Risk assessment method for high-pressure common-rail fuel injection system of low-speed machine

Abstract

The invention discloses a risk assessment method for a high-pressure common rail fuel injection system of a low-speed machine. Differentiated assessment suggestions of experts with different functions in the same field are collected through questionnaire survey; introducing an optimal cloud entropy model to process fuzziness and randomness existing in an evaluation process, and obtaining basic probability distribution of each risk index by solving a membership degree; calculating an expert conflict degree of a single fault mode, generating a reliability weight, and fusing the reliability weight and an objective weight through game combination weighting to form a dynamic weight; utilizing dynamic evidence reasoning to fuse multi-expert opinions, generating a set belief degree and mapping the set belief degree into a prior probability; then, constructing a Bayesian network; and finally, verifying the stability and robustness of the improved method by adopting sensitivity analysis. According to the method, the accuracy of risk assessment of the high-pressure common-rail fuel injection system of the low-speed machine can be improved, a quantitative basis is provided for reasonable configuration and risk pre-control of operation and maintenance resources of the low-speed machine, and the method has good expandability and engineering applicability.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of mechanical system safety risk assessment and prediction, and particularly relates to a risk assessment method for a low-speed engine high-pressure common rail fuel injection system based on an improved FMEA coupled with an optimal cloud entropy-dynamic evidence reasoning-Bayesian network. PRIOR ART

[0002] Traditional risk assessment methods have been widely used in the field of diesel engines, such as fault tree analysis (FTA), event tree analysis (ETA), hazard analysis and quantitative risk assessment (QRA), hazard and operability study (HAZOP), failure mode and effects analysis (FMEA), and Bayesian network. Among them: FTA relies on a complete fault probability database; HAZOP is more suitable for qualitative analysis of process deviations; QRA requires the construction of high-precision numerical models and the input of multi-dimensional parameters, which has the limitations of high computational complexity and high economic cost.

[0003] In view of the typical characteristics of the low-speed engine fuel injection system, such as multi-physical field coupling and insufficient fault data accumulation, the structured method of FMEA has obvious advantages. It not only can systematically evaluate the failure modes of each component to provide a basis for developing preventive maintenance strategies, but also can reduce the dependence on historical data by combining expert experience scoring. Therefore, FMEA has been widely used in the field of low-speed engine fuel injection systems.

[0004] Although researchers have made some progress in using FMEA to conduct risk assessment of low-speed engine fuel injection systems, there are still some limitations, such as FMEA serving mainly in the design and assembly stages, with less consideration in the operation stage. Even a few scholars consider from the operation perspective, but still rely on the risk priority number (RPN) calculated by the design experts, which is calculated by multiplying the occurrence probability level (O), the severity level (S), and the detection difficulty level (D) to obtain the value of RPN, and the result's reliability is difficult to guarantee. Other scholars in the field have tried to introduce methods such as fuzzy logic (FL), Dempster-Shafer theory (D-S), BN, and grey correlation analysis to overcome the shortcomings of traditional FMEA. Among them, fuzzy Bayesian network is commonly used, but still has the following shortcomings:

[0005] (1) Fuzzy logic cannot balance fuzziness and randomness: FL can effectively describe linguistic fuzzy uncertainty, but it is difficult to handle random uncertainty caused by incomplete information or expert subjective differences;

[0006] (2) Expert belief degree acquisition difficulty: The assignment of expert belief degree usually relies on personal experience, lacks uniform standards, and different experts have different understandings of belief degree, resulting in strong subjectivity and difficulty in scoring process;

[0007] (3) Expert opinion conflict is not considered: Existing evidence reasoning methods mostly use equal or fixed weights, ignoring the differences in background, experience and knowledge reserves of experts. For complex systems, the evaluation ability of a single expert may differ significantly under different failure modes, but existing research does not introduce differentiated weight distribution for different failure modes, and cannot effectively handle expert opinion conflicts. This simplification ignores conflict management mechanisms, which may increase decision bias and reduce the reliability and explainability of the fusion results. SUMMARY

[0008] To solve the problems in existing FMEA methods such as the inability of fuzzy logic to balance fuzziness and randomness, the difficulty in obtaining expert belief degree, and the failure to consider opinion conflicts in expert weight calculation, the present application proposes an improved FMEA risk assessment method for low-speed engine high-pressure common rail fuel injection systems, which is coupled with "optimal cloud entropy-dynamic evidence reasoning-Bayesian network". The improved FMEA method is used for risk assessment of low-speed engine high-pressure common rail fuel injection systems in the operation stage, to provide a scientific and quantitative risk assessment method, and to provide quantitative basis for the rational allocation of low-speed engine operation and maintenance resources and risk pre-control.

[0009] The technical solution is as follows: First, collect the differentiated evaluation opinions of experts with different functions in the same field through questionnaire survey to optimize the analysis basis of traditional FMEA; then, introduce the optimal cloud entropy model (CM) to handle the fuzziness and randomness existing in the evaluation process, and obtain the basic probability assignment (BPA) of each risk indicator by solving the membership; in view of the possible conflicts in different expert opinions, calculate the expert conflict degree of a single failure mode, generate a reliability weight, and fuse the reliability weight and the objective weight to form a dynamic weight through game combination weighting; use dynamic evidence reasoning (ER) to fuse multiple expert opinions, generate a set belief degree and map it to a prior probability; then, derive the conditional probability based on the confidence rule base, construct a Bayesian network (BN), and realize the visual and quantitative sorting of the risk values of each failure mode; finally, verify the stability and robustness of the improved method by sensitivity analysis, compare the improved method with the equal weight fusion method (ignoring expert conflicts and giving the same weight to all expert evaluations) and the global dynamic weighting method (aggregating the expert conflicts of all failure modes and applying a unified weight adjustment strategy), and verify the feasibility and superiority of the method.

[0010] A low-speed engine high-pressure common rail fuel injection system risk assessment method, comprising:

[0011] Step 1: combing the failure modes of the system to be predicted and obtaining expert score values;

[0012] Step 2: calculating the fuzzy membership degree of each risk indicator using the optimal cloud entropy model, and converting it into a basic probability assignment;

[0013] Step 2.1: according to the grade score interval and the expert evaluation value, the entropy En is solved by using the optimal cloud entropy model algorithm, and the index cloud membership function is established;

[0014] Step 2.2: according to the membership function, the average certainty degree of the evaluation value is iteratively calculated as the final membership degree, and the final membership value of the evaluation value is determined; the basic probability assignment is calculated according to the final membership value;

[0015] Step 2.3: calculating the membership of each parameter and converting it into a basic probability assignment;

[0016] Step 3: generating a set of beliefs by fusing expert opinions using dynamic evidence reasoning, and mapping it into a prior probability;

[0017] Step 4: based on the confidence rule base, calculating the conditional probability, using Bayesian network to calculate the risk value of each failure mode, and realizing risk quantitative evaluation;

[0018] Step 4.1: establishing a Bayesian network according to the FMEA table;

[0019] Step 4.2: converting the prior into a probability using a linear probability function according to the set of beliefs;

[0020] Step 4.3: obtaining a confidence rule base based on a proportionally distributed confidence degree, and calculating the conditional probability;

[0021] Step 4.4: based on the prior probability and the conditional probability, carrying out rule-based aggregation to obtain the marginal probability of each node;

[0022] Step 4.5: solving the linear utility value according to the marginal probability;

[0023] Step 5: based on sensitivity analysis, verifying the robustness and stability of the proposed method; and based on multi-method comparison analysis, verifying the reliability and superiority of the proposed method.

[0024] Step 1 specifically includes:

[0025] Step 1.1, establishing an FMEA table; according to the structure and hierarchy of the marine low-speed engine high-pressure common rail fuel injection system, combining literature, maintenance manual, maintenance record, and combining field investigation and analysis of typical failure modes, effects and causes of each component, the FMEA table is determined;

[0026] The hardware FMEA of the marine low-speed engine high-pressure common rail fuel injection system is divided into initial agreement level, first agreement level, second agreement level and lowest agreement level;

[0027] The initial agreement level is a subsystem level, i.e. an electronically controlled common rail fuel injection system;

[0028] The first agreement level is an "outfield replaceable unit", i.e. a component set constituting the electronically controlled common rail system, including five modules of adjusting tooth set and adjusting tooth rod, fuel pump, common rail pipe, fuel injector and electromagnetic valve and electronic speed regulator;

[0029] The second agreement level is an "indoor replaceable unit", i.e. a functional component constituting each component set, including a pump oil system component of the electronically controlled fuel pump and a needle valve pair of the fuel injector;

[0030] The lowest agreement level is a component, including a pump oil system component such as a plunger and a return spring;

[0031] Step 1.2, dividing the risk level and risk parameter level of the failure mode and the scoring interval;

[0032] Step 1.3, obtaining expert opinions, and constructing a diversified expert evaluation group.

[0033] Step 2 specifically includes:

[0034] Step 2.1, according to the grade scoring interval and the expert evaluation value, using the optimal cloud entropy model algorithm to solve the entropy En, and establishing an index cloud membership function;

[0035] The digital characteristics and membership functions of the standard cloud C(Ex, En, He) are defined; according to the risk parameter level and the grade interval, a suitable cloud model feature conversion method is selected to calculate the digital characteristics, and the expected value Ex is the average of the sum of C min and C max

[0036]

[0037] En is solved according to the "3En" criterion *

[0038]

[0039] or using the "50% correlation degree" criterion to solve En ** ;

[0040]

[0041] The super-entropy He is set to a constant value λ,

[0042] ​Step 2.2. According to the membership function, iteratively calculate the average certainty of the evaluation value as the final membership, determine the final membership value of the evaluation value, and calculate the basic probability distribution according to the final membership value;

[0043] Assuming that there are J evaluation levels for the evaluation index, the goal of the cloud entropy optimization algorithm is to minimize the sum of the maximum deviation of the certainty of each evaluation level, as shown in formula (4). If L experts score the index, the optimal cloud entropy can be solved respectively:

[0044]

[0045] wherein, is the maximum certainty of level j calculated by the "50% correlation degree" criterion, is the minimum certainty of level j calculated by the "3En" criterion, μ(x) j is the certainty of level j corresponding to the optimized entropy;

[0046] Step 2.3: Calculate the membership of each parameter and convert it into a basic probability distribution; solve the cloud digital characteristics of each level according to formulas (1)-(3), and use the formula μ = exp(-(x-Ex) 2 / 2(En′) 2 Establish the standard cloud membership function of CM; for the parameter x i (i = 1, 2, …, n) in level j (j = 1, 2, …, J), the membership μ ij is calculated by the cloud model. n The randomness generated by E′ ij makes the μ ij value present small fluctuations, so the iteration is calculated k = 1, 2, …, K times, and a random entropy En′ ij (k) ~ N(En ij , He 2 ) is generated each time, and its average certainty is calculated as the final membership, and the calculation formula is as follows:

[0047]

[0048] In order to solve the sum of the membership of the parameters in different levels, the index level distribution uncertainty probability φ ij is introduced, and the cloud model index membership is converted into BPA conforming to the definition of evidence theory, i.e. m(x ij ),

[0049]

[0050] Calculate the membership of each parameter belonging to different levels by the expert score value, and calculate the basic probability distribution of each parameter belonging to different levels by the formula.

[0051] Step 3 specifically includes:

[0052] Step 3.1: Objective weight: when determining the objective weight of the expert, the professional position, tenure, education level can be considered to determine the initial weight;

[0053] Step 3.2: Reliability weight:

[0054] Step 3.3: Game theory combination strategy to calculate dynamic weight. Linear model is used to combine objective weight and reliability, w = a1w0 + a2r * , a1 and a2 are combination coefficients of objective weight and reliability weight, in order to consider the objective weight and reliability of the expert, a game theory combination weight model is established to solve the dynamic weight w, so that the deviation of w and the objective weight and reliability weight is minimized,

[0055]

[0056] Its solution is equivalent to solving a linear equation group:

[0057]

[0058] Where w0 = [w 01 ,w 02 ,…,w 0L ] T is the initial weight vector, is the reliability vector, μ1 = w0, μ2 = r * ,

[0059] The final dynamic weight is generated by the normalized combination coefficient:

[0060]

[0061] Step 3.4: Dynamic evidence reasoning to calculate the belief degree of the set.

[0062] Step 3.2 specifically includes:

[0063] Step 3.2.1: Expert conflict degree calculation: Let e l and e h be two members in the expert group, their BPA functions of parameter x t under fault mode FM i are m l (x ij ) and m h (x ij ), and the conflict degree TC lh is defined as:

[0064] TC lh = dlh ………(10)

[0065] where d lh is the distance between e l and e h , calculated by Jousselme distance,

[0066]

[0067] where the 1 / 2 in the formula is to normalize the distance between BPA to ensure it is between [0,1], and are the m l and m h corresponding vector representation, D is a 2 J x 2 J matrix, whose elements are determined according to the formula:

[0068]

[0069] e h and other experts is calculated by formula (28)

[0070]

[0071] Step 3.2.2: Gaussian function reliability mapping: select Gaussian function as the conversion function between non-average conflict and reliability and normalize it to r * ,

[0072]

[0073] where the parameter σ is used to adjust the tolerance of conflict, which can be calculated according to the set conflict threshold and its corresponding reliability.

[0074] Step 4 specifically includes:

[0075] Step 4.1: Establishing Bayesian network according to the FMEA table: determine the failure mode category, each failure mode category contains its internal failure mode; then, establish Bayesian network, where the failure mode is the root node, the failure mode category is the intermediate node, and the general risk is the leaf node;

[0076] Step 4.2: Use linear probability function formula to convert set BPA to prior probability BetP m (H j ) of root node O, S, D, which satisfies the single subset probability sum of 1,

[0077]

[0078] where |A| is the cardinality of the subset A,

[0079] Step 4.3: Obtain the confidence rule base according to a proportionally distributed confidence distribution, and calculate the conditional probability;

[0080] Step 4.4: Perform rule-based aggregation according to the prior probability and the conditional probability to obtain the marginal probability of each node.

[0081] After the prior probability and the CPT are determined, assuming that the set of parameters is {O, S, D}, and the number of levels is R, S, and T respectively, the probability distribution of the root node X can be calculated by equation (38),

[0082]

[0083] p(O r )(r=1,2,…R) is the prior probability of the parameter O belonging to level r, where p(S s )(s=1,2,…S) is the prior probability of the parameter S belonging to level s, where p(D t )(t=1,2,…T) is the prior probability of the parameter D belonging to level t.

[0084] The marginal overall probability p(Y j ) of the failure mode at the intermediate node is calculated by equation (39), where m is the number of leaf nodes pointing to the intermediate node,

[0085]

[0086] Step 4.5: Solve the linear utility value according to the marginal probability;

[0087] In order to prioritize the failures in the risk model, the utility value of the leaf node and the intermediate node Y j needs to be determined. Take the root node X j as an example, the calculation formula of the expected utility value CV is as follows:

[0088]

[0089] where U j is the utility value of X, and the utility value of state X j is U j =j.

[0090] Step 5 specifically includes:

[0091] Step 5.1 Sensitivity analysis, verify whether the Bayesian network satisfies the following three axioms, and verify the robustness and stability of the model:

[0092] Axiom 1: Small changes in input node prior probabilities result in corresponding changes in output node posterior probabilities.

[0093] Axiom 2: The influence of applying the same magnitude of probability change to premise attributes should be proportional to the attribute weights;

[0094] Axiom 3: Sub-nodes can have multiple parent nodes (e.g., O and D), and the influence of individual parent nodes is less than their combined effect;

[0095] Step 5.2: Comparative analysis. To verify the feasibility and superiority of the proposed model, the system compares three methods:

[0096] (1) Equal weight fusion method: ignore expert conflicts, and assign the same weight to all expert evaluations;

[0097] (2) Global dynamic weighting method: aggregate expert conflicts for all failure modes, and apply a unified weight adjustment strategy;

[0098] (3) The proposed failure mode-specific dynamic weighting method: evaluate expert conflicts for each failure mode separately, and determine the corresponding dynamic weights.

[0099] Also includes step 6: risk value visualization and sorting:

[0100] Step 6.1 visualizes the risk values output by the Bayesian network;

[0101] Step 6.2 quantitatively sorts the failure modes according to the risk values, and outputs a list of failure modes for priority processing;

[0102] Step 6.3 provides quantitative basis for maintenance and risk prevention during the operation phase of the low-speed machine based on the sorting results.

[0103] Compared with the prior art, the present application can improve the accuracy of risk assessment of the high-pressure common rail fuel injection system of the low-speed machine, provide quantitative basis for the rational allocation of low-speed machine operation and maintenance resources and risk prevention control, and has good scalability and engineering applicability. BRIEF DESCRIPTION OF DRAWINGS

[0104] Figure 1 is the overall flowchart of the present application;

[0105] Figure 2 is a structure diagram of the high-pressure common rail fuel injection system;

[0106] Figure 3 is a structure level division diagram of the high-pressure common rail fuel injection system of the low-speed machine. DETAILED DESCRIPTION

[0107] As Figure 1As shown, a low-speed engine high-pressure common rail fuel injection system risk prediction method, comprising:

[0108] Step 1: Sort out the failure modes of the system to be predicted and obtain expert score values;

[0109] Step 2: Calculate the fuzzy membership of each risk indicator using the optimal cloud entropy model (CM), and convert it into basic probability assignment (BPA);

[0110] Step 3: Generate set belief degree by fusing expert opinions using dynamic evidence reasoning (ER), and map it to prior probability;

[0111] Step 4: Based on the confidence rule base, calculate the conditional probability, use Bayesian network (BN) to calculate the risk value of each failure mode, and realize risk quantitative evaluation.

[0112] Step 5: Based on sensitivity analysis, verify the robustness and stability of the proposed method. Based on multi-method comparative analysis, verify the reliability and superiority of the proposed method.

[0113] For step 1, the determination of failure modes and the construction of Bayesian network.

[0114] Step 1.1, FMEA table. According to the structure and hierarchy of the marine low-speed engine high-pressure common rail fuel injection system, combined with literature, maintenance manual, maintenance records, and combined with field investigation and analysis of typical failure modes, effects and causes of each component, the FMEA table is determined.

[0115] The hierarchy involved in the hardware FMEA of the marine low-speed engine high-pressure common rail fuel injection system is divided into initial agreed hierarchy,

[0116] subsystem level, first agreed hierarchy, second agreed hierarchy and lowest agreed hierarchy.

[0117] The initial agreed hierarchy is the subsystem level, i.e. the electronic control common rail fuel injection system.

[0118] The first agreed hierarchy is "field replaceable unit (LRU)", i.e. the component set that constitutes the electronic control common rail system, such as the adjustment tooth set and adjustment tooth rod, fuel pump, common rail pipe, fuel injector, solenoid valve and electronic speed regulator five modules.

[0119] The second agreed hierarchy is "shop replaceable unit (SRU)", i.e. the functional components that constitute each component set, such as the pump oil system components of the electronic fuel pump, the needle valve components of the fuel injector, etc.

[0120] The lowest agreed hierarchy is the component, such as the pump oil system components, such as the plunger, return spring, etc.

[0121] Step 1.2, score level and interval division. According to GJB / Z 1391-2006, FMEA standard of quality requirement system QS9000 and the Application Guide for Failure Mode and Effects Analysis 2017 issued by China Classification Society, the risk level of failure mode, risk parameter level and score interval are divided.

[0122] Step 1.3, expert opinion acquisition. Through questionnaire survey or structured interview, invite design engineers, after-sales service engineers, university experts and sailors in different functional fields to build a diversified expert evaluation group.

[0123] Step 2: calculate the fuzzy membership degree of each risk index by using the optimal cloud entropy model (CM), and convert it into the basic probability allocation (BPA) method, which includes:

[0124] Step 2.1, according to the grade score interval and the expert evaluation value, the entropy En is solved by using the optimal cloud entropy model algorithm, and the index cloud membership function is established.

[0125] The digital characteristics and membership function of the standard cloud C(Ex, En, He) are defined. According to the risk parameter level and the grade interval, the appropriate cloud model feature conversion method is selected to calculate the digital characteristics, and the expectation Ex is the mean of the sum of C min and C max

[0126]

[0127] According to the "3En" criterion, En *

[0128]

[0129] or the "50% correlation degree" criterion to solve En ** .

[0130]

[0131] The hyper entropy He is set to a constant value λ,

[0132] Step 2.2, according to the membership function, the average certainty of the evaluation value is calculated as the final membership degree, and the final membership value of the evaluation value is determined; the basic probability allocation is calculated according to the final membership value.

[0133] ​The "3En" criterion focuses on the explicitness of the boundary value of the evaluation grade, while the "50% correlation degree" criterion is more inclined to the fuzziness of the boundary value, which may lead to conflicts in state conclusions. In order to balance the explicitness and fuzziness of the grade division, this paper uses the cloud entropy optimization algorithm to solve the entropy En. Assuming that there are J evaluation grades for the evaluation index. The goal of the cloud entropy optimization algorithm is to make the difference between the maximum deviation of the certainty degree of each evaluation grade and the minimum value as shown in equation (4). If L experts score the index, the optimal cloud entropy can be solved respectively.

[0134]

[0135] wherein, is the maximum certainty degree of grade j calculated by the "50% correlation degree" criterion, is the minimum certainty degree of grade j calculated by the "3En" criterion, μ(x) j is the certainty degree of grade j corresponding to the optimized entropy; Δμ(x) is the difference between the maximum deviation of the certainty degree of each evaluation grade and the minimum value, s.t. is the constraint condition.

[0136] Step 2.3: Calculate the membership of each parameter and convert it to the basic probability assignment. According to equations (1)-(3), the cloud digital features of each grade are solved, and the formula μ = exp(-(x-Ex) 2 / 2(En′) 2 is used to convert the cloud membership function to the standard cloud membership function of CM. For the parameter x i (i = 1, 2, …, n) in grade j (j = 1, 2, … J), the membership μ ij is calculated. Since E′ n produces randomness, the μ ij value presents a small fluctuation, so the iteration is calculated k = 1, 2, …, K times, and a random entropy En′ ij (k) ~ N(En ij , He ij 2 is generated each time. The average certainty degree is calculated as the final membership, and the calculation formula is as follows:

[0137]

[0138] In order to solve the problem that the sum of the membership of the parameters in different grades is not 1, the index grade allocation uncertainty probability φ ij is introduced. Equation 23 is used to convert the cloud model index membership to BPA that meets the definition of evidence theory, i.e. m(x ij ).

[0139]

[0140] ​The membership degree of each parameter to different levels is calculated based on the expert score, and the basic probability allocation of each parameter to different levels is calculated using a formula.

[0141] Step 3: Dynamic Evidence Reasoning

[0142] In evidential reasoning, the appropriate allocation of expert weights has a decisive impact on the outcome of evidence fusion. Due to differences in experts' knowledge backgrounds, their evaluation opinions often exhibit varying degrees of conflict.

[0143] Step 3.1: Objective Weighting. When determining the objective weights of experts, their professional titles, tenure, and education levels can be comprehensively considered to determine their initial weights.

[0144] Step 3.2: Reliability Weights. The expert reliability weights are calculated based on the "consensus reliability" principle (i.e., experts with higher consensus with the majority of experts have higher reliability). This is modeled after (Liu, Z., Zhao, Y., and Liu, P. (2023), "A Comprehensive FMEA Framework Considering Expert Reliability and Its Application in Aircraft Power Systems," *Artificial Intelligence Engineering Applications*, 123106319, https: / / doi.org / 10.1016 / j.engappai.2023.106319) regarding the transformation of expert conflict into reliability, with improvements. Specifically, considering the differences in experts' understanding of the failure modes of various system components, the average conflict among experts is calculated for each failure mode, rather than calculating the expert conflict for all failure modes.

[0145] Step 3.2.1: Calculation of Expert Conflict Level. Assume L experts perform the evaluation process; the expert set can be defined as E = {e1, e2, ..., e...} l ,…,e L The expert weight set is represented by w = {w1, w2, ..., w}. L The set of evaluation levels is H = {H1, H2, ..., H}. j ,…,H J}. e l and e h They are two members of the expert group, specializing in Failure Mode and Effects (FM). t The lower parameter x i The BPA functions are m l (x ij ) and m h (x ij ), its level of conflict TC lh Defined as:

[0146] TC lh =d lh ………(25)

[0147] Where, dlh is e l and e h The distance between e

[0148]

[0149] where the 1 / 2 in the formula is to normalize the distance between BPA to ensure it is between [0, 1], and are the m l and m h corresponding vector representation, D is a 2 J x 2 J matrix, and T is the transpose of the vector, the elements of which are determined according to the formula:

[0150]

[0151] e h The average conflict of e

[0152]

[0153] Step 3.2.2: Gaussian function reliability mapping. The average conflict CD h,t of the expert group opinion is an important indicator of its reliability: the larger the CD h,t , the more serious the disagreement between experts, the lower the consensus degree, and the less reliable the group's judgment of the current problem. In addition, when the average conflict CD h,t tends to 0 (the expert opinions are highly consistent), the reliability r smoothly tends to the maximum value 1 (highly reliable); when the conflict CD h,t increases, the reliability r continuously and smoothly decreases, and the decline is steep in the high conflict area. Therefore, the Gaussian function is selected as the conversion function between the average conflict and reliability and is normalized to r * , as shown in formula (29).

[0154]

[0155] where the parameter σ is used to adjust the tolerance of the conflict, which can be calculated according to the set conflict threshold and its corresponding reliability.

[0156] Step 3.3: Game theory combined strategy calculation of dynamic weight. A linear model is used to combine the objective weight and reliability, w = a1w0 + a2r * , a1 and a2 are the combination coefficients of the objective weight and the reliability weight, and a game theory combined weight model is established to take into account the objective weight and the reliability of the experts. The dynamic weight w is solved so that the deviation of w from the objective weight and the reliability weight is minimized.

[0157]

[0158] Its solution is equivalent to solving a linear equation system:

[0159]

[0160] where w0= [w 01 ,w 02 ,…,w 0L ] T is the initial weight vector, is the reliability vector, μ1= w0, μ2= r * .

[0161] The final dynamic weights are generated by the normalized combination coefficients:

[0162]

[0163] Step 3.4: Calculate the belief degree of the set of evidence. The evidence reasoning (equations (15)-(18)) is used to fuse different expert opinions to determine the set belief degree of each failure mode parameter.

[0164] Step 3.4.1: Weighted evidence synthesis. The evaluation of the expert e l is weighted to obtain the weighted basic probability assignment m j,l , and the unassigned probability m H,l is calculated.

[0165] m j,l = w l * β j,l … (33)

[0166]

[0167] where m j,l is the weighted basic probability assignment of the expert e l to the parameter evaluation level H j . m H,l represents the basic probability assigned by the expert e l to the parameter not assigned to any level. represents the remaining probability function not assigned due to weights; represents the probability function not assigned due to ignorance, which is caused by incomplete evaluation.

[0168] Step 3.4.2: Recursively synthesize the opinions of L experts using the Dempster combination rule to obtain the set belief degree.

[0169] m j,I(l+1) = K I(l+1)(m j,I(l) m j,I(l+1) +m j,I(l) m H,(l+1) +m H,l(l) m j,(l+1) )………(35)

[0170]

[0171] where K I(l+1) is the normalization coefficient, m j,I(l+1) is the basic probability assignment fused with the evaluation made by the l+1th expert according to the relevant parameters.

[0172] Step 4: Quantify the risk values of each failure mode using the Bayesian network, which specifically includes:

[0173] Step 4.1: Establish the Bayesian network according to the FMEA table. Determine the failure mode categories, each of which contains its internal failure modes. Then, establish the Bayesian network, where the failure modes are the root nodes, the failure mode categories are the intermediate nodes, and the general risks are the leaf nodes.

[0174] Step 4.2: Convert the prior probability into probability using the linear probability function (based on Dempster-Shafer evidence theory and grey relational projection method, a new failure mode and effects analysis model, Engineering Applications of Artificial Intelligence, 76, 13-20, https: / / doi.org / 10.1016 / j.engappai.2018.08.010) according to the set belief degree.

[0175] Convert the set BPA into the prior probability BetP m (H j ) of the root nodes O, S, and D using the linear probability function (37) …… (37), which satisfies the single subset probability sum of 1.

[0176]

[0177] where |A| is the cardinality (number of elements) of the subset A,

[0178] Step 4.3: Obtain the confidence rule base based on the proportional allocation of the belief degree distribution and calculate the conditional probability.

[0179] Confidence rule base obtains conditional probability: Considering that the accumulated knowledge of failures in the low-speed field is less, we borrow the calculation of a belief degree distribution based on proportional allocation proposed by (Z. Yang, Bayesian reasoning method based on fuzzy rules for priority ranking of failures in FMEA, IEEE Transactions on Reliability, 2008) and others.

[0180] Step 4.4: Rule-based aggregation based on the prior probability and conditional probability to obtain the marginal probability of each node.

[0181] After the prior probability and CPT are determined, assuming the set of parameters is {O, S, D}, and the number of levels is R, S, T respectively, the probability distribution of the root node X can be calculated by equation (38).

[0182]

[0183] p(O r )(r = 1, 2, … R) is the prior probability of parameter O belonging to level r, where p(S s )(s = 1, 2, … S) is the prior probability of parameter S belonging to level s, where p(D t )(t = 1, 2, … T) is the prior probability of parameter D belonging to level t.

[0184] The marginal population probability of the failure mode at the intermediate node p(Y j ) is calculated by equation (39), where m is the number of leaf nodes pointing to the intermediate node.

[0185]

[0186] Step 4.5: Solve the linear utility value according to the marginal probability.

[0187] In order to prioritize the failures in the risk model, the utility value of the leaf node and the intermediate node Y j needs to be determined. Take the root node X j as an example, the calculation formula of the expected utility value CV is as follows:

[0188]

[0189] Where, U j is the utility value determined by X, and the utility value of state X j is U j = j.

[0190] Step 5: Sensitivity analysis and comparative analysis method, specifically including:

[0191] Step 5.1 Sensitivity analysis, verify whether the Bayesian network satisfies the following three axioms, verify the robustness and stability of the model:

[0192] Axiom 1: Small changes in the prior probability of the input node will cause corresponding changes in the posterior probability of the output node.

[0193] Axiom 2: The influence of the same magnitude of probability change on a premise attribute should be proportional to the attribute weight.

[0194] Axiom 3: A child node can have multiple parent nodes (e.g., O and D), and the influence of an individual parent node is less than the combined effect.

[0195] Step 5.2: Comparative analysis. To verify the feasibility and superiority of the proposed model, the system compares three methods:

[0196] (1) Equal weight fusion method: ignore expert conflicts, and assign the same weight to all expert evaluations;

[0197] (2) Global dynamic weighting method: aggregate expert conflicts for all failure modes and apply a unified weight adjustment strategy;

[0198] (3) Proposed failure mode-specific dynamic weighting method: evaluate expert conflicts for each failure mode separately and determine the corresponding dynamic weights.

[0199] Step 6: Risk value visualization and sorting

[0200] Step 6.1 Visualize the risk values output by the Bayesian network;

[0201] Step 6.2 Quantitatively sort the failure modes according to the risk values and output a list of failure modes for priority handling;

[0202] Step 6.3 Provide quantitative basis for maintenance and risk prevention during the low-speed machine operation phase based on the sorting results.

Claims

1. A risk assessment method for a low-speed engine high-pressure common rail fuel injection system, characterized in that: include: Step 1: Identify the failure modes of the system to be predicted and obtain expert scores; Step 2: Calculate the fuzzy membership degree of each risk indicator using the optimal cloud entropy model and convert it into a basic probability assignment; Step 2.1: Based on the grade scoring range and the expert evaluation value, use the optimal cloud entropy model algorithm to solve for the entropy En and establish the indicator cloud membership function; Step 2.2: Based on the membership function, iteratively calculate the average degree of certainty of the evaluation value as the final membership degree, and determine the final membership degree value of the evaluation value; calculate the basic probability assignment based on the final membership degree value. Step 2.3: Calculate the membership of each parameter and convert it into a basic probability assignment; Step 3: Use dynamic evidence reasoning to fuse expert opinions to generate a set of belief degrees and map them to prior probabilities; Step 4: Based on the confidence rule base, calculate the conditional probability, and use a Bayesian network to calculate the risk value of each failure mode to achieve quantitative risk assessment; Step 4.1: Construct a Bayesian network based on the FMEA table; Step 4.2: Based on the set of beliefs, transform the prior knowledge into probability using a linear probability function; Step 4.3: Obtain a confidence rule base based on a confidence distribution based on proportional allocation, and calculate the conditional probability; Step 4.4: Perform rule-based aggregation based on the prior probabilities and conditional probabilities to obtain the marginal probabilities of each node; Step 4.5: Solve for the linear utility value based on the marginal probabilities; Step 5: Based on sensitivity analysis, verify the robustness and stability of the proposed method; The reliability and superiority of the proposed method are verified through multi-method comparative analysis.

2. The risk assessment method for low-speed engine high-pressure common rail fuel injection system according to claim 1, characterized in that: Step 1 specifically includes: Step 1.1: Establish the FMEA table; Based on the structural composition and hierarchical division of the marine low-speed engine high-pressure common rail fuel injection system, combined with literature, maintenance manuals, maintenance records, and on-site investigation and analysis of the typical failure modes, effects and causes of each component, determine the FMEA table. The hardware FMEA of the marine low-speed engine high-pressure common rail fuel injection system is divided into the initial agreement level, the first agreement level, the second agreement level, and the lowest agreement level. The initial agreement level is the subsystem level, namely the electronically controlled common rail fuel injection system; The first agreed level is "field replaceable unit", which is the component that constitutes the electronically controlled common rail system, including five major modules: adjusting sleeve and adjusting rack, fuel pump, common rail pipe, injector, solenoid valve and electronic governor; The second agreed level is "internal replaceable unit", which is the functional component that constitutes each part, including the pump system component of the electronic fuel pump and the needle valve assembly of the injector; The lowest agreed level is components, including components of the oil pump system, such as plungers and return springs; Step 1.2: Classify the risk level, risk parameter level, and scoring range of the failure mode; Step 1.3: Obtain expert opinions and build a diversified expert evaluation group.

3. The risk assessment method for low-speed engine high-pressure common rail fuel injection system according to claim 1, characterized in that: Step 2 specifically includes: Step 2.1: Based on the grade scoring range and the expert evaluation value, use the optimal cloud entropy model algorithm to solve for the entropy En and establish the indicator cloud membership function; Define the numerical features and membership functions of the standard cloud C(Ex,En,He); select an appropriate cloud model feature transformation method based on the risk parameter level and level range, calculate the numerical features, and expect Ex to be a subset of C. min and C max The mean of the sums, i.e. Solve for En according to the "3En" criterion. * Alternatively, the "50% correlation" criterion can be used to solve for En. ** ; The hyperentropy He is set to a constant λ. Step 2.2: Based on the membership function, iteratively calculate the average degree of certainty of the evaluation value as the final membership degree, and determine the final membership degree value of the evaluation value; calculate the basic probability assignment based on the final membership degree value. Assuming there are J evaluation levels for the evaluation indicators, the goal of the cloud entropy optimization algorithm is to minimize the sum of the differences in the maximum certainty deviations under each evaluation level, as shown in equation (4). If L experts score the indicators, the optimal cloud entropy can be calculated separately: in, This refers to the maximum certainty of level j calculated using the "50% correlation" criterion. This refers to the minimum degree of determination of rank j, μ(x), calculated using the "3En" criterion. j This refers to the degree of certainty of the level j corresponding to the optimized entropy; Step 2.3: Calculate the membership of each parameter and convert it into a basic probability assignment; solve for the cloud digital characteristics of each level according to equations (1)-(3), and use the formula μ=exp(-(x-ex)) 2 / 2(En′) 2 Establish the standard cloud membership function for CM; for parameter x i The membership degree μ of (i = 1, 2, ..., n) at level j (j = 1, 2, ..., J) ij Because of E′ n The resulting randomness makes μ ij The value exhibits relatively small fluctuations, therefore the iteration is performed k = 1, 2, ..., K times, generating a random entropy En′ each time. ij (k)~N(En ij He ij 2 The average degree of certainty is calculated as the final membership degree, and the calculation formula is as follows: To address the issue that the sum of membership degrees of parameters at different levels is not equal to 1, an uncertainty probability φ for index level assignment is introduced. ij Equation 5 transforms the membership degree of the cloud model index into a BPA that conforms to the definition of evidence theory, i.e., m(x ij ), The membership degree of each parameter to different levels is calculated based on the expert score, and the basic probability allocation of each parameter to different levels is calculated using a formula.

4. The risk assessment method for low-speed engine high-pressure common rail fuel injection system according to claim 1, characterized in that: Step 3 specifically includes: Step 3.1: Objective weights: When determining the objective weights of experts, their professional positions, tenure, and education levels can be comprehensively considered to determine their initial weights; Step 3.2: Reliability Weights: Step 3.3: Calculate dynamic weights using game theory combined strategies: A linear model is used, combining objective weights and reliability, w = α1w0 + α2r * α1 and α2 are the combined coefficients of objective weight and reliability weight. To balance the objective and reliability weights of experts, a game-theoretic combined weight model is established to solve for the dynamic weight w, which minimizes the deviation of w from the objective and reliability weights of experts. Its solution is equivalent to solving a system of linear equations: Where w0 = [w 01 ,w 02 ,…,w 0L ] T The initial weight vector, Let μ1 = w0 and μ2 = r be the reliability vectors. * , The final dynamic weights are generated from the normalized combination coefficients: Step 3.4: Calculate the belief degree of the dynamic evidence reasoning set.

5. The risk assessment method for low-speed engine high-pressure common rail fuel injection system according to claim 4, characterized in that: Step 3.2 specifically involves: Step 3.2.1: Calculation of the degree of expert conflict: Let e l and e h They are two members of the expert group, specializing in Failure Mode and Effects (FM). t The lower parameter x i The BPA functions are m l (x ij ) and m h (x ij ), its level of conflict TC lh Defined as: TC lh =d lh ………(10) Where, d lh It is e l and e h The distance between them is calculated using the Jousselme distance. The 1 / 2 in the formula normalizes the distance between BPA to ensure it lies within the range [0,1]. and They are m l and m h The corresponding vector representation, D, is a 2 K ×2 K The elements of the matrix are determined according to the formula: e h The average conflict with other experts is calculated by equation (13). Step 3.2.2: Gaussian Function Reliability Mapping: Select a Gaussian function as the transformation function between non-uniform conflict and reliability, and normalize it to r. * As shown in equation (14)…………(14), The parameter σ is used to adjust the tolerance for conflict, and can be calculated based on the set conflict threshold and its corresponding reliability.

6. The risk assessment method for low-speed engine high-pressure common rail fuel injection system according to claim 4, characterized in that: Step 3.4 specifically involves: Step 3.4.1: Weighted Evidence Synthesis: For expert e l The evaluation is weighted to obtain the weighted basic probability assignment m. j,l And calculate the unassigned probability m H,l , m j,l =w l *b j,l ……(15) Where m j,l Is it an expert e l The parameter evaluation level is H. j The weighted basic probability assignment; m H,l Expert e l Assign values ​​to the base probability parameters that are not assigned to any level; This represents the remaining probability function for those not assigned due to weighting; The probability function representing the failure to assign due to ignorance is caused by incomplete evaluation; Step 3.4.2: Recursively synthesize the opinions of L experts using the Dempster combination rule to obtain the set's belief degree; m j,I(l+1) =K I(l+1) (m j,I(l) m j,I(l+1) +m j,I(l) m H,(l+1) +m H,I(l) m j,(l+1) )………(17) Among them, K I(l+1) Represents the normalization coefficient, m j,I(l+1) This is a basic probability assignment that incorporates the evaluation made by the (l+1)th expert based on relevant parameters.

7. The risk assessment method for low-speed engine high-pressure common rail fuel injection system according to claim 1, characterized in that: Step 4 specifically includes: Step 4.1: Establish a Bayesian network based on the FMEA table: determine the failure mode categories, each failure mode category contains its internal failure modes; then, establish a Bayesian network, where failure modes are the root nodes, failure mode categories are the intermediate nodes, and general risks are the leaf nodes. Step 4.2: Transform the set BPA into the prior probabilities BetP of the root nodes O, S, and D using the linear probability function (19). m (H j ), satisfying the condition that the sum of the probabilities of a single subset is 1. Where |A| is the cardinality (number of elements) of subset A. Step 4.3: Obtain a confidence rule base based on a confidence distribution based on proportional allocation, and calculate the conditional probability; Step 4.4: Perform rule-based aggregation based on the prior probabilities and conditional probabilities to obtain the marginal probabilities of each node; After the prior probabilities and CPT are determined, assuming the set of parameters is {O,S,D} and the number of levels is R, S, and T respectively, the probability distribution of the root node X can be calculated using equation (20). p(O r (r=1,2,…R) is the prior probability that parameter O belongs to class r, where p(S s (s=1,2,…S) is the prior probability that parameter S belongs to class s, where p(D) t (t=1,2,…T) is the prior probability that parameter D belongs to rank t; The marginal overall probability p(Y) of the failure mode at the intermediate node j ) is calculated by equation (21), where m is the number of leaf nodes pointing to the intermediate node. Step 4.5: Solve for the linear utility value based on the marginal probabilities; To prioritize faults in the risk model, the leaf nodes and intermediate nodes Y need to be determined. j The utility value, with root node X j For example, the formula for calculating its expected utility value (CV) is as follows: Among them, U j The utility value determined for X, state X j The utility value is U j =j.

8. The risk assessment method for low-speed engine high-pressure common rail fuel injection system according to claim 1, characterized in that: Step 5 specifically includes: Step 5.1 Sensitivity analysis verifies whether the Bayesian network satisfies the following three axioms, thus verifying the robustness and stability of the model: Axiom 1: A small change in the prior probability of an input node will result in a corresponding change in the posterior probability of an output node; Axiom 2: When the probability of a given attribute is changed by the same magnitude, its effect on the result should be proportional to the attribute weight. Axiom 3: A child node may have multiple parent nodes (such as O and D), and the influence of a single parent node is less than its combined effect; Step 5.2: Comparative Analysis: To verify the feasibility and superiority of the proposed model, three methods were systematically compared: (1) Equal weighting method: Ignore expert conflicts and assign equal weight to all expert evaluations; (2) Global dynamic weighting method: aggregate expert conflicts of all failure modes and apply a unified weight adjustment strategy; (3) The proposed dynamic weighted method for fault modes: evaluate expert conflict separately for each fault mode and determine the corresponding dynamic weight.

9. The risk assessment method for low-speed engine high-pressure common rail fuel injection system according to claim 1, characterized in that: It also includes step 6: Risk value visualization and sorting: Step 6.1 Visualize the risk values ​​output by the Bayesian network; Step 6.2 Quantify and sort the failure modes according to their risk values, and output a list of failure modes that should be prioritized for handling; Step 6.3 Based on the sorting results, provide quantitative basis for maintenance and risk prevention during the low-speed machine operation phase.

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