-making. By employing a series of multi-criteria decision-making methods, the FMEA model can be improved, overcoming the inherent shortcomings of traditional FMEA, especially in the decision-making process where subjective factors often lead to reference dependence or loss aversion. Specifically, methods such as triangular fuzzy hierarchical analysis, standard deviation analysis, trapezoidal fuzzy numbers, and comprehensive weighting can fully consider and synthesize the subjective and objective weights of risk factors, thereby reducing the influence of subjective factors and considering the relative importance of risk factors.

[0004] Combining the Multi-Attribute Decision Making Method (TODIM) with FMEA can incorporate decision-making behavior into the decision model, fully considering the psychological characteristics of decision-makers, thereby improving the accuracy of problem analysis and decision-making. However, in the application of TODIM, there is a problem of insufficient consideration of the interrelationships between failure modes.

[0005] Furthermore, FMEA is overly complex in its use during failure mode identification and classification. The FMEA worksheet is also quite complicated, making it difficult for frontline workers or untrained operators to intuitively obtain failure modes and risk priorities. Summary of the Invention

[0006] This invention is made to solve the above-mentioned problems, and aims to provide an improved FMEA method and analysis and evaluation system that considers the interrelationship of failure modes and subjective factors.

[0007] This invention improves the classic TODIM model by incorporating the concept of entropy weight, thus taking into account the influence weights between different failure modes to a certain extent. Furthermore, machine learning methods enable precise data analysis. Machine learning, a branch of artificial intelligence, has wide and in-depth applications in data science. Clustering, based on similarity measures, organizes a set of data with multidimensional features into different groups. It can detect and identify significant categories from large amounts of data, analyze the internal structure of the data, and classify it. Applying clustering to failure mode classification helps distinguish key points and can play a certain auxiliary role in FMEA model analysis. Bisecting K-means clustering addresses the issue that the clustering results of the traditional K-means algorithm are easily affected by the selection of initial cluster centers, overcoming the algorithm's tendency to get trapped in local optima. Therefore, this invention chooses to use this clustering to analyze the ranking results of the improved FMEA failure mode and impact analysis, classifying the risks of the digital twin system and taking corresponding measures to reduce or improve risks based on the classification, thereby improving its reliability.

[0008] This invention provides an improved FMEA method that considers the interrelationships of failure modes and subjective factors, and has the following features:

[0009] Step S1: Obtain the scoring results of the potential failure modes of the system to be analyzed, and obtain the evaluation results of the risk factors for each potential failure mode; wherein, the evaluation result of the risk factor for the p-th potential failure mode is expressed as (S p O p D p p = 1, 2, ..., n, where n is the number of potential failure modes of the system to be analyzed, S represents severity, O represents occurrence, and D represents detectability;

[0010] Step S2: Determine the subjective weights of risk factors S, O, and D based on the triangular fuzzy analytic hierarchy process (AHP), determine the objective weights of risk factors S, O, and D based on the standard deviation method and trapezoidal fuzzy numbers, and obtain the comprehensive weight w of risk factors S, O, and D using a comprehensive weighting method based on the subjective and objective weights. j ;

[0011] Step S3: Determine the comprehensive ranking value R corresponding to each potential failure mode according to the TODIM method improved by the entropy weight method. p And according to the comprehensive sorting value R pThe potential failure modes are sorted.

[0012] Step S4: Average and synthesize the scoring results of the potential failure modes, and then calculate the weights based on the comprehensive weights w. j w j The W-RPN value, obtained by weighting the result and multiplying the S, O, and D values, is combined with the overall ranking value R. p The potential failure modes are clustered using the binary K-means clustering method, and corresponding prevention and response measures are formulated for each potential failure mode.

[0013] The improved FMEA method considering the interrelationships of failure modes and subjective factors provided by this invention may also have the following feature: wherein, in step S1, the scoring results of the potential failure modes of the system to be analyzed are obtained through the following process:

[0014] Step Sa1: Obtain the system to be analyzed, form an FMEA team based on the type and application field of the system to be analyzed, and obtain the operation mode of the system to be analyzed;

[0015] Step Sa2: The FMEA team determines n potential failure modes FM1, FM2, ..., FM3 based on the operating mode of the system to be analyzed. n ;

[0016] Step Sa3: Using a seven-granularity scoring model, establish scoring standards for S, O, and D risk factors;

[0017] Step Sa4: Based on the established scoring criteria, the FMEA team obtains the evaluation results of the importance of each potential failure mode under the S, O, and D risk factors.

[0018] The improved FMEA method considering the interrelationships of failure modes and subjective factors provided by this invention may also have the following feature: wherein the method for determining the subjective weights of risk factors S, O, and D based on the triangular fuzzy hierarchical analysis method in step S2 includes:

[0019] Step S211: Establish importance scoring criteria for risk factors S, O, and D. The FMEA team then conducts expert scoring of the importance of risk factors S, O, and D based on these scoring criteria.

[0020] Step S212: Based on the importance scoring criteria of risk factors S, O, and D, establish the corresponding triangular fuzzy language set and triangular fuzzy number;

[0021] Step S213: Calculate the risk factor consistency index CI based on the expert scores and the triangular fuzzy number;

[0022] Step S214: Query the random consistency index table, obtain the consistency index RI based on the number of risk factors, and calculate the consistency ratio using the consistency ratio formula. Obtain the consistency ratio CR to perform a consistency test on the expert scores. If the consistency ratio is less than 0.1, it means that the expert scores are valid. Then, the expert scores are combined according to the expert weight and the process proceeds to step S215. Otherwise, the expert scores are re-evaluated and the process returns to step S213.

[0023] Step S215: Repeat steps S213 to S214 with the synthesized expert scores to check if the consistency ratio is less than 0.1. If so, the subjective weights of risk factors S, O, and D are obtained. Otherwise, the expert scoring is repeated, and the process returns to step S213.

[0024] The improved FMEA method considering the interrelationships of failure modes and subjective factors provided by this invention may also have the following feature: wherein the method for determining the objective weights of risk factors S, O, and D based on the standard deviation method and trapezoidal fuzzy numbers in step S2 includes:

[0025] Step S221: Based on the S, O, D risk factor scoring criteria established in step Sa3, establish a trapezoidal fuzzy evaluation language;

[0026] Step S222: Based on the trapezoidal fuzzy evaluation language, the scores given by each member of the FMEA team for the potential failure mode according to the S, O, D risk factor scoring standard are converted into expert fuzzy language evaluation results.

[0027] Step S223: Based on the expert fuzzy language evaluation results, construct an evaluation index matrix P. After standardizing the evaluation index matrix P, calculate the standard deviation of each potential failure mode, and obtain the objective weight based on the standard deviation and mean of each potential failure mode.

[0028] The improved FMEA method considering the interrelationships of failure modes and subjective factors provided by this invention may also have the following feature: wherein, in step S2, the comprehensive weighting method is used to obtain the comprehensive weight w of risk factors S, O, and D. j The methods include:

[0029] Step S231: Introduce an adjustment coefficient θ, θ∈[0,1], and calculate the comprehensive weight.

[0030] The improved FMEA method considering the interrelationships of failure modes and subjective factors provided by this invention may also have the following feature: wherein step S3 includes:

[0031] Step S31, based on the combined weight w of risk factors S, O, and D j Calculate the relative weights ω′ of the risk factors j ;

[0032] Step S32: Normalize the evaluation index matrix P constructed in step S223 to obtain the normalized matrix G;

[0033] Step S33, based on the relative weights ω′ of the risk factors j And the normative matrix G, respectively calculate the dominance matrix V under risk factors S, O, and D. j ;

[0034] Step S34, based on the dominance matrix V under risk factors S, O, and D. j Calculate the overall dominance between each pair of failure modes to obtain the overall dominance matrix V;

[0035] Step S35: Calculate the comprehensive ranking value R based on the comprehensive dominance matrix V. P And according to the comprehensive sorting value R p Sort the values ​​in descending order.

[0036] The improved FMEA method considering the interrelationships of failure modes and subjective factors provided by this invention may also have the following feature: wherein step S4 includes:

[0037] Step S41: Utilize the comprehensive weights obtained in step S231 The scoring results of the potential failure modes are weighted, and the S, O, and D values ​​of each potential failure mode are multiplied together to obtain the W-RPN, which is used as the first feature value.

[0038] Step S42, the comprehensive ranking value R obtained in step S35 is... p As the second eigenvalue;

[0039] Step S43: Normalize the first feature value and the second feature value;

[0040] Step S44: Obtain the description matrix P′=(p′) based on the normalized first and second eigenvalues. pf ) n×2 Let p' represent n two-dimensional data points. p1 p′ is the first eigenvalue after normalization. p2 The second eigenvalue after normalization;

[0041] Step S45: Cluster the n two-dimensional data points into K classes using the binary K-means clustering method to obtain the clustering results;

[0042] Step S46: Based on the clustering results, analyze the potential failure modes, and based on the operation mode of the system to be analyzed, the magnitude of the first feature value, and the magnitude of the second feature value, provide corresponding prevention and response measures for each potential failure mode.

[0043] This invention also provides an analysis and evaluation system that uses the improved FMEA method described above, which considers the interrelationships of failure modes and subjective factors, and has the following features:

[0044] The scoring acquisition unit acquires the scoring results of the potential failure modes of the system to be analyzed, and obtains the evaluation results of the risk factors for each potential failure mode; wherein, the evaluation result of the risk factor for the p-th potential failure mode is represented as (S p O p D p p = 1, 2, ..., n, where n is the number of potential failure modes of the system to be analyzed, S represents severity, O represents occurrence, and D represents detectability;

[0045] The comprehensive weight calculation unit determines the subjective weights of risk factors S, O, and D based on the triangular fuzzy analytic hierarchy process (AHP), determines the objective weights of the risk factors S, O, and D based on the standard deviation method and trapezoidal fuzzy numbers, and obtains the comprehensive weight w of risk factors S, O, and D using a comprehensive weighting method based on the subjective and objective weights. j ;

[0046] The ranking unit determines the comprehensive ranking value R corresponding to each potential failure mode according to the TODIM method improved based on the entropy weight method. p And according to the comprehensive sorting value R p The potential failure modes are sorted.

[0047] The analysis results generation unit averages and synthesizes the scores of the potential failure modes, based on the comprehensive weight w. j The W-RPN value, obtained by weighting the result and multiplying the S, O, and D values, is combined with the overall ranking value R. p The potential failure modes are clustered using the binary K-means clustering method, and corresponding prevention and response measures are generated for each potential failure mode.

[0048] The analysis and evaluation system provided by this invention may also have the following features: It further includes:

[0049] The storage unit stores the corresponding rules between different categories of potential failure modes and their prevention and response measures, wherein the different categories are divided according to the classification results of the cluster analysis.

[0050] The role and effect of invention

[0051] The improved FMEA method and analysis and evaluation system of this invention, which considers the interrelationships of failure modes and subjective factors, improves the traditional FMEA method based on triangular fuzzy hierarchical analysis, trapezoidal fuzzy numbers, standard deviation method, comprehensive weighting method, TODIM method improved based on entropy weight, and bisection K-means clustering analysis. First, a seven-granularity evaluation method is used to score failure modes. Second, triangular fuzzy hierarchical analysis is used to determine subjective weights, and standard deviation method and trapezoidal fuzzy numbers are combined to determine objective weights. Then, the comprehensive weighting method is used to calculate the comprehensive weight of risk factors, thus solving the problems of strong subjectivity and failure to consider the relative importance of risk factors in traditional FMEA methods. Next, TODIM is improved and used to rank failure modes, overcoming the deficiency of the classic TODIM method in not considering the interrelationships between failure modes. Finally, bisection K-means clustering analysis is used to cluster failure modes based on W-RPN values ​​and comprehensive ranking values. Therefore, the improved FMEA method and analysis and evaluation system of this invention, which considers the interrelationships of failure modes and subjective factors, can fully consider expert scoring preferences and the interrelationships between failure modes and improve accuracy. Attached Figure Description

[0052] Figure 1 This is a flowchart of the improved FMEA method in an embodiment of the present invention; and

[0053] Figure 2 This is a schematic diagram illustrating the failure modes of the intelligent gas digital twin system based on binary K-means clustering in an embodiment of the present invention. Detailed Implementation

[0054] To make the technical means, creative features, objectives and effects of this invention easier to understand, the following embodiments, in conjunction with the accompanying drawings, specifically illustrate the improved FMEA method and analysis and evaluation system of this invention that considers the interrelationship of failure modes and subjective factors.

[0055] <Example 1>

[0056] The improved FMEA method in this embodiment, which considers the interrelationships of failure modes and subjective factors, is used to analyze and evaluate a smart gas digital twin system (DTS).

[0057] Figure 1 This is a flowchart of the improved FMEA method in an embodiment of the present invention.

[0058] like Figure 1 As shown, this method first obtains the scoring results of the potential failure modes of the system to be analyzed; secondly, it determines the subjective weights based on the triangular fuzzy hierarchical analysis method, determines the objective weights based on the standard deviation method and trapezoidal fuzzy numbers, and calculates the comprehensive weights of risk factors based on the comprehensive weighting method; thirdly, it sorts the failure modes based on the entropy weight improved TODIM method; and finally, it uses the binary K-means clustering method to perform cluster analysis on the failure modes.

[0059] Specifically, the improved FMEA method in this embodiment, which considers the interrelationships of failure modes and subjective factors, includes the following steps:

[0060] Step S1: Obtain the scoring results of the potential failure modes of the system to be analyzed, and obtain the evaluation results of the risk factors for each potential failure mode. Each potential failure mode's risk factor includes severity (S), occurrence (O), and detection (D). The evaluation result of the risk factor for the p-th potential failure mode is expressed as (S... p O p D p p = 1, 2, ..., n, where n is the number of potential failure modes of the system to be analyzed.

[0061] Specifically, a seven-granularity scoring model is used to score failure modes and obtain scoring results, including:

[0062] Step Sa1: Obtain the system to be analyzed. Based on the type and application field of the system to be analyzed, form an FMEA team and use multiple methods to gain a comprehensive understanding of the system to be analyzed and obtain information on how the system operates.

[0063] In this embodiment, the FMEA team consists of Technical Manager A, Implementation Consultant B, Senior Manager of DTS Information Project C, and D, a scholar from a university researching DTS reliability and risk assessment.

[0064] Step Sa2: Based on the operation of the system under analysis, the FMEA team identifies n potential failure modes FM1, FM2, ..., FM3. n .

[0065] To summarize the failure modes of the smart gas digital twin system, it is necessary to start from the expected effects of various functions under each functional module of the digital twin system, to further divide the functions of each module, and after brainstorming by the FMEA team, the basic functional modules and failure modes of the smart gas digital twin system are summarized in Table 1 below:

[0066] Table 1. Basic functional modules and failure modes of the intelligent gas digital twin system.

[0067]

[0068] For ease of description, the above failure modes are designated by the number FM. p (p=1,2,…25) indicates that the causes of failure are divided into five categories: human error, hardware failure, network problems, software errors, and modeling errors. The impact of each failure mode is summarized in Table 2 below:

[0069] Table 2. Failure Mode Effects and Causes

[0070]

[0071]

[0072] Step Sa3 involves establishing the scoring criteria for the S, O, and D risk factors using a seven-granularity scoring model, as shown in Table 3:

[0073] Table 3 FMEA Scoring Criteria

[0074]

[0075] Step Sa4: Based on the established scoring criteria, the FMEA team obtains the evaluation results of the importance of each potential failure mode under the S, O, and D risk factors. The evaluation result of the risk factor for the p-th potential failure mode is expressed as (S p O p D p ), p = 1, 2, ..., 25.

[0076] In this embodiment, each member of the FMEA team scores the 25 potential failure modes according to the scoring criteria shown in Table 3 above. Then, the average score of each member's score is taken to obtain the score for each potential failure mode. The final scoring results are shown in Table 4 below:

[0077] Table 4 FMEA Scoring Results

[0078]

[0079] Risk factors are scored from 1 to 10, with 1 indicating the least impact of the failure mode on the system being analyzed and 10 indicating the most severe impact. RPN is the product of the S, O, and D scores for each failure mode, used to measure the risk level of each failure mode. The higher the score, the higher the risk level of the failure mode and the more urgent the need for control.

[0080] Step S2: Determine the subjective weights of risk factors S, O, and D based on the triangular fuzzy analytic hierarchy process (AHP), determine the objective weights of risk factors S, O, and D based on the standard deviation method and trapezoidal fuzzy numbers, and obtain the comprehensive weight w of risk factors S, O, and D using a comprehensive weighting method based on the subjective and objective weights. j w j ∈w, w=(w1,w2,w3).

[0081] In step S2, the method for determining the subjective weights of risk factors S, O, and D based on the triangular fuzzy analytic hierarchy process includes:

[0082] Step S211: Establish importance scoring criteria for risk factors S, O, and D. The FMEA team then uses these criteria to conduct expert scoring of the importance of risk factors S, O, and D. The importance scoring criteria for risk factors S, O, and D are shown in Table 5.

[0083] Table 5 Risk Factor Importance Scoring Criteria

[0084] Importance score Meaning of scores (comparison between horizontal risk factors and vertical factors) 1 Extremely unimportant 2 unimportant 3 Equally important 4 important 5 Extremely important

[0085] Step S212: Based on the importance scoring criteria of risk factors S, O, and D, establish the corresponding triangular fuzzy language set and triangular fuzzy number, as shown in Table 6:

[0086] Table 6. Triangular Fuzzy Numbers Corresponding to the Importance of Risk Factors

[0087] Importance score Meaning of scores (comparing horizontal factors and vertical factors) Triangular fuzzy number 1 Extremely unimportant (0.1，0.1，0.2) 2 unimportant (0.2，0.3，0.4) 3 Equally important (0.5，0.5，0.5) 4 important (0.6，0.7，0.8) 5 Extremely important (0.8，0.9，0.9)

[0088] Step S213: Calculate the risk factor consistency index CI based on the expert scores and the triangular fuzzy number;

[0089] Specifically, select The evaluation method constructs a complementary judgment matrix for each expert score. Its corresponding element This represents the triangular fuzzy number corresponding to the importance of the i-th risk factor relative to the j-th risk factor, and then the expectation formula is applied. Calculate the expectation matrix Among them, since the experts held a neutral attitude, ε = 0.5. The element in the i-th row and j-th column is represented as The element in row j and column i is represented as The expectation matrix is ​​processed to obtain the fuzzy reciprocal judgment matrix. The weight vector of the matrix is ​​then calculated using summation and integration. Then calculate the consistency index. These represent the weight vectors respectively. The i-th and j-th components, i, j = 1, 2, 3, m = 3, where m represents the total number of risk factors.

[0090] Step S214: Query the random consistency index table, obtain the consistency index RI based on the total number of risk factors m, and calculate the consistency ratio using the consistency ratio formula. The consistency ratio (CR) was obtained to perform a consistency test on the expert scores. A consistency ratio less than 0.1 indicates the test passed. The expert scores were then aggregated according to their respective weights. In this embodiment, the weights of all experts were 0.25, with no significant difference. The random consistency index (RI) is shown in Table 7.

[0091] Table 7 Random Consistency Index Values

[0092] m 1 2 3 4 5 6 7 8 9 10 … RI 0 0 0.58 0.90 1.12 1.24 1.32 1.41 1.45 1.49 …

[0093] Step S215: Repeat steps S213-S214 with the synthesized expert scores to perform a consistency test (CR < 0.1). If the result meets the preset value, the subjective weights of risk factors S, O, and D are obtained. As shown in Table 8:

[0094] Table 8 Subjective Weights of Risk Factors

[0095] Risk factors S O D CR Subjective weight 0.648 0.215 0.137 0.0015

[0096] In step S2, the method for determining the objective weights of risk factors S, O, and D based on the standard deviation method and trapezoidal fuzzy numbers includes:

[0097] Step S221: Based on the S, O, and D risk factor scoring criteria established in step Sa3, a trapezoidal fuzzy evaluation language is established, as shown in Table 9:

[0098] Table 9. Trapezoidal Fuzzy Evaluation Language

[0099] Rating results Evaluation language Trapezoidal fuzzy number 1，2 Extremely low (VL) (0，0，1，3) 3，4 Low (L) (1，3，4，5) 5，6 Medium (M) (4，5，5，6) 7，8 High (H) (5，6，7，9) 9，10 Extremely high (VH) (7，9，10，10)

[0100] Step S222: Based on the trapezoidal fuzzy evaluation language, the scores given by each member of the FMEA team for potential failure modes according to the S, O, D risk factor scoring criteria are converted into expert fuzzy language evaluation results.

[0101] In this embodiment, the scores given by experts A, B, C, and D for the above 25 potential failure modes are converted into expert fuzzy language evaluation results, as shown in Table 10:

[0102] Table 10 Expert evaluation results of fuzzy language

[0103]

[0104]

[0105] Step S223: Defuzzify and synthesize the expert fuzzy language evaluation results to construct the evaluation index matrix P. Here, n represents the total number of failure modes, and m represents the total number of risk factors, which are 25 and 3 respectively in this embodiment. After standardizing this matrix P, matrix B is obtained, and the standard deviation σ of each potential failure mode is calculated. j To obtain objective weights

[0106] Table 11 Objective Weights of Risk Factors

[0107] Risk factors S O D Objective weight 0.331 0.317 0.352

[0108] In step S2, the comprehensive weighting method is used to obtain the comprehensive weights w of risk factors S, O, and D. j The methods include:

[0109] Step S231: Introduce an adjustment coefficient θ, θ∈[0,1], and calculate the comprehensive weight. As shown in Table 12:

[0110] Table 12 Overall Weights of Risk Factors

[0111] Risk factors S O D Subjective weight 0.648 0.215 0.137 Objective weight 0.331 0.317 0.352 Overall weight 0.490 0.265 0.245

[0112] Step S3: Determine the comprehensive ranking value R corresponding to each potential failure mode according to the TODIM method improved by the entropy weight method. p And based on the comprehensive ranking value R p Sort the potential failure modes.

[0113] Specifically, step S3 includes:

[0114] Step S31, based on the combined weight w of risk factors S, O, and D j The relative weights ω′ of the risk factors are calculated according to the following formula. j :

[0115]

[0116] Where, ω j The combined weight w of risk factors S, O, and D obtained in step S2 j j = 1, 2, ..., m, where m represents the total number of risk factors; ω * As a reference weight, ω * =max(ω1, ω2, ..., ω m ).

[0117] In this embodiment, the relative weights ω′ of the risk factors are obtained.j As shown in Table 13:

[0118] Table 13 Relative Weights of Risk Factors

[0119]

[0120] Step S32: Normalize the evaluation index matrix P constructed in step S223 to obtain the normalized matrix G. Wherein, the evaluation index matrix P = [x...] pj ] n×m The normalized matrix G = [g pj ] n×m Here, n represents the total number of failure modes, and m represents the total number of risk factors. In this embodiment, they are 25 and 3 respectively. The specific calculation formula is as follows:

[0121]

[0122]

[0123]

[0124] In this embodiment, the obtained normalization matrix G is as follows:

[0125]

[0126] Step S33, based on the relative weights ω′ of the risk factors j Given the normalization matrix G, calculate the dominance matrix V for risk factors S, O, and D, respectively. j =[v j (F p F l )] n×n v j (F p F l ) indicates failure mode F p Compared to F under risk factor j l Advantages, v j (F p F l Calculate according to the following formula:

[0127]

[0128] In the formula, ρ is the loss decay coefficient, which is generally taken as 2.25.

[0129] In this embodiment, the dominance matrix under risk factor S is shown in Table 14:

[0130] Table 14 Dominance matrix under risk factor S

[0131] 0.000 0.103 0.133 -0.07 0.173 -0.14 -0.07 0.196 0.084 -0.07 0.160 -0.05 0.196 -0.07 0.084 0.000 -0.14 -0.14 -0.11 -0.07 0.103 0.059 -0.07 0.059 0.146 -0.09 0.000 0.084 -0.12 0.138 -0.16 -0.12 0.166 -0.05 -0.12 0.122 -0.10 0.166 -0.12 -0.05 -0.09 -0.16 -0.16 -0.14 -0.12 0.000 -0.07 -0.12 -0.07 0.103 -0.12 -0.07 0.000 -0.40 0.109 -0.18 -0.14 0.143 -0.09 -0.14 0.088 -0.13 0.143 -0.14 -0.09 -0.12 -0.18 -0.18 -0.16 -0.14 -0.07 -0.10 -0.14 -0.10 0.059 0.084 0.133 0.158 0.000 0.192 -0.11 0.000 0.213 0.119 0.000 0.181 0.059 0.213 0.000 0.119 0.084 -0.11 -0.11 -0.08 0.000 0.133 0.103 0.000 0.103 0.169 -0.15 -0.12 -0.09 -0.17 0.000 -0.21 -0.17 0.091 -0.13 -0.17 -0.06 -0.16 0.091 -0.17 -0.13 -0.15 -0.21 -0.21 -0.19 -0.17 -0.12 -0.14 -0.17 -0.14 -0.08 0.155 0.186 0.204 0.130 0.232 0.000 0.130 0.249 0.176 0.130 0.223 0.143 0.249 0.130 0.176 0.155 0.000 0.000 0.084 0.130 0.186 0.166 0.130 0.166 0.213 0.084 0.133 0.158 0.000 0.192 -0.11 0.000 0.213 0.119 0.000 0.181 0.059 0.213 0.000 0.119 0.084 -0.11 -0.11 -0.08 0.000 0.133 0.103 0.000 0.103 0.169 -0.17 -0.15 -0.12 -0.19 -0.08 -0.22 -0.19 0.000 -0.16 -0.19 -0.10 -0.18 0.000 -0.19 -0.16 -0.17 -0.22 -0.22 -0.21 -0.19 -0.15 -0.16 -0.19 -0.16 -0.11 -0.07 0.059 0.103 -0.10 0.151 -0.16 -0.10 0.176 0.000 -0.10 0.136 -0.09 0.176 -0.10 0.000 -0.07 -0.16 -0.16 -0.13 -0.10 0.059 -0.05 -0.10 -0.05 0.119 0.084 0.133 0.158 0.000 0.192 -0.11 0.000 0.213 0.119 0.000 0.181 0.059 0.213 0.000 0.119 0.084 -0.11 -0.11 -0.08 0.000 0.133 0.103 0.000 0.103 0.169 -0.14 -0.11 -0.08 -0.16 0.065 -0.20 -0.16 0.112 -0.12 -0.16 0.000 -0.15 0.112 -0.16 -0.12 -0.14 -0.20 -0.20 -0.18 -0.16 -0.11 -0.13 -0.16 -0.13 -0.05 0.059 0.119 0.146 -0.05 0.183 -0.12 -0.05 0.204 0.103 -0.05 0.171 0.000 0.204 -0.05 0.103 0.059 -0.12 -0.12 -0.09 -0.05 0.119 0.084 -0.05 0.084 0.158 -0.17 -0.15 -0.12 -0.19 -0.08 -0.22 -0.19 0.000 -0.16 -0.19 -0.10 -0.18 0.000 -0.19 -0.16 -0.17 -0.22 -0.22 -0.21 -0.19 -0.15 -0.16 -0.19 -0.16 -0.11 0.084 0.133 0.158 0.000 0.192 -0.11 0.000 0.213 0.119 0.000 0.181 0.059 0.213 0.000 0.119 0.084 -0.11 -0.11 -0.08 0.000 0.133 0.103 0.000 0.103 0.169 -0.07 0.059 0.103 -0.10 0.151 -0.16 -0.10 0.176 0.000 -0.10 0.136 -0.09 0.176 -0.10 0.000 -0.07 -0.16 -0.16 -0.13 -0.10 0.059 -0.05 -0.10 -0.05 0.119 0.000 0.103 0.133 -0.07 0.173 -0.14 -0.07 0.196 0.084 -0.07 0.160 -0.05 0.196 -0.07 0.084 0.000 -0.14 -0.14 -0.11 -0.07 0.103 0.059 -0.07 0.059 0.146 0155 0186 0204 0130 0232 0000 0130 0249 0176 0130 0223 0143 0249 0130 0176 0155 0000 0000 0084 0130 0186 0166 0130 0166 0213 0155 0186 0204 0130 0232 0000 0130 0249 0176 0130 0223 0143 0249 0130 0176 0155 0000 0000 0084 0130 0186 0166 0130 0166 0213 0.125 0.162 0.183 0.091 0.213 -0.08 0.091 0.232 0.151 0.091 0.203 0.109 0.232 0.091 0.151 0.125 -0.08 -0.08 -0.00 0.091 0.162 0.138 0.091 0.138 0.192 0.084 0.133 0.158 0.000 0.192 -0.11 0.000 0.213 0.119 0.000 0.181 0.059 0.213 0.000 0.119 0.084 -0.11 -0.11 -0.08 0.000 0.133 0.103 0.000 0.103 0.169 -0.09 0.000 0.084 -0.12 0.138 -0.16 -0.12 0.166 -0.05 -0.12 0.122 -0.10 0.166 -0.12 -0.05 -0.09 -0.16 -0.16 -0.14 -0.12 0.000 -0.07 -0.12 -0.07 0.103 -0.05 0.084 0.119 -0.09 0.162 -0.15 -0.09 0.186 0.059 -0.09 0.148 -0.07 0.186 -0.09 0.059 -0.05 -0.15 -0.15 -0.12 -0.09 0.084 0.000 -0.09 0.000 0.133 0.084 0.133 0.158 0.000 0.192 -0.11 0.000 0.213 0.119 0.000 0.181 0.059 0.213 0.000 0.119 0.084 -0.11 -0.11 -0.08 0.000 0.133 0.103 0.000 0.103 0.169 -005 0084 0119 -009 0162 -015 -009 0186 0059 -009 0148 -007 0186 -009 0059 -005 -015 -015 -012 -009 0084 0000 -009 0000 0133 -0.13 -0.09 -0.05 -0.15 0.091 -0.19 -0.15 0.130 -0.10 -0.15 0.065 -0.14 0.130 -0.15 -0.10 -0.13 -0.19 -0.19 -0.17 -0.15 -0.09 -0.12 -0.15 -0.12 0.000

[0132] In this embodiment, the dominance matrix under risk factor O is shown in Table 15:

[0133] Table 15 Dominance matrix under risk factor O

[0134] 0.000 -0.12 -0.17 0.051 -0.24 0.106 -0.08 -0.19 -0.12 0.072 -0.14 0.106 -0.20 0.000 -0.20 0.051 0.132 0.132 0.106 0.106 -0.12 0.000 0.072 -0.17 -0.17 0.072 0.000 -0.12 0.088 -0.21 0.128 0.051 -0.14 0.000 0.101 -0.08 0.128 -0.17 0.072 -0.17 0.088 0.150 0.150 0.128 0.128 0.000 0.072 0.101 -0.12 -0.12 0.102 0.072 0.000 0.114 -0.17 0.147 0.088 -0.08 0.072 0.124 0.051 0.147 -0.12 0.102 -0.12 0.114 0.166 0.166 0.147 0.147 0.072 0.102 0.124 0.000 0.000 -0.08 -0.14 -0.19 0.000 -0.26 0.093 -0.12 -0.20 -0.14 0.051 -0.17 0.093 -0.22 -0.08 -0.22 0.000 0.121 0.121 0.093 0.093 -0.14 -0.08 0.051 -0.19 -0.19 0.147 0.128 0.106 0.155 0.000 0.181 0.138 0.093 0.128 0.164 0.118 0.181 0.078 0.147 0.078 0.155 0.197 0.197 0.181 0.181 0.128 0.147 0.164 0.106 0.106 -0.17 -0.21 -0.24 -0.15 -0.30 0.000 -0.19 -0.26 -0.21 -0.13 -0.23 0.000 -0.27 -0.17 -0.27 -0.15 0.078 0.078 0.000 0.000 -0.21 -0.17 -0.13 -0.24 -0.24 0.051 -0.08 -0.14 0.072 -0.23 0.118 0.000 -0.17 -0.08 0.088 -0.12 0.118 -0.19 0.051 -0.19 0.072 0.141 0.141 0.118 0.118 -0.08 0.051 0.088 -0.14 -0.14 0.114 0.088 0.051 0.124 -0.15 0.155 0.102 0.000 0.088 0.134 0.072 0.155 -0.08 0.114 -0.08 0.124 0.174 0.174 0.155 0.155 0.088 0.114 0.134 0.051 0.051 0.072 0.000 -0.12 0.088 -0.21 0.128 0.051 -0.14 0.000 0.101 -0.08 0.128 -0.17 0.072 -0.17 0.088 0.150 0.150 0.128 0.128 0.000 0.072 0.101 -0.12 -0.12 -0.12 -0.17 -0.20 -0.08 -0.27 0.078 -0.14 -0.22 -0.17 0.000 -0.19 0.078 -0.24 -0.12 -0.24 -0.08 0.110 0.110 0.078 0.078 -0.17 -0.12 0.000 -0.20 -0.20 0.088 0.051 -0.08 0.101 -0.19 0.138 0.072 -0.12 0.051 0.114 0.000 0.138 -0.14 0.088 -0.14 0.101 0.158 0.158 0.138 0.138 0.051 0.088 0.114 -0.08 -0.08 -0.17 -0.21 -0.24 -0.15 -0.30 0.000 -0.19 -0.26 -0.21 -0.13 -0.23 0.000 -0.27 -0.17 -0.27 -0.15 0.078 0.078 0.000 0.000 -0.21 -0.17 -0.13 -0.24 -0.24 0.124 0.101 0.072 0.134 -0.13 0.164 0.114 0.051 0.101 0.144 0.088 0.164 0.000 0.124 0.000 0.134 0.181 0.181 0.164 0.164 0.101 0.124 0.144 0.072 0.072 0.000 -0.12 -0.17 0.051 -0.24 0.106 -0.08 -0.19 -0.12 0.072 -0.14 0.106 -0.20 0.000 -0.20 0.051 0.132 0.132 0.106 0.106 -0.12 0.000 0.072 -0.17 -0.17 0.124 0.101 0.072 0.134 -0.13 0.164 0.114 0.051 0.101 0.144 0.088 0.164 0.000 0.124 0.000 0.134 0.181 0.181 0.164 0.164 0.101 0.124 0.144 0.072 0.072 -0.08 -0.14 -0.19 0.000 -0.26 0.093 -0.12 -0.20 -0.14 0.051 -0.17 0.093 -0.22 -0.08 -0.22 0.000 0.121 0.121 0.093 0.093 -0.14 -0.08 0.051 -0.19 -0.19 -0.22 -0.25 -0.27 -0.20 -0.33 -0.13 -0.23 -0.29 -0.25 -0.18 -0.26 -0.13 -0.30 -0.22 -0.30 -0.20 0.000 0.000 -0.13 -0.13 -0.25 -0.22 -0.18 -0.27 -0.27 -0.22 -0.25 -0.27 -0.20 -0.33 -0.13 -0.23 -0.29 -0.25 -0.18 -0.26 -0.13 -0.30 -0.22 -0.30 -0.20 0.000 0.000 -0.13 -0.13 -0.25 -0.22 -0.18 -0.27 -0.27 -0.17 -0.21 -0.24 -0.15 -0.30 0.000 -0.19 -0.26 -0.21 -0.13 -0.23 0.000 -0.27 -0.17 -0.27 -0.15 0.078 0.078 0.000 0.000 -0.21 -0.17 -0.13 -0.24 -0.24 -0.17 -0.21 -0.24 -0.15 -0.30 0.000 -0.19 -0.26 -0.21 -0.13 -0.23 0.000 -0.27 -0.17 -0.27 -0.15 0.078 0.078 0.000 0.000 -0.21 -0.17 -0.13 -0.24 -0.24 0.072 0.000 -0.12 0.088 -0.21 0.128 0.051 -0.14 0.000 0.101 -0.08 0.128 -0.17 0.072 -0.17 0.088 0.150 0.150 0.128 0.128 0.000 0.072 0.101 -0.12 -0.12 0.000 -0.12 -0.17 0.051 -0.24 0.106 -0.08 -0.19 -0.12 0.072 -0.14 0.106 -0.20 0.000 -0.20 0.051 0.132 0.132 0.106 0.106 -0.12 0.000 0.072 -0.17 -0.17 -0.12 -0.17 -0.20 -0.08 -0.27 0.078 -0.14 -0.22 -0.17 0.000 -0.19 0.078 -0.24 -0.12 -0.24 -0.08 0.110 0.110 0.078 0.078 -0.17 -0.12 0.000 -0.20 -0.20 0.102 0.072 0.000 0.114 -0.17 0.147 0.088 -0.08 0.072 0.124 0.051 0.147 -0.12 0.102 -0.12 0.114 0.166 0.166 0.147 0.147 0.072 0.102 0.124 0.000 0.000 0.102 0.072 0.000 0.114 -0.17 0.147 0.088 -0.08 0.072 0.124 0.051 0.147 -0.12 0.102 -0.12 0.114 0.166 0.166 0.147 0.147 0.072 0.102 0.124 0.000 0.000

[0135] In this embodiment, the dominance matrix under risk factor D is shown in Table 16:

[0136] Table 16 Dominance matrix under risk factor D

[0137] 0.000 -0.14 -0.14 0.000 0.146 0.146 0.082 0.171 0.000 0.146 0.000 0.100 -0.21 0.171 0.100 0.000 0.171 0.171 0.146 0.116 0.100 0.116 0.158 0.000 0.000 0.082 0.000 0.000 0.082 0.167 0.167 0.116 0.189 0.082 0.167 0.082 0.129 -0.14 0.189 0.129 0.082 0.189 0.189 0.167 0.142 0.129 0.142 0.178 0.082 0.082 0.082 0.000 0.000 0.082 0.167 0.167 0.116 0.189 0.082 0.167 0.082 0.129 -0.14 0.189 0.129 0.082 0.189 0.189 0.167 0.142 0.129 0.142 0.178 0.082 0.082 0.000 -0.14 -0.14 0.000 0.146 0.146 0.082 0.171 0.000 0.146 0.000 0.100 -0.21 0.171 0.100 0.000 0.171 0.171 0.146 0.116 0.100 0.116 0.158 0.000 0.000 -0.26 -0.30 -0.30 -0.26 0.000 0.000 -0.27 0.089 -0.26 0.000 -0.26 -0.19 -0.33 0.089 -0.19 -0.26 0.089 0.089 0.000 -0.16 -0.19 -0.16 0.061 -0.26 -0.26 -0.26 -0.30 -0.30 -0.26 0.000 0.000 -0.43 0.089 -0.26 0.000 -0.26 -0.19 -0.33 0.089 -0.19 -0.26 0.089 0.089 0.000 -0.16 -0.19 -0.16 0.061 -0.26 -0.26 -0.14 -0.21 -0.21 -0.14 0.121 0.121 0.000 0.150 -0.14 0.121 -0.14 0.058 -0.25 0.150 0.058 -0.14 0.150 0.150 0.121 0.082 0.058 0.082 0.135 -0.14 -0.14 -0.31 -0.34 -0.34 -0.31 -0.16 -0.16 -0.36 0.000 -0.31 -0.16 -0.31 -0.25 -0.37 0.000 -0.25 -0.31 0.000 0.000 -0.16 -0.22 -0.25 -0.22 -0.11 -0.31 -0.31 0.000 -0.14 -0.14 0.000 0.146 0.146 0.082 0.171 0.000 0.146 0.000 0.100 -0.21 0.171 0.100 0.000 0.171 0.171 0.146 0.116 0.100 0.116 0.158 0.000 0.000 -0.26 -0.30 -0.30 -0.26 0.000 0.000 -0.41 0.089 -0.26 0.000 -0.26 -0.19 -0.33 0.089 -0.19 -0.26 0.089 0.089 0.000 -0.16 -0.19 -0.16 0.061 -0.26 -0.26 0.000 -0.14 -0.14 0.000 0.146 0.146 0.082 0.171 0.000 0.146 0.000 0.100 -0.21 0.171 0.100 0.000 0.171 0.171 0.146 0.116 0.100 0.116 0.158 0.000 0.000 -0.18 -0.23 -0.23 -0.18 0.106 0.106 -0.43 0.138 -0.18 0.106 -0.18 0.000 -0.27 0.138 0.000 -0.18 0.138 0.138 0.106 0.058 0.000 0.058 0.122 -0.18 -0.18 0.116 0.082 0.082 0.116 0.186 0.186 0.142 0.206 0.116 0.186 0.116 0.153 0.000 0.206 0.153 0.116 0.206 0.206 0.186 0.164 0.153 0.164 0.196 0.116 0.116 -0.31 -0.34 -0.34 -0.31 -0.16 -0.16 -0.40 0.000 -0.31 -0.16 -0.31 -0.25 -0.37 0.000 -0.25 -0.31 0.000 0.000 -0.16 -0.22 -0.25 -0.22 -0.11 -0.31 -0.31 -0.18 -0.23 -0.23 -0.18 0.106 0.106 -0.35 0.138 -0.18 0.106 -0.18 0.000 -0.27 0.138 0.000 -0.18 0.138 0.138 0.106 0.058 0.000 0.058 0.122 -0.18 -0.18 0.000 -0.14 -0.14 0.000 0.146 0.146 0.082 0.171 0.000 0.146 0.000 0.100 -0.21 0.171 0.100 0.000 0.171 0.171 0.146 0.116 0.100 0.116 0.158 0.000 0.000 -0.31 -0.34 -0.34 -0.31 -0.16 -0.16 -0.44 0.000 -0.31 -0.16 -0.31 -0.25 -0.37 0.000 -0.25 -0.31 0.000 0.000 -0.16 -0.22 -0.25 -0.22 -0.11 -0.31 -0.31 -0.31 -0.34 -0.34 -0.31 -0.16 -0.16 -0.44 0.000 -0.31 -0.16 -0.31 -0.25 -0.37 0.000 -0.25 -0.31 0.000 0.000 -0.16 -0.22 -0.25 -0.22 -0.11 -0.31 -0.31 -0.26 -0.30 -0.30 -0.26 0.000 0.000 -0.43 0.089 -0.26 0.000 -0.26 -0.19 -0.33 0.089 -0.19 -0.26 0.089 0.089 0.000 -0.16 -0.19 -0.16 0.061 -0.26 -0.26 -0.21 -0.25 -0.25 -0.21 0.089 0.089 -0.43 0.125 -0.21 0.089 -0.21 -0.10 -0.29 0.125 -0.10 -0.21 0.125 0.125 0.089 0.000 -0.10 0.000 0.108 -0.21 -0.21 -0.18 -0.23 -0.23 -0.18 0.106 0.106 -0.39 0.138 -0.18 0.106 -0.18 0.000 -0.27 0.138 0.000 -0.18 0.138 0.138 0.106 0.058 0.000 0.058 0.122 -0.18 -0.18 -0.21 -0.25 -0.25 -0.21 0.089 0.089 -0.40 0.125 -0.21 0.089 -0.21 -0.10 -0.29 0.125 -0.10 -0.21 0.125 0.125 0.089 0.001 -0.10 0.001 0.108 -0.21 -0.21 -0.28 -0.32 -0.32 -0.28 -0.11 -0.11 -0.41 0.063 -0.28 -0.11 -0.28 -0.22 -0.35 0.063 -0.22 -0.28 0.063 0.063 -0.11 -0.19 -0.22 -0.19 0.000 -0.28 -0.28 0.000 -0.14 -0.14 0.000 0.146 0.146 0.082 0.171 0.000 0.146 0.000 0.100 -0.21 0.171 0.100 0.000 0.171 0.171 0.146 0.116 0.100 0.116 0.158 0.000 0.000 0.000 -0.14 -0.14 0.000 0.146 0.146 0.082 0.171 0.000 0.146 0.000 0.100 -0.21 0.171 0.100 0.000 0.171 0.171 0.146 0.116 0.100 0.116 0.158 0.000 0.000

[0138] Step S34, based on the dominance matrix V under risk factors S, O, and D. j Calculate the overall dominance v(F) between each pair of failure modes. p F l ), v(F p F l ) indicates failure mode F p Compared to F l The degree of advantage, n represents the total number of failure modes, and the overall dominance matrix V = [v pl ] n×n As shown in Table 17:

[0139] Table 17 Comprehensive Advantage Matrix

[0140] 0.000 -0.16 -0.18 -0.02 0.072 0.111 -0.08 0.176 -0.03 0.141 0.012 0.152 -0.22 0.094 -0.02 0.051 0.162 0.162 0.139 0.145 0.083 0.175 0.153 -0.11 -0.02 0.060 0.000 -0.03 0.048 0.091 0.126 0.045 0.208 0.027 0.148 0.119 0.149 -0.15 0.140 -0.09 0.076 0.171 0.171 0.148 0.149 0.129 0.137 0.159 -0.11 0.065 0.062 -0.00 0.000 -0.20 0.099 0.129 0.060 0.247 0.060 0.148 0.221 0.144 -0.12 0.148 -0.08 0.074 0.170 0.170 0.148 0.145 0.125 0.135 0.159 -0.02 0.141 -0.00 -0.16 -0.18 0.000 0.077 0.121 -0.03 0.175 -0.02 0.197 0.010 0.253 -0.22 0.085 -0.00 0.084 0.175 0.175 0.156 0.209 0.086 0.134 0.209 -0.08 -0.02 -0.27 -0.30 -0.29 -0.28 0.000 -0.02 -0.30 0.274 -0.27 -0.01 -0.20 -0.17 -0.16 0.061 -0.25 -0.26 0.076 0.076 -0.01 -0.15 -0.19 -0.16 0.050 -0.30 -0.24 -0.28 -0.33 -0.34 -0.29 -0.07 0.000 -0.49 0.077 -0.30 -0.00 -0.27 -0.04 -0.36 0.040 -0.29 -0.26 0.167 0.167 0.084 -0.03 -0.22 -0.17 0.060 -0.34 -0.29 -0.01 -0.16 -0.20 -0.07 0.082 0.121 0.000 0.193 -0.11 0.209 -0.08 0.235 -0.23 0.201 -0.01 0.007 0.173 0.173 0.155 0.200 0.106 0.236 0.224 -0.19 -0.12 -0.37 -0.40 -0.42 -0.37 -0.40 -0.23 -0.45 0.000 -0.38 -0.22 -0.34 -0.28 -0.46 -0.07 -0.49 -0.36 -0.05 -0.05 -0.21 -0.26 -0.31 -0.28 -0.17 -0.42 -0.37 -0.00 -0.08 -0.16 -0.02 0.082 0.114 0.024 0.200 0.000 0.139 0.050 0.134 -0.20 0.134 -0.07 0.011 0.161 0.161 0.137 0.135 0.160 0.133 0.151 -0.17 -0.00 -0.30 -0.34 -0.35 -0.35 -0.08 -0.03 -0.56 0.076 -0.31 0.000 -0.27 -0.05 -0.36 -0.03 -0.31 -0.26 0.081 0.081 -0.00 -0.08 -0.22 -0.17 0.061 -0.37 -0.30 -0.05 -0.20 -0.31 -0.06 0.013 0.082 -0.01 0.163 -0.07 0.095 0.000 0.083 -0.24 0.094 -0.17 -0.04 0.127 0.127 0.100 0.089 0.040 0.069 0.108 -0.22 -0.14 -0.30 -0.33 -0.33 -0.39 -0.01 -0.02 -0.68 0.082 -0.29 -0.07 -0.24 0.000 -0.34 -0.09 -0.17 -0.27 0.087 0.087 0.006 0.003 -0.09 -0.03 -0.06 -0.34 -0.27 0.063 0.033 0.024 0.057 -0.02 0.124 0.062 0.257 0.057 0.137 0.101 0.131 0.000 0.138 -0.00 0.073 0.161 0.161 0.139 0.134 0.104 0.119 0.147 0.018 0.070 -0.22 -0.33 -0.35 -0.26 -0.21 -0.17 -0.49 0.022 -0.31 -0.08 -0.27 -0.08 -0.37 0.000 -0.34 -0.17 0.014 0.014 -0.13 -0.12 -0.23 -0.12 -0.04 -0.37 -0.31 -0.13 -0.07 -0.05 -0.15 0.126 0.110 -0.34 0.366 -0.08 0.141 0.042 0.069 -0.10 0.154 0.000 -0.12 0.160 0.160 0.133 0.113 0.161 0.128 0.158 -0.16 0.009 -0.08 -0.19 -0.20 -0.07 0.058 0.098 -0.11 0.158 -0.06 0.120 -0.01 0.139 -0.24 0.009 -0.04 0.000 0.152 0.152 0.126 0.132 0.056 0.090 0.132 -0.13 -0.04 -0.37 -0.41 -0.41 -0.38 -0.26 -0.29 -0.55 -0.04 -0.38 -0.21 -0.35 -0.23 -0.43 -0.09 -0.37 -0.35 0.000 0.000 -0.20 -0.22 -0.31 -0.28 -0.17 -0.42 -0.37 -0.37 -0.41 -0.41 -0.38 -0.26 -0.29 -0.55 -0.04 -0.38 -0.21 -0.35 -0.23 -0.43 -0.09 -0.37 -0.35 0.000 0.000 -0.20 -0.22 -0.31 -0.28 -0.17 -0.42 -0.37 -0.31 -0.35 -0.36 -0.33 -0.09 -0.08 -0.53 0.060 -0.32 -0.03 -0.29 -0.08 -0.38 0.002 -0.31 -0.29 0.083 0.083 -0.00 -0.06 -0.24 -0.20 0.022 -0.37 -0.31 -0.30 -0.33 -0.34 -0.36 -0.02 -0.02 -0.62 0.078 -0.30 -0.04 -0.26 -0.04 -0.35 -0.05 -0.26 -0.28 0.086 0.086 0.005 0.000 -0.18 -0.07 -0.02 -0.35 -0.28 -0.20 -0.23 -0.27 -0.21 0.029 0.065 -0.46 0.157 -0.23 0.086 -0.14 0.019 -0.28 0.089 -0.22 -0.18 0.119 0.119 0.087 0.065 0.000 0.053 0.103 -0.38 -0.19 -0.26 -0.29 -0.30 -0.25 0.004 0.044 -0.58 0.121 -0.27 0.067 -0.20 -0.07 -0.32 0.031 -0.25 -0.21 0.107 0.107 0.069 0.013 -0.14 0.001 0.086 -0.38 -0.24 -0.32 -0.36 -0.37 -0.37 -0.19 -0.15 -0.56 0.050 -0.34 -0.11 -0.29 -0.08 -0.38 -0.05 -0.34 -0.28 0.055 0.055 -0.11 -0.11 -0.26 -0.21 0.000 -0.39 -0.32 0.047 0.007 -0.02 0.019 0.130 0.142 0.076 0.272 0.132 0.177 0.199 0.171 -0.14 0.179 0.039 0.059 0.187 0.187 0.167 0.169 0.257 0.218 0.189 0.000 0.133 -0.03 -0.17 -0.20 -0.03 0.060 0.099 0.016 0.215 -0.03 0.117 0.116 0.104 -0.20 0.119 -0.12 -0.01 0.144 0.144 0.118 0.109 0.078 0.096 0.129 -0.12 0.000

[0141] Step S35: Calculate the overall ranking value R based on the overall dominance matrix V. P And according to R P Sort the values ​​in descending order.

[0142] First, normalize matrix V to obtain normalized matrix U = [u pl ], Secondly, calculate the failure mode F. p Among n failure modes, relative to failure mode F l The proportion of dominance Next, calculate the dominance entropy value of the l-th failure mode out of n failure modes. Then, the dominance weight of the l-th failure mode is calculated. The results are shown in Table 18; finally, the comprehensive ranking value was calculated. n represents the total number of failure modes, and according to R pSort in descending order, R p The larger the value, the greater the risk of the corresponding failure mode. The results are shown in Table 18.

[0143] Table 18. Dominance Entropy Values, Failure Mode Dominance Weights, Overall Dominance of Failure Modes, and Ranking

[0144] FM <![CDATA[E k ]]> <![CDATA[W k ]]> Overall dominance Sort FM1 0.9007 0.0650 1.2493 7 FM2 0.8995 0.0658 1.4065 4 FM3 0.8996 0.0657 1.4247 3 FM4 0.8875 0.0737 1.4874 2 FM5 0.9714 0.0187 0.1875 21 FM6 0.9536 0.0304 0.2894 16 FM7 0.9176 0.0539 1.0615 9 FM8 0.9406 0.0389 0.0257 25 FM9 0.8952 0.0686 1.3496 5 FM10 0.9432 0.0372 0.2847 17 FM11 0.8979 0.0669 1.0866 8 FM12 0.9510 0.0321 0.2671 18 FM13 0.9351 0.0425 0.9369 11 FM14 0.9186 0.0533 0.3327 15 FM15 0.9586 0.0271 0.5186 14 FM16 0.9092 0.0595 1.0419 10 FM17 0.9673 0.0214 0.0305 23 FM18 0.9673 0.0214 0.0305 23 FM19 0.9476 0.0343 0.2454 20 FM20 0.9507 0.0323 0.2599 19 FM21 0.9084 0.0600 0.7825 12 FM22 0.9227 0.0506 0.5429 13 FM23 0.9480 0.0340 0.1802 22 FM24 0.8877 0.0735 1.7282 1 FM25 0.8957 0.0683 1.2677 6

[0145] As shown in Table 18, the three modes with the highest impact weight are FM4, FM9, and FM24, corresponding to the failure modes of incorrect auxiliary operation parameter determination, incorrect maintenance strategy selection, and incorrect user requirement analysis, which are more likely to affect the normal operation of other functions. The three modes with the lowest impact weight are FM5, FM17, and FM18, corresponding to the failure modes of missing integrity data, incorrect hazard warning, and remote control failure, which only affect the functions of the modules they belong to and are easy to find.

[0146] As shown in Table 18, the three modes with the highest overall dominance are FM3, FM4, and FM24, while the three modes with the lowest dominance are FM8, FM17, and FM18. This is similar to the results of the highest and lowest influence weights, indicating that the overall influence of failure modes with high mutual influence is usually also at a high level.

[0147] Step S4, based on the comprehensive weight w j And the comprehensive ranking value R p We use the binary K-means clustering method to perform cluster analysis on potential failure modes and provide corresponding prevention and response measures for each potential failure mode.

[0148] Specifically, step S4 includes:

[0149] Step S41: Utilize the comprehensive weights obtained in step S231 The scoring results of the potential failure modes are weighted, and the S, O, and D values ​​of each potential failure mode are multiplied together to obtain the W-RPN, which is used as the first feature value.

[0150] Step S42, the comprehensive ranking value R obtained in step S35 is... p As the second eigenvalue.

[0151] Step S43: Normalize the first eigenvalue and the second eigenvalue.

[0152] Step S44: Obtain the description matrix P' = (p') based on the normalized first and second eigenvalues. pf ) n×2 Let p' represent n two-dimensional data points. p1 p' is the first eigenvalue after normalization. p2This is the second eigenvalue after normalization.

[0153] Step S45: Cluster the n two-dimensional data points into K classes using the binary K-means clustering method to obtain the clustering results.

[0154] Step S46: Based on the clustering results, analyze the potential failure modes, and based on the operation mode of the system to be analyzed, the magnitude of the first eigenvalue, and the magnitude of the second eigenvalue, provide corresponding prevention and response measures for each potential failure mode.

[0155] Clustering algorithms can intuitively and efficiently classify and segment failure modes at different risk levels, grouping similar-risk failure modes together for priority-based improvement. Compared to the widely used K-means algorithm, the binary K-means clustering employed in this invention has a faster convergence speed and overcomes the algorithm's tendency to get trapped in local optima. Regarding failure levels, since clustering failure levels cannot reflect the differences between individual failure modes and other failure modes, this invention categorizes causes into four levels: extreme risk, high risk, medium risk, and low risk. The clustering results are as follows: Figure 2 As shown in the figure, the failure causes in the "extreme risk", "high risk", "medium risk" and "low risk" areas all include four reasons: network problems, hardware failure, human error and software error.

[0156] The "Extreme Risk" zone includes seven failure modes: FM24, FM2, FM3, FM9, FM4, FM1, and FM25, involving the user service module, pipeline design module, and pipeline integrity management module. These failure modes have high W-RPN and overall ranking values, significantly impacting the system. Therefore, substantial resources and effort should be invested in addressing these failure modes and their corresponding modules. Among the causes of these failures, human error is the primary reason, followed by hardware failure and modeling errors. In the future, it is essential to strengthen the training and supervision of operators, and to regularly test and optimize hardware to improve operational efficiency. Furthermore, the modeling process and data should be regularly reviewed to ensure the consistency and accuracy of the digital twin.

[0157] The "high-risk" areas include FM7, FM21, FM15, FM11, FM16, and FM13. The combined ranking value and W-RPN for these six failure modes are all medium to high, indicating they are significant but not as severe as "extreme risk." Therefore, excessive resources should not be allocated, but sufficient attention should still be given. The failure modes are located in the pipeline integrity management module, gas inspection module, and transmission and distribution dispatch management module. All five causes of failure are involved, but human error is the primary cause. Therefore, strengthening workforce training is the top priority in addressing these failure modes.

[0158] The "medium-risk" zone includes FM5, FM6, FM10, FM12, FM14, FM19, FM20, FM22, and FM23. These failure modes have W-RPN and composite ranking values ​​in the lower middle range. Therefore, some resources and attention should be provided to failure modes in this area to the best of our ability. However, FM22, supply forecasting error, stands out in the "medium-risk" zone, with its composite ranking value and W-RPN significantly higher than other modes within the medium-risk range. Correspondingly, demand forecasting error FM21 belongs to the high-risk range, but is at a lower level compared to other high-risk modes. There is a causal relationship between FM21 and FM22; the occurrence of FM21 will also lead to the occurrence of FM22. Therefore, the significance of FM21 is significantly higher than that of FM22, and it should be classified into a higher-risk category for treatment.

[0159] The "low-risk" zones include FM8, FM18, and FM17, all of which have low W-RPN and low overall ranking values. Therefore, this category requires minimal resources and attention. Maintenance is only needed when these failure modes occur, rather than requiring regular resource allocation.

[0160] In this embodiment, the parts not described in detail are well-known technologies in the art.

[0161] <Example 2>

[0162] This embodiment provides an analysis and evaluation system that uses the improved FMEA method described above, which considers the interrelationships of failure modes and subjective factors. The system includes:

[0163] The scoring acquisition unit acquires the scoring results of the potential failure modes of the system to be analyzed, and obtains the evaluation results of the risk factors for each potential failure mode; wherein, the evaluation result of the risk factor for the p-th potential failure mode is represented as (S p O p D p p = 1, 2, ..., n, where n is the number of potential failure modes of the system to be analyzed, S represents severity, O represents occurrence, and D represents detectability.

[0164] The comprehensive weight calculation unit determines the subjective weights of risk factors S, O, and D based on the triangular fuzzy analytic hierarchy process (AHP), determines the objective weights of the risk factors S, O, and D based on the standard deviation method and trapezoidal fuzzy numbers, and obtains the comprehensive weight w of risk factors S, O, and D using a comprehensive weighting method based on the subjective and objective weights. j .

[0165] The ranking unit determines the comprehensive ranking value R corresponding to each potential failure mode according to the TODIM method improved based on the entropy weight method. pAnd according to the comprehensive sorting value R p The potential failure modes are sorted.

[0166] The analysis results generation unit averages and synthesizes the scores of the potential failure modes, based on the comprehensive weight w. j The W-RPN value, obtained by weighting the result and multiplying the S, O, and D values, is combined with the overall ranking value R. p The potential failure modes are clustered using the binary K-means clustering method, and corresponding prevention and response measures are generated for each potential failure mode.

[0167] The storage unit stores the corresponding rules between different categories of potential failure modes and their prevention and response measures, wherein the different categories are divided according to the classification results of the cluster analysis.

[0168] It should be understood that the various parts of the analysis and evaluation system described in Embodiment 2 correspond to the various steps of the improved FMEA method described in Embodiment 1. Therefore, the operations, features, and advantages described above for each step of the improved FMEA method are also applicable to the various parts of the analysis and evaluation system. For the sake of brevity, some operations, features, and advantages will not be repeated here.

[0169] The role and effect of the embodiments

[0170] The improved FMEA method and analysis and evaluation system provided in the above embodiments, which considers the interrelationships of failure modes and subjective factors, improves the traditional FMEA method based on triangular fuzzy hierarchical analysis, trapezoidal fuzzy numbers, standard deviation method, comprehensive weighting method, TODIM method improved based on entropy weight, and bisection K-means clustering analysis. This method first uses a seven-granularity evaluation method to score failure modes; secondly, it uses triangular fuzzy hierarchical analysis to determine subjective weights, and uses standard deviation method and trapezoidal fuzzy numbers to determine objective weights. The subjective and objective weights are combined to calculate the comprehensive weight of risk factors, thus solving the problems of strong subjectivity and failure to consider the relative importance among risk factors in traditional FMEA methods. Thirdly, it improves TODIM and ranks failure modes accordingly, overcoming the deficiency of the classic TODIM method in not considering the interrelationships between failure modes. Finally, based on W-RPN values ​​and comprehensive ranking values, it uses bisection K-means clustering to perform cluster analysis on failure modes. This embodiment uses this method and system to conduct reliability and risk assessment analysis on a smart gas digital twin system, and the results verify the effectiveness and applicability of the method.

[0171] The above embodiments are preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention.

Claims

1. An improved FMEA method for analyzing intelligent gas digital twin systems, considering the interrelationships of failure modes and subjective factors, characterized in that: include: Step S1: Obtain the scoring results of the potential failure modes of the system to be analyzed, and obtain the evaluation results of the risk factors for each potential failure mode; wherein, the evaluation result of the risk factor for the p-th potential failure mode is expressed as (S p O p D p p = 1, 2, ..., n, where n is the number of potential failure modes of the system to be analyzed, S represents severity, O represents occurrence, and D represents detectability. Step S2: Determine the subjective weights of risk factors S, O, and D based on the triangular fuzzy analytic hierarchy process (AHP), determine the objective weights of risk factors S, O, and D based on the standard deviation method and trapezoidal fuzzy numbers, and obtain the comprehensive weight w of risk factors S, O, and D using a comprehensive weighting method based on the subjective and objective weights. j ; Step S3: Determine the comprehensive ranking value R corresponding to each potential failure mode according to the TODIM method improved by the entropy weight method. p And according to the comprehensive sorting value R p The potential failure modes are sorted. Step S3 includes: Step S31, based on the combined weight w of risk factors S, O, and D j Calculate the relative weights ω′ of the risk factors j ; Step S32: Normalize the evaluation index matrix P to obtain the normalized matrix G; Step S33, based on the relative weights ω′ of the risk factors j And the normative matrix G, respectively calculate the dominance matrix V under risk factors S, O, and D. j ; Step S34, based on the dominance matrix V under risk factors S, O, and D. j Calculate the overall dominance between each pair of failure modes to obtain the overall dominance matrix V; Step S35: Calculate the comprehensive ranking value R based on the comprehensive dominance matrix V. p And according to the comprehensive sorting value R p Sort the values ​​in descending order; Step S4: Average and synthesize the scoring results of the potential failure modes, and then calculate the weights based on the comprehensive weights w. j The W-RPN value, obtained by weighting the result and multiplying the S, O, and D values, is combined with the overall ranking value R. p The potential failure modes are clustered using the binary K-means clustering method, and corresponding prevention and response measures are formulated for each potential failure mode. Step S4 includes: Step S41, using the comprehensive weights The scoring results of the potential failure modes are weighted, and the S, O, and D values ​​of each potential failure mode are multiplied together to obtain W-RPN, which is used as the first feature value. Step S42, the comprehensive ranking value R obtained in step S35 is... p As the second eigenvalue; Step S43: Normalize the first feature value and the second feature value; Step S44: Obtain the description matrix P' = (p') based on the normalized first and second eigenvalues. pf ) n×2 Let p' represent n two-dimensional data points. p1 p′ is the first eigenvalue after normalization. p2 The second eigenvalue after normalization; Step S45: Cluster the n two-dimensional data points into K classes using the binary K-means clustering method to obtain the clustering results; Step S46: Based on the clustering results, analyze the potential failure modes, and based on the operation mode of the system to be analyzed, the magnitude of the first feature value, and the magnitude of the second feature value, provide corresponding prevention and response measures for each potential failure mode.

2. The improved FMEA method for analyzing intelligent gas digital twin systems, considering failure mode interrelationships and subjective factors, as described in claim 1. Its features are: in, In step S1, the scoring results of the potential failure modes of the system to be analyzed are obtained through the following process: Step Sa1: Obtain the system to be analyzed, form an FMEA team based on the type and application field of the system to be analyzed, and obtain the operation mode of the system to be analyzed; Step Sa2: The FMEA team determines n potential failure modes FM1, FM2, ..., FM3 based on the operating mode of the system to be analyzed. n ; Step Sa3: Using a seven-granularity scoring model, establish scoring standards for S, O, and D risk factors; Step Sa4: Based on the established scoring criteria, the FMEA team obtains the evaluation results of the importance of each potential failure mode under the S, O, and D risk factors.

3. The improved FMEA method for analyzing intelligent gas digital twin systems, considering failure mode interrelationships and subjective factors, as described in claim 2. Its features are: in, The method for determining the subjective weights of risk factors S, O, and D based on triangular fuzzy analytic hierarchy process in step S2 includes: Step S211: Establish importance scoring criteria for risk factors S, O, and D. The FMEA team then conducts expert scoring of the importance of risk factors S, O, and D based on these scoring criteria. Step S212: Based on the importance scoring criteria of risk factors S, O, and D, establish the corresponding triangular fuzzy language set and triangular fuzzy number; Step S213: Calculate the risk factor consistency index CI based on the expert scores and the triangular fuzzy number; Step S214: Query the random consistency index table, obtain the consistency index RI based on the number of risk factors, and calculate the consistency ratio using the consistency ratio formula. Obtain the consistency ratio CR to perform a consistency test on the expert scores. If the consistency ratio is less than 0.1, it means that the expert scores are valid. Then, the expert scores are combined according to the expert weights and the process proceeds to step S215. Otherwise, the expert scores are re-evaluated and the process returns to step S213. Step S215: Repeat steps S213 to S214 with the synthesized expert scores to check if the consistency ratio is less than 0.

1. If so, the subjective weights of risk factors S, O, and D are obtained. Otherwise, the expert scoring is repeated, and the process returns to step S213.

4. The improved FMEA method for analyzing intelligent gas digital twin systems, considering failure mode interrelationships and subjective factors, as described in claim 2. Its features are: in, The method for determining the objective weights of risk factors S, O, and D based on the standard deviation method and trapezoidal fuzzy numbers in step S2 includes: Step S221: Based on the S, O, D risk factor scoring criteria established in step Sa3, establish a trapezoidal fuzzy evaluation language; Step S222: Based on the trapezoidal fuzzy evaluation language, the scores given by each member of the FMEA team for the potential failure mode according to the S, O, D risk factor scoring standard are converted into expert fuzzy language evaluation results. Step S223: Based on the expert fuzzy language evaluation results, construct an evaluation index matrix P. After standardizing the evaluation index matrix P, calculate the standard deviation and mean of each potential failure mode, and obtain the objective weight based on the standard deviation and mean of each potential failure mode.

5. The improved FMEA method for analyzing intelligent gas digital twin systems, considering failure mode interrelationships and subjective factors, as described in claim 1, is characterized in that: in, In step S2, the comprehensive weighting method is used to obtain the comprehensive weight w of risk factors S, O, and D. j The methods include: Step S231: Introduce an adjustment coefficient θ, θ∈[0,1], and calculate the comprehensive weight.

6. An analysis and evaluation system, using the improved FMEA method according to any one of claims 1-5 for analyzing intelligent gas digital twin systems, considering failure mode interrelationships and subjective factors, characterized in that, include: The scoring acquisition unit acquires the scoring results of the potential failure modes of the system to be analyzed, and obtains the evaluation results of the risk factors for each potential failure mode; wherein, the evaluation result of the risk factor for the p-th potential failure mode is represented as (S p O p D p P = 1, 2, ..., n, where n is the number of potential failure modes of the system to be analyzed, S represents severity, O represents occurrence, and D represents detectability. The comprehensive weight calculation unit determines the subjective weights of risk factors S, O, and D based on the triangular fuzzy analytic hierarchy process (AHP), determines the objective weights of the risk factors S, O, and D based on the standard deviation method and trapezoidal fuzzy numbers, and obtains the comprehensive weight w of risk factors S, O, and D using a comprehensive weighting method based on the subjective and objective weights. j ; The ranking unit determines the comprehensive ranking value R corresponding to each potential failure mode according to the TODIM method improved based on the entropy weight method. i And according to the comprehensive sorting value R i The potential failure modes are sorted. The analysis results generation department averages and synthesizes the expert scores, based on the aforementioned comprehensive weight w. j The W-RPN value, obtained by weighting the result and multiplying the S, O, and D values, is combined with the overall ranking value R. p The potential failure modes are clustered using the binary K-means clustering method, and corresponding prevention and response measures are generated for each potential failure mode.

7. The analysis and evaluation system according to claim 6, characterized in that, Also includes: The storage unit stores the corresponding rules between different categories of potential failure modes and their prevention and response measures, wherein the different categories are divided according to the classification results of the cluster analysis.

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