Equipment failure risk analysis method based on probability hesitant fuzzy evidence theory

Abstract

The invention discloses an equipment failure risk analysis method based on a probability hesitant fuzzy evidence theory, and relates to the field of failure risk analysis, and the method comprises the steps: S1, building a fault tree structure, and constructing a reference failure rate set of basic events in a fault tree; s2, acquiring evaluation data of an expert on a reference failure rate set of the basic event, and obtaining an adjustment score and a tendency degree of the basic event; s3, converting the adjustment score into an evaluation probability by using a score conversion rule; s4, establishing a qualification weight according to the qualification of the expert; quantizing and adjusting the uncertainty of the score and the tendency degree to obtain an evaluation uncertainty weight, and carrying out weighted summation on the two weights to synthesize a total weight; s5, based on the evaluation probability and the total weight, synthesizing a final evaluation probability through a Dempster-Shafer evidence theory; and S6, performing fault tree analysis based on the final evaluation probability. According to the method, the probability hesitant fuzzy set and the Dempster-Shafer evidence theory are introduced, the diversity and uncertainty of expert evaluation are reserved, and conflicts and consistency between evidences are effectively processed.

Description

TECHNICAL FIELD

[0001] The present application relates to failure risk analysis, in particular to a device failure risk analysis method based on probability hesitant fuzzy evidence theory. BACKGROUND

[0002] Failure risk analysis of complex industrial systems is the core of safety management, which converts the fuzzy hidden risk into a measurable quantitative index through scientific methods, identifies the weak links of the system, provides the basis for safety decision-making, and realizes the transition from "passive response" to "active prevention" to improve system reliability.

[0003] Fault tree analysis (FTA) as a classic core structured deductive method in the field of failure risk analysis lays a logical foundation for risk quantification and decision support, and provides a standardized framework for failure cause tracing. In engineering practice, fault probability acquisition faces the difficulties of data scarcity, boundary fuzziness and small sample bias, and FTA is limited because it relies on accurate probability input. Since fuzzy technology has the advantage of handling fuzzy and inaccurate information, FTA and fuzzy mathematical theory are combined to form fuzzy fault tree analysis (FFTA), which uses fuzzy numbers to describe the occurrence probability of events, reducing the difficulty of obtaining accurate values of fault occurrence probability, and has certain adaptability.

[0004] Under the framework of FFTA, expert evaluation is an important means to obtain the fuzzy probability of basic events, which provides key input in data-scarce scenarios, but introduces subjective uncertainty due to differences in expert knowledge background and subjective cognition. This uncertainty will lead to bias in the evaluation of basic event probability, and further affect the accuracy of the evaluation of top event probability. At the same time, FFTA relies on triangular / trapezoidal fuzzy numbers to describe event probability, which cannot well describe the multi-peak distribution characteristics of expert opinions, ignores the distribution characteristics and weight differences of probability values, and often forces the assumption of symmetry, which is easy to cause the truncation of the high-risk tail. FFTA lacks conflict detection mechanism in practice, cannot handle differences in expert opinions, and smoothes conflicting opinions, which leads to dilution of key evaluation and reduces the reliability of FFTA in risk quantification. SUMMARY

[0005] To solve the above problems, the present application provides a device failure risk analysis method based on probability hesitant fuzzy evidence theory, constructs a probability hesitant fuzzy set of expert opinions, aggregates the probability hesitant fuzzy set form of expert opinions through Dempster-Shafer evidence theory, and weights and sums the qualification weight and evaluation uncertainty weight to synthesize the total weight for generating the final evaluation probability, which retains the diversity and uncertainty of expert evaluation, can handle differences in expert opinions, and solves the problem that existing solutions often ignore the influence of low-quality evaluation of high-weight experts by taking expert qualifications as the total allocation weight.

[0006] The device failure risk analysis method based on the probabilistic hesitant fuzzy evidence theory comprises the following steps:

[0007] S1, a fault tree structure of the device is built, and a reference failure rate set of basic events in the fault tree is constructed;

[0008] S2, a probabilistic hesitant fuzzy set of expert evaluation data of the reference failure rate set is obtained; the membership degree of the probabilistic hesitant fuzzy set is an adjustment score of the basic event obtained by the expert evaluation on the reference failure rate set of the basic event; and the probability weight of the probabilistic hesitant fuzzy set is a tendency degree corresponding to the adjustment score;

[0009] S3, the adjustment score is converted into an evaluation probability by using a score conversion rule;

[0010] S4, a qualification weight is constructed according to the qualification of the expert; the uncertainty of the adjustment score and the tendency degree is quantified to obtain an evaluation uncertainty weight; and the qualification weight and the evaluation uncertainty weight are weighted and summed to synthesize a total weight;

[0011] S5, based on the evaluation probability and the total weight, a final evaluation probability of the basic event is synthesized by using the Dempster-Shafer evidence theory;

[0012] S6, based on the final evaluation probability of the basic event, a fault tree analysis is performed to obtain a failure rate of a top event in the fault tree and an importance degree of the basic event, and the device failure risk analysis is completed.

[0013] Preferably, the reference event comprises a basic event with a reference event and a basic event without a reference event; and the score conversion rule is specifically as follows:

[0014] For the basic event without the reference event, a reference probability is obtained by using a weighted average as a value in the reference failure rate set; and the reference probability is represented as:

[0015]

[0016] wherein, the reference probability of the basic event without the reference event; v related,b the evaluation probability of the bth similar basic event selected by the expert; p related,b the corresponding tendency degree of v related,b ; and h represents the number of evaluations.

[0017] The evaluation probability is calculated by using the score conversion rule; and the evaluation probability is represented as:

[0018]

[0019] wherein, v arepresents the evaluation probability of the a-th adjustment score after conversion; c represents an interval parameter, and the value interval is [0, 1]; score a represents the a-th adjustment score; P ref represents the reference probability, for the basic event without reference event, f(score a ) represents a conversion function.

[0020] Preferably, the adjustment score is a plurality of scores or score intervals between 10 and -10, which are independent of each other; when the score is positive, it means that the reference failure rate is increased; when the score is 0, it means that no adjustment is needed; when the score is negative, it means that the reference failure rate is reduced; the conversion function satisfies: f(0)=0, f(5)=1, f(-5)=-0.5, f(-10)=-1, and the conversion function is strictly monotonically increasing in the independent variable interval.

[0021] Preferably, the analytic hierarchy process (AHP) is used to calculate the qualification weight of the expert; the qualification includes field relevance, education, title and length of service.

[0022] Preferably, the qualification weight and the evaluation uncertainty weight are weighted and summed to synthesize the total weight, which is represented as:

[0023] w total =α·w q +β·w u

[0024] β=1-α

[0025] wherein, w total represents the total weight; w q represents the qualification weight; w u represents the evaluation uncertainty weight; q i represents the qualification weight of the i-th expert; q j represents the qualification weight of the j-th expert; α represents the qualification weight distribution ratio; β represents the evaluation uncertainty weight distribution ratio; n represents the number of experts; t represents a strict index for controlling the change sensitivity of the qualification difference, t∈[0, 1].

[0026] Preferably, the uncertainty of the quantitative adjustment score and the degree of inclination is quantified to obtain the evaluation uncertainty weight, which is as follows:

[0027] The dispersion degree of the adjustment score of the expert for the same basic event is calculated to obtain the dispersion evaluation;

[0028] The Shannon entropy of the inclination degree distribution of the expert is calculated and normalized to obtain the hesitation evaluation;

[0029] The discrete evaluation and the hesitant evaluation are combined into a total uncertainty entropy, denoted as:

[0030] E total = E d + E h - E d · E h

[0031] wherein E total denotes the total uncertainty entropy; E d denotes the discrete evaluation; E h denotes the hesitant evaluation;

[0032] An evaluation uncertainty weight is calculated according to the total uncertainty entropy, denoted as:

[0033]

[0034] w u = [u1, u2, … u i , … u n ]

[0035] wherein w u denotes the evaluation uncertainty weight, i.e. a vector composed of all u i ; u i denotes the evaluation uncertainty weight of the ith expert; E total,i denotes the total uncertainty entropy of the ith expert; E total,k denotes the total uncertainty entropy of the kth expert; and n denotes the number of experts.

[0036] Preferably, the discrete degree of the adjustment score of the experts to the same basic event is calculated to obtain the discrete evaluation, specifically as follows:

[0037] The weighted distance D between the evaluation probabilities of the same basic event is calculated with the tendency degree as the weight.

[0038] The maximum value of the weighted distance when the data is uniformly distributed at both ends is calculated, denoted as:

[0039]

[0040] wherein D max denotes the maximum value of the weighted distance; range(v) denotes the range of the probability set, and v denotes the evaluation probability.

[0041] A relative scale factor is calculated, denoted as:

[0042]

[0043] wherein σ denotes the relative scale factor; P refa reference failure rate representing a basic event; s represents a sensitivity factor not less than 0, controlling the influence degree of relative scale in the discreteness evaluation;

[0044] a discreteness evaluation obtained by normalizing the weighted distance based on the relative scale factor; represented as:

[0045]

[0046] wherein, E d represents the discreteness evaluation.

[0047] Preferably, the final evaluation probability is synthesized by Dempster-Shafer evidence theory based on the evaluation probability and the total weight, specifically as follows:

[0048] The evaluation probability of each expert is extended with an allowable degree, and the extended interval after the interval extension is used to construct the recognition framework of each basic event;

[0049] The basic assignment probability (BPA) value of the extended interval in the recognition framework is calculated; represented as:

[0050]

[0051] wherein, m k (I l ) represents the BPA value of the kth expert to the lth extended interval I l ; p k,d represents the v d th tendency value of the kth expert, v d represents the dth adjustment value in the same recognition framework; p k,p represents the pth tendency value of the kth expert; N k represents the total number of tendency values of the kth expert;

[0052] The discounted BPA value is obtained by evidence discounting processing according to the total weight; represented as:

[0053] m′ k (I l ) = w total,k ·m k (I l )

[0054] wherein, m′ k (I l ) represents the discounted BPA value of the kth expert to the lth extended interval; w total,k represents the total weight of the kth expert;

[0055] The discounted BPA values of the experts are fused by using the Dempster combination rule to obtain the final probability of the basic event.

[0056] Preferably, the interval expansion with allowance is performed on the evaluation probability to obtain an evaluation probability interval with allowance, and the interval expansion with allowance is specifically as follows:

[0057] All the evaluation probabilities are sorted in ascending order;

[0058] The smallest evaluation probability after sorting is expanded and expressed as:

[0059] I = [(1-ε)v1, (1+ε)v1]

[0060] wherein I represents an initial generated expansion interval; ε represents the allowance; and v1 represents the smallest evaluation probability;

[0061] Interval overlap judgment is performed, and v1 is used as an interval center value v c If a subsequent evaluation probability v2 is not included in the interval I, the interval expansion is performed on v2 to obtain an independent expansion interval; and if v2 is included in the interval I, the expansion interval is merged, and expressed as:

[0062] I' = [(1-ε)v1, (1+ε)v2]

[0063] wherein I' represents the merged expansion interval;

[0064] The center value of the merged expansion interval is updated, and expressed as:

[0065]

[0066] wherein v c ' represents the center value of the merged expansion interval;

[0067] The interval overlap judgment is performed on the subsequent evaluation probability until the interval expansion of all the evaluation probabilities is completed.

[0068] Preferably, the discount BPA value of the expert is fused by using the Dempster combination rule to obtain the final probability of the basic event, and the fusion is specifically as follows:

[0069] The joint support degree of the same proposition in the recognition framework is calculated based on the Dempster combination rule, and the conflict coefficient is used as a normalization factor to process the conflict between evidences;

[0070] When the conflict coefficient is less than a preset conflict coefficient threshold, it is a low conflict situation, and the final probability of the basic event is a center value corresponding to an expansion interval with the highest joint support degree;

[0071] ​When the conflict coefficient reaches or exceeds the preset conflict coefficient threshold value, the high conflict situation is used, the center value of all extension intervals in the identification framework is weighted with the corresponding discount BPA using the weighted average processing, and the final probability of the basic event is represented as:

[0072]

[0073] wherein, represents the final probability of the basic event; n represents the number of experts; z represents the number of extension intervals; v c,l represents the center value of the lth extension interval.

[0074] Compared with the prior art, the present application has the following beneficial effects:

[0075] (1) The probability hesitant fuzzy set applied to the decision-making method is adaptively modified and the characteristics of expert evaluation opinions are introduced, the diversity and uncertainty of expert evaluation are retained, the information loss caused by forced simplification due to opinion disagreement is avoided, and a data basis is provided for subsequent uncertainty quantification;

[0076] (2) The present application constructs a multi-source expert evidence fusion framework driven by DS evidence theory, aggregates the expert opinions in the form of probability hesitant fuzzy set through Dempster synthesis rule, formulates evidence conflict fusion strategy, can process expert opinion disagreement, forms an integrated fusion mechanism of "opinion expression-weight distribution-conflict resolution", and significantly improves the robustness and reliability of the fusion result;

[0077] (3) The present application establishes a double-weight evaluation system of expert qualification and evaluation uncertainty, describes the objective condition difference with the expert qualification weight, describes the subjective evaluation quality with the evaluation uncertainty weight, perfects the weight distribution scheme, provides an interpretable decision for the conflict situation, and solves the problem that the existing scheme often takes the expert qualification as the total distribution weight and ignores the influence of low-quality evaluation of high-weight experts;

[0078] (4) The present application establishes a complete and perfect failure risk analysis system, constructs a whole-chain technical framework of "data collection-weight calibration-evidence fusion-risk quantification", realizes the precise quantification and decision support of failure risk through the synergistic innovation of double-weight evaluation and PHFS-DS, and makes the fault tree analysis still have reliability in the scene of lacking data. BRIEF DESCRIPTION OF DRAWINGS

[0079] The present application will be further described in detail below with reference to the accompanying drawings;

[0080] Figure 1 The flowchart of the equipment failure risk analysis method based on the probability hesitant fuzzy evidence theory of the embodiment of the present application;

[0081] Figure 2An implementation flowchart of the device failure risk analysis method based on the probabilistic hesitant fuzzy evidence theory of the embodiments of the present application is shown in the figure.

[0082] Figure 3 A multi-source evidence fusion strategy diagram of the device failure risk analysis method based on the probabilistic hesitant fuzzy evidence theory of the embodiments of the present application is shown in the figure.

[0083] Figure 4 A basic event identification framework diagram of the device failure risk analysis method based on the probabilistic hesitant fuzzy evidence theory of the embodiments of the present application is shown in the figure.

[0084] Figure 5 A probabilistic hesitant fuzzy evidence theory processing main program of the device failure risk analysis method based on the probabilistic hesitant fuzzy evidence theory of the embodiments of the present application is shown in the figure.

[0085] Figure 6 A fault tree analysis main program of the device failure risk analysis method based on the probabilistic hesitant fuzzy evidence theory of the embodiments of the present application is shown in the figure.

[0086] Figure 7 A fault tree structure diagram of the offshore wind turbine variable pitch system of the device failure risk analysis method based on the probabilistic hesitant fuzzy evidence theory of the embodiments of the present application is shown in the figure.

[0087] Figure 8 A probabilistic importance consistency analysis diagram of the device failure risk analysis method based on the probabilistic hesitant fuzzy evidence theory of the embodiments of the present application is shown in the figure.

[0088] Figure 9 An offshore wind turbine variable pitch system reliability curve diagram of the device failure risk analysis method based on the probabilistic hesitant fuzzy evidence theory of the embodiments of the present application is shown in the figure. DETAILED DESCRIPTION

[0089] The present application is further described below through specific embodiments.

[0090] As shown in the figures, Figure 1 and Figure 2 the device failure risk analysis method based on the probabilistic hesitant fuzzy evidence theory has the following specific steps:

[0091] S1, a fault tree structure of a device is built, and a reference failure rate set of basic events in the fault tree is constructed.

[0092] S11, the functional structure of the device is analyzed, and human factors, environmental factors, etc. are combined to construct a fault tree according to the failure mechanism and event relationship;

[0093] S12, find relevant literature and historical data or apply stress analysis method, counting method and other reliability prediction methods to establish a reference failure rate set of basic events. For events lacking reference failure rate, leave empty for expert evaluation.

[0094] S2, obtain a probability hesitant fuzzy set of expert evaluation data of the reference failure rate set; a membership degree of the probability hesitant fuzzy set is an adjusted score of the basic event obtained by the expert evaluating the reference failure rate set of the basic event; and a probability weight of the probability hesitant fuzzy set is a tendency degree corresponding to the adjusted score.

[0095] S21, invite multiple experts to evaluate failure rates of basic events in the current application environment according to knowledge and experience, score adjustment degrees of the reference failure rates, and assign corresponding tendency degrees.

[0096] S22, for events lacking reference failure rates, the experts select events similar in probability or failure mechanism as references for evaluation.

[0097] The evaluation content of the expert for each basic event includes a reference event, an adjusted score and a corresponding tendency degree.

[0098] Reference event: before inviting the expert to evaluate, a reference failure rate set of the basic event is established by searching relevant literature, historical data or stress analysis method, counting method and other reliability prediction methods. For basic events providing reference failure rates, the events or other events can be selected as references. For basic events lacking reference failure rates, events similar in probability or failure mechanism are selected as references.

[0099] Adjusted score: the assignment interval of the adjusted score is -10-10, and the expert can assign multiple scores. When the score is positive, the reference failure rate is increased, when the score is 0, no adjustment is needed, and when the score is negative, the reference failure rate is reduced. The definition of the score in each range is shown in Table 1.

[0100] Table 1: Definition of expert adjustment score.

[0101]

[0102] Tendency degree: for each adjusted score of the same basic event, the tendency degree needs to be assigned. The value interval of the tendency degree is 0-1 (0 is not included), the smaller the value, the lower the tendency, the larger the value, the higher the tendency, and the closer to 0.5, the more hesitant the judgment. In the evaluation of the same event, the sum of the tendency degrees of all the adjusted scores is 1.

[0103] Table 2: Definition of expert tendency degree.

[0104]

[0105] Each adjustment score needs to be converted into an adjustment factor according to the set rules, and the adjustment factor corrects the reference failure rate to obtain the evaluation probability, that is, the purpose of preprocessing is to convert all adjustment scores of each basic event into evaluation probability according to certain rules.

[0106] S3, converting the adjustment score into evaluation probability using the score conversion rule.

[0107] S31, formulating the conversion rule between the score and the adjustment degree;

[0108] S32, for the event with reference failure rate, the evaluation probability = reference probability × (1 + adjustment degree); for the event lacking reference failure rate, the evaluation of the reference event needs to be weighted as the reference probability first, and then the calculation of the current event probability is performed.

[0109] According to the adjustment score definition and the overall evaluation opinion, the score conversion rule is formulated, and the conversion function S is defined adj = f(score), according to the definition, the function needs to meet: f(0) = 0, f(5) = 1, f(-5) = -0.5, f(-10) = -1, and the function is strictly monotonically increasing in the independent variable interval.

[0110] The evaluation probability = reference probability × (1 + adjustment factor), in order to make the adjustment factor have higher flexibility to adapt to more scenarios, the definite integral is introduced in the calculation of the evaluation probability v b The conversion method of the a-th adjustment score into evaluation probability when the basic event has reference failure rate is:

[0111]

[0112] Wherein, the value range of c is [0, 1].

[0113] When preprocessing the basic event lacking reference failure rate, the reference value is obtained by weighting and averaging all evaluation probabilities of the specified reference event according to the corresponding tendency degree: The subsequent score conversion rule is unchanged.

[0114] S4, constructing the qualification weight according to the qualification of the expert; quantifying the uncertainty of the adjustment score and the tendency degree to obtain the evaluation uncertainty weight, and weighting and summing the qualification weight and the evaluation uncertainty weight to synthesize the total weight.

[0115] S41, scoring each qualification of each expert, and prescribing the weight, and applying the analytic hierarchy process (AHP) to calculate the qualification weight;

[0116] S42, Analyze and quantify the uncertainty of the evaluation opinions based on the evaluation results of each expert and assign uncertainty weights;

[0117] S43, determine the allocation ratio of qualification weight and uncertainty weight in the synthesis based on the differences in expert qualifications.

[0118] The Analytic Hierarchy Process (AHP) is applied to calculate qualification weights.

[0119] The experts (n) are scored based on their field relevance, education, professional title, years of service, and other qualifications (m items). A judgment matrix is ​​constructed for the k-th qualification:

[0120]

[0121] in, Solve for A k The largest eigenvalue and eigenvector are used as the judgment vector, and normalization is performed to obtain α. k .

[0122] The combination of judgment vectors for m qualifications is:

[0123]

[0124] Meanwhile, the matrix can be viewed as a combination of the initial qualification vectors β of n experts.

[0125] Define the proportion of each qualification in the assessment as γ = [c1, c2, ..., c m ],

[0126] The qualification weight q of the i-th expert i =β i T ·γ, i.e., the qualification weight vector w q =[q1,q2,…q n ].

[0127] Discreteness evaluation: In the traditional probabilistic hesitant fuzzy set (PHFS), fuzzy entropy and hesitant entropy are commonly used to describe the uncertainty of data. Fuzzy entropy focuses on the degree of membership close to 0.5. The closer the degree of membership is to 0.5, the higher the fuzziness. However, this evaluation criterion is not suitable for describing the uncertainty of multiple small probability values.

[0128] The essence of hesitation entropy is to describe the discrete degree of membership contained in the probability hesitant fuzzy element. Experts can give multiple adjustment scores in the evaluation of the same basic event. The number of scores and the difference between scores reflect the concentration of expert opinions. When the scores are concentrated, the expert opinions are more explicit. When the scores are dispersed, the expert opinions are more fuzzy. Therefore, the evaluation method of hesitation entropy can be used to evaluate the concentration of each expert's evaluation results, reflecting the degree of disagreement between scores.

[0129] The preprocessing step has converted the adjustment scores into evaluation probabilities. The distance between each evaluation probability v of the same basic event is calculated, and the weighted sum is calculated with the corresponding tendency p as the weight:

[0130]

[0131] The range of the probability set is range(v). When the data is uniformly distributed at both ends, the weighted distance reaches the maximum value:

[0132]

[0133] If the reference failure rate of a basic event is 1×10 -5 , the discrete evaluation of the intuitive evaluation {1×10 -5 (0.5), 1.2×10 -5 (0.5)} is smaller than that of {1×10 -5 (0.5), 1.5×10 -5 (0.5)}. If D max is used directly, the discrete evaluation results of both evaluation opinions reach the maximum value 1, so the expert evaluation scale will be eliminated. A relative scale factor needs to be introduced:

[0134]

[0135] where P ref is the reference failure rate of the basic event, and s is a sensitivity factor not less than 0, which controls the influence of the relative scale in the discrete evaluation.

[0136] Therefore, the definition of the discrete evaluation after normalization of the weighted distance is:

[0137]

[0138] Hesitation evaluation: Shannon entropy, as a classic index for measuring information uncertainty in information theory, can quantify the total amount of uncertainty in probability distribution. Tendency describes the distribution of expert opinions in evaluation. When the tendency is concentrated on one state, the hesitation is the lowest, and the Shannon entropy is 0. When the tendency is uniformly distributed in all states, the hesitation is the highest, and the Shannon entropy reaches the maximum value. The calculation method of the Shannon entropy of the evaluation opinion is:

[0139]

[0140] wherein C s is the number of scores made by experts on a certain basic event, and the hesitation evaluation is obtained after normalization:

[0141]

[0142] Evaluation synthesis: combined with the probability synthesis method, the calculation method of total uncertainty entropy is:

[0143] E total = E d + E h - E d · E h

[0144] Weight calculation: according to the information entropy theory, the smaller the entropy value, the more important the corresponding evaluation index; on the contrary, the greater the entropy value, the less important the evaluation index. Therefore, the calculation formula of the evaluation uncertainty weight of expert i is as follows:

[0145]

[0146] That is, the evaluation uncertainty weight vector w u = [u1, u2, … u i , … u n ].

[0147] When the expert qualifications are close, the difference in evaluation opinions evaluated by the qualification level is small, at this time, the uncertainty and quality of the evaluation opinions of each expert need to be analyzed; when the difference between the expert qualifications is large, the expert with deeper qualification should obtain more weight distribution, at this time, the qualification weight should be given priority.

[0148] In the scoring link of expert qualifications, there are different degrees of strictness in different scenarios. The higher the strictness, the easier it is to increase the difference between the qualifications of experts, therefore, the strictness index t is introduced to control the sensitivity of the change of the difference between the qualifications, and the difference between the qualifications of each expert is taken as the evaluation standard of the distribution proportion, and the calculation formula of the distribution proportion of the qualification weight and the evaluation uncertainty weight is as follows:

[0149] β = 1 - α

[0150] Wherein, t ∈ [0, 1], α is the distribution proportion of the qualification weight, β is the distribution proportion of the evaluation uncertainty weight, and the total weight is:

[0151] w total = α·w q + β·w u

[0152] S5, synthesizing the final assessment probability of the basic event by Dempster-Shafer evidence theory based on the assessment probability and the total weight.

[0153] S51, extending the interval of the assessment probability of each expert and merging the interval center according to the interval overlap to construct the recognition framework of each basic event;

[0154] S52, calculating the BPA of each interval in the recognition framework and performing evidence discounting processing according to the weight of each expert;

[0155] S53, calculating the joint support degree and the conflict coefficient based on the Dempster combination rule, taking the center value of the maximum support interval as the final probability for the low conflict case, and performing weighted average processing on the center value of each interval for the high conflict case.

[0156] In Dempster-Shafer (DS) evidence theory, the recognition framework θ defines the problem boundary and all possible basic hypotheses, which has mutual exclusivity and completeness. Each basic event corresponds to a recognition framework, which needs to include the assessment probability of all experts. However, the core of DS evidence theory is the analysis of set intersection, and if the single-point probability is directly fused, the zero intersection and conflict problems may occur, especially for the events lacking reference failure rate. Due to the different references of experts, even if the evaluation opinions are similar, the numerical values are not equal, which still leads to conflict.

[0157] To solve this problem, the single-point value of the assessment probability v is extended to an interval with a tolerance ε to expand the interval to a recognition framework to perform Dempster-Shafer evidence theory, as shown in Figure 3 , specifically as follows:

[0158] Sort all assessment probabilities from small to large, and first extend the smallest assessment probability:

[0159] I=[(1-ε)v1,(1+ε)v1]

[0160] and take v1 as the interval center value v c , if the subsequent assessment probability v2∈I, merge the interval:

[0161] I'=[(1-ε)v1,(1+ε)v2]

[0162] and update the interval center value as:

[0163]

[0164] If , form an independent extended interval and repeat the interval overlap judgment until the extension of all single-point assessment probabilities is completed. The overall process of interval expansion is as followsFigure 4 as shown.

[0165] Basic Probability Assignment (BPA), also known as mass function, is used to quantify the degree of confidence of evidence on a proposition, and the BPA of expert k on extended interval I l is calculated as:

[0166]

[0167] In traditional DS evidence theory, all sources of evidence have equal weight, but due to the differences in expert qualifications and the quality of evaluation results, the credibility of evidence is different. In order to avoid the deviation of the synthesis result from the truth, evidence discounting is needed based on the total weight:

[0168] m′ k (I l )=w total,k ·m k (I l )

[0169] When multiple independent evidences support the same proposition in the identification framework, the joint support of the proposition needs to be calculated based on the Dempster combination rule to synthesize each independent evidence, and the conflict between evidences is handled by a normalization factor to ensure that the synthesis result satisfies the probability sum of 1. The discounted BPA of the first expert is used as the initial result, and the discounted BPA of other experts is sequentially fused with the current synthesis result:

[0170]

[0171] where K is the conflict coefficient, which is represented as:

[0172]

[0173] The conflict coefficient threshold is defined, and when it is less than the threshold, it is a low conflict situation, and the extended interval with the highest joint support is taken, which is represented as:

[0174] I max =argmaxm combined (I l )

[0175] The final probability of the basic event is the center value corresponding to this extended interval.

[0176] When it reaches or exceeds the threshold, it is a high conflict situation, and the strategy is downgraded to weighted average processing. The center value of all extended intervals in the identification framework is weighted with the corresponding discounted BPA. If there are n experts in total and s extended intervals in the identification framework, the final probability of the basic event is:

[0177]

[0178] S6, based on the final assessment probability of the basic event, a fault tree analysis is performed to obtain the failure rate of the top event in the fault tree and the importance of the basic event, and the failure risk analysis of the equipment is completed.

[0179] S61, Monte Carlo simulation is applied to the final probability of the event to assess the probability of occurrence of the top event;

[0180] S62, the importance of the basic event is analyzed and the weak link is identified.

[0181] The failure rate of the basic event is transmitted and synthesized through the logic gate, Monte Carlo simulation is performed on the constructed fault tree model, the unreliability F(t) is calculated through digital simulation test and the failure rate λ is solved, and for the equipment with exponential distribution of life, the relationship between the unreliability and the failure rate is as follows:

[0182] F(t)=1-e -λt

[0183] The number of failures caused by each basic event is counted, the importance of the basic event is calculated to identify the weak link of the system, wherein the probability importance reflects the sensitivity of the occurrence probability of the basic event, and the calculation formula is:

[0184]

[0185] The FV importance reflects the contribution share of the minimum cut set containing the basic event in the top event, and the calculation formula is:

[0186]

[0187] Wherein, C k is the minimum cut set containing the event i.

[0188] The main program for processing the probability hesitant fuzzy evidence theory is shown in Figure 5 , and the main program for fault tree analysis is shown in Figure 6 .

[0189] In summary, to reduce the impact of subjective uncertainty, this embodiment introduces probability hesitant fuzzy sets and DS evidence theory. Probability hesitant fuzzy sets allow elements to have multiple possible probability values in the form of a set of membership degrees to the set, rather than a single numerical value or traditional fuzzy numbers, fully reflecting the diversity and uncertainty of expert opinions and avoiding information loss due to simplification. At the same time, the uncertainty of expert evaluation opinions can be quantitatively analyzed to allocate opinion weights and reduce the impact of opinion differences. DS evidence theory provides a systematic framework for fusing fault probability information given by different experts based on probability hesitant fuzzy sets, and uses the Dempster combination rule to fuse the evidence of multiple experts, effectively handling conflicts and consistency between evidence.

[0190] Based on the probability hesitant fuzzy evidence theory method, subjective uncertainty and conflict scenarios in expert evaluation can be effectively handled in the complex system fault probability acquisition link, enhancing the reliability and practicality of fault tree analysis method in complex industrial scenarios for failure risk assessment, and providing more convincing quantitative basis for safety decision-making.

[0191] Specific case:

[0192] Wind power is a high-quality new energy, and the sea area has abundant wind energy resources. The installed capacity of offshore wind power continues to increase, but the wind power system is large and complex, and is prone to failure and cannot operate normally. The variable pitch system adjusts the angle of the wind turbine blades to maintain stable output power of the generator, and the system failure rate is as high as 13.3%. Therefore, it has practical engineering value to analyze the failure risk of the variable pitch system to improve the weak link.

[0193] Based on the maintenance records of H120-2.0MW type wind turbines in 2021, the structure and function of the variable pitch system of offshore wind turbines are analyzed, and a fault tree is built as shown in Figure 7 The basic events and structure of the fault tree are shown in Tables 3 and 4.

[0194] Table 3: Basic events of offshore wind turbine variable pitch system.

[0195]

[0196] Table 4: Fault tree structure of offshore wind turbine variable pitch system.

[0197]

[0198] Consult literature and data to collect basic event probabilities as a reference, and invite three experts in the relevant field to evaluate the occurrence probability of the basic events based on the technical characteristics of the current type of wind turbine, service environment, etc. The evaluation opinions are shown in Table 5. Each expert's evaluation includes the specified reference event, the correction score and the corresponding inclination degree. N_BE represents the weighted average event.

[0199] Table 5: Expert evaluation opinions of basic events of the pitch system fault tree.

[0200]

[0201]

[0202] According to the evaluation opinions of each expert, the modified amplification factor of all basic events is not greater than 5, so the conversion function is defined as:

[0203]

[0204] The score is converted into evaluation probability according to the pre-processing steps introduced in the principle part.

[0205] To calculate the qualification weight, the qualifications of the three experts are scored according to their field relevance, education, title and length of service, and the proportions of each qualification are determined as γ = [0.25, 0.25, 0.25, 0.25] T , and the qualification scoring is as follows:

[0206] Table 6: Expert qualification scoring table.

[0207]

[0208] The expert qualification weight w q = [0.3340, 0.3317, 0.3343] is calculated.

[0209] The evaluation opinions of each expert are analyzed by the formula in the above method, the dispersion evaluation E d = [0.6136, 0.6453, 0.6361], the hesitation evaluation E h = [0.9410, 0.9441, 0.9370], the evaluation opinions of expert 1 are more concentrated, and the evaluation opinions of expert 3 have the lowest hesitation, the synthesized evaluation E total = [0.9772, 0.9802, 0.9771], the lower the evaluation value, the higher the weight, and the evaluation uncertainty weight w u = [0.3479, 0.3023, 0.3497].

[0210] The proportion allocated by the qualification weight is α = 0.5513, β = 0.4487, and the total weight w total = [0.3402, 0.3185, 0.3412].

[0211] After evidence fusion, the final probability of each basic event is shown in Table 7.

[0212] Table 7: Final probability of basic events of offshore wind turbine pitch system.

[0213]

[0214] Therefore, the method based on the probability hesitant fuzzy evidence theory is used to complete and correct the basic event probability value to a certain extent, and a Monte Carlo simulation with a time length of 8760 hours and a number of 10000 times is carried out according to the probability data, the probability of the top event is 84.17%, that is, the overall failure rate of the offshore wind turbine variable pitch system is 2.1042*10 -4 , and the mean time between failures (MTBF) is 4752.4 hours. The probability importance consistency analysis obtained by simulation is shown in Figure 8 , and the reliability curve of the offshore wind turbine variable pitch system is shown in Figure 9 .

[0215] According to the consistency of the event probability importance ranking obtained by analyzing the failure statistics of the H120-2.0MW type part of the wind turbine in 2021, the Spearman correlation coefficient is greater than 0.8, which has strong correlation, and verifies the rationality of the simulation result.

[0216] The above is only a specific embodiment of the present application, but the design concept of the present application is not limited thereto, and any non-essential modification of the present application using this concept shall be deemed as an infringement of the protection scope of the present application.

Claims

1. A method of probabilistic Dempster-Shafer theory based equipment failure risk analysis, characterized in that, The method comprises the following steps: S1, constructing a fault tree structure of the equipment, and constructing a reference failure rate set of basic events in the fault tree; S2, obtaining a probability hesitating fuzzy set of expert evaluation data of the reference failure rate set; The membership of the probability hesitating fuzzy set is an adjusted score of the basic event obtained by the expert evaluating the reference failure rate set of the basic event; The probability weight of the probability hesitating fuzzy set is a tendency degree corresponding to the adjusted score; S3, converting the adjusted score into an evaluation probability by using a score conversion rule; S4, constructing a qualification weight according to the qualification of the expert, quantifying the uncertainty of the adjusted score and the tendency degree to obtain an evaluation uncertainty weight, and performing weighted summation of the qualification weight and the evaluation uncertainty weight to synthesize a total weight; S5, synthesizing a final evaluation probability of the basic event by using Dempster-Shafer evidence theory based on the evaluation probability and the total weight; S6, performing fault tree analysis based on the final evaluation probability of the basic event to obtain a top event failure rate and an importance degree of the basic event in the fault tree, and completing the failure risk analysis of the equipment.

2. The probabilistic hesitant fuzzy evidence theory based equipment failure risk analysis method according to claim 1, characterized in that, The reference event comprises a basic event with a reference event and a basic event without a reference event; the score conversion rule is specifically as follows: For the basic event without the reference event, a reference probability is obtained by using weighted average as the value of the basic event in the reference failure rate set; and the reference probability is represented as: wherein, represents the reference probability of the basic event with no reference event; v related,b represents the evaluation probability of the selected b-th similar basic event by the expert; p related,b represents the corresponding tendency degree of v related,b ; h represents the number of evaluations made; The evaluation probability is calculated by using the score conversion rule; and the evaluation probability is represented as: Wherein, v a represents the evaluation probability of the a-th adjustment score after conversion; c represents the interval parameter, and the value interval is [0, 1]; score a represents the a-th adjustment score; P ref represents the reference probability, for the basic event without reference event, f(score a ) represents the conversion function.

3. The probabilistic hesitant fuzzy evidence theory based equipment failure risk analysis method according to claim 2, characterized in that, The adjusted score is a plurality of scores or score intervals between 10 and -10 which are independent of each other, the score is a positive value, the reference failure rate is increased, the score is 0, the reference failure rate is not adjusted, the score is a negative value, the reference failure rate is reduced, the conversion function satisfies f(0) = 0, f(5) = 1, f(-5) = -0.5, f(-10) = -1, and the conversion function is strictly monotonically increasing in the independent variable interval.

4. The probabilistic hesitant fuzzy evidence theory based equipment failure risk analysis method according to claim 1, characterized in that, The qualification weight of the expert is calculated by using an analytic hierarchy process (AHP); and the qualification comprises a field correlation degree, an educational background, a professional title and a service length.

5. The probabilistic hesitant fuzzy evidence theory based equipment failure risk analysis method according to claim 1, characterized in that, The weighted summation of the qualification weight and the evaluation uncertainty weight to synthesize the total weight is represented as: w total = a · w q + β · w u wherein w total denotes the total weight; w q denotes the qualification weight; w u denotes the assessment uncertainty weight; q i denotes the qualification weight of the i-th expert; q j denotes the qualification weight of the j-th expert; a denotes the qualification weight distribution proportion; b denotes the assessment uncertainty weight distribution proportion; n denotes the number of experts; t denotes a strictness index that controls the change sensitivity of the qualification difference, t e [0, 1].

6. The probabilistic hesitant fuzzy evidence theory based equipment failure risk analysis method according to claim 1, characterized in that, The evaluation uncertainty weight is obtained by quantifying the uncertainty of the adjusted score and the tendency degree; and the evaluation uncertainty weight is specifically as follows: A dispersion evaluation of the adjusted score of the expert to the same basic event is calculated; A hesitating evaluation of the tendency degree distribution of the expert is calculated and normalized to obtain; A total uncertainty entropy is synthesized by the dispersion evaluation and the hesitating evaluation; and the total uncertainty entropy is represented as: E total = E d + E h - E d • E h wherein E total represents the total uncertainty entropy; E d represents the dispersion evaluation; E h represents the hesitancy evaluation; The evaluation uncertainty weight is calculated according to the total uncertainty entropy; and the evaluation uncertainty weight is represented as: w u = [u1, u2,... u i ,... u n ] where w u represents the evaluation uncertainty weight, i.e., all u i constitute a vector; u i represents the evaluation uncertainty weight of the i-th expert; E total,i represents the total uncertainty entropy of the i-th expert; E total,k represents the total uncertainty entropy of the k-th expert; n represents the number of experts.

7. The probabilistic hesitant fuzzy evidence theory based equipment failure risk analysis method according to claim 1, characterized in that, The dispersion evaluation of the adjusted score of the expert to the same basic event is calculated; and the dispersion evaluation is specifically as follows: A weighted distance D between each evaluation probability of the same basic event is calculated by using the tendency degree as a weight; A maximum value of the weighted distance when the data is uniformly distributed at both ends is calculated; and the maximum value is represented as: where D max denotes the maximum of the weighted distances; range(v) denotes the range of the probability set, v denotes the evaluation probability; A relative scale factor is calculated; and the relative scale factor is represented as: where σ denotes a relative scale factor; P ref denotes a reference failure rate of a basic event; s denotes a sensitivity factor not less than 0, controlling the degree of influence of the relative scale in the discreteness evaluation; The dispersion evaluation is obtained by normalizing the weighted distance based on the relative scale factor; and the dispersion evaluation is represented as: wherein E d represents a discrete evaluation.

8. The probabilistic hesitant fuzzy evidence theory based equipment failure risk analysis method according to claim 1, characterized in that, The final evaluation probability is synthesized by using Dempster-Shafer evidence theory based on the evaluation probability and the total weight; and the final evaluation probability is specifically as follows: The evaluation probability of each expert is extended with an allowable degree to obtain an extended interval, and an identification framework of each basic event is constructed based on the extended interval; A basic assignment probability (BPA) value of the extended interval in the identification framework is calculated and expressed as: wherein, m k (I l ) represents the BPA value of the kth expert to the lth extended interval I l ; p k,d represents the v d th tendency value of the kth expert, v d represents the dth adjustment score in the same identification framework; p k,p represents the pth tendency value of the kth expert; N k represents the total number of tendency values of the kth expert; An evidence discounting process is performed according to the total weight to obtain a discounted BPA value, which is expressed as: m' k (I l )=w total,k ·m k (I l ) where m' = m - 1 k (I l ) denotes the discounted BPA value of the kth expert for the lth extension interval; w total,k denotes the total weight of the kth expert; The discounted BPA values of the experts are fused by using a Dempster combination rule to obtain the final probability of the basic event.

9. The probabilistic hesitant fuzzy evidence theory based equipment failure risk analysis method according to claim 8, characterized in that, The evaluation probability is extended with an allowable degree to obtain an evaluation probability interval with an allowable degree, and the specific process is as follows: All the evaluation probabilities are sorted in ascending order; The smallest evaluation probability after sorting is extended and expressed as: I = [(1-ε)v1, (1+ε)v1] where I represents an initial generated extended interval, ε represents an allowable degree, and v1 represents the smallest evaluation probability; Interval overlap judgment is performed with v1 as the interval center value v c If the subsequent evaluation probability v2 is extended into an independent extended interval; if v2 ∈ I, the extended interval is merged, denoted as: I' = [(1-ε)v1, (1+ε)v2] where I' represents a merged extended interval; The center value of the merged extended interval is updated and expressed as: wherein v c represents the center value of the merged extended interval; The above interval overlap judgment is performed on the subsequent evaluation probabilities until the interval extension of all the evaluation probabilities is completed.

10. The probabilistic hesitant fuzzy evidence theory based equipment failure risk analysis method according to claim 9, characterized in that, The discounted BPA values of the experts are fused by using a Dempster combination rule to obtain the final probability of the basic event, and the specific process is as follows: The joint support of the same proposition in the identification framework is calculated based on the Dempster combination rule, and a conflict coefficient is used as a normalization factor to process the conflict between the evidences; When the conflict coefficient is less than a preset conflict coefficient threshold, it is a low conflict situation, and the final probability of the basic event is the center value corresponding to the extended interval with the highest joint support; When the conflict coefficient reaches or exceeds the preset conflict coefficient threshold, it is a high conflict situation, and a weighted average is used to process, the center value of all the extended intervals in the identification framework is weighted with the corresponding discounted BPA, and the final probability of the basic event is expressed as: wherein, represents the final probability of the basic event; n represents the number of experts; z represents the number of extension intervals; v c,l represents the center value of the lth extension interval.

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