Machine tool maintenance priority ranking method based on z number-CRITIC-grey relational degree

Abstract

The invention provides a machine tool maintenance priority ranking method based on z-number-CRITIC-grey relational degree, which comprises the following steps: firstly, proposing distance measurement of the z-number, improving a CRITIC weight model based on total utility (TU value) of the z-number to enable the CRITIC weight model to be fused with a z-number decision language, and secondly, improving a grey relational degree model based on the distance measurement of the z-number to enable the grey relational degree model to be fused with the z-number decision language. According to the method, the reliability of decision information is considered, and finally, the maintenance units are subjected to priority ranking through a z-number-CRITIC-grey relational degree decision model, and the problems of fuzziness, reliability and the like of expert decision languages are fully considered.

Description

Technical Field

[0001] The invention relates to the technical field of machine tool maintenance, and in particular to a machine tool maintenance priority sorting method based on z number-CRITIC-grey correlation degree. Background Art

[0002] Failures in CNC machine tools can seriously affect the efficiency of machine tools. Failures may cause production stagnation, extend downtime, and increase maintenance costs, ultimately affecting the overall operation of the production line and product quality. Failure to repair the fault in a timely manner may also cause more equipment damage, thereby affecting production progress and company profits; CNC machine tools are highly integrated and complex mechanical devices. In order to perform timely, effective and reasonable maintenance, this paper proposes a machine tool maintenance priority sorting method based on z-number-CRITIC-grey correlation. Summary of the invention

[0003] In view of the shortcomings of the above-mentioned technology, the present invention proposes a machine tool maintenance priority sorting method and usage method based on z-number-CRITIC-grey correlation, which fully considers the fuzziness and reliability of decision-making information, so that the sorting result has higher accuracy and rationality.

[0004] In order to realize the above technical features, the object of the present invention is achieved as follows: a machine tool maintenance priority sorting method based on z number-CRITIC-grey correlation degree comprises the following steps:

[0005] Step 1: Establish a maintenance priority ranking evaluation system;

[0006] Step 2: Establish a z-number evaluation language table;

[0007] Step 3: Construct the decision matrix D nxm ;

[0008] Step 4: Normalize the decision matrix D nxm ;

[0009] Step 5: Use the z-critic method to calculate the weights of q evaluation indicators;

[0010] Step 6: Calculate the maintenance unit approximation and sort them based on the improved z-number-grey relational method.

[0011] Preferably, the distance measure between the first components A is solved based on the cut set theory, as follows:

[0012]

[0013] Where: and Respectively represent A i α-cut and

[0014] Preferably, the distance measure between the second components B is solved based on the cut set theory, as follows:

[0015]

[0016] Where: and Respectively represent B i β-cut and

[0017] Preferably, the hidden probability distribution p is solved based on the maximum entropy model XA The distance between them is as follows:

[0018]

[0019] Where: p zij represents the hidden probability distribution p between Z1 and Z2 XA .

[0020] Preferably, define the distance measure between two Z1, Z2:

[0021]

[0022] Where: λ is a (0-1) parameter, which represents the decision maker's preference for fuzzy ranging and reliability ranging of z-number information.

[0023] Preferably, it is characterized in that:

[0024] Step 4: Normalize the decision matrix:

[0025] Cost indicators:

[0026]

[0027] Interest-based indicators:

[0028]

[0029] in, Fuzziness Component Reliability Component constant.

[0030] Preferably, step 5 needs to further improve the CRITIC method so that it can be integrated with the z number information. The specific formula is as follows:

[0031]

[0032] Where: TU(Zij ) is a transformation of the z-number form, which contains all the information of the z-number;

[0033]

[0034] is the mean of the total utility of the z-number of each indicator;

[0035]

[0036] TU(S j ) represents the variability of the jth indicator;

[0037]

[0038] TU(r ij ) represents the correlation between indicators;

[0039]

[0040] TU(R j ) represents the conflict of the jth indicator;

[0041] TU(C j )=TU(S j )×TU(R j );

[0042] TU(C j ) represents the amount of information contained in the jth evaluation index, TU(C j ) is larger, the greater its role in the entire evaluation system, and the more weight it should be given;

[0043]

[0044] ω j is the objective weight of the jth evaluation index.

[0045] Preferably, step 6 needs to further improve the grey relational decision model, which is defined as follows:

[0046]

[0047] Among them, (A ij ,B ij ) is expressed in the form of z number; X O As a reference sequence, X 1。。。m As a comparison sequence;

[0048]

[0049] It is the minimum difference between two levels and the maximum difference between two levels;ρ is the resolution coefficient, ρ∈(0,1), c((A 0j ,B 0j ),(A ij ,B ij )) is the comparison sequence (A ij ,B ij ) and the reference sequence (A 0j ,B 0j ) between the correlation coefficient, Δ 0i (j) is equivalent to the distance measure between two z numbers;

[0050]

[0051] Where: d(X0,X i ) is the comparison sequence (A ij ,B ij ) and the reference sequence (A 0j ,B 0j ), W j Represents the weight of the evaluation index, 0≤w j ≤1;

[0052]

[0053] X + is a positive ideal sequence, X - is a negative ideal sequence; usually X + and X - As a reference sequence;

[0054]

[0055] According to the approximation μ i Sort the values.

[0056] Beneficial effects of the present invention:

[0057] 1. Aiming at the problems of fuzziness, reliability and lack of maintenance resource (maintenance time, maintenance cost, etc.) indicators in the maintenance priority sorting process, the present invention proposes a machine tool maintenance priority sorting method based on z-number-CRITIC-grey correlation, so as to rationalize the use of maintenance resources. The meta-action theory is used to decompose the CNC machine tool from the perspective of function-motion-action, and the meta-action unit is obtained as the maintenance object; and the maintenance priority evaluation system is established by considering the indicators such as maintenance cost, maintenance time, and maintenance difficulty; in view of the fuzziness and reliability of expert evaluation information, the -CRITIC method is used to calculate the objective weight of the evaluation index, which expands the application of z-number in the field of multi-attribute decision-making models and reduces the subjectivity of decision-making information; and combined with the defined z-number generalized distance and grey correlation model, the transformation and defuzzification of z-number in the calculation process are avoided, the original decision information of z-number is retained, and the problem of information distortion in the operation of z-number is prevented, and the effectiveness and feasibility of the proposed method are verified.

[0058] 2. The present invention is based on the fact that the machine tool maintenance priority ranking is also a multi-attribute maintenance decision problem. First, a z-number distance measure is proposed, and the CRITIC weight model is improved based on the total utility (TU value) of the z-number, so that it is integrated with the z-number decision language. Secondly, the gray correlation model is improved based on the z-number distance measure, and the reliability of the decision information is taken into account. Finally, the maintenance units are prioritized through the z-number-CRITIC-gray correlation decision model, and the fuzziness and reliability of the expert decision language are fully considered. The machine tool maintenance priority ranking has higher accuracy and rationality. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0060] Figure 1 Schematic diagram of the evaluation system.

[0061] Figure 2 Flowchart of the proposed machine tool maintenance priority sorting method based on z-number-CRITIC-grey correlation.

[0062] Figure 3 Schematic diagram of z-number reliability levels. DETAILED DESCRIPTION

[0063] The embodiments of the present invention are further described below in conjunction with the accompanying drawings.

[0064] Embodiment 1:

[0065] like Figure 1-3As shown in the figure, a machine tool maintenance priority sorting method based on z-number-CRITIC-grey correlation is presented. Machine tool maintenance priority sorting is also a multi-attribute maintenance decision problem. Firstly, a z-number distance measure is proposed, and the CRITIC weight model is improved based on the total utility (TU value) of the z-number to integrate it with the z-number decision language. Secondly, the grey correlation model is improved based on the z-number distance measure to take the reliability of the decision information into consideration. Finally, the maintenance units are prioritized through the z-number-CRITIC-grey correlation decision model, which fully considers the fuzziness and reliability of the expert decision language.

[0066] The evaluation method comprises the following steps:

[0067] Step 1: Establish a maintenance priority ranking evaluation system;

[0068] Step 2: Establish a z-number evaluation language table;

[0069] Step 3: Construct the decision matrix D nxm ;

[0070] Step 4: Normalize the decision matrix D nxm ;

[0071] Step 5: Use the z-critic method to calculate the weights of q evaluation indicators;

[0072] Step 6: Calculate the maintenance unit approximation and sort them based on the improved z-number-grey relational method.

[0073] Preferably, the distance measure between the first components A is solved based on the cut set theory, as follows:

[0074]

[0075] Where: and Respectively represent A i α-cut and

[0076] Preferably, the distance measure between the second components B is solved based on the cut set theory, as follows:

[0077]

[0078] Where: and Respectively represent B i β-cut and

[0079] Preferably, the hidden probability distribution p is solved based on the maximum entropy modelXA The distance between them is as follows:

[0080]

[0081] Where: p zij represents the hidden probability distribution p between Z1 and Z2 XA .

[0082] Preferably, define the distance measure between two Z1, Z2:

[0083]

[0084] Where: λ is a (0-1) parameter, which represents the decision maker's preference for fuzzy ranging and reliability ranging of z-number information.

[0085] Preferably, it is characterized in that:

[0086] Step 4: Normalize the decision matrix:

[0087] Cost indicators:

[0088]

[0089] Interest-based indicators:

[0090]

[0091] in, Fuzziness Component Reliability Component constant.

[0092] Preferably, step 5 needs to further improve the entropy value (CRITIC) method to merge it with the z number information. The specific formula is as follows:

[0093]

[0094] Where: TU(Z ij ) is a transformation of the z-number form, which contains all the information of the z-number;

[0095]

[0096] is the mean of the total utility of the z-number of each indicator;

[0097]

[0098] TU(S j ) represents the variability of the jth indicator;

[0099]

[0100] TU(r ij ) represents the correlation between indicators;

[0101]

[0102] TU(R j ) represents the conflict of the jth indicator;

[0103] TU(C j )=TU(S j )×TU(R j );

[0104] TU(C j ) represents the amount of information contained in the jth evaluation index, TU(C j ) is larger, the greater its role in the entire evaluation system, and the more weight it should be given;

[0105]

[0106] ω j is the objective weight of the jth evaluation index.

[0107] Preferably, step 6 needs to further improve the grey relational decision model, which is defined as follows:

[0108]

[0109] Among them, (A ij ,B ij ) is expressed in the form of z number; X O As a reference sequence, X 1。。。m As a comparison sequence;

[0110]

[0111] It is the minimum difference between two levels and the maximum difference between two levels; ρ is the resolution coefficient, ρ∈(0,1), usually chosen ρ =0.5, c((A 0j ,B 0j ),(A ij ,B ij )) is the comparison sequence (A ij ,B ij ) and the reference sequence (A 0j ,B 0j ) between the correlation coefficient, Δ 0i (j) is equivalent to the distance measure between two z numbers;

[0112]

[0113] Where: d(X0,X i ) is the comparison sequence (A ij ,B ij ) and the reference sequence (A 0j ,B 0j ), W j Represents the weight of the evaluation index, 0≤w j ≤1;

[0114]

[0115] X + is a positive ideal sequence, X - is a negative ideal sequence; usually X + and X - As a reference sequence;

[0116]

[0117] According to the approximation μ i Sort the values.

[0118] Embodiment 3:

[0119] As one of the core components of CNC machine tools, CNC turntables are mainly used to realize the rotation or tilting movement of workpieces during processing, so as to facilitate multi-faceted processing or processing of complex shapes. The stability and reliability of its operating conditions are crucial to the entire processing and production process. Timely maintenance and regular inspections can effectively reduce the negative impact of CNC turntable failures on machine tool operation; according to Figure 1 Establish a maintenance unit evaluation system.

[0120] By performing FMA decomposition on the CNC turntable, it is found that the CNC machine tool has a total of seven units, namely: rotating body movement unit MU1, worm rotation unit MU2, gear shaft rotation unit MU3, rotating body rotation unit MU4, claw movement unit MU5, push rod movement unit MU6 and motor rotation unit MU7.

[0121] There are 6 evaluation indicators in the evaluation system to measure the maintenance priority from the perspective of maintenance resources and failure risks: maintenance cost C1, danger level C2, maintenance time C3, maintenance difficulty C4, failure frequency C5 and detectability C6;

[0122] Experts based on the fuzziness rating table in Table 1 and Figure 3 Schematic diagram of z-number reliability level, establishing decision matrix D nxm As shown in Table 2.

[0123] Table 1. Table of fuzziness levels of z numbers

[0124]

[0125] Table 2 Decision matrix D nxm

[0126]

[0127] Step 4, normalize the decision matrix; C1 to C6 are all interest indicators;

[0128] Step 5 Calculate the total utility TU(Z ij ), as shown in Table 3.

[0129] Table 3 Total utility of z number

[0130]

[0131] Step 5 calculates the evaluation index weights according to the improved z-number-CRITIC method.

[0132] ω=(ω1,ω2...ω6)=(0.131,0.121,0.115,0.113,0.364,0.155);

[0133] Step 6: Calculate the scores according to the z-number-CRITIC-grey relational model and sort them.

[0134] Positive ideal sequence X + :

[0135] ((0.625,0.750,0.875),(0.6,0.8,1))((0.625,0.75,0.875),(0.6,0.8,1))((0.75,0.875,1),(0.6,0.8,1))

[0136] ((0.750,0.875,1.000),(0.6,0.8,1))((0.750,0.875,1.000),(0.6,0.8,1))((0.75,0.875,1),(0.6,0.8,1))

[0137] Negative ideal sequence X - :

[0138] ((0,0.125,0.25),(0.6,0.8,1))((0,0.125,0.25),(0.6,0.8,1))((0,0.125,0.25),(0.6,0.8,1))

[0139] ((0,0.125,0.25),(0.6,0.8,1))((0,0.125,0.25),(0.6,0.8,1))((0,0.125,0.25),(0.4,0.6,0.8))

[0140] λ=0.5 means that the experts believe that the information reliability limit and the fuzziness limit are in the same position; further calculation of the maintenance unit d(X + ,X i ) and d(X - ,X i ):

[0141] d(X + ,X1)=0.702 d(X + ,X2)=0.522 d(X + ,X3)=0.508 d(X + ,X4)=0.656

[0142] d(X + ,X5)=0.675 d(X + ,X6)=0.608 d(X + ,X7)=0.647

[0143] d(X - ,X1)=0.507 d(X - ,X2)=0.661 d(X - ,X3)=0.760 d(X - ,X4)=0.398

[0144] d(X - ,X5)=0.581 d(X - ,X6)=0.725 d(X - ,X7)=0.549

[0145] Calculate the approximation μ i :

[0146] μ1=0.581 μ2=0.442 μ3=0.400 μ4=0.623 μ5=0.538

[0147] μ6=0.456 μ7=0.541

[0148] According to the similarity CC i + The values ​​are sorted, and the results are as follows:

[0149] MU4>MU1>MU7>MU5>MU6>MU2>MU3.

Claims

1. A machine tool maintenance priority sorting method based on z-number-CRITIC-grey correlation, characterized in that: The following steps are involved: Step 1: Establish a maintenance priority ranking evaluation system; Step 2: Establish a z-number evaluation language table; Step 3: Construct the decision matrix D nxm ; Step 4: Normalize the decision matrix D nxm ; Step 5: Use the z-critic method to calculate the weights of q evaluation indicators; Step 6: Calculate the maintenance unit approximation and sort them based on the improved z-number-grey relational method.

2. A machine tool maintenance priority sorting method based on z number-CRITIC-grey correlation according to claim 1, characterized in that: Based on the cut set theory, the distance measure between the first component A is solved as follows: Where: and Respectively represent A i α-cut and 3. A machine tool maintenance priority sorting method based on z number-CRITIC-grey correlation according to claim 2, characterized in that: Based on the cut set theory, the distance measure between the second component B is solved as follows: Where: and Respectively represent B i β-cut and 4. A machine tool maintenance priority sorting method based on z number-CRITIC-grey correlation according to claim 3, characterized in that: Solving the hidden probability distribution p based on the maximum entropy model XA The distance between them is as follows: Where: p Zij represents the hidden probability distribution p between Z1 and Z2 XA .

5. A machine tool maintenance priority sorting method based on z number-CRITIC-grey correlation according to claim 4, characterized in that: Define the distance measure between two Z1 and Z2: Where: λ is a (0-1) parameter, which represents the decision maker's preference for fuzzy ranging and reliability ranging of z-number information.

6. A machine tool maintenance priority sorting method based on z number-CRITIC-grey correlation according to claim 5, characterized in that: Step 4: Normalize the decision matrix: Cost indicators: Interest-based indicators: in, Fuzziness Component Reliability Component constant.

7. A machine tool maintenance priority sorting method based on z number-CRITIC-grey correlation according to claim 6, characterized in that: Step 5 requires further improvement of the CRITIC method to integrate it with the z-number information. The specific formula is as follows: Where: TU(Z ij ) is a transformation of the z-number form, which contains all the information of the z-number; is the mean of the total utility of the z-number of each indicator; TU(S j ) represents the variability of the jth indicator; TU(r ij ) represents the correlation between indicators; TU(R j ) represents the conflict of the jth indicator; YOU(C j )=TU(S j )×TU(R j ); TU(C j ) represents the amount of information contained in the jth evaluation index, TU(C j ) is larger, the greater its role in the entire evaluation system, and the more weight it should be given; ω j is the objective weight of the jth evaluation index.

8. A machine tool maintenance priority sorting method based on z number-CRITIC-grey correlation according to claim 7, characterized in that: Step 6 requires further improvement of the grey relational decision model, which is defined as follows: Among them, (A ij ,B ij ) is expressed in the form of z number; X O As a reference sequence, X 1。。。m As a comparison sequence; It is the minimum difference between two levels and the maximum difference between two levels; ρ is the resolution coefficient, ρ∈(0,1), c((A 0j ,B 0j ),(A ij ,B ij )) is the comparison sequence (A ij ,B ij ) and the reference sequence (A 0j ,B 0j ) between the correlation coefficient, Δ 0i (j) is equivalent to the distance measure between two z numbers; Where: d(X 0, X i ) is the comparison sequence (A ij ,B ij ) and the reference sequence (A 0j ,B 0j ), W j Represents the weight of the evaluation index, 0≤w j ≤1; X + is a positive ideal sequence, X - is a negative ideal sequence; usually X + and X - As a reference sequence; According to the approximation μ i Sort the values.

Images