An improved FMEA method based on evidence distance and its application

Abstract

The present invention discloses an improved FMEA method based on evidence distance. First, we obtain a new BPA by modeling the expert's evaluation results using triangular fuzzy numbers, then calculate the inverse of BPA, then calculate the expert's weight by evidence distance, and finally we fuse the final result by using Murphy combination rules. In short, this method considers how to fuse conflicting evidence from experts, and correspondingly considers the differences in relative weights between experts due to the uncertainty of expert evaluation. It has been verified by experiments that the method of the present invention has high accuracy.

Description

Technical Field

[0001] The invention relates to the technical field of data processing, and in particular to an improved FMEA method based on triangular fuzzy numbers, the inverse of BPA and evidence distance in DS evidence theory. Background Art

[0002] Failure Mode and Effects Analysis (FMEA) was first proposed by NASA in the 1960s. It is a risk analysis and management tool designed to allocate limited resources to projects with the highest risk. FMEA can improve the quality, safety and reliability of products. Due to its significant advantages, FMEA has been widely used in various fields, such as steel production, fishing boat propulsion systems, sewage treatment, and medical fields. The most commonly used tool for FMEA is the risk priority number (RPN), which is expressed as the product of occurrence (O), severity (S), and detection rate (D). Although FMEA has significant advantages, with the increasing complexity of the evaluation system, there is a lot of uncertainty in the evaluation results, which greatly affects the final risk analysis.

[0003] First, different risk factors can produce the same RPN value. For example, (O:9, S:2, D:5) and (O:2, S:9, D:5) have the same final RPN value, but the occurrence and severity of the two are very different.

[0004] Secondly, the traditional risk priority number considers O, S and D as equally important, but in fact their weights may be different. Finally, the level of each risk factor is rated as [1,2,3,4,5,6,7,8,9,10], so that the final RPN value will be between 1 and 1000, but not all numbers between them can represent the RPN value, in fact there are only 120 discrete values.

[0005] When we do FMEA, we need to deal with uncertain information. So how to improve the existing FMEA and increase the accuracy of the application of this FMEA. Summary of the invention

[0006] In view of the above problems existing in the prior art, the technical problem to be solved by the present invention is: how to improve the existing FMEA and improve the accuracy of the application of the FMEA.

[0007] In order to solve the above technical problems, the present invention adopts the following technical solution: an improved FMEA method based on evidence distance, comprising the following steps:

[0008] S1: Assume there are J experts in FMEA and N failure modes: E1,...E J ;FM1,...FM N, the identification framework of the i-th risk factor of the n-th failure mode is as follows:

[0009]

[0010] in, represents the lowest evaluation level of J experts on the i-th risk factor of the n-th failure mode, and also satisfies the following constraints:

[0011]

[0012] S2: Construct BPA as follows:

[0013] Let X represent the single possible rating of the ith risk factor of the nth failure mode, and the BPA is expressed as follows:

[0014]

[0015] Then, the identification framework of the i-th risk factor of the n-th failure mode is expressed as:

[0016] S3: Calculate the inverse of the BPA constructed in S2 using the following formula, and the inverse function satisfies:

[0017]

[0018] in, is the BPA function m i The inverse function of

[0019] S4: For J experts, the distance matrix d between the i-th risk factor and the n-th failure mode can be defined as follows:

[0020]

[0021] in, They represent the inverse functions of the BPA function obtained by experts 1, 2, ..., J for the risk factor i in the nth failure mode;

[0022] S5: Similarity indicates the degree of similarity between two evidence bodies. The similarity matrix is ​​defined as follows:

[0023]

[0024] Use Formula 7 to calculate the p-th evidence body to get the support Sup(m ip ):

[0025]

[0026] Among them, mip represents the BPA function in the p-th evidence body of the ith risk factor, m iq represents the BPA function in the qth body of evidence of the ith risk factor, where n is a positive integer, p = 1, 2, 3, ..., n, q = 1, 2, 3, ..., n;

[0027] The support Sup(m ip ) is normalized using Formula 8 to obtain the credibility Crd(m ip ):

[0028]

[0029] S6: Using credibility as the weight of the average BPA, we get the following for the scoring criteria A represented by the subset of propositions:

[0030]

[0031] Among them, the value range of A is from 1 to 10. Then, after n-1 rounds of iterations of the Murphy combination rule, the fused BPA value is obtained.

[0032] S7: In the nth failure mode, suppose RPN has several different levels, each level corresponds to a different probability, defined as follows:

[0033]

[0034]

[0035] in, represents the fusion value of risk factor i based on the evaluation results of n experts.

[0036] and They respectively represent: the expert evaluation fusion value of risk sequence number O (risk frequency Occurrence), the expert evaluation fusion value of S (risk severity level Severity), and the expert evaluation fusion value of D (risk detectability).

[0037] A failure mode The larger the value, the higher the overall risk of this failure mode.

[0038] Specifically, after n-1 rounds of iterations using the Murphy combination rule in S6, the fused BPA value is obtained. The specific steps are as follows:

[0039] For n independent mass functions m1, m2...m n(n>2), Murphy calculated the average value of the mass function of n groups as m avg , and then iterate (n-1) times to get a new quality function. The Murphy combination rule is defined as follows:

[0040] m 1 =F DS (m avg ,m avg ) Formula (12)

[0041] m n =F DS (m n-1 ,m avg )(n≥2) Formula (13)

[0042] Among them, F DS represents the Dempster combination rule, which is defined as follows:

[0043] For two independent sets of mass functions m1 and m2, the following Dempster combination rule is used for fusion:

[0044]

[0045]

[0046]

[0047] An improved FMEA method based on evidence distance is applied to the potential failure risk of aircraft turbine rotor blades. The improved FMEA method based on evidence distance is as described above and includes the following steps:

[0048] Step 1: Assume J = 3, and three experts use the proposed FMEA method to conduct risk analysis on the potential failure modes of aircraft turbine rotor blades:

[0049] Based on the evaluation results of the risk factor O of the first failure mode, the risk level identification framework is determined. Similarly, the risk level identification framework is determined for the risk factors S and D of the first failure mode.

[0050] Step 2: Construct the BPA of risk factor O, the BPA of risk factor S, and the BPA of risk factor D based on the evaluation data of the three experts;

[0051] Step 3: Calculate the inverse function of BPA for the risk factors O, S and D respectively;

[0052] Step 4: For risk factors O, S, and D, calculate the evidence distance between experts based on the inverse function of BPA;

[0053] Step 5: Construct a distance matrix based on the evidence distance between experts. The smaller the distance between two pieces of evidence, the higher their similarity; conversely, the larger the evidence distance, the smaller the similarity.

[0054]

[0055] The support is calculated using the similarity matrix formula 6' and formula 7;

[0056] Then, we use Formula 8 to normalize the obtained support to obtain the credibility of the evidence;

[0057] Step 6: Based on the credibility calculated in step 5 as the weight of BPA, the evaluation results of risk factors O, S and D based on the improved method are calculated using formula 9;

[0058] The final quality function of each risk factor is obtained using Murphy's combination rule;

[0059] Step 7: Calculate the RPN values ​​of all aircraft turbine rotor blade potential failure modes based on equations 10 and 11;

[0060] Step 8: Sort all potential failure modes of aircraft turbine rotor blades according to the RPN value. The larger the RPN value, the higher the risk of the corresponding failure mode.

[0061] Compared with the prior art, the present invention has at least the following advantages:

[0062] The present invention proposes an improved FMEA method based on triangular fuzzy numbers, the inverse of BPA and the evidence distance. First, we obtain a new BPA by modeling the expert's evaluation results using triangular fuzzy numbers, then calculate the inverse of BPA, then calculate the expert's weight by the evidence distance, and finally we fuse the final result by using Murphy's combination rule. In short, this method considers how to fuse conflicting evidence from experts, and correspondingly considers the differences in relative weights between experts due to the uncertainty of expert evaluation. The method of the present invention has been verified to be highly accurate by experiments.

[0063] The functional expression of the inverse information of expert evaluation information is obtained through the inverse of BPA, which improves the utilization efficiency of FMEA expert evaluation information; the differences between different expert evaluations are measured by evidence distance, and then modeled as the credibility of risk assessment information, and the subjective evaluation of experts is scientifically quantified, so that the improved FMEA method has better scientific and quantitative characteristics; on the basis of the above, the Murphy combination rule is used to fuse FMEA expert evaluation information to overcome the limitations of a single expert, improve the reliability of the evaluation results, and thus improve the accuracy of the risk analysis method. DETAILED DESCRIPTION

[0064] The present invention is further described in detail below in conjunction with embodiments.

[0065] Embodiment 1: An improved FMEA method based on evidence distance, characterized in that it comprises the following steps:

[0066] S1: Assume there are J experts in FMEA and N failure modes: E1,...E J ;FM1,...FM N , in this case, the identification framework of the ith risk factor of the nth failure mode can be written as:

[0067]

[0068] Obviously, we can observe that the number of identification frameworks is 3N. Since different experts have little difference in their evaluation of the ith risk factor of the nth failure mode, in practical applications, the identification framework of the ith risk factor of the nth failure mode is simplified as follows:

[0069]

[0070] in, represents the lowest evaluation level of J experts on the i-th risk factor of the n-th failure mode, and also satisfies the following constraints:

[0071]

[0072] S2: Construct BPA as follows:

[0073] Let X represent the single possible rating of the ith risk factor of the nth failure mode, and the BPA is expressed as follows:

[0074]

[0075] Then, the identification framework of the i-th risk factor of the n-th failure mode is expressed as:

[0076] In order to solve the conflict of combined evidence, we use triangular fuzzy numbers to construct a more flexible BPA and fully consider the uncertainty of experts in their evaluation. Since the evaluation of risk factor i of the nth failure mode by different experts is not much different, we can choose two adjacent set values ​​to construct the BPA function.

[0077] Based on the above discussion, we construct a triangular fuzzy number that fits this description well. In this example, we define ω = 2 / 3, a2-a1 = 1, a4-a3 = 2. There are two reasons: (1) The triangular fuzzy number covers two adjacent integer values, and the corresponding function value of the other integer is 0. (2) The sum of these two adjacent integer values ​​is 1, which meets the basic definition of the quality function.

[0078] Assuming we denote by X a single possible rating for the ith risk factor of the nth failure mode, the new BPA will be expressed as follows:

[0079]

[0080] Then the recognition framework can be expressed as:

[0081] Assume that the severity (S) of the nth failure mode given by two experts (E1, E2) are and Using formula 15, we can get the conflict coefficient k = 1. However, according to our experience, level 3 and level 4 are not completely conflicting. Then using triangular fuzzy numbers, we can get a new BPA:

[0082] E1:

[0083] E2:

[0084] Using equation (15) again, we can get k = 0.78. Obviously, using triangular fuzzy numbers can effectively reduce evidence conflicts.

[0085] S3: Calculate the inverse of the BPA constructed in S2 using the following formula:

[0086]

[0087] in, is the BPA function m i The inverse function of

[0088] S4: In this step, we need to get the evidence distances between experts. Then, using these distances, we construct a distance matrix.

[0089] For J experts, the distance matrix d between the i-th risk factor and the n-th failure mode can be defined as follows:

[0090]

[0091] in, They represent the inverse functions of the BPA function evaluated by experts 1, 2…J for the risk factor i in the nth failure mode.

[0092] S5: Because we perform an inverse operation on BPA, the larger the evidence distance, the smaller the similarity. Similarity indicates the degree of similarity between two evidence bodies. The similarity matrix is ​​defined as follows:

[0093]

[0094] Similarity reflects the degree to which a body of evidence is supported by other bodies of evidence. Use Formula 7 to calculate the support Sup(m ip ):

[0095]

[0096] Among them, m ip represents the BPA function in the p-th evidence body of the ith risk factor, m iq represents the BPA function in the qth body of evidence of the ith risk factor, where n is a positive integer, p = 1, 2, 3, ..., n, q = 1, 2, 3, ..., n;

[0097] The purpose of normalization is to make the final result more accurate. ip ) is normalized using Formula 8 to obtain the credibility Crd(m ip ):

[0098]

[0099] S6: Using credibility as the weight of the average BPA, we get the following for the scoring criteria A represented by the subset of propositions:

[0100]

[0101] Among them, the value range of A is from 1 to 10. Then, after n-1 rounds of iterations of the Murphy combination rule, the fused BPA value is obtained. Specifically, calculate the BPA value after fusion The specific steps are as follows:

[0102] For n independent mass functions m1, m2…m n (n>2), Murphy calculated the average value of the mass function of n groups as m avg , and then iterate (n-1) times to get a new quality function. The Murphy combination rule is defined as follows:

[0103] m 1 =F DS (m avg,m avg ) Formula (12)

[0104] m n =F DS (m n-1 ,m avg )(n≥2) Formula (13)

[0105] where F DS represents the Dempster combination rule, which is defined as follows:

[0106] For two independent sets of mass functions m1 and m2, the following Dempster combination rule is used for fusion:

[0107]

[0108]

[0109]

[0110] Wherein, k represents the conflict coefficient.

[0111] S7: In the nth failure mode, suppose RPN has several different levels, each level corresponds to a different probability, and the average value of RPN can be used to compare the overall risk of each failure mode. The specific definition is as follows:

[0112]

[0113]

[0114] in, represents the fusion value of risk factor i based on the evaluation results of n experts.

[0115] and They respectively represent: the expert evaluation fusion value of risk sequence number O (risk frequency Occurrence), the expert evaluation fusion value of S (risk severity level Severity), and the expert evaluation fusion value of D (risk detectability).

[0116] A failure mode The larger the value, the higher the overall risk of this failure mode.

[0117] Embodiment 2: An improved FMEA method based on evidence distance is applied to the potential failure risk of aircraft turbine rotor blades, characterized in that the improved FMEA method based on evidence distance is as described in claim 2, comprising the following steps:

[0118] Step 1: Assume J = 3, and three experts use the proposed FMEA method to conduct risk analysis on the potential failure modes of aircraft turbine rotor blades:

[0119] For the evaluation result of the risk factor O of the first failure mode (i.e., i=O, the other two risk factors are S and D), the risk level identification framework is determined. Similarly, the risk level identification framework is determined for the risk factor S and risk factor D of the first failure mode.

[0120] For example: O1 (3, 40%; 4, 60%), O2 (3, 90%; 4, 10%), O3 (3, 80%; 4, 20%). This means that the risk level is 3 and 4. For the risk factor O of the first failure mode, the identification framework for determining the risk level can be simplified to:

[0121] Similarly, the risk level identification framework of risk factors S and D can be obtained.

[0122] Step 2: Construct the BPA of risk factor O, the BPA of risk factor S, and the BPA of risk factor D based on the evaluation data of the three experts;

[0123] Step 3: Calculate the inverse function of BPA for the risk factors O, S and D respectively;

[0124] According to Formula 3, the new BPA constructed from the data in the existing literature is shown in Table 1. As for the risk factor O of the first failure mode, the results are shown in Table 2. The inverse operation of BPA is performed using Formula 17, and the results are shown in Table 3.

[0125] In the theory of evidence, Yagar proposed the concept of the inverse function of probability distribution, as follows:

[0126]

[0127] where n represents the number of critical factors, and satisfy:

[0128]

[0129]

[0130] Table 1 RPN values ​​obtained using triangular fuzzy numbers

[0131]

[0132]

[0133] Table 2 Evaluation information of three experts

[0134]

[0135] Table 3 Inverse evaluation information of three experts

[0136]

[0137]

[0138] Step 4: For risk factors O, S, and D, calculate the evidence distance between experts based on the inverse function of BPA;

[0139] We start by calculating the evidence distance between the three experts. By using equations 3.11 and 3.12, we get the evidence distance;

[0140]

[0141] In the recognition framework Θ with n elements, the evidence distance (m1, m2) between two evidence bodies can be defined as:

[0142]

[0143] in D Is a 2 N Row and 2 N The elements in the matrix are:

[0144]

[0145] The smaller the distance between two pieces of evidence, the higher their similarity. By using Equation 6, we get the similarity matrix between the three experts:

[0146]

[0147] Support reflects the degree of mutual support between evidence. We use the similarity matrix and formula 7 to obtain support, and the results are shown in Table 4. Then we use formula 8 to normalize the results to obtain credibility, as shown in Table 5. The higher the degree to which a body of evidence is supported by other bodies of evidence, the more credible the evidence is.

[0148] Step 5: Use Formula 5 to construct a distance matrix based on the evidence distance between experts. The smaller the distance between two pieces of evidence, the higher their similarity; conversely, the larger the evidence distance, the smaller the similarity.

[0149] We get the similarity matrix between the three experts:

[0150]

[0151] Support reflects the degree of mutual support between evidence. We use the similarity matrix and formula 7 to obtain support, and the results are shown in Table 4. Then we use formula 8 to normalize the results to obtain credibility, as shown in Table 5. The higher the degree to which a body of evidence is supported by other bodies of evidence, the more credible the evidence is.

[0152] Table 4 Support for each body of evidence

[0153] Expert <![CDATA[E1]]> <![CDATA[E2]]> <![CDATA[E3]]> Support Degree 1.1 1.1 1.5

[0154] Table 5 Credibility of each body of evidence

[0155] Expert <![CDATA[E1]]> <![CDATA[E2]]> <![CDATA[E3]]> Credibility 0.275 0.350 0.375

[0156] Step 6: We use credibility as the weight to calculate BPA The specific calculation process is as follows:

[0157]

[0158] Next, we use the Murphy combination rule to obtain the final quality function, as shown in Table 6. The average value of the O risk factor is obtained using the following formula.

[0159]

[0160] Similarly, we can find the average values ​​of S and D risk factors. We list the results in Table 7.

[0161] Table 6 RPN values ​​obtained based on Murphy combination rule

[0162]

[0163] Table 7 Average values ​​of three risk factors of RPN

[0164]

[0165] Step 7: Calculate the RPN values ​​of all potential failure modes of aircraft turbine rotor blades; sort all potential failure modes of aircraft turbine rotor blades according to the RPN values. The larger the RPN value, the higher the risk of the corresponding failure mode.

[0166]

[0167] Table 8 RPN values ​​obtained based on different methods

[0168] FMEA AMWRPN MVRPN MVRPN2 <![CDATA[RPN avg ]]> <![CDATA[RPN avg2 ]]> <![CDATA[FM1]]> 5.1551 42.56 42.56 45.81 46.39 <![CDATA[FM2]]> 5.3171 64.00 64.05 70.27 70.28 <![CDATA[FM3]]> 3.8634 30.00 30.00 34.95 34.95 <![CDATA[FM4]]> 3.3302 18.00 17.97 20.61 20.42 <![CDATA[FM5]]> 1.6529 4.17 3.14 4.00 3.99 <![CDATA[FM6]]> 5.0964 60.00 60.00 65.94 65.94 <![CDATA[FM7]]> 3.3567 21.00 21.00 24.58 24.58 <![CDATA[FM8]]> 3.2975 15.00 15.00 17.42 17.37 <![CDATA[FM9]]> 8.3797 78.92 79.57 81.65 81.64 <![CDATA[FM 10 ]]> 5.0964 60.00 60.00 68.66 68.66 <![CDATA[FM 11 ]]> 4.7399 50.00 50.00 57.42 57.42 <![CDATA[FM 12 ]]> 5.0973 50.00 50.00 63.13 60.89 <![CDATA[FM 13 ]]> 4.9447 50.00 50.00 56.85 56.52 <![CDATA[FM 14 ]]> 5.4187 60.00 60.04 68.13 68.13 <![CDATA[FM 15 ]]> 5.9509 42.00 42.09 46.22 45.96 <![CDATA[FM 16 ]]> 3.7560 23.88 23.86 25.02 24.77 <![CDATA[FM 17 ]]> 5.0554 30.05 30.05 32.92 32.97

[0169] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solution of the present invention, which should be included in the scope of the claims of the present invention.

Claims

1. An improved FMEA method based on evidence distance, characterized in that: The steps include: S1: Assume there are J experts in FMEA, and N potential failure modes of aircraft turbine rotor blades: E1,…E J ;FM1,…FM N , the identification framework of the i-th risk factor of the n-th failure mode is as follows: in, represents the lowest evaluation level of J experts on the i-th risk factor of the n-th failure mode, and also satisfies the following constraints: S2: Construct a BPA with corresponding risk factors for the potential failure modes of aircraft turbine rotor blades, as follows: Let X represent the single possible rating of the ith risk factor of the nth failure mode, and the BPA is expressed as follows: Then, the identification framework of the i-th risk factor of the n-th failure mode is expressed as: S3: Use the following formula to calculate the inverse of the BPA of the corresponding risk factor constructed in S2, and the inverse function satisfies: in, is the BPA function m i The inverse function of S4: For J experts, the distance matrix d between the i-th risk factor and the n-th failure mode can be defined as follows: in, They represent the inverse functions of the BPA functions obtained by experts 1, 2…J for the risk factor i in the nth failure mode; S5: Similarity indicates the degree of similarity between two evidence bodies. The similarity matrix is ​​defined as follows: Use formula (7) to calculate the p-th evidence body to get the support Sup(m ip ): Among them, m ip represents the BPA function in the p-th evidence body of the ith risk factor, m iq represents the BPA function in the qth body of evidence of the ith risk factor, where n is a positive integer, p = 1, 2, 3, ..., n, q = 1, 2, 3, ..., n; The support Sup(m ip ) is normalized using formula (8) to obtain the credibility Crd(m ip ): S6: Using credibility as the weight of the average BPA, we get the following for the scoring criteria A represented by the subset of propositions: Among them, the value range of A is from 1 to 10. Then, after n-1 rounds of iterations of the Murphy combination rule, the fused BPA value is obtained. S7: In the nth failure mode, suppose RPN has several different levels, each level corresponds to a different probability, defined as follows: in, represents the fusion value of risk factor i based on the evaluation results of n experts; and They represent: the expert evaluation fusion value of risk order number O, the expert evaluation fusion value of S, and the expert evaluation fusion value of D; The potential failure modes of all aircraft turbine rotor blades are calculated using equations (10) and (11). The larger the value of a certain failure mode, the higher the overall risk of this failure mode.

2. The improved FMEA method based on evidence distance as claimed in claim 1, characterized in that: After n-1 rounds of iterations using the Murphy combination rule in S6, the fused BPA value is obtained. The specific steps are as follows: For n independent mass functions m1, m2...m n (n>2), Murphy calculated the average value of n groups of mass functions as m avg , and then iterate (n-1) times to get a new quality function. The Murphy combination rule is defined as follows: m 1 =F DS (m avg ,m avg ) Formula (12) m n =F DS (m n-1 ,m avg )(n≥2) Formula (13) where F DS represents the Dempster combination rule, which is defined as follows: For two independent sets of mass functions m1 and m2, the following Dempster combination rule is used for fusion:

3. An improved FMEA method based on evidence distance is applied to the potential failure risk of aircraft turbine rotor blades, characterized in that: The improved FMEA method based on evidence distance as claimed in claim 2 comprises the following steps: Step 1: Assume J = 3, and three experts use the proposed FMEA method to conduct risk analysis on the potential failure modes of aircraft turbine rotor blades: Based on the evaluation results of the risk factor O of the first failure mode, the risk level identification framework is determined. Similarly, the risk level identification framework is determined for the risk factors S and D of the first failure mode. Step 2: Construct the BPA of risk factor O, the BPA of risk factor S, and the BPA of risk factor D based on the evaluation data of the three experts; Step 3: Calculate the inverse function of BPA for the risk factors O, S and D respectively; Step 4: For risk factors O, S, and D, calculate the evidence distance between experts based on the inverse function of BPA; Step 5: Construct a distance matrix based on the evidence distance between experts. The smaller the distance between two pieces of evidence, the higher their similarity. Conversely, the larger the evidence distance, the smaller the similarity. The support is calculated using the similarity matrix formula (6') and formula (7); Then, the obtained support is normalized using formula (7) to obtain the credibility of the evidence; Step 6: Based on the credibility calculated in step 5 as the weight of BPA, the evaluation results of risk factors O, S and D based on the improved method are calculated using formula (9); The final quality function of each risk factor is obtained using Murphy's combination rule; Step 7: Calculate the RPN values ​​of all potential failure modes of aircraft turbine rotor blades based on equations (10) and (11); Step 8: Sort all potential failure modes of aircraft turbine rotor blades according to the RPN value. The larger the RPN value, the higher the risk of the corresponding failure mode.

Images