基于AHP和模糊综合评判的润滑油状态评估

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Sep．2013机 床 与 液 压Hydromechatronics Engineering Ve1．41 No．18DOI：10．3969／j．issn．1001-3881．2013．18．018Lubricant Oil Condition Assessment Based on AHPand Fuzzy Comprehensive EvaluationDU Chuanbin ，WANG Juxianga．Graduate Students’Brigade；b．Department of Airborne Vehicle Engineering，Naval Aeronautical Engineering Institute，Yantai 264001，China1．IntroductionAbstract：Lubricant oil condition assessment is a multi-index evaluation problem ，and it should besolved by considering indexes comprehensively that charactering oil condition．In this paper，oilphysical and chemical property indexes，oil prope~y deteriorating indexes，and wear metal ele‘ment indexes were used to assess oil condition comprehensively．Hierarchy of lubricant oil condi‘tion assessment and weight of each index were determined by AHP method．Secondary oil con。

dition assessment was achieved by fuzzy comprehensive evaluation method．Firstly，oil physicaland chemicaI condition．oil property deteriorating condition，and wear condition were assessed byfirst．grade fuzzy comprehensive evaluation．and then Iubricant oil condition were determined bysecond．grade fuzzy comprehensive evaluation．The example showed that the oil condition can beassessed effectively by applying these two methods.

Key words：Iubricant oil condition，AHP，fuzzy comprehensive evaluationEngines rely highly on lubricant oil to operateproperly． The film of lubricant oil between enginecomponents can reduce friction and provide an addi-tional pathway for heat transfer，thereby assisting theengine in maintaining its mechanical efficiency，pro—longing its life，and guaranteeing its normal operation[1—2]．Engines can not work without lubricant oil，and lubricant oil quality determines the work condi—tion of engine．At the same time，many wear parti‘cles，which are the products of engine componentsfriction，suspend in lubricant oil． On the basis ofwear metal elements types and concentrations，thecondition of component that contains these elements，can be determined． Apparently，acquiring real timeoil quality and wear metal elements information，andtaking in time measures，can guarantee that the en。

Received：2013—05—16$DU Chuanbin．E—mail：836027552### qq．comgine is in good state.

According to the above analysis，Lubricant oilcondition assessment is a multi．index evaluation prob-lem．and it is very hard to assess oil condition byconsidering single index． Therefore， it should besolved by considering indexes comprehensively thatcharacterizing oil condition.

In this paper．1ubricant oil of a missile launch-ing vehicle and guarantee vehicle is investigated.

Through physical and chemical analysis．FTIR analysis，and AES analysis，oil physical and chemical in—dexes，oil property deteriorating indexes，and wearmetal elements indexes can be acquired．These inde—xes characterize oil condition from different respects.

By using AHP[3—4](Analytic Hierarchy Process)and fuzzy comprehensive evaluation[5]，these inde—xes are considered comprehensively to assess lubri’a r】t oi】condition.

2．Analysis of lubricant oil condition assess-ment process based on AHPIn 1980，AHP was proposed by T．L．Saty toDU Chuanbin，et al：Lubricant Oil Condition Assessment Based on AHPand Fuzzy Comprehensive Evaluation 89organize and synthesize people subjective judgment，which can also transforn3 qualitative problem to quan—titative problem，and make complex problem system—atical and hierarchica1．There are four steps to assesslubricant oil condition process using AHP．① Ana—lyze relationship between factors of assessmentprocess，and build hierarchy．② Compare every twofactors of every layer，and construct judgment ma-trix．③ According to the judgment matrix，computerelative weight of factors．④ Check consistency of theiudgment matrix.

2．1．Hierarchy of lubricant oil condition assess-mentIn the process of lubricant oil condition assess—ment，firstly，three testings are conducted，and elev—en indexes that characterize oil condition are ac-quired；secondly，on the basis of some indexes，oilphysical and chemical condition，oil property deterio-rating condition，and wear condition can be deter—mined；lastly，according to these conditions，lubri—cant oil condition can be assessed comprehensively.

So the hierarchy of oil condition assessment can beconstructed．and illustrated with Fig．1.

Lubricant oilconditionPhysical and chemicalcondition U，Propery deterioratingcondition U2W ear conditionChange rate ofVlscosity llAcid number“l2Acid numbervalue．added“0xidation1evel“21NitratiOllevel nW ater pollutionlevel“23============= Diesel pollution1evel“24COncentrati0n ofFe”31C0ncentrati0n ofAI“32C0ncentratiOn ofCu 3==========：== COncentratiOn ofSi“34Fig．1 Hierarchy of lubricant oil condition assessment2．2．Establish of judgment matrix of factorsAfter construction of hierarchy，comparison ofevery two factors is taken to determine relative impor—tance of every factor，and quantify the relative impor‘tance with 1—9 scales proposed by Satty to establishjudgment matrix．For example，judgment matrix A=(a )n x rt of layer B relative to layer A is established，and a is the quantified scale between the ith factorand the jth factor of layer B according to their relativeimportance to layer A.

2．3．Computation of factor weightAccording to judgment matrix A，preferentialweight of factors can be determined by computing themaximum eigenvalue of matrix A and its correspond—ing eigenvector．The eigenvector W =(w1，w2，? ，w )represents the ratio of weight distribution．Eig-envector can be obtained by root method as folows：= .

1 nAmaxL
， 。
： 2．4．Consistency checkw i ，i= 1，2，? ，rt(1)(2)While calculating the maximum matrix eigenval—He A Ⅱ，consistency check must be made so as toguarantee the accuracy and reliability of calculationresult．consistency indicat0ris = ，checkc。eficient is CR=丽CI
， and RI is average rand0mconsistency indicator． When CR < 0．1，matrix Ameets the consistency requirement．Some values of R／are listed in Tab．1.

Tab．1 Average random consistency indicator R／3．Fuzzy comprehensive evaluationAccording to the hierarchy of lubricant oil condi—tion assessment．the assessment process is divided in—to three layers．Evaluation starts from the bottom．1ay—er sub—factors，and then on the basis of this layer e—valuation． further evaluation is conducted． Thus，multi—fuzzy comprehensive evaluation model is nee—ded.

Multi．fuzzy comprehensive evaluation model isaccording to the features of objects，to set up indexsystem ．to divide all the factors with special features.

In accordance with the lower to higher，firstly do thecomprehensive evaluation for every section， andnext，do the senior comprehensive evaluation for ev-cry lower result，and finally get the realistic results.

∑ 7 ) 。

∑㈦Hydromechatronics EngineeringConcrete steps are shown as follows：3．1．Setting element set and comment set1)Seting up evaluation objects’element setU． Divide Uin to several subsets with special fea—tures，denoted U1， ，? ，U meeting with， U =U，U n = (i≠ )．Every subsets are divided in—to several evaluation elements， U{ 订，“ ，?， m}，i=1，2，?，n.

2)Seting up comment set V={ 1， ，?， ).

3．2．Determining the weight of every elementEvery U represents characteristics of U，as apart of U．According to different importance，gets theweight distribution A = {01，a2，?，a )， meansweight Vect0r ：{ 02，?，an}， ai=1，andweight vector of subset U ／s A ={0n，a ，? ，口 )，。 。

3．3．Determining single element fuzzy matrixAccording to fuzzy theory ，every element’smembership of U is calculated with formula．The ap-praisal ofjth single factor is =( l， ，?， )，where is the fuzzy membership degree of factorto grade v ．The overall fuzzy evaluation matrix of alm factors is“ ]= ? l， ==，3．4．Multi-fuzzy comprehensive evaluationSince the hierarchy of lubricant oil condition as-sessment is divided into three layers．a model of see-ondary fuzzy comprehensive evaluation can be built.

Firstly，do the comprehensive evaluation for every el—ement in the botom layer．and then do it for thehigher layer.

1)First—grade fuzzy comprehensive evaluationSupposing the weight vector of elements in sub。

set U is A ={口 a 2，?，D )，with fuzzy operatorM(V，^)，carry matrix synthetic operation onweight vector A and fuzzy evaluation matrix R ，thematrix elements aye that b = V
，
(。 ^ )，(i：1，2，?，n； =1，2，?，p)．The first—grade con。

Drehensive evaluation resuh of the th element subsetU is shown as follows：惯 ]whereB = A 。R = [b1，b2，? ，b
p
] (4)b = V (0 八1 1Finally，according to maximum membership de。

gree method，evaluation result is the comment ele。

ment corresponding to the maximum of b (i=1，2，?
，P).

4．Lubricant oil condition assessmentSamples investigated are CD一15W／40 lubricant0il．and collected from one launching vehicle and oneguarantee vehicle．Through physical and chemical a—nalysis[6，7]，FTIR analysis[8，9]，and AES analy—sis『10]，oil physical and chemical indexes，oilproperty deteriorating indexes，and wear metal ele。

ments indexes are acquired．The results are listed inTab 2.

Tab．2 Lubricant oil testing resultsDU Chuanbin，et al：Lubricant Oil Condition Assessment Based on AHPand Fuzzy Comprehensive EvaluationBased on theory analyzed in section 2 and 3
， lu.

bricant oil condition is assessed in this section．Theassessment takes physical and chemical condition，oilproperty deteriorating condition，and wear condition.

： 3 ： =into account comprehensively． as illustrated withFig．1.

4．1．Establish of element set and comment setAccording to the hierarchy of lubricant oil condi.

tion assessment，element set of oil condition assess—ment is U={ l， ， }．In our research，the finaloil condition assessment result is divided into threelevels，which are‘normal”，“abnormal”．and “oilchange”． So the corresponding comment set is de.

fined as V：{normal，abnormal，oilchange}.

The element set has three subsets：U1
， ， ，where U1={U U12，U13}，U2={ 1， 2， 3，}，and ={ l， 2， 3， 4}．Theirs COl~e—sponding comment sets are V1={normal，atention，alarm}， ={normal，atention，alarm}， ：{nor-maZwear，abnormalwear，$everewear}.

4．2．Determining fuzzy evaluation matrixThe first-grade fuzzy evaluation matrix R is de.

termined by calculating every element’S membershipof Ui with form ula．Th e membership used in this pa—per is defined as follows：， =1 il，k：21 ≤一 z 孚椰z 一 ，c 2 ?『nl c ≤z 孚柑，／《 ]。

z ? ／口1『a，≤÷ a，÷ < ≤aa1< ≤ 02(5)(6)O2[≤／《 ] ～：一z(x-a2- 柑 。2< ≤。2+Where，i means th subset Ui， means the jth ele—ment U ，k means kth comment level，a1 and a2 areconstant number that divide factors into grade． Onbasis of lots of experiments，al and a2 for each factorcan be found in Tab．3.

Tab．3 Grade divisions Of factorsAccording to formula(5)一(7)and grade divi.

sion table，first．grade fuzzy evaluation matrix can b0determined as follows.

First—grade fuzzy evaluation matrixes for launch—ing vehicle lubricant oil condition are：r0．986 2 0．013 8 0 1R1=l 0．005 0 0．995 0 0 l0 0．795 2 0．204 8、 一+ > + 一十 92 Hydromechatronics Engineering0．966 2 0]0．130 0 0 l
0 0 lo．030 9 oj0 O0．2l0 0 00．224 4 00．423 2 0First-grade fuzzy evaluation matrixes for guaran·-tee vehicle lubricant oil condition are：1 0
；0．358 40．456 70．231 50．624 200．O80．031 20．843 24．3．Determining weight vectorWeight vectors are calculated from judgment ma-trix generated from AHP．Based on the results of tes-ting，relationship between indexes，and theirs influ—ence on lubricant oil condition，judgment matrixesare determined iS Tab．4～7.

Tab．4 Judgment matrix Of physical and chemicalproperties indexesTab．5 Judgment matrix of property deteriorating indexesTab．6 Judgment matrix of wearing element indexesU1 Consistency checkThe weight vectors are：A =(0．539 0 0．297 2 0．163 8)A。=f0．483 7 0．297 3 0．109 5 0．109 5)A =(0．502 6 0．205 4 0．205 4 0．086 6)A=f0．320 2 0．557 2 0．122 6)4．4．First-grade fuzzy evaluationTaking first—grade fuzzy evaluation matrix andweight vector to formula(3)，and according to themaximum membership degree method，the first-gradefuzzy evaluation result Can be determined.

First—grade fuzzy evaluation result of launchingvehicle lubricant oil condition is：B1=(0．539 0 0．297 2 0．163 8)，physicaland chemical property condition is“normal”；B2=(0．297 3 0．483 7 0．000 0)，propertydeteriorating condition is“attention”；B3 = (0．502 6 0．205 4 0．000 0)， wearcondition lS no 口 wear ． 一 · · “ T ”First-grade fuzzy evaluation result of guaranteevehicle lubricant oil condition iS：B =(0．539 0 0．297 2 0．000 0)，physicaland chemical property condition iS“normal”：B2=(0．483 7 0．358 4 0．000 0)，propertydeteriorating condition iS“normal”：B = (0．502 6 0．088 6 0．000 0)。 wearC0na】t】On 1s n0 r】 r上￡ erzr ． 1·。· · “ "4．5．Second-grade fuzzy evaluationSecond-grade fuzzy evaluation result of launch·-ing vehicle lubricant oil condition is：B=(0．320 2 0．483 7 0．163 8)Second-grade fuzzy evaluation result of guaran-tee vehicle lubricant oil condition iS8 0 1 3 O 9 3 7 1 6 0 8 9
0 0 O —．。．．．，．。． ．．。．．．．。．。L =2 R0 6 8 0 5 6 1 9 7 7 7 5
O 0 O —。．．．． ．．．．．．．．．．．．．L ：3 R6 3 5 8 l 3 8 5 4 4 6 76 5 7 3 0 O 0 0 —．．．．．。．．．．．．．．．．．．L =2 R8 8 ● 醯
0 0 ：3 R DU Chuanbin，et al：Lubricant Oil Condition Assessment Based on AHPand Fuzzy Comprehensive Evaluation 93B=f0．483 7 0．358 4，0．000 0)According to the maximum membership degreemethod．1ubricant oil condition of launching vehicleand guarantee vehicle is“attention” and “normaf”respectively．The first—grade fuzzy evaluation result oflaunching vehicle shows that property deterioratingcondition is“attention”．and so it can be concludedthat lubricant oi1 “attention” condition is mainlycaused by oil property deteriorating．It has been sur—veyed that the launching vehicle engine bears moreload than guarantee vehicle engine，and its workingenvironment is worse．therefore its antioxidant addi—tive and antiwear additive are consumed more quick—ly．In the future．the lubricant oil of launching vehi—cle should be given more attention， especialy itsproperty deteriorating condition，and the time interval0f oil monitoring should be reduced.

5．ConclusionsLubricant oil experiences a lot of change in use，and many indexes that characterizing its property mayshow different change trend．so it is very hard to as-sess oil condition by considering single index．There—fore．1ubricant oil condition assessment is a multi—in—dex evaluation problem ，and it should be solved bycomprehensive evaluation．In our research．oil physi—cal and chemical property indexes，oil property dete—riorating indexes．and wear indexes are consideredcomprehensively， AHP and fuzzy comprehensive e—valuation methods are used to assess oil condition.

The example shows that the methods give the reasona-ble results that according with actual oil condition.

According to the assessment，engine lubrication stateis acquired，and engine maintenance support deci-sion-making can be provided.

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基于AHP和模糊综合评判的润滑油状态评估杜传斌 ，王菊香海军航空工程学院 a．研究生管理大队；b．飞行器工程系 ，山东 烟台 264001摘要：利用润滑油的理化性质指标＼性能衰变指标和磨损金属元素指标分析了润滑油的状态。根据润滑油状态评估过程 ，利用层次分析法(AHP)建立润滑油状态评估的分级结构，利用模糊综合评判方法对润滑油状态做 出两级评估。首先应用一级模糊综合评判，评估润滑油理化性质状态、润滑油性质衰变状态和磨损状态；然后利用二级模糊综合评判评估润滑油的状态。实例证明：应用这 2种方法都能有效地评估润滑油的状态。

关键词 ：润滑油状态评估；AHP；模糊综合评判中图分类号：TH137