Underwater control module FMEA analysis method based on spherical fuzzy set

Abstract

The invention relates to the technical field of offshore oil engineering, in particular to an underwater control module FMEA analysis method based on a spherical fuzzy set, and the method comprises the steps: obtaining the risk assessment information of an underwater control module, constructing a decision matrix based on the converted spherical fuzzy set, carrying out the preprocessing of the decision matrix, and obtaining the risk assessment information of the underwater control module. And deriving a three-branch decision threshold according to the loss function, dividing three-branch decision domains of the failure mode by using the three-branch decision threshold and the conditional probability, carrying out risk sorting on the failure mode based on the expected loss function in each three-branch decision domain, and outputting risk grading and priority results of the failure mode of the underwater control module. According to the method, the three decision threshold values are deduced through the loss function, risk sorting is carried out in each decision domain based on the corresponding expected loss function, a risk disposal strategy with a clear level is formed, and the scientificity and pertinence of reliability management of the underwater control module are improved.

Description

Technical Field

[0001] This invention relates to the field of marine oil engineering technology, and in particular to an underwater control module FMEA analysis method based on spherical fuzzy sets. Background Technology

[0002] In the field of offshore oil engineering, the Subsea Control Module (SCM) is the core control unit of the subsea production system. Its operational reliability directly determines the safety and stability of the entire subsea production process. Once the subsea control module fails, it may not only cause the interruption of oil and gas production and huge economic losses, but also cause serious environmental accidents such as crude oil spills. Therefore, it is crucial to conduct scientific and effective failure mode and effects analysis (FMEA) on the subsea control module.

[0003] Currently, the mainstream FMEA analysis method in the industry still relies on the traditional Risk Priority Number (RPN) calculation model. This model determines the risk level of a failure mode by multiplying the severity, occurrence, and detectability of three risk factors. While this method is simple to operate and widely used, it has gradually revealed significant shortcomings when adapting to the complex operating scenarios of underwater control modules, making it difficult to meet the requirements of high-precision reliability management. First, the primary flaw of the traditional FMEA method lies in the unreasonable allocation of risk factor weights. This method implicitly assumes that the weights of severity, occurrence, and detectability are completely equal, failing to consider the differences in risk criteria during the actual operation of underwater control modules. For example, underwater control modules operate in high-pressure deep-sea environments, and the severity of their failures, such as environmental hazards caused by oil spills, contributes significantly to system risk compared to conventional equipment. Traditional equal-weighting methods fail to reflect this difference, leading to significant discrepancies between risk assessment results and actual risk levels. This can result in misjudgments of high-risk failure modes or excessive focus on low-risk failure modes, affecting the accurate allocation of subsequent reliability management resources. Furthermore, traditional FMEA methods lack sufficient index scalability and decision-making hierarchy, making them ill-suited to the complex risk management needs of modern underwater control modules. Therefore, a spherical fuzzy set-based FMEA analysis method for underwater control modules is currently needed. Summary of the Invention

[0004] To address the aforementioned problems, the purpose of this invention is to provide an underwater control module FMEA analysis method based on spherical fuzzy sets, which solves the problems of low accuracy and insufficient adaptability of traditional FMEA analysis methods in underwater control module evaluation. To achieve the above objectives, the present invention adopts the following technical solution: an underwater control module FMEA analysis method based on spherical fuzzy sets, comprising: acquiring risk assessment information of the underwater control module and converting expert language evaluations in the risk assessment information into spherical fuzzy sets; constructing a decision matrix based on the converted spherical fuzzy sets, preprocessing the decision matrix, and calculating the weights of each risk factor using the MEREC method; defining a scoring function using the membership and non-membership degrees of the spherical fuzzy sets, and determining the ideal and non-ideal solutions of the failure modes under each risk factor based on the scoring function, calculating the regret and gratification functions of the failure modes by combining the distance between spherical fuzzy sets, and then calculating the conditional probabilities of the failure modes being in high-risk and low-risk states; constructing a loss function for the failure modes under different decision actions and risk states based on the risk factor weights, and calculating the expected loss function by combining the conditional probability; deriving a three-branch decision threshold based on the loss function, and dividing the failure modes into three decision domains using the three-branch decision thresholds and conditional probabilities; ranking the failure modes by risk based on the expected loss function within each three-branch decision domain, and outputting the risk classification and priority results of the underwater control module failure modes.

[0005] Furthermore, the conversion of expert linguistic evaluations in the risk assessment information into spherical fuzzy sets includes defining a spherical fuzzy set S under the universal set X based on the acquired risk assessment information. The risk assessment information includes risk factors, failure modes, and linguistic evaluations of the underwater control module. A pre-established correspondence table between linguistic evaluation terms and spherical fuzzy numbers is constructed, mapping the linguistic evaluations of each failure mode under each risk factor to spherical fuzzy numbers conforming to the definition of a spherical fuzzy set. The expression for the spherical fuzzy set S is: and , in, Let X be any element in the universal set X. Let x be the membership degree of element x to the spherical fuzzy set S. Let x be the degree of non-membership of the element x with respect to the spherical fuzzy set S. Let x be the degree of hesitation of element x with respect to the spherical fuzzy set S.

[0006] Furthermore, the preprocessing of the decision matrix includes establishing a p×q-dimensional decision matrix based on a spherical fuzzy set to characterize the fuzzy evaluation relationship between failure modes and risk factors. Based on the decision matrix, risk factors are categorized into benefit-type risk factors and cost-type risk factors. The spherical fuzzy numbers corresponding to cost-type risk factors are then reverse-transformed to unify them into benefit-type spherical fuzzy numbers, resulting in the transformed spherical fuzzy number decision matrix. hesitancy after conversion The calculation formula is: , Where i is the failure mode number and j is the risk factor number and , Let i be the membership degree of the i-th failure mode under the j-th risk factor. For the corresponding non-membership degree, For the corresponding degree of hesitation, The transformed membership degree. This represents the non-membership degree after transformation.

[0007] Furthermore, the calculation of the weights of each risk factor using the MEREC method includes using the preprocessed benefit-type spherical fuzzy number decision matrix as the data basis. For the i-th failure mode, the overall performance of its membership benchmark, non-membership benchmark, and hesitation benchmark under all q risk factors are calculated respectively. For the j-th risk factor, it is removed from the set of all risk factors one by one, and the sum of the absolute deviations of the corresponding overall performance after removing each risk factor is calculated. Based on the sum of the absolute deviations, the weights of the membership dimension, non-membership dimension, and hesitation dimension are obtained respectively. Then, a weighted average is performed on each weight to obtain the comprehensive weight of each risk factor.

[0008] Furthermore, the calculation of the regret and gratification functions of failure modes by combining the distance between spherical fuzzy sets includes defining a scoring function using the membership and non-membership degrees of the spherical fuzzy sets. For each risk factor j, the scoring function value of all failure modes under that factor is calculated. The failure mode with the largest scoring function value is the ideal solution for that risk factor, and the failure mode with the smallest scoring function value is the non-ideal solution for that risk factor. The Euclidean distance between the spherical fuzzy number corresponding to the i-th failure mode and the ideal and non-ideal solutions is calculated. An avoidance coefficient is introduced, and the regret and gratification functions of the failure modes are calculated based on the Euclidean distances. The expressions for the regret and gratification functions are as follows: , , in, For the regret function value, To avoid coefficient, Let Euclidean distance be the distance between the failure mode and the ideal solution. For the target failure mode, This is the ideal solution under risk factors. For the pleasing function value, This is a non-ideal solution under risk factors. Let be the Euclidean distance between the failure mode and the non-ideal solution.

[0009] Furthermore, the calculation of the conditional probability of a failure mode being in a high-risk state and a low-risk state includes defining the dominance and subordination relationships between failure modes based on the regret function value and the gratification function value, determining the dominance class and subordination class of the i-th failure mode based on the dominance and subordination relationships, and calculating the conditional probability of the failure mode being in a high-risk state and the conditional probability of it being in a low-risk state based on the number of elements in the dominance class and the number of elements in the subordination class. The expression for the conditional probability of the high-risk state is as follows: , in, For the j-th failure mode, Let j be the dominant class of the failure mode. Let be the number of elements in the class that dominates the j-th failure mode. For the j-th failure mode, Let be the number of elements in the class dominated by the j-th failure mode. For the j-th failure mode, This is a high-risk situation. As a relationship of domination, It is a subordinate relationship.

[0010] Furthermore, the calculation of the expected loss function using conditional probability includes determining the decision action and the risk state type, wherein the decision action includes priority actions for high-risk failure modes. Delayed decision-making actions for critical risk failure modes and risk acceptance actions for low-risk failure modes Using the comprehensive weight of each risk factor as the core parameter, a differentiated loss function is constructed for different combinations of decision actions and risk states. The expected loss function is then calculated using conditional probability. The loss functions for each scenario are weighted and summed according to their corresponding probabilities to obtain the expected loss function for each decision action. The expression for the expected loss function of the priority action is as follows: , in, Prioritize actions targeting high-risk failure modes. To take the i-th failure mode Expected losses To take measures in high-risk situations The proper handling of losses during the operation To take measures under low-risk conditions Over-handling of the action resulted in losses. and Let represent the conditional probabilities of the i-th failure mode being in a high-risk or low-risk state, respectively.

[0011] Furthermore, the construction of the differentiated loss function includes: defining the correct decision loss, which occurs when the failure mode is in a high-risk state C and priority actions are taken. At that time, properly handle the loss When the failure mode is in a low-risk state And take risk-acceptance actions When to accept losses correctly Define the loss from a wrong decision when the failure mode is in a high-risk state (C) but a risk-accepting action is taken. At that time, the loss was incorrectly missed. When the failure mode is in a low-risk state However, priority action was taken. At times, excessive handling of losses Define the loss from delayed decision-making and the action of delayed decision-making. The loss is the median of the loss from a correct decision and the loss from a wrong decision; where, The overall weight of the j-th risk factor is... Let be the Euclidean distance between the ideal solution of the i-th failure mode and the j-th risk factor. Let be the benefit-type spherical fuzzy number of the i-th failure mode under the j-th risk factor. For the j-th risk factor, For the j-th risk factor, the non-ideal solution is... To properly handle losses in high-risk situations, This refers to the proper acceptance of losses under low-risk conditions.

[0012] Furthermore, the three-branch decision domain, which utilizes three decision thresholds and conditional probabilities to divide failure modes, includes calculating high-risk determination thresholds based on differentiated loss functions. Low-to-medium risk threshold and low-risk determination threshold A complete three-branch decision threshold system was obtained, and with As the classification criterion, the conditional probability of the i-th failure mode being in a high-risk state is considered. Establish a comparison rule between the threshold and the conditional probability. Specifically, the comparison rule is as follows: when... and When this happens, the failure mode is classified into the positive domain. and When, it falls into the negative domain. and Then it belongs to the boundary domain.

[0013] Furthermore, the risk ranking of failure modes based on the expected loss function includes using the expected loss function as the core ranking indicator, whereby the expected loss includes the expected loss of taking priority actions for each failure mode. Expected losses from delaying decision-making and the expected losses from taking risk-accepting actions. Then, based on the three different decision domains, the corresponding target expected loss function is matched and sorted according to the ascending order of the corresponding target expected loss function values.

[0014] The present invention has the following advantages due to the adoption of the above technical solutions: 1. This invention transforms the linguistic evaluations of experts in underwater control module FMEA analysis into spherical fuzzy sets, and uses three parameters—membership, non-membership, and hesitation—to fully characterize the fuzziness and uncertainty in the evaluation information. This breaks through the limitations of traditional FMEA relying on precise numerical evaluations, avoids the distortion of risk assessment caused by the fuzziness of expert subjective judgments, and achieves accurate quantification of fuzzy evaluation information, providing a data foundation that is more in line with actual evaluation scenarios for subsequent risk analysis.

[0015] 2. Based on the preprocessed benefit-oriented spherical fuzzy number decision matrix, this invention uses the MEREC method to determine the weights by calculating the overall performance deviation before and after the removal of risk factors. It does not require subjective weighting and can objectively reflect the actual contribution of different risk factors (such as failure probability, loss cost, detection difficulty, etc.) to the failure risk of underwater control modules. It solves the problem of equalizing the weights of risk factors in traditional FMEA and makes the risk assessment more in line with the complex risk composition characteristics of underwater control modules.

[0016] 3. This invention utilizes the scoring function of a spherical fuzzy set to determine the ideal and non-ideal solutions of failure modes under various risk factors. It combines Euclidean distance to calculate the regret and gratification functions, and then quantifies the relative risk relationship of failure modes through the dominant and dominated classes. Finally, it obtains the conditional probabilities of high and low risk states, transforming the risk level of failure modes from a qualitative description to a quantitative probability, providing an objective basis for risk classification, and avoiding the subjectivity and fuzziness of traditional FMEA risk ranking.

[0017] 4. This invention constructs a differentiated loss function based on risk factor weights, covering correct decisions, incorrect decisions, and delayed decisions. It also calculates expected losses by combining the conditional probability of risk states. This comprehensively considers the costs of decision-making actions, risk state matching, and mismatch scenarios, making the quantification of decision losses more closely aligned with the actual cost composition of underwater control module operation and maintenance (such as failure losses from high-risk missed detections and resource waste from low-risk over-handling), providing accurate cost references for subsequent decisions.

[0018] 5. This invention derives three decision thresholds through a loss function, dividing failure modes into positive, boundary, and negative domains. Within each decision domain, risks are ranked based on the corresponding expected loss function. This breaks through the binary decision-making limitations of traditional FMEA, forming a risk management strategy with clear hierarchies. Differentiated control schemes are formulated for failure modes of different risk levels of underwater control modules, ensuring that high-risk modes are handled first while avoiding excessive investment in low-risk modes, thus improving the scientific and targeted nature of underwater control module reliability management. Attached Figure Description

[0019] Figure 1 This is a schematic diagram of the overall process of an underwater control module FMEA analysis method based on spherical fuzzy sets according to an embodiment of the present invention; Figure 2 This is an architecture diagram of an underwater control module FMEA analysis method based on spherical fuzzy sets according to an embodiment of the present invention. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the described embodiments of the present invention are within the scope of protection of the present invention.

[0021] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0022] Example 1 Reference Figure 1 This embodiment of an underwater control module FMEA analysis method based on spherical fuzzy sets includes: S1. Obtain the risk assessment information of the underwater control module and convert the expert language evaluation in the risk assessment information into a spherical fuzzy set; S2. Construct a decision matrix based on the transformed spherical fuzzy set. After preprocessing the decision matrix, calculate the weight of each risk factor using the MEREC method. S3. Define the scoring function using the membership and non-membership of the spherical fuzzy set, and determine the ideal and non-ideal solutions of the failure mode under each risk factor based on the scoring function. Combine the distance between the spherical fuzzy sets to calculate the regret function and gratification function of the failure mode, and then calculate the conditional probability of the failure mode being in a high-risk state and a low-risk state. S4. Based on the risk factor weights, construct the loss function of the failure mode under different decision actions and risk states, and calculate the expected loss function in combination with conditional probability. S5. Derive the three-branch decision threshold based on the loss function, and use the three-branch decision threshold and conditional probability to divide the three-branch decision domain of the failure mode. S6. Within each of the three decision domains, the failure modes are ranked by risk based on the expected loss function, and the risk classification and priority results of the underwater control module failure modes are output.

[0023] Specifically, an underwater control module FMEA analysis method based on spherical fuzzy sets includes the following steps: like Figure 1 , Figure 2 As shown, S1, obtain the risk assessment information of the underwater control module, and convert the expert language evaluation in the risk assessment information into a spherical fuzzy set; A comprehensive risk assessment information system is constructed through multi-dimensional information collection methods: combining the design specifications of the underwater control module, historical fault records, and industry reliability reports, the core risk factors and typical failure modes of the module are identified. Risk factors must cover key dimensions such as the probability of failure, the severity of failure consequences, and the difficulty of fault detection. These can be expanded into multiple specific risk indicators based on the functional characteristics of the underwater control module. Typical failure modes must be selected based on failure types that significantly impact module reliability, occur frequently during operation and maintenance, or have severe consequences, ensuring the comprehensiveness and representativeness of the risk assessment objects. Subsequently, standardized language evaluation terms are used to conduct expert evaluations of the performance of each failure mode under each risk factor. The language evaluation terms must predefine semantic levels; this embodiment uses extremely low, low, low-medium, medium, medium-high, high, and extremely high to ensure consistency in expert evaluations, ultimately forming a set of expert language evaluation information covering all evaluation units.

[0024] Based on the acquired risk assessment information, we first define a universal set X, which is the set of all failure modes and risk factor evaluation units in the underwater control module FMEA analysis. The mathematical expression is: ,in, Let p be the i-th failure mode, and p be the total number of failure modes. Let q be the j-th risk factor, and q be the total number of risk factors. Let X be the specific evaluation unit for the i-th failure mode under the j-th risk factor. The total number of elements in the set X is p×q, covering all risk evaluation objects to be analyzed.

[0025] Based on the universal set X, a spherical fuzzy set S is defined to quantitatively characterize the fuzziness and uncertainty of expert language evaluation. The mathematical expression of the spherical fuzzy set S is: , And the core constraints must be met. , in, Let X be any element in the universal set X. Let x be the membership degree of element x to the spherical fuzzy set S, and the functional mapping relationship is as follows: The value range is [0,1], representing the degree of expert recognition that the evaluation unit x meets the characteristics of high risk. Let x be the non-membership degree of the element x with respect to the spherical fuzzy set S, and the functional mapping relationship is as follows: The value range is [0,1], representing the degree of expert disapproval that the evaluation unit x meets the high-risk characteristics. Let x be the degree of hesitation of element x with respect to the spherical fuzzy set S, and the functional mapping relationship is as follows: The value range is [0,1], representing the degree of uncertainty of experts' judgment on the risk level of evaluation unit x, and is determined by the membership degree μ(x) and non-membership degree ν(x) through the formula. It is derived that...

[0026] Based on the definition of spherical fuzzy sets and the semantic strength of language evaluation terms, a standardized correspondence table is pre-constructed. The construction principle is that the semantic strength of language is positively correlated with membership degree and negatively correlated with non-membership degree. The specific technical logic is as follows: 1. For each preset language evaluation term (such as "extremely low, low, low-medium, medium, medium-high, high, extremely high"), match the corresponding membership degree μ and non-membership degree ν according to its semantic connotation. The higher the semantic strength (such as extremely high), the larger the value of μ and the smaller the value of ν; the lower the semantic strength (such as extremely low), the smaller the value of μ and the larger the value of ν.

[0027] 2. Based on Calculate the degree of hesitation π corresponding to each language evaluation term, ensuring that μ, ν, and π satisfy the constraints of a spherical fuzzy set. ; 3. Map language evaluation terms one-to-one with their corresponding (μ,ν,π) triples (i.e., spherical fuzzy numbers) to form a complete correspondence table, which serves as a unified standard for subsequent mapping and transformation, thus avoiding subjective bias in expert evaluation and interpretation.

[0028] Then, based on the constructed correspondence table, a mapping transformation process is executed, traversing the expert language evaluation information set and extracting each evaluation unit. For the corresponding language evaluation term, consult the correspondence table to find the spherical fuzzy number that matches the language evaluation term. ,in, Let i be the membership degree of the i-th failure mode under the j-th risk factor. To correspond to non-membership degree, To correspond to the degree of hesitation, the spherical fuzzy number is then verified to ensure it meets the constraints. If it does, the mapping is confirmed to be valid; otherwise, if it does not (e.g., exceeding the limits due to data errors), the semantic logic is corrected based on the corresponding relation table. or Until the constraints are met and the mapping transformation of all evaluation units is completed, an initial quantitative dataset with spherical fuzzy numbers as elements is formed. This dataset fully preserves the fuzziness and uncertainty information in the expert language evaluation, and all data conform to the mathematical specifications of spherical fuzzy sets.

[0029] S2. Construct a decision matrix based on the transformed spherical fuzzy set. After preprocessing the decision matrix, calculate the weight of each risk factor using the MEREC method. Using the spherical fuzzy numbers corresponding to all failure modes and risk factor evaluation units in step S1 as data elements, a p×q-dimensional decision matrix is ​​constructed to characterize the relationship between failure modes and risk factor fuzzy evaluation. Where p is the total number of failure modes of the underwater control module, q is the total number of risk factors, and the mathematical expression of the decision matrix is: The element in the i-th row and j-th column of the matrix Here, i is the failure mode number and j is the risk factor number and , Let i be the membership degree of the i-th failure mode under the j-th risk factor. For the corresponding non-membership degree, To correspond to the degree of hesitation, this decision matrix integrates the scattered failure modes and risk factors into a structured data format using spherical fuzzy numbers.

[0030] Then the decision matrix Risk factors are categorized into two types based on their evaluation logic: benefit-based risk factors and cost-based risk factors. Benefit-based risk factors are defined by their membership degree in the spherical fuzzy number. The larger the value of a risk factor (such as the direct cost of failure, environmental impact, etc., the higher the risk level of the failure mode), the higher the risk level of that factor. Cost-type risk factors refer to the membership degree in the spherical fuzzy number corresponding to that factor. The larger the value, the lower the risk level of the failure mode. For example, the lower the detection difficulty, the easier it is to find the fault, and the lower the risk. Therefore, the higher the detection difficulty, the lower the risk. The larger the value, the lower the actual risk.

[0031] To unify the evaluation direction of all risk factors, it is necessary to define the spherical fuzzy numbers corresponding to cost-type risk factors. Perform a reverse transformation to obtain the benefit-type spherical fuzzy number. The transformation rule is: the transformed membership degree By subtracting the original membership degree from 1, the negative correlation between membership degree and risk level in cost-type risk factors is transformed into a benefit-type relationship where membership degree and risk level are positively correlated; the transformed non-membership degree Similarly, the original logic of the relationship between non-membership degree and risk level is reversed to ensure that the degree of negation of risk level by non-membership degree is consistent with the logic of benefit-based evaluation; the transformed degree of hesitation The calculation needs to be derived based on the constraints of spherical fuzzy sets, and the formula is as follows: This formula ensures that by subtracting the square root of the sum of the squared membership degrees and the squared non-membership degrees after transformation from 1, the formula is correct. The value of conforms to the mathematical constraints of spherical fuzzy sets and accurately reflects the degree of hesitation of the evaluation unit after transformation. After performing the above transformation operation on the spherical fuzzy numbers corresponding to all cost-type risk factors in the decision matrix, a benefit-type spherical fuzzy number decision matrix with unified evaluation direction for all risk factors is obtained. .

[0032] For the i-th failure mode, calculate its membership baseline overall performance under all q risk factors. Overall performance of non-membership benchmark and overall performance of the hesitation benchmark This serves as the benchmark value for measuring the overall evaluation status of failure modes across various dimensions. The overall performance is calculated using the logarithmic average method to avoid excessive influence of extreme values ​​from a single risk factor on the overall evaluation. The specific formula is as follows: Overall performance of membership benchmark: ,in, The transformed benefit-type membership degree. The average factor is used to ensure that the results reflect the average performance under all risk factors.

[0033] Overall performance of non-membership benchmark: ,in, The converted benefit-type non-membership degree has a calculation logic that is consistent with the overall performance of the membership degree benchmark, and is used to characterize the comprehensive evaluation status of the failure mode in the non-membership degree dimension. Overall performance of the hesitation benchmark: ,in, The transformed benefit-oriented hesitation degree is used to characterize the comprehensive evaluation status of failure modes in the hesitation degree dimension.

[0034] For the j-th risk factor Each of the q risk factors is removed one by one, and then the membership degree of the i-th failure mode under the remaining q-1 risk factors is calculated and compared with the overall performance. Overall performance of non-membership comparison Comparison of overall performance in terms of hesitation To analyze the impact of removing this risk factor on the overall performance of the failure mode, the specific formula is as follows: Overall performance in membership comparison: Where k is the risk factor number, This is the averaged coefficient after removing one risk factor. The meanings of the remaining parameters are consistent with the overall performance formula of the benchmark. Non-membership degree is compared with overall performance: Hesitation level compared to overall performance: Then, the impact of the j-th risk factor on the overall performance of all failure modes is calculated. By summing the absolute differences between the baseline overall performance and the comparative overall performance of all p failure modes, the sum of the absolute deviations of the membership degree, the sum of the absolute deviations of the non-membership degree, and the sum of the absolute deviations of the hesitation degree of the j-th risk factor are obtained. The larger the sum of the deviations, the more significant the impact of the risk factor on the overall performance of the failure mode, and the higher its importance in the corresponding dimension.

[0035] Based on the sum of absolute deviations, the dimensional weights of the j-th risk factor are calculated in three dimensions: membership, non-membership, and hesitation. The membership dimension weight is... ,in, It is the sum of the absolute deviations of the membership degrees. Let be the sum of the absolute deviations of the membership degrees of all q risk factors. The sum of absolute deviations is converted into a weight value within the interval [0,1] by the ratio of the sum of the absolute deviations of the j-th risk factor to the sum of the absolute deviations of all risk factors. A larger weight indicates a higher importance of the risk factor in the membership dimension. The weights for non-membership dimensions are... ,in, It is the sum of the absolute deviations of the non-membership degrees. The sum of the absolute deviations of the non-membership degrees of all risk factors is used, and the calculation logic is consistent with the weighting of the membership dimension; the weighting of the hesitation dimension is... ,in, This is the sum of the absolute deviations in the degree of hesitation. It is the sum of the absolute deviations of hesitation for all risk factors.

[0036] Subsequently, a weighted average is calculated on the weights of the three dimensions to obtain the comprehensive weight of the j-th risk factor. Membership, non-membership, and hesitation are all core dimensions of spherical fuzzy sets, and their contributions to risk assessment are equally important. Therefore, the arithmetic mean method is used to calculate the comprehensive weight, and the specific formula is as follows: In the formula, 1 / 3 represents the average weight coefficient of the three dimensions; through this calculation, the comprehensive weight of all q risk factors is finally obtained. And satisfy This ensures the normalization properties of the weights.

[0037] S3. Define the scoring function using the membership and non-membership of the spherical fuzzy set, and determine the ideal and non-ideal solutions of the failure mode under each risk factor based on the scoring function. Combine the distance between the spherical fuzzy sets to calculate the regret function and gratification function of the failure mode, and then calculate the conditional probability of the failure mode being in a high-risk state and a low-risk state. S31. To quantify the risk level of the failure mode and risk factor evaluation unit, a scoring function is constructed using the membership and non-membership degrees of the spherical fuzzy set defined in step S1. This function is calculated by the difference between the squared membership degree and the squared non-membership degree. The core logic is: squared membership degree The weight of the contribution of the characterization expert to the recognition that the evaluation unit meets the high-risk characteristics, and the square of the non-membership degree. The negative contribution weight of the characterization experts to the evaluation unit's high-risk characteristics is considered; the larger the difference between the two, the more significant the high-risk attribute of the evaluation unit and the higher the risk level. The mathematical expression of the scoring function is: ,in, Let i be the benefit-type spherical fuzzy number corresponding to the i-th failure mode under the j-th risk factor. The score value is directly related to the core parameters of the spherical fuzzy set, ensuring that the score value can objectively reflect the risk tendency in the expert evaluation.

[0038] S32. Based on the benefit-oriented spherical fuzzy number decision matrix For each risk factor j, perform the following operations to determine the ideal and non-ideal solutions: First, using the scoring function defined in step S3.1, calculate the spherical fuzzy number corresponding to all p failure modes under that risk factor. The scores are then ranked, and the failure mode with the highest score is identified as the ideal solution for that risk factor. This represents the upper limit of risk under this risk factor. The failure mode with the lowest score is identified as the non-ideal solution under this risk factor. This represents the lower limit of risk for that risk factor.

[0039] S33. To quantify the degree of difference between any two spherical fuzzy numbers, based on the triplet structure (membership, non-membership, hesitation) of spherical fuzzy sets, the Euclidean distance between spherical fuzzy sets is defined; for the benefit-type spherical fuzzy number of the i-th failure mode under the j-th risk factor. The Euclidean distance between the ideal solution and the non-ideal solution under this risk factor is calculated using the following formula: , in, Let be the Euclidean distance between the ideal solution of the i-th failure mode and the j-th risk factor. Ideal solutions Corresponding to the benefit-type membership degree, non-membership degree, and hesitation degree of the spherical fuzzy number, this distance formula simultaneously considers the three dimensions of the spherical fuzzy set, ensuring that the distance value can fully reflect the differences between the two fuzzy evaluation units. The larger the distance, the more significant the difference in risk characteristics between the failure mode and the ideal solution (or non-ideal solution).

[0040] S34. Introducing an avoidance coefficient To modulate the decision-maker's sensitivity to the gap between the failure mode and the ideal / non-ideal solution. The larger the value, the more sensitive the decision-maker is to the gap. The smaller the value, the less sensitive the perception. Based on the Euclidean distance calculated in step S33, a regret function and a gratification function are constructed respectively. The regret function characterizes the degree of regret caused by the difference between the failure mode and the ideal solution. The larger the difference, that is, the lower the risk level of the failure mode is compared with the ideal solution, the larger the value of the regret function. Its mathematical expression is: ,in, Let be the regret function value of the target failure mode s. To avoid coefficient, Let be the Euclidean distance between the target failure mode s and the ideal solution of the corresponding risk factor.

[0041] The euphoria function characterizes the degree of euphoria arising from the difference between the failure mode and the non-ideal solution. The larger the difference, i.e., the higher the risk level of the failure mode compared to the non-ideal solution, the larger the euphoria function value. Its mathematical expression is: ,in, Let be the euphoria function value of the target failure mode s. Let S be the Euclidean distance between the target failure mode s and the corresponding non-ideal solution of the risk factor. The two functions use the decreasing bounded property of the exponential function to convert the distance value into a function value in the interval [0,1), ensuring that the results are comparable. At the same time, the introduction of the avoidance coefficient enables the function to adapt to the risk preferences of different decision-making scenarios.

[0042] S35. Regret function value calculated based on step S3.4 With the value of the joy function Define the dominance and subordinate relationships between failure modes. For any two failure modes... and ,in, ,like ,show The risk level is no less than Then define right A dominance relationship exists, denoted as ,in, For the set of all dominance relationships, ,like ,show The risk level is no higher than Then define right A subordinate relationship exists, denoted as ,in, Let be the set of all subordinate relationships; based on the above relationships, determine the i-th failure mode. Dominant class With the dominated class Dominant class For all those The dominant set of failure modes, namely: , The number of elements in the dominating class represents Total number of controllable failure modes; controlled classes For all domination The set of failure modes, i.e. By dividing failure modes into dominant and dominated classes, the relative risk relationships between failure modes are transformed into a set form, providing countable quantifiable objects for calculating conditional probabilities.

[0043] S36. Based on the dominant and dominated classes, calculate the i-th failure mode. High-risk state C and low-risk state Conditional probability: Conditional probability of a high-risk state Characterization in the known Under the premise of a dominance relationship, the probability of it belonging to a high-risk state is calculated by the logic of "the proportion of the number of dominance elements to the total number of dominance and subordinate elements". The higher the proportion, the higher the risk. The more failure modes a system can control, the more significant its high-risk attributes, and the greater its conditional probability; its mathematical expression is: , in, For the i-th failure mode, Let i be the dominant class of the failure mode. Let be the number of elements in the class dominated by the i-th failure mode. For the i-th failure mode, Let be the number of elements in the dominant class of the i-th failure mode. For the i-th failure mode, This is a high-risk situation. As a relationship of domination, The relationship is one of subordination, and the conditional probability of a low-risk state is given. This is obtained by subtracting the conditional probability of the high-risk state from 1, i.e. This probability calculation method is based entirely on the objective dominance relationship between failure modes, avoiding subjective assignment bias and ensuring that the probability results can objectively reflect the relative risk level of failure modes.

[0044] S4. Based on the risk factor weights, construct the loss function of the failure mode under different decision actions and risk states, and calculate the expected loss function in combination with conditional probability. Based on the risk management requirements of the underwater control module FMEA, three types of decision-making actions and two types of risk states are identified: decision-making actions include priority actions for high-risk failure modes. Delayed decision-making actions for critical risk failure modes Risk acceptance actions for low-risk failure modes ,in, This refers to high-intensity actions that can quickly eliminate high risks, such as immediate shutdown for maintenance and emergency replacement of spare parts. This refers to medium-intensity actions that require sustained attention, such as strengthening dynamic monitoring and shortening testing cycles. This refers to low-intensity actions such as incorporating into routine maintenance and not taking additional action for the time being; the risk status is the high-risk status and low-risk status defined in step S3.

[0045] The comprehensive weight of the j-th risk factor calculated in step S2 Using the core parameters and combining the ideal and non-ideal solutions determined in step S32 with the Euclidean distance calculated in step S3.3, a differentiated loss function is constructed for six combined scenarios of decision-making actions and risk states, specifically including: The loss from a correct decision refers to the loss in a scenario where the decision action perfectly matches the risk state. Since there is no additional risk or waste of resources in this scenario, the loss value is set to a baseline of 0: when the failure mode is in a high-risk state C and priority actions are taken. At that time, define the correct handling of losses ,in, Under high-risk conditions The loss of the action is represented by a value of 0, indicating that timely handling of high-risk situations results in no loss; when the failure mode is in a low-risk state and a risk-acceptance action is taken. At that time, define the correct acceptance of loss. ,in, Under low-risk conditions The loss of the action, with a value of 0 representing accepting low risk and no waste of resources; this definition provides a benchmark for the loss of wrong decisions and delayed decisions, ensuring the relativity and rationality of loss quantification.

[0046] Define the loss from erroneous decisions. This loss refers to the loss in a scenario where the decision-making action is mismatched with the risk state. The consequences of this mismatch need to be quantified by combining the weights of risk factors and Euclidean distance. For example, when the failure mode is in a high-risk state C, but a risk-accepting action is taken... At that time, the loss was incorrectly missed. When the failure mode is in a low-risk state However, priority action was taken. At times, excessive handling of losses ; Define delayed decision loss as the loss incurred when a decision is made after a delay. Losses in the scenario, due to Action intensity between and Therefore, the loss value is set as the median of the losses from a correct decision and an incorrect decision. When the failure mode is in high-risk state C and a delayed decision-making action is taken... Define the loss due to delayed processing. ,in, For risk aversion coefficient, For the loss of incorrect omission, and satisfying the following conditions: When the failure mode is in a low-risk state and delayed decision-making actions are taken When, define the delayed acceptance loss. ,in, This is due to excessive handling of losses.

[0047] Priority action Expected loss function Characterizing the i-th failure mode The average loss of an action is calculated using the following formula: , in, for Expected losses of the operation and Let represent the conditional probabilities of the i-th failure mode being in a high-risk or low-risk state, respectively. Similarly, for delayed decision-making actions... Expected loss function Actions to accept risk Expected loss function ,in, , To delay the handling and acceptance of losses, To mitigate the losses from erroneous omissions, the aforementioned expected loss function integrates the losses from different risk states through probability weighting, transforming deterministic losses into probabilistic average losses.

[0048] S5. Derive the three-branch decision threshold based on the loss function, and use the three-branch decision threshold and conditional probability to divide the three-branch decision domain of the failure mode. First, clarify the inherent logical relationships between the various loss functions defined in step S4 to make correct loss decisions. The loss from wrong decisions satisfies The consequences of overlooking high-risk cases are more severe than the over-handling of low-risk cases; delayed decision-making results in losses. The loss from delayed action lies between that of a correct and a wrong decision. Based on this logical relationship, high-risk judgment thresholds are calculated respectively. Low-to-medium risk threshold and low-risk determination threshold High-risk determination threshold The core logic behind determining whether a failure mode should be classified into the positive domain is based on the implementation of priority actions. The expected loss is less than or equal to the decision to delay action. When the expected loss is reached, the failure mode needs to be managed as a high-risk condition. Based on the expected loss function in step S4, a high-risk threshold is obtained. Calculation formula This formula transforms the loss difference into a probability threshold within the [0,1] interval by using the ratio of the difference between the loss from incorrect decisions and the loss from delayed decisions. The higher the value, the more stringent the conditions for classifying it as high-risk.

[0049] Low-to-medium risk threshold Used to help define the boundary between the positive and negative domains, the core logic is to take priority actions. If the expected loss is less than or equal to the risk acceptance action When considering the expected loss, the failure mode needs to be classified into the high / medium risk category. After processing, the low / medium risk threshold is obtained. The calculation formula is Low-risk threshold The core logic for determining whether a failure mode should be classified into the negative domain is: "When the expected loss from taking risk-accepting action is less than or equal to the expected loss from taking delayed decision-making action, the failure mode should be managed as a low-risk mode, and the low-risk judgment threshold can be obtained after processing." .

[0050] High-risk determination threshold Low-to-medium risk threshold and low-risk determination threshold To establish the classification criteria, and based on the conditional probability of the i-th failure mode being in a high-risk state calculated in step S3, the following threshold and probability comparison rule is established to divide all failure modes into three decision domains: positive domain POS(S), boundary domain BND(S), and negative domain NEG(S): The comparison rule is specifically as follows: when and When the failure mode is classified into the positive domain, the technical logic of this rule is that "when the high-risk probability of the failure mode exceeds a stringent threshold..." At that time, the expected loss from prioritizing disposal is the lowest, and it should be managed with the highest priority. and When the probability of a failure mode being high-risk is below a lenient threshold, it falls into the negative domain. The technical logic behind this rule is that when the probability of a failure mode being high-risk is below a lenient threshold... At this point, the expected loss is lowest, and no additional action is required. and If the value is within the boundary domain, it falls between the thresholds of the positive and negative domains. The technical logic is that the expected losses for prioritizing treatment and accepting risk are both high at this point, while the expected loss for delaying the decision (strengthening monitoring) is optimal. Through the above division, all failure modes are classified into a unique decision domain, and the division process is entirely based on the loss function and conditional probability of the preceding steps, without subjective intervention, ensuring the objectivity and scientific nature of the decision domain division. At the same time, the three decision domains correspond to differentiated management strategies for prioritizing treatment, temporarily suspending observation, and accepting risk.

[0051] S6. Within each of the three decision domains, the failure modes are ranked by risk based on the expected loss function, and the risk classification and priority results of the underwater control module failure modes are output.

[0052] This step, based on the three decision domains defined in step S5 and combined with the expected loss function calculated in step S4, performs targeted risk ranking within each decision domain. Finally, it integrates these results to form the risk classification and priority of the underwater control module failure modes, completing the closed loop of the entire FMEA analysis process. The specific technical implementation process is as follows: Because different decision domains correspond to differentiated control strategies, the expected loss function under that strategy needs to be matched as the core ranking indicator—the positive domain POS(S) corresponds to the priority action. Therefore, the expected loss of the priority action calculated in step S4 is... The target indicator directly reflects the cost of prioritizing high-risk scenarios; a smaller value indicates a higher urgency of action. The boundary domain BND(S) corresponds to delayed decision-making actions. Therefore, the expected loss is due to delayed decision-making. For target indicators, the smaller the value, the higher the priority for close monitoring; the negative domain NEG(S) corresponds to risk acceptance actions. Therefore, the expected loss is based on risk-acceptance actions. The smaller the value of the target indicator, the higher the level of routine attention required in the low-risk mode. By accurately matching the decision domain with the objective function, we can ensure that the ranking logic and control strategy are highly consistent and avoid the ranking indicator from becoming disconnected from actual decision-making needs.

[0053] Secondly, risk ranking is performed within each decision domain: for all failure modes in the positive domain POS(S), according to... Sort by ascending order, i.e. Failure modes with smaller values ​​rank higher in the positive domain, indicating a higher urgency for handling and requiring priority allocation of operational resources. For failure modes in the boundary domain (BND(S), the ranking is based on... The failure modes are sorted in ascending order. Failure modes that appear earlier in the list require more monitoring resources to dynamically track risk changes, such as low-voltage accumulator performance degradation. The smallest value is the key observation target within the boundary domain; for failure modes in the negative domain NEG(S), according to... The ascending order rule sorts failure modes, with those listed earlier in the order, to be checked first in routine maintenance to prevent low-risk modes from accumulating into high-risk ones. The core function of this ascending order rule is to assign the highest priority to the least expected loss, ensuring that the sorting results directly serve the optimal allocation of resources. This aligns with the actual needs of controllable maintenance costs and risk priority for underwater control modules.

[0054] Finally, the risk classification and priority results are output: Integrating the decision domain division results from step S5 and the domain ranking results from step S6, a three-level output system of decision domain-risk level-priority is constructed. All failure modes within the positive domain are uniformly classified as high-risk, with the top 30% of failure modes marked as High-Risk Level I, requiring immediate initiation of emergency response procedures (such as shutdown for maintenance and spare parts replacement); the bottom 70% of failure modes are marked as High-Risk Level II, requiring completion of response planning within 24 hours. All failure modes within the boundary domain are uniformly classified as medium-risk, with the top 50% of failure modes marked as Medium-Risk Level I, requiring the detection cycle to be shortened to 50% of the original cycle; the bottom 50% of failure modes are marked as Medium-Risk Level II, requiring enhanced data recording according to the original detection cycle. Within the negative domain… All failure modes are uniformly classified as low-risk, requiring only routine maintenance checks (e.g., monthly, quarterly) without additional resource investment. Simultaneously, a complete result is output in the form of a visual report, including key information such as the failure mode name, its decision domain, risk level, handling priority, target expected loss function value, and recommended control measures. The target expected loss function value must be clearly marked to provide a quantitative basis for subsequent maintenance resource allocation and review of handling effectiveness. This output achieves both scientific classification of failure modes and clarifies the handling priorities and specific measures for different levels of modes, effectively supporting underwater control module reliability management decisions and completing a closed-loop process from risk assessment to decision implementation, ensuring the engineering practicality and operability of the entire FMEA analysis method.

[0055] Example 2 The difference between this embodiment and Embodiment 1 is that this embodiment provides a specific implementation process for an underwater control module FMEA analysis method based on spherical fuzzy sets: The underwater control module is one of the key components of the underwater production system. Such failures can lead to serious economic and environmental losses. Based on a comprehensive evaluation of the key components and subsystems of the underwater control module, this case study selects 10 common failure modes of the underwater control module, namely: F1 SEM power loss, F2 SCM casing rupture, F3 high-voltage DCV leakage, F4 high-voltage accumulator failure, F5 low-pressure shuttle valve severe leakage, F6 complete loss of SEM signal, F7 high-voltage filter failure, F8 low-pressure DCV severe leakage, F9 high-pressure shuttle valve severe leakage, and F10 low-pressure accumulator failure.

[0056] The failure modes listed are based on the internal components of the underwater control module and the requirements for providing specific functions. Failures caused by installation, testing, and transportation are not within the scope of this case. The three risk factors of occurrence (O), severity (S), and detectability (D) in traditional FMEA analysis are further divided as shown in Table 1.

[0057] Table 1. Assessment Criteria for Extended Traditional FMEA Risk Factors

[0058] Expert evaluation information on each failure mode was collected, and failure modes were described using linguistic information such as VH (Very High), H (high), MH (Medium High), M (Medium), ML (Medium Low), L (Low), and VL (Very Low), as shown in Table 2.

[0059] Table 2 Expert Evaluation Information for Each Failure Mode of the Underwater Control Module

[0060] The transformation converts the expert fuzzy language into a spherical fuzzy set according to the corresponding rules: ; The decision matrix can be obtained through expert fuzzy language information and transformation table. , decision matrix The cost-related factors are transformed into benefit-related factors, resulting in a decision matrix. As shown in Table 3.

[0061] Table 3 Decision Matrix

[0062]

[0063] Based on the obtained decision matrix The membership degree performance of each failure mode was calculated. Non-membership degree representation Hesitation level performance Based on the obtained decision matrix Calculate the membership performance after removing a certain risk factor. Non-membership degree representation Hesitation level performance Based on the calculations , , and , , This yields the performance difference before and after removing a certain influencing factor, and the sum of membership biases. The sum of non-membership degree deviations The sum of hesitation deviations As shown in Table 4.

[0064] Table 4 Performance Difference Table of Influencing Factors

[0065] The sum of the calculated membership degree deviations The sum of non-membership degree deviations The sum of hesitation deviations Then, the weights of each influencing factor are calculated.

[0066] The regret function and euphoria function for each failure mode were calculated. as follows: .

[0067] Based on the calculation , And classify each failure mode into dominant and dominated classes and calculate the corresponding states of each failure mode. and state The conditional probabilities are shown in Table 5.

[0068] Table 5 Conditional probabilities of each failure mode

[0069] Based on the calculated weights of each influencing factor The relative loss functions for each failure mode are calculated and shown in Table 6.

[0070] Table 6 Conditional probabilities of each failure mode

[0071] Based on the expected loss function and conditional probability of each failure mode, the expected loss function for taking action is calculated as shown in Table 7.

[0072] Table 7 Expected loss function for taking action on each failure mode

[0073] Based on the relative loss function of each failure mode, the three-branch decision threshold is calculated, as shown in Table 8.

[0074] Table 8 Three-branch decision thresholds for each failure mode

[0075] Based on the three-branch decision thresholds and expected loss functions for each failure mode, the three decision domains are divided, and the classification results are as follows: , , .

[0076] The failure modes are ranked according to their expected loss functions, and the ranking results are as follows: According to the final classification and ranking results, the following three failure modes are in the high-risk range: F1 (SEM power loss), F3 (high-voltage DCV leakage), and F8 (severe low-voltage DCV leakage), indicating serious potential consequences or significant overall risk. F5 (severe low-pressure shuttle valve leakage), F9 (severe high-pressure shuttle valve leakage), and F10 (low-pressure accumulator failure) are in the medium-risk range, indicating manageable risk and low overall impact. F2 (SCM casing rupture), F4 (high-voltage accumulator failure), F6 (complete SEM signal loss), and F7 (high-pressure filter failure) are in the low-risk range, indicating sufficient safety redundancy and low probability of occurrence or low impact. This invention effectively overcomes the problems of fixed risk weights and insufficient fuzzy information processing capabilities in traditional FMEA, enabling priority ranking and hierarchical decision-making for underwater control module failure modes.

[0077] The above are all preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Therefore, all equivalent changes made in accordance with the structure, shape and principle of the present invention should be covered within the scope of protection of the present invention.

Claims

1. A method for underwater control module FMEA analysis based on spherical fuzzy sets, characterized in that, include: Obtain risk assessment information for the underwater control module and convert the expert language evaluation in the risk assessment information into a spherical fuzzy set; A decision matrix is ​​constructed based on the transformed spherical fuzzy set. After preprocessing the decision matrix, the weights of each risk factor are calculated using the MEREC method. The score function is defined by the membership and non-membership of spherical fuzzy sets. The ideal and non-ideal solutions of failure modes under each risk factor are determined based on the score function. The regret function and gratification function of failure modes are calculated by combining the distance between spherical fuzzy sets. Then, the conditional probability of failure modes being in high-risk and low-risk states is calculated. Based on the risk factor weights, a loss function for failure modes under different decision actions and risk states is constructed, and the expected loss function is calculated by combining conditional probability. The three-branch decision threshold is derived based on the loss function, and the three-branch decision domain of the failure mode is divided using the three-branch decision threshold and conditional probability. Within each of the three decision domains, the failure modes are ranked by risk based on the expected loss function, and the risk classification and priority results of the underwater control module failure modes are output.

2. The underwater control module FMEA analysis method based on spherical fuzzy sets according to claim 1, characterized in that, The process of converting expert linguistic evaluations from risk assessment information into spherical fuzzy sets includes defining a spherical fuzzy set S under a universal set X based on the acquired risk assessment information. The risk assessment information includes risk factors, failure modes, and linguistic evaluations of the underwater control module. A pre-established correspondence table between linguistic evaluation terms and spherical fuzzy numbers is used to map the linguistic evaluations of each failure mode under each risk factor to spherical fuzzy numbers conforming to the definition of a spherical fuzzy set. The expression for the spherical fuzzy set S is: and , in, Let X be any element in the universal set X. Let x be the membership degree of element x to the spherical fuzzy set S. Let x be the degree of non-membership of the element x with respect to the spherical fuzzy set S. Let x be the degree of hesitation of element x with respect to the spherical fuzzy set S.

3. The underwater control module FMEA analysis method based on spherical fuzzy sets according to claim 1, characterized in that, The preprocessing of the decision matrix includes establishing a p×q dimensional decision matrix based on a spherical fuzzy set to characterize the fuzzy evaluation relationship between failure modes and risk factors. Based on the decision matrix, risk factors are categorized into benefit-type risk factors and cost-type risk factors. The spherical fuzzy numbers corresponding to cost-type risk factors are then reverse-transformed to unify them into benefit-type spherical fuzzy numbers, resulting in the transformed spherical fuzzy number decision matrix. hesitancy after conversion The calculation formula is: ， Where i is the failure mode number and j is the risk factor number and , Let i be the membership degree of the i-th failure mode under the j-th risk factor. For the corresponding non-membership degree, For the corresponding degree of hesitation, The transformed membership degree. This represents the non-membership degree after transformation.

4. The underwater control module FMEA analysis method based on spherical fuzzy sets according to claim 1, characterized in that, The method of calculating the weights of each risk factor using MEREC includes using the preprocessed benefit-type spherical fuzzy number decision matrix as the data basis. For the i-th failure mode, the overall performance of the membership benchmark, the overall performance of the non-membership benchmark, and the overall performance of the hesitation benchmark under all q risk factors are calculated respectively. For the j-th risk factor, it is removed from the set of all risk factors one by one, and the sum of the absolute deviations of the corresponding overall performance after removing each risk factor is calculated. Based on the sum of the absolute deviations, the weights of the membership dimension, the non-membership dimension, and the hesitation dimension are obtained respectively. The weights are then weighted and averaged to obtain the comprehensive weight of each risk factor.

5. The underwater control module FMEA analysis method based on spherical fuzzy sets according to claim 1, characterized in that, The calculation of the regret and gratification functions for failure modes by combining the distances between spherical fuzzy sets includes defining a scoring function using the membership and non-membership degrees of the spherical fuzzy sets. For each risk factor j, the scoring function values ​​of all failure modes under that factor are calculated. The failure mode with the largest scoring function value is the ideal solution for that risk factor, and the failure mode with the smallest scoring function value is the non-ideal solution for that risk factor. The Euclidean distance between the spherical fuzzy number corresponding to the i-th failure mode and the ideal and non-ideal solutions is calculated. An avoidance coefficient is introduced, and the regret and gratification functions of the failure modes are calculated based on the Euclidean distances. The expressions for the regret and gratification functions are as follows: ， ， in, For the regret function value, To avoid coefficient, Let Euclidean distance be the distance between the failure mode and the ideal solution. For the target failure mode, This is the ideal solution under risk factors. For the pleasing function value, This is a non-ideal solution under risk factors. Let be the Euclidean distance between the failure mode and the non-ideal solution.

6. The underwater control module FMEA analysis method based on spherical fuzzy sets according to claim 1, characterized in that, The calculation of the conditional probabilities of a failure mode being in a high-risk state and a low-risk state includes defining the dominance and subordination relationships between failure modes based on regret and euphoria function values, determining the dominance and subordination classes of the i-th failure mode based on these relationships, and calculating the conditional probabilities of the failure mode being in a high-risk state and the conditional probabilities of it being in a low-risk state based on the number of elements in the dominance and subordination classes. The expression for the conditional probability of the high-risk state is as follows: ， in, For the j-th failure mode, Let j be the dominant class of the failure mode. Let be the number of elements in the class that dominates the j-th failure mode. For the j-th failure mode, Let be the number of elements in the class dominated by the j-th failure mode. For the j-th failure mode, This is a high-risk situation. As a relationship of domination, It is a subordinate relationship.

7. The underwater control module FMEA analysis method based on spherical fuzzy sets according to claim 1, characterized in that, The calculation of the expected loss function using conditional probability includes determining the decision action and the risk state type, wherein the decision action includes priority actions for high-risk failure modes. Delayed decision-making actions for critical risk failure modes and risk acceptance actions for low-risk failure modes Using the comprehensive weight of each risk factor as the core parameter, a differentiated loss function is constructed for different combinations of decision actions and risk states. The expected loss function is then calculated using conditional probability. The loss functions for each scenario are weighted and summed according to their corresponding probabilities to obtain the expected loss function for each decision action. The expression for the expected loss function of the priority action is as follows: ， in, Prioritize actions targeting high-risk failure modes. To take the i-th failure mode Expected losses To take measures in high-risk situations The proper handling of losses during the operation To take measures under low-risk conditions Over-handling of the action resulted in losses. and Let represent the conditional probabilities of the i-th failure mode being in a high-risk or low-risk state, respectively.

8. The underwater control module FMEA analysis method based on spherical fuzzy sets according to claim 7, characterized in that, The construction of the differential loss function includes: Define the loss of correct decision-making when the failure mode is in a high-risk state C and priority actions are taken. At that time, properly handle the loss When the failure mode is in a low-risk state And take risk-acceptance actions When to accept losses correctly ; Define the loss from a wrong decision as the loss incurred when the failure mode is in a high-risk state (C) but a risk-accepting action is taken. At that time, the loss was incorrectly missed. When the failure mode is in a low-risk state However, priority action was taken. At times, excessive handling of losses ; Define the loss of delayed decision-making and the action of delayed decision-making. The loss is the median of the loss from a correct decision and the loss from a wrong decision. in, The overall weight of the j-th risk factor is... Let be the Euclidean distance between the ideal solution of the i-th failure mode and the j-th risk factor. Let be the benefit-type spherical fuzzy number of the i-th failure mode under the j-th risk factor. For the j-th risk factor, For the j-th risk factor, the non-ideal solution is... To properly handle losses in high-risk situations, This refers to the proper acceptance of losses under low-risk conditions.

9. The underwater control module FMEA analysis method based on spherical fuzzy sets according to claim 1, characterized in that, The three-branch decision domain, which uses three decision thresholds and conditional probabilities to divide failure modes, includes calculating high-risk determination thresholds based on differentiated loss functions. Low-to-medium risk threshold and low-risk determination threshold A complete three-branch decision threshold system was obtained, and with As the classification criterion, the conditional probability of the i-th failure mode being in a high-risk state is considered. Establish a comparison rule between the threshold and the conditional probability. Specifically, the comparison rule is as follows: when... and When this happens, the failure mode is classified into the positive domain. and When, it falls into the negative domain. and If it is, then it belongs to the boundary domain.

10. The underwater control module FMEA analysis method based on spherical fuzzy sets according to claim 1, characterized in that, The risk ranking of failure modes based on the expected loss function includes using the expected loss function as the core ranking indicator, whereby the expected loss includes the expected loss of taking priority actions for each failure mode. Expected losses from delaying decision-making and the expected losses from taking risk-acceptance actions Then, based on the three different decision domains, the corresponding target expected loss function is matched and sorted according to the ascending order of the corresponding target expected loss function values.

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