CN110057581B - Rotary machine fault diagnosis method based on interval type credibility rule reasoning - Google Patents

Rotary machine fault diagnosis method based on interval type credibility rule reasoning Download PDF

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CN110057581B
CN110057581B CN201910354802.5A CN201910354802A CN110057581B CN 110057581 B CN110057581 B CN 110057581B CN 201910354802 A CN201910354802 A CN 201910354802A CN 110057581 B CN110057581 B CN 110057581B
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徐晓滨
夏俊涛
侯平智
胡燕祝
李建宁
黄大荣
韩德强
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Hangzhou Dianzi University
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Abstract

The invention relates to a fault diagnosis method for a rotary machine based on interval-type credibility rule reasoning. The method can classify the fault characteristic data acquired under various fault modes, and construct an interval type reliability rule base of fault characteristic parameters and fault types; acquiring the matching degree of the characteristic input parameters and the reference value on line, and calculating rule activation weight; correcting the interval type reliability by using the activation weight to obtain new interval type reliability; by usingDempsterAnd the rule fuses the activated interval type credibility to obtain a new interval type credibility, and obtains the fault type corresponding to the online fault feature according to a decision criterion under the interval evidence. The method adopts interval reliability to describe the support degree of the fault characteristic signal to the fault mode, and the obtained fault decision result contains more information capacity, thereby being more beneficial to decision makers to make judgments.

Description

Rotary machine fault diagnosis method based on interval type credibility rule reasoning
Technical Field
The invention relates to a rotary machine fault diagnosis method based on interval-type credibility rule reasoning, and belongs to the field of machine fault diagnosis and maintenance.
Background
In modern industrial production, rotary mechanical equipment cannot be separated, equipment faults are reduced to the greatest extent through fault diagnosis technology, loss is reduced, and the rotary mechanical equipment plays a vital role in reducing equipment maintenance cost and improving working efficiency of the rotary mechanical equipment. Especially for some large-scale rotating machinery equipment, the structure is complicated, the maintenance cost is high, the time period is long, and once serious faults occur, serious harm is easily caused. Therefore, the method utilizes the fault diagnosis technology to judge the occurrence of the fault in advance, and has important practical significance for improving the safety of equipment.
The operation of mechanical equipment can not be separated in modern industrial production, the probability caused by equipment failure is reduced to the greatest extent before the equipment fails, and the loss is reduced, so that the maintenance cost of the equipment is reduced, the working efficiency of the equipment is improved, and the equipment has a vital effect, especially on some large-scale rotating mechanical equipment, the structure is complex, the maintenance cost is high, the time period is long, and once serious failure occurs, serious harm is easily caused. Therefore, the occurrence of the fault is judged in advance, and the method has great significance for maintaining the life and property safety of people.
Two key problems are faced in fault diagnosis of rotary mechanical equipment, one is that due to interference in a measurement environment or real-time change of an operation state of the equipment, collected fault characteristic signals for fault diagnosis generally have strong uncertainty, and uncertainty of a fault judgment result is caused. Therefore, the interval reliability is adopted to describe the support degree of the fault characteristic signal to the fault mode, so that the uncertainty of the fault can be more objectively described; secondly, when various characteristic signals are used for judging fault modes, due to the influence of uncertainty, the judgment reliability result given by a single characteristic is inevitably inaccurate and unilateral, so that corresponding information fusion methods are needed to be adopted for fusing the interval reliability provided by each single-source characteristic signal, and the accuracy of fault decision is improved.
Disclosure of Invention
The invention aims to provide a rotary machine fault diagnosis method based on interval type reliability rule reasoning, which is characterized in that corresponding fault characteristic data are sampled and analyzed under different types of fault modes, the fault characteristic data are converted into reliability of each fault type, and fault decisions are made according to the reliability intervals obtained after fusion through fusion of multi-source reliability intervals.
The invention provides a fault diagnosis method for rotary mechanical equipment based on interval evidence fusion, which comprises the following steps:
the fault diagnosis method for the rotating machinery based on interval type credibility rule reasoning comprises the following steps:
(1) setting an identification frame theta ═ zeta { zeta } of a rotating machinery fault diagnosis method based on interval confidence rule reasoning1,ζ2,ζ3Therein ζ1Indicating an imbalance fault in the rotating machine, ζ2Showing an asymmetrical fault, ζ, in a rotating machine3Indicating a base loosening failure in a rotating machine.
(2) Setting the rotating speed of the rotating mechanical equipment as p, unit: the method comprises the steps that rotation per minute (r/min), wherein p belongs to [1000r/min,3000r/min ], a vibration acceleration sensor arranged on a base or a support and the like can acquire time domain vibration acceleration signals at intervals of delta t belonging to [16s,48s ], under various fault modes, and a signal sequence omega (r) is obtained, wherein r is 1, 2.
(3) Performing fast Fourier transform on the time domain vibration signal sequence omega (r) obtained in the step (2) to transform the time domain vibration signal sequence omega (r) into a corresponding frequency domain spectrogram, and then selecting amplitudes of 1-time fundamental frequency, 2-time fundamental frequency and 3-time fundamental frequency as fault characteristic parameters which are respectively recorded as x1(r)、x2(r)、x3(r)。
(4) Establishing interval type credibility rule base for describing characteristic parameter variable x1、x2、x3And failure mode, wherein the k-th rule RkIs expressed as follows:
Figure BDA0002045063220000021
in the formula (1), the reaction mixture is,
Figure BDA0002045063220000022
for inputting characteristic parameter variable xi(i-1, 2,3) set of input reference values, wherein the elements satisfy
Figure BDA0002045063220000023
qiThe number of the values of the reference value of the corresponding characteristic parameter is represented,
Figure BDA0002045063220000024
and
Figure BDA0002045063220000025
for x in various failure modesiMaximum and minimum values of βj,k(j 1,2,3, k 1, 2.., L) is the failure mode ζjAnd j is 1,2,3, the section reliability given:
βj,k＝[aj,bj](2)
wherein a isjMinimum value representing the effective confidence of the interval, bjRepresents the maximum value of the interval effective reliability, and is more than or equal to 0 and less than or equal to aj≤bjLess than or equal to 1 and satisfies the constraint condition
Figure BDA0002045063220000026
And is
Figure BDA0002045063220000027
(5) Characteristic parameter sample x obtained for the r-th sampling periodi(r) substituting into the k-th rule defined in step (4) to obtain xiInputting a reference value according to the kth rule
Figure BDA0002045063220000031
The matching degree of (2):
① when
Figure BDA0002045063220000032
Or
Figure BDA0002045063220000033
When xiFor the
Figure BDA0002045063220000034
And
Figure BDA0002045063220000035
degree of matching of
Figure BDA0002045063220000036
The values are all 1, and the matching degree values of other reference values are all 0.
② when
Figure BDA0002045063220000037
When xiFor the
Figure BDA0002045063220000038
And
Figure BDA0002045063220000039
degree of matching of
Figure BDA00020450632200000310
The values of (A) are respectively as follows:
Figure BDA00020450632200000313
Figure BDA00020450632200000314
the matching degree values of other reference values are all 0.
(6) According to equation (3), calculating the activation weight of each rule in the interval confidence rule base:
Figure BDA00020450632200000311
in the formula (4), the reaction mixture is,
Figure BDA00020450632200000312
l is the number of rules in the rule base, θkThe initial rule weight is 0 ≦ thetak≤1，iInputting the initial attribute weight of the characteristic parameter, wherein the weight is less than or equal to 0i≤1。
(7) And fusing the activated rules in the interval confidence rule base by adopting a Dempster combination rule to obtain an interval confidence value of each fault mode, wherein the method specifically comprises the following steps:
(7-1) activation weight obtained according to the formula (4), interval type reliability β in the k rulej,kAnd (3) carrying out discount to obtain the discounted interval type reliability:
mj,k(ζj)＝wkβj,k，j＝1,2,3,k＝1,2,...,L
mΘ,k(Θ)＝1-wk(5)
wherein m isj,kIs the jth interval confidence level after discount, mΘ,kExpressed as interval-type confidence of the corpus elements.
(7-2) confidence level (m) of interval type corresponding to the 1 st and 2 nd rules obtained in the step (7-1)j,1,mΘ,1) And (m)j,2,mΘ,2) And fusing the two by using the following Dempster combination rule to obtain the fused interval type credibility as follows:
Figure BDA0002045063220000041
the above interval type reliability combined operation can be realized by fmincon optimization function in MATLAB.
(7-3) results obtained from formula (6)
Figure BDA0002045063220000042
And (m)j,3,mΘ,3) Continuing to use Dempster combination rule fusion in the step (7-2) to obtain new interval type credibility
Figure BDA0002045063220000043
Sequentially fusing to obtain final interval confidence
Figure BDA0002045063220000044
Figure BDA0002045063220000045
Where k represents the number of rules in the system.
(8) According to the interval type reliability judgment set type decision result obtained by Dempster rule combination, the fault type can be determined to be zeta when the following two conditions are metj，j＝1,2,3：
(8-1)
Figure BDA0002045063220000046
The left and right end points of the reliability interval are respectively larger than the left and right end points of the interval type reliability of other fault modes.
(8-2)
Figure BDA0002045063220000047
Are all less than 0.3.
The invention provides a rotary machine fault diagnosis method based on interval type credibility rule reasoning, which divides fault characteristic monitoring data acquired under different fault modes and constructs a mapping relation rule base of fault characteristic parameters and fault types; matching the acquired characteristic input parameters with reference values, and calculating activation weights; discounting the interval type reliability to obtain a new interval type reliability; and fusing the activated interval type credibility by using a Dempster rule to obtain a new interval type credibility, and obtaining a fault type corresponding to the online fault feature according to a decision criterion under an interval evidence.
The invention has the beneficial effects that:
firstly, due to the uncertainty of input information, the uncertainty of a fault judgment result is also caused, so that the method adopts interval type credibility to describe the support degree of fault characteristic signals for fault mode occurrence, and the obtained fault decision result contains more information capacity, thereby being more beneficial to decision makers to judge.
Secondly, because of the influence of uncertainty when various characteristic signals are used for judging, the judgment given by a single characteristic cannot be reliable to the result, so that the method adopts a corresponding information fusion method to fuse the credibility of the single characteristic signal, thereby increasing the accuracy of decision.
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FIG. 1 is a block flow diagram of the method of the present invention.
FIG. 2 is a block diagram of a motor rotor fault diagnostic system in an embodiment of the method of the present invention.
Detailed Description
The fault diagnosis method for the rotating machinery based on interval type credibility rule reasoning comprises the following steps:
(1) setting an identification frame theta ═ zeta { zeta } of a rotating machinery fault diagnosis method based on interval confidence rule reasoning1,ζ2,ζ3Therein ζ1Indicating an imbalance fault in the rotating machine, ζ2Showing an asymmetrical fault, ζ, in a rotating machine3Indicating a base loosening failure in a rotating machine.
(2) Setting the rotating speed of the rotating mechanical equipment as p, unit: the method comprises the steps that rotation per minute (r/min), wherein p belongs to [1000r/min,3000r/min ], a vibration acceleration sensor arranged on a base or a support and the like can acquire time domain vibration acceleration signals at intervals of delta t belonging to [16s,48s ], under various fault modes, and a signal sequence omega (r) is obtained, wherein r is 1, 2.
(3) Performing fast Fourier transform on the time domain vibration signal sequence omega (r) obtained in the step (2) to transform the time domain vibration signal sequence omega (r) into a corresponding frequency domain spectrogram, and then selecting amplitudes of 1-time fundamental frequency, 2-time fundamental frequency and 3-time fundamental frequency as fault characteristic parameters which are respectively recorded as x1(r)、x2(r)、x3(r)。
(4) Establishing interval type credibility rule base for describing characteristic parameter variable x1、x2、x3And failure mode, wherein the k-th rule RkIs expressed as follows:
Figure BDA0002045063220000051
in the formula (1), the reaction mixture is,
Figure BDA0002045063220000061
for inputting characteristic parameter variable xi(i-1, 2,3) set of input reference values, wherein the elements satisfy
Figure BDA0002045063220000062
qiThe number of the values of the reference value of the corresponding characteristic parameter is represented,
Figure BDA0002045063220000063
and
Figure BDA0002045063220000064
for x in various failure modesiβj,k(j 1,2,3, k 1, 2.., L) is the failure mode ζjAnd j is 1,2,3, the section reliability given:
βj,k＝[aj,bj](2)
wherein a isjMinimum value representing the effective confidence of the interval, bjRepresents the maximum value of the interval effective reliability, and is more than or equal to 0 and less than or equal to aj≤bjLess than or equal to 1 and satisfies the constraint condition
Figure BDA0002045063220000065
And is
Figure BDA0002045063220000066
To facilitate understanding of the interval-type belief rule base, it is assumed that the example is given here
Figure BDA0002045063220000067
Each reference value in (1) is taken as
Figure BDA0002045063220000068
Each reference value in (1) is taken as
Figure BDA0002045063220000069
Each reference value in (1) is taken as
Figure BDA00020450632200000610
A total of 64 rules results,
setting an initial θk＝1,1＝2＝31, wherein the rule form in part is as follows:
R1: if x10.05 and x20.035 and x30.28, then β1,1＝[0.5632,0.9672],β2,1＝[0.1246,0.1365],β3,1＝[0.1126,0.1365]
R2: if x10.05 and x20.125 and x30.42, then β1,2＝[0.5631,0.9463],β2,2＝[0.1258,0.2367],β3,2＝[0.1248,0.3365]
R3: if x10.05 and x20.25 and x30.67, then β1,3＝[0.6321,0.9532]，β2,3＝[0.1124,0.3236)],β3,3＝[0.1214,0.2362]
......
R62: if x10.38 and x20.035 and x30.28, then β1,62＝[0.1129,0.2563],β2,62＝[0.2145,0.4259],β3,62＝[0.4569,0.9653]
R63: if x10.05 and x20.45 and x30.42, then β1,63＝[0.1127,0.3896],β2,63＝[0.1116,0.3256],β3,63＝[0.6563,0.9782]
R64: if x10.05 and x20.46 and x30.48, then β1,64＝[0.3456,0.4569],β2,64＝[0.3213,0.4452],β3,64＝[0.4563,0.9863]
(5) Characteristic parameter sample x obtained for the r-th sampling periodi(r) substituting into the k-th rule defined in step (4) to obtain xiInputting a reference value according to the kth rule
Figure BDA0002045063220000071
The matching degree of (2):
① when
Figure BDA0002045063220000072
Or
Figure BDA0002045063220000073
When xiFor the
Figure BDA0002045063220000074
And
Figure BDA0002045063220000075
degree of matching of
Figure BDA0002045063220000076
The values are all 1, and the matching degree values of other reference values are all 0.
② when
Figure BDA0002045063220000077
When xiFor the
Figure BDA0002045063220000078
And
Figure BDA0002045063220000079
degree of matching of
Figure BDA00020450632200000710
The values of (A) are respectively as follows:
Figure BDA00020450632200000711
Figure BDA00020450632200000712
the matching degree values of other reference values are all 0.
(6) According to equation (3), calculating the activation weight of each rule in the interval confidence rule base:
Figure BDA00020450632200000713
in the formula (4), the reaction mixture is,
Figure BDA00020450632200000714
l is the number of rules in the rule base, θkThe initial rule weight is 0 ≦ thetak≤1，
iInputting the initial attribute weight of the characteristic parameter, wherein the weight is less than or equal to 0i≤1。
For the sake of understanding, it is exemplified here that, taking the model in step (4) as an example, the activation weight of each rule is calculated for each input variable, and the activation weight w of each rule in the interval-type credibility rule system can be calculated using equations (3) and (4)kAssume an input variable x1(r)＝0.1663，x2(r)＝0.1612，x3(R) 0.1221 rule R can be activated21、R22、R25、R26、R37、R38、R41、R42Calculating the resulting activation weight wkComprises the following steps: w is a1＝0.075、w2＝0.64、w3＝0.0171、w4＝0.16、w5＝0.0092、w6＝0.0838、w7＝0.011、w8And when the interval confidence level rule base is not equal to 0.0035, the rest are all 0, namely 8 rules in the interval confidence level rule base are activated.
(7-1) activation weight obtained according to the formula (4), interval type reliability β in the k rulej,kAnd (3) carrying out discount to obtain the discounted interval type reliability:
mj,k(ζj)＝wkβj,k，j＝1,2,3,k＝1,2,...,L
mΘ,k(Θ)＝1-wk(5)
wherein m isj,kIs the jth interval confidence level after discount, mΘ,kThe interval type confidence L expressed as a complete set element is the number in the rule base.
To facilitate the understanding of equation (5), let us assume w1＝0.075，w2＝0.64，w3＝0.0171，w4＝0.16，w5＝0.0092，w6＝0.0838，w7＝0.011，w8＝0.0035；β1,1＝[0.5632,0.9672]，
β2,1＝[0.1246,0.1365],β3,1＝[0.1126,0.1256],β1,2＝[0.4263,0.9236],β2,2＝[0.1362,0.2423]，β3,2＝[0.1213,0.2352],β1,3＝[0.5631,0.9463],β2,3＝[0.1258,0.2367],β3,3＝[0.1248,0.3365]，β1,4＝[0.6321,0.9532],β2,4＝[0.1124,0.3236],β3,4＝[0.1214,0.2362],β1,5＝[0.1263,0.9542]，β2,5＝[0.1236,0.2354],β3,5＝[0.1124,0.2263],β1,6＝[0.1213,0.2145],β2,6＝[0.4569,0.9653]，Β3,6＝[0.1123,0.3563],β1,7＝[0.7563,0.9782],β2,7＝[0.1563,0.2687],β3,7＝[0.1129,0.2563]，β1,8＝[0.1012,0.1818],β2,8＝[0.5623,0.9016],β3,8＝[0.1456,0.1569]；
According to formula (5):
mj,1(ζj)＝{[0.0422,0.0725],[0.0093,0.0102],[0.0084,0.0094]},mj,2(ζj)＝{[0.2728,0.5911],[0.0872,0.1551],[0.0776,0.1505]},mj,3(ζj)
＝{[0.0096,0.0162],[0.0022,0.0040],[0.0021,0.0058]},mj,4(ζj)＝{[0.1011,0.1525],[0.0180,0.0518],[0.0194,0.0378]},
mj,5(ζj)＝{[0.0012,0.0088],[0.0011,0.0022],[0.0010,0.0021]},mj,6(ζj)
＝{[0.0102,0.0180],[0.0383,0.0809],[0.0094,0.0299]},mj,7(ζj)
＝{[0.0083,0.0108],[0.0017,0.0030],[0.0012,0.0028]},mj,8(ζj)
＝{[0.0004,0.0006],[0.0020,0.0032],[0.0005,0.0005]}；mΘ,1(Θ)＝0.925，mΘ,2(Θ)
＝0.36，mΘ,3(Θ)＝0.9829，mΘ,4(Θ)＝0.84，mΘ,5(Θ)＝0.9908，mΘ,6(Θ)＝0.9162，
mΘ,7(Θ)＝0.989，mΘ,8(Θ)＝0.9965；
(7-2) confidence level (m) of interval type corresponding to the 1 st and 2 nd rules obtained in the step (7-1)j,1,mΘ,1) And (m)j,2,mΘ,2) The fusion is carried out by using the following Dempster rule combination, and the fusion interval type credibility is obtained:
Figure BDA0002045063220000091
the above interval type reliability combined operation can be realized by fmincon optimization function in MATLAB.
(7-3) results obtained from formula (6)
Figure BDA0002045063220000092
And (m)j,3,mΘ,3) Continuing to use Dempster combination rule fusion in the step (7-2) to obtain new interval type credibility
Figure BDA0002045063220000093
Sequentially fusing to obtain final interval confidence
Figure BDA0002045063220000094
Figure BDA0002045063220000095
Where k represents the number of rules in the system.
To enhance the understanding of equation (6), an example is given here, assuming mj,1(ζj)＝{[0.0205,0.0669],[0.014,0.0199],[0.0092,0.0166]}，mθ,1(Θ)＝[0.9298,0.9298]，mj,2(ζj)＝{[0.2061,0.6330],[0.1040,0.1697],[0.1151,0.1698]}，mθ,2(Θ)＝[0.3591,0.3591]，mj,3(ζj)＝{[0.0073,0.1065],[0.0033,0.0039],[0.0021,0.0049]}，mθ,3(Θ)＝[0.9829,0.9829]，mj,4(ζj)＝{[0.0420,0.1478],[0.0190,0.0383],[0.0213，0.0425]}，mθ,4(Θ)＝[0.8438,0.8438]，mj,5(ζj)＝{[0.0051,0.0090],[0.0014,0.0033],[0.0010,0.0027]}，mθ,5(Θ)＝[0.9908,0.9908]，mj,6(ζj)＝{[0.0388,0.0797],[0.0105,0.0199],[0.0096,0.0189]}，mθ,6(Θ)＝[0.9162,0.9162]，mj,7(ζj)＝{[0.0014,0.0019]，[0.0003,0.0007],[0.0003,0.0007]}，mθ,7(Θ)＝[0.9978,0.9978]，mj,8(ζj)＝{[0.0029,0.0052],[0.0118,0.0183],[0.0030,0.0046]}，mθ,8(Θ)＝[0.9796,0.9796]；
Obtaining the product according to the Dempster combination rule in the step (7-2)
Figure BDA0002045063220000101
Figure BDA0002045063220000102
0.3437]Then the obtained results are summed up with (m)j,3,mΘ,3) Fusing according to Dempster combination rules in the step (7-2) to obtain final interval type credibility
Figure BDA0002045063220000103
Figure BDA0002045063220000104
Figure BDA0002045063220000105
Where k represents the number of rules in the system.
(8) The decision method based on evidence reasoning is widely applied to the fields of target identification, system evaluation, fault diagnosis and the like, and the interval type reliability determination fault type zeta can be obtained by meeting the following two conditions according to the interval type reliability judgment set type decision result obtained by Dempster rule combinationj，j＝1,2,3：
(8-1)
Figure BDA0002045063220000106
The left and right end points of the reliability interval are respectively larger than the left and right end points of the interval type reliability of other fault modes.
(8-2)
Figure BDA0002045063220000107
Are all less than 0.3.
Embodiments of the method of the present invention are described in detail below with reference to the accompanying drawings:
the flow chart of the method of the invention is shown in figure 1, and the core part is as follows: obtaining a frequency domain spectrogram from the time domain signal through fast Fourier transform, and selecting different fundamental frequencies as fault characteristic input parameters; constructing an interval type reliability rule base to describe the nonlinear mapping relation between the input variable and the fault characteristic mode; discounting the obtained interval type reliability to obtain new interval type reliability; obtaining a decision result of interval type reliability fusion by using a Dempster rule, and accurately describing the type of the fault by using a decision criterion;
1. setting an identification frame theta ═ zeta { zeta } of a rotating machinery fault diagnosis method based on interval confidence rule reasoning1,ζ2,ζ3Therein ζ1Indicating an imbalance fault in the rotating machine, ζ2Showing an asymmetrical fault, ζ, in a rotating machine3Indicating a base loosening failure in a rotating machine.
2. The method shown in fig. 2 is used for acquiring data, setting the rotation speed of the rotary mechanical equipment to be 1500r/min, setting the time interval Δ t of the vibration acceleration sensor installed on the base or the bracket and the like to be 16s, acquiring time-domain vibration acceleration signals in three fault modes, and obtaining a signal sequence ω (r), wherein r is 1, 2.
3. Performing fast Fourier transform on the time domain vibration signal sequence omega (r) obtained in the step (2) to transform the time domain vibration signal sequence omega (r) into a corresponding frequency domain spectrogram, and then selecting amplitudes of 1-time fundamental frequency, 2-time fundamental frequency and 3-time fundamental frequency as fault characteristic parameters which are respectively recorded as x1(r)、x2(r)、x3(r), r 1,2, n, which, for the sake of a specific explanation,a total of 40 acquisitions n.
4. Establishing interval type credibility rule base for describing characteristic parameter variable x1、x2、x3Nonlinear mapping relationship with failure mode:
selecting semantic values of input variables:
x1(r) fuzzy variables are described as: minimum (PS1), minimum (PM1), normal (PN1), maximum (PQ1),
x2(r) fuzzy variables are described as: minimum (PS2), minimum (PM2), normal (PN2), maximum (PQ2),
x3(r) fuzzy variables are described as: minimum (PS3), minimum (PM3), normal (PN3), maximum (PQ3), with specific assignments as shown in tables 1-3:
TABLE 1 x1Semantic value and reference value of (r)
Figure BDA0002045063220000111
TABLE 2 x2Semantic value and reference value of (r)
Figure BDA0002045063220000112
TABLE 3 x3Semantic value and reference value of (r)
Figure BDA0002045063220000113
Defining and constructing a regional reliability rule base according to reference values in tables 1-3 and meeting constraint conditions
Figure BDA0002045063220000114
And is
Figure BDA0002045063220000115
Are respectively at
Figure BDA0002045063220000116
Extract an element as x1(r),x2(r),x3Reference values of (r), thus combined into rules, may yield, in total, a rule base construct of L4 × 4 × 4 as shown in table 4:
TABLE 4 Interval confidence rule base
Figure BDA0002045063220000117
Figure BDA0002045063220000121
Figure BDA0002045063220000131
5. Combining given inputs x1、x2、x3And step (7) obtaining the discounted interval type reliability, namely obtaining the final interval type reliability;
firstly, obtaining the matching degree of an input characteristic parameter and a kth rule input reference value according to a formula (3), then obtaining the activation weight of each rule in an interval confidence rule base according to a formula (4), then obtaining the interval confidence after discount through a step (7), and finally fusing the activated rules and obtaining the final interval confidence by utilizing a Dempster combination rule
Figure BDA0002045063220000132
Figure BDA0002045063220000133
As shown in tables 5-7.
TABLE 5 x1(r) sample Interval fusion confidence
Figure BDA0002045063220000134
TABLE 6 x2(r) sample Interval fusion confidence
Figure BDA0002045063220000141
TABLE 7 x3(r) sample Interval fusion confidence
Figure BDA0002045063220000142
6. After tables 5-7 are obtained, the true fault type can be determined according to the interval fusion decision criterion of step (8) of the method of the present invention.

Claims (1)

1. The fault diagnosis method of the rotating machinery based on interval type credibility rule reasoning is characterized by comprising the following steps:
(1) setting an identification frame theta ═ zeta { zeta } of a rotating machinery fault diagnosis method based on interval confidence rule reasoning1,ζ2,ζ3Therein ζ1Indicating an imbalance fault in the rotating machine, ζ2Showing an asymmetrical fault, ζ, in a rotating machine3Indicating a base loosening fault in a rotating machine;
(2) setting the rotating speed of the rotating mechanical equipment as p, unit: the method comprises the steps that rotation per minute, wherein p belongs to [1000r/min,3000r/min ], a vibration acceleration sensor arranged on a base or a support can acquire time domain vibration acceleration signals at intervals of delta t belonging to [16s,48s ], and signal sequences omega (r) are obtained, wherein r is 1,2, n, n is the number of sampling periods;
(3) performing fast Fourier transform on the time domain vibration signal sequence omega (r) obtained in the step (2) to transform the time domain vibration signal sequence omega (r) into a corresponding frequency domain spectrogram, and then selecting amplitudes of 1-time fundamental frequency, 2-time fundamental frequency and 3-time fundamental frequency as fault characteristic parameters which are respectively recorded as x1(r)、x2(r)、x3(r)；
(4) Establishing interval type credibility rule base for describing characteristic parameter variable x1、x2、x3And failure mode, wherein the k-th rule RkIs expressed as follows:
Figure FDA0002612245340000011
in the formula (1), the reaction mixture is,
Figure FDA0002612245340000012
for inputting characteristic parameter variable xiOf the input reference value set, wherein the elements satisfy
Figure FDA0002612245340000013
qiThe number of the values of the reference value of the corresponding characteristic parameter is represented,
Figure FDA0002612245340000014
and
Figure FDA0002612245340000015
for x in various failure modesiMaximum and minimum values of βj,kTo fault mode ζjAssigned interval type reliability:
βj,k＝[aj,bj](2)
wherein a isjMinimum value representing the effective confidence of the interval, bjRepresents the maximum value of the interval effective reliability, and is more than or equal to 0 and less than or equal to aj≤bjLess than or equal to 1 and satisfies the constraint condition
Figure FDA0002612245340000016
And is
Figure FDA0002612245340000017
(5) Characteristic parameter sample x obtained for the r-th sampling periodi(r) substituting into the k-th rule defined in step (4) to obtain xiInputting a reference value according to the kth rule
Figure FDA0002612245340000021
Figure FDA0002612245340000022
The matching degree of (2):
① when
Figure FDA0002612245340000023
Or
Figure FDA0002612245340000024
When xiFor the
Figure FDA0002612245340000025
And
Figure FDA0002612245340000026
degree of matching of
Figure FDA0002612245340000027
Values are all 1, and values of matching degrees of other reference values are all 0;
② when
Figure FDA0002612245340000028
When xiFor the
Figure FDA0002612245340000029
And
Figure FDA00026122453400000210
degree of matching of
Figure FDA00026122453400000211
The values of (A) are respectively as follows:
Figure FDA00026122453400000212
Figure FDA00026122453400000213
the matching degree values of other reference values are all 0;
(6) according to equation (3), calculating the activation weight of each rule in the interval confidence rule base:
Figure FDA00026122453400000214
in the formula (4), the reaction mixture is,
Figure FDA00026122453400000215
l is the number of rules in the rule base, θkThe initial rule weight is 0 ≦ thetak≤1，iInputting the initial attribute weight of the characteristic parameter, wherein the weight is less than or equal to 0i≤1；
(7) And fusing the activated rules in the interval confidence rule base by adopting a Dempster combination rule to obtain an interval confidence value of each fault mode, wherein the method specifically comprises the following steps:
(7-1) activation weight obtained according to the formula (4), interval type reliability β in the k rulej,kAnd (3) carrying out discount to obtain the discounted interval type reliability:
mj,k(ζj)＝wkβj,k
mΘ,k(Θ)＝1-wk(5)
wherein m isj,kIs the jth interval confidence level after discount, mΘ,kInterval type confidence expressed as a corpus element;
(7-2) confidence level (m) of interval type corresponding to the 1 st and 2 nd rules obtained in the step (7-1)j,1,mΘ,1) And (m)j,2,mΘ,2) And fusing the two by using the following Dempster combination rule to obtain the fused interval type credibility as follows:
Figure FDA0002612245340000031
(7-3) results obtained from formula (6)
Figure FDA0002612245340000032
And (m)j,3,mΘ,3) Continuing to use Dempster combination rule fusion in the step (7-2) to obtain new interval type credibility
Figure FDA0002612245340000033
Sequentially fusing to obtain final interval confidence
Figure FDA0002612245340000034
Figure FDA0002612245340000035
Wherein k' represents the number of rules in the system;
(8) according to the interval type reliability judgment set type decision result obtained by Dempster rule combination, the fault type can be determined to be zeta when the following two conditions are metj：
(8-1)
Figure FDA0002612245340000036
The left end point and the right end point of the reliability interval are respectively larger than the left end point and the right end point of the interval type reliability of other fault modes;
(8-2)
Figure FDA0002612245340000037
are all less than 0.3.
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