三角直覺逼近在模糊系統(tǒng)可靠性上的應(yīng)用

李舒陽, 李洪興, 孫凱彪

(1. 海軍大連艦艇學(xué)院 基礎(chǔ)部, 遼寧 大連 116018; 2. 大連理工大學(xué) 控制科學(xué)與工程學(xué)院, 遼寧 大連 116024)

0 引言

隨著高科技產(chǎn)業(yè)的快速發(fā)展,工程系統(tǒng)越來越大型化和復(fù)雜化,系統(tǒng)可靠性分析已經(jīng)成為工程領(lǐng)域的研究熱點(diǎn)與難點(diǎn)之一.故障樹分析方法是系統(tǒng)可靠性分析方法中一種應(yīng)用最為廣泛的分析方法.很多系統(tǒng)存在大量的模糊不確定性,要得到基本事件的確切概率是困難的.因此，Tanaka等[1]將模糊理論引入故障樹分析,用模糊概率代替?zhèn)鹘y(tǒng)可靠性分析中的精確概率值.文獻(xiàn)[2]用三角形直覺模糊數(shù)表示系統(tǒng)部件失效概率,提出一種直覺模糊故障樹分析算法計(jì)算系統(tǒng)部件的故障區(qū)間,為管理人員找到最關(guān)鍵的系統(tǒng)部件提供決策參考,并將此算法應(yīng)用到印刷電路板裝配中.文獻(xiàn)[3]提出一種直覺模糊故障樹分析方法解決液化天然氣終端緊急關(guān)閉系統(tǒng)的故障分析問題.文獻(xiàn)[4]通過L-R型三角直覺模糊集表示的直覺模糊故障樹分析計(jì)算機(jī)安全系統(tǒng)的可靠性.文獻(xiàn)[5]利用故障樹分析部件用梯形直覺模糊數(shù)表示的船舶動(dòng)力裝置的可靠性.文獻(xiàn)[6]修改文獻(xiàn)[1]模糊故障樹的定義,應(yīng)用故障樹分析、三角直覺模糊數(shù)的α-截集和建立在三角直覺模糊數(shù)代數(shù)運(yùn)算上的弱t-范數(shù),得到了系統(tǒng)的故障區(qū)間和可靠區(qū)間.

在模糊系統(tǒng)可靠性分析中,很多成果都是假設(shè)一個(gè)系統(tǒng)所有部件的故障率是相同類型的直覺模糊數(shù),然而,這種情況很少發(fā)生.在實(shí)際問題中,系統(tǒng)部件的可靠性往往用不同類型的直覺模糊數(shù)描述.文獻(xiàn)[7]給出一種算法，分析了部件用不同類型的直覺模糊數(shù)表示的系統(tǒng)的模糊可靠性.通過非線性規(guī)劃方法計(jì)算直覺模糊函數(shù)解決模糊系統(tǒng)可靠性問題,數(shù)值例子用的是三角和梯形直覺模糊數(shù).文獻(xiàn)[8]給出基于α-和β-截集的直覺模糊數(shù)的代數(shù)運(yùn)算,由此得到一種系統(tǒng)部件的可靠性用不同類型直覺模糊數(shù)表示的模糊系統(tǒng)可靠性分析的方法.該文獻(xiàn)里的數(shù)值例子中用的也是三角和梯形直覺模糊數(shù).文獻(xiàn)[9]針對(duì)用不同類型直覺模糊數(shù)表示部件直覺模糊故障率的系統(tǒng),提出構(gòu)建串并聯(lián)系統(tǒng)模糊可靠性隸屬函數(shù)和非隸屬函數(shù)的算法,這種算法是通過非線性規(guī)劃方法用直覺模糊函數(shù)實(shí)現(xiàn)的.數(shù)值例子用的是三角形和梯形直覺模糊數(shù)說明評(píng)估過程和方法,從而減少計(jì)算量.文獻(xiàn)[10]用弱t-范數(shù)的方法對(duì)用不同類型的直覺模糊數(shù)表示所有部件故障率的系統(tǒng)進(jìn)行了可靠性分析;但是這種方法需要對(duì)直覺模糊數(shù)的截集進(jìn)行代數(shù)運(yùn)算,計(jì)算量較大.文獻(xiàn)[11]考慮部件的故障率是用三角和梯形直覺模糊數(shù)表示的,使用可信性理論計(jì)算直覺模糊函數(shù),提出一種分析串聯(lián)和并聯(lián)系統(tǒng)模糊可靠性的方法.

雖然關(guān)于模糊系統(tǒng)可靠性的研究成果很多,但是仍然有各自的不足之處.如果能有一種評(píng)估模糊系統(tǒng)可靠性的方法,不僅評(píng)估過程相對(duì)簡(jiǎn)單,計(jì)算量小,而且能解決系統(tǒng)部件用不同類型的直覺模糊數(shù)(包括一般直覺模糊數(shù))表示的可靠性評(píng)估問題,將對(duì)模糊系統(tǒng)可靠性的發(fā)展有著深遠(yuǎn)的意義.本文提出一種解決實(shí)際問題中遇到的系統(tǒng)部件故障率用不同類型直覺模糊數(shù)表示模糊系統(tǒng)的可靠性問題的方法,并用直覺模糊數(shù)的代數(shù)運(yùn)算分析模糊系統(tǒng)的可靠性,比已有方法的計(jì)算量小.最后通過印刷電路板組件(PCBA)故障分析表明,應(yīng)用本文所給出的梯形直覺逼近方法處理數(shù)據(jù)后,所得的結(jié)果與其它的計(jì)算結(jié)果相比縮小了直覺模糊數(shù)截集的區(qū)間長(zhǎng)度,提高了結(jié)果的可信度.

1 預(yù)備知識(shí)

1.1形直覺逼近

定義1[12-13]設(shè)X是一個(gè)給定的非空集合,A={〈x,μA(x),νA(x)〉:x∈X},μA:X→[0,1],νA:X→[0,1],且對(duì)?x∈X有0≤μA(x)+νA(x)≤1,稱A為X上的直覺模糊集.

如果直覺模糊集A滿足一定的條件,那么稱A為正規(guī)直覺模糊集.

定義2[14]設(shè)A={〈x,μA(x),νA(x)〉:x∈X}是論域X上的直覺模糊集，如果至少存在2點(diǎn)x1,x2∈X，使得μA(x1)=1,νA(x2)=1，則稱直覺模糊集A是正規(guī)的.

直覺模糊集的一種特殊情形稱為直覺模糊數(shù).

定義3[14]設(shè)A={〈x,μA(x),νA(x)〉:x∈R}是實(shí)軸R上的一個(gè)直覺模糊子集,如果下面條件成立:

1)μA(x)是模糊凸的，即對(duì)?x1,x2∈R,λ∈[0,1],有

μA(λx1+(1-λ)x2)≥

min{μA(x1),μA(x2)},

νA(x)是模糊凹的，即對(duì)?x1,x2∈R,λ∈[0,1],有

νA(λx1+(1-λ)x2)≤max{νA(x1),νA(x2)};

2)A是正規(guī)的;

3)μA是上半連續(xù)的,νA是下半連續(xù)的;

4) SupA={x∈R:μA(x)>0,νA(x)<1}是有界的.

則稱A為一個(gè)直覺模糊數(shù).

如果μA和1-νA是梯形模糊數(shù),那么稱直覺模糊數(shù)A=〈μA,νA〉是梯形直覺模糊數(shù);如果μA和1-νA是三角形模糊數(shù),那么稱直覺模糊數(shù)A=〈μA,νA〉是三角形直覺模糊數(shù).如果A=〈μA,νA〉是一個(gè)直覺模糊數(shù),T△(A)=〈μT△,νT△〉是距離A=〈μA,νA〉最近的那個(gè)三角形直覺模糊數(shù),稱T△(A)=〈μT△,νT△〉為A=〈μA,νA〉的三角直覺逼近.

(μA)U(α))dα,

(1)

(2)

(3)

(1-νA)U(α))dα,

(4)

(5)

(6)

(μT△)α=[s1-(1-α)s2,s1+(1-α)s3],

?

(7)

圖1串聯(lián)系統(tǒng)
Fig.1Seriessystem

圖 2 并聯(lián)系統(tǒng)Fig.2 Parallel system

?

(8)

2 算例分析

給出一個(gè)印刷電路板組件(PCBA)的例子說明所提出來的逼近方法分析系統(tǒng)模糊可靠性的過程,并與文獻(xiàn)[17-18]的方法比較.圖3的PCBA故障樹和數(shù)據(jù)來自臺(tái)灣新竹科學(xué)園區(qū)一個(gè)中型制造廠[2].這里使用PCBA作為故障樹的頂部事件.印刷電路板組件故障的故障樹如圖3所示,子事件和底部事件詳見表1和表2.

圖 3 印刷電路板組件故障樹的圖像Fig.3 The fault-tree diagram of PCBA fault

由于基本事件的故障率數(shù)據(jù)不完全,故障率密度函數(shù)類型不同等原因,根據(jù)專家的觀點(diǎn)給出了故障樹底部事件的故障率,故障率用以下的不同類型的直覺模糊數(shù)表示.

A1=〈μA1,νA1〉是三角形直覺模糊數(shù),有

(μA1)α=

[0.000 7+0.000 4α,0.001 24-0.000 14α],

(1-νA1)α=

[0.000 58+0.000 52α,0.001 51-0.000 41α].

A2=〈μA2,νA2〉是三角形直覺模糊數(shù),

(μA2)α=

[0.000 96+0.000 14α,0.001 34-0.000 24α],

(1-νA2)α=

[0.000 72+0.000 38α,0.001 49-0.000 39α].

表 1 PCBA故障子事件的說明Tab.1 The descriptions of the sub-events of PCBA fault

表 2 PCBA故障底部事件的說明Tab.2 The descriptions of the bottom events of PCBA fault

A3=〈μA3,νA3〉是三角形直覺模糊數(shù),

(μA3)α=[0.004 11+0.000 62α,0.005 13-0.000 4α],

(1-νA3)α=[0.002 89+0.001 84α,0.005 57-0.000 84α].

B=〈μB,νB〉是梯形直覺模糊數(shù),

(μB)α=

[0.001 11+0.000 09α,0.001 78-0.000 08α],

(1-νB)α=

[0.000 89+0.000 31α,0.001 92-0.000 22α].

C=〈μC,νC〉是正態(tài)型直覺模糊數(shù),

(μC)α=(1-νC)α=[0.000 99-

D=〈μD,νD〉是尖γ型直覺模糊數(shù),

(μD)α=

(1-νD)α=

E1=〈μE1,νE1〉是正態(tài)型直覺模糊數(shù),

(μE1)α=(1-νE1)α=

E2=〈μE2,νE2〉是正態(tài)型直覺模糊數(shù),

(μE2)α=(1-νE2)α=[0.000 77-

E3=〈μE3,νE3〉是尖γ型直覺模糊數(shù),

(μE3)α=

(1-νE3)α=

F1=〈μF1,νF1〉是三角形直覺模糊數(shù),

(μF1)α=

[0.001+0.000 1α,0.001 62-0.000 52α],

(1-νF1)α=[0.000 683+0.000 417α,

0.001 82-0.000 72α].

F2=〈μF2,νF2〉是三角形直覺模糊數(shù),

(μF2)α=[0.001 85+0.000 35α,

0.002 59-0.000 39α],

(1-νF2)α=[0.001 49+0.000 71α,

0.002 99-0.000 79α].

G1=〈μG1,νG1〉是梯形直覺模糊數(shù),

(μG1)α=[0.000 496+0.000 024α,

0.000 79-0.000 09α],

(1-νG1)α=[0.000 273+0.000 247α,

0.000 86-0.000 7α].

G2=〈μG2,νG2〉是梯形直覺模糊數(shù),

(μG2)α=[0.002 54+0.000 46α,

0.003 95-0.000 55α],

(1-νG2)α=[0.000 233+0.002 763α,

0.004 61-0.001 21α].

G3=〈μG3,νG3〉是梯形直覺模糊數(shù),

(μG3)α=[0.000 96+0.000 04α,

0.001 71-0.000 11α],

(1-νG3)α=[0.000 517+0.000 483α,

0.002 07-0.000 47α].

H1=〈μH1,νH1〉是尖γ型直覺模糊數(shù),

H2=〈μH2,νH2〉是正態(tài)型直覺模糊數(shù),

(μH2)α=(1-νH2)α=[0.002 97-

H3=〈μH3,νH3〉是尖γ型直覺模糊數(shù),

(μH3)α=

(1-νH3)α=

I1=〈μI1,νI1〉是正態(tài)型直覺模糊數(shù),

(μI1)α=(1-νI1)α=[0.003 3-

I2=〈μI2,νI2〉是正態(tài)型直覺模糊數(shù),

(μI2)α=(1-νI2)α=[0.003 3-

I3=〈μI3,νI3〉是正態(tài)型直覺模糊數(shù),

(μI3)α=(1-νI3)α=[0.002 42-

J1=〈μJ1,νJ1〉是三角形直覺模糊數(shù),

(μJ1)α=[0.004 41+0.000 21α,

0.004 95-0.000 33α],

(1-νJ1)α=[0.001 88+0.002 74α,

0.005 51-0.000 89α].

J2=〈μJ2,νJ2〉是三角形直覺模糊數(shù),

(μJ2)α=[0.001 94+0.000 7α,

0.002 85-0.000 21α],

(1-νJ2)α=[0.001 88+0.000 76α,

0.002 91-0.000 27α].

K=〈μK,νK〉是尖γ型直覺模糊數(shù),

(μK)α=

L=〈μL,νL〉是三角形直覺模糊數(shù),

(μL)α=[0.001 06+0.000 15α,

0.001 68-0.000 47α],

(1-νL)α=[0.000 83+0.000 38α,

0.002 05-0.000 84α].

M1=〈μM1,νM1〉是三角形直覺模糊數(shù),

(μM1)α=[0.004 61+0.001 22α,

0.005 92-0.000 09α],

(1-νM1)α=[0.002 59+0.003 24α,

0.006 17-0.000 34α].

M2=〈μM2,νM2〉是三角形直覺模糊數(shù),

(μM2)α=[0.000 203+0.000 017α,

0.000 28-0.000 06α],

(1-νM2)α=[0.000 184+0.000 36α,

0.000 45-0.000 23α].

M3=〈μM3,νM3〉是三角形直覺模糊數(shù),

(μM3)α=[0.001 19+0.000 24α,

0.001 61-0.000 18α],

(1-νM3)α=[0.001 02+0.000 41α,

0.001 93-0.000 5α].

N1=〈μN(yùn)1,νN1〉是三角形直覺模糊數(shù),

(μN(yùn)1)α=[0.001 97+0.000 34α,

0.002 58-0.000 27α],

(1-νN1)α=[0.001 91+0.000 4α,

0.002 73-0.000 42α].

N2=〈μN(yùn)2,νN2〉是三角形直覺模糊數(shù),

(μN(yùn)2)α=[0.001 04+0.000 28α,

0.001 39-0.000 07α],

(1-νN2)α=[0.000 862+0.000 458α,

0.001 42-0.000 1α].

N3=〈μN(yùn)3,νN3〉是三角形直覺模糊數(shù),

(μJ1)α=[0.001 45+0.000 31α,

0.001 88-0.000 12α],

(1-νJ1)α=[0.001 17+0.000 59α,

0.002 51-0.000 45α].

O=〈μO,νO〉是尖γ型直覺模糊數(shù),

(μO)α=

(1-νO)α=

P=〈μP,νP〉是梯形直覺模糊數(shù),

(μP)α=

[0.002 58+0.000 12α,0.003 06-0.000 12α],

(1-νP)α=[0.002 11+0.000 59α,

0.003 27-0.000 33α].

Q=〈μQ,νQ〉是正態(tài)型直覺模糊數(shù),

(μQ)α=(1-νQ)α=

R=〈μR,νR〉是尖γ型直覺模糊數(shù),

(μR)α=

(1-νR)α=

S=〈μS,νS〉是正態(tài)型直覺模糊數(shù),

(μS)α=(1-νS)α=[0.004 18-

下面用不同的方法對(duì)PCBA故障模型進(jìn)行可靠性評(píng)估,并對(duì)結(jié)果進(jìn)行對(duì)比分析.對(duì)系統(tǒng)基本事件故障率數(shù)據(jù)不完整的情況,文獻(xiàn)[17]提出了直覺模糊故障樹分析的方法.根據(jù)專家的知識(shí)和經(jīng)驗(yàn)對(duì)底部事件的故障率用三角形直覺模糊數(shù)進(jìn)行代數(shù)運(yùn)算,計(jì)算頂部事件PCBA故障的可能性是:

q=〈0.040 794,0.055 720,0.069 499;

0.032 797,0.055 720,0.075 212〉.

當(dāng)α=0,0.1,0.2,…,1時(shí),根據(jù)直覺模糊數(shù)的α-截集計(jì)算出頂部事件CBA故障的信任隸屬區(qū)間和非隸屬區(qū)間,如表3所示.這種方法只能對(duì)用三角形直覺模糊數(shù)表示的故障率進(jìn)行運(yùn)算,有很大的局限性.

表 3 PCBA故障在不同截集水平的模糊故障率[17]Tab.3 Fuzzy failure probability of PCBA fault at different level[17]

文獻(xiàn)[18]根據(jù)直覺模糊集的區(qū)間代數(shù)運(yùn)算評(píng)估模糊系統(tǒng)的可靠性,需要先計(jì)算35個(gè)底部事件,當(dāng)α=0,0.1,0.2,…,1時(shí)的770個(gè)α-截集;然后當(dāng)α=0,0.1,0.2,…,1時(shí),對(duì)這些截集再進(jìn)行區(qū)間代數(shù)運(yùn)算,得出頂部事件PCBA故障的信任隸屬區(qū)間和非隸屬區(qū)間在α=0,0.1,0.2,…,1時(shí)的情況,如表4所示,這種方法計(jì)算量比較大.

表 4 PCBA故障在不同截集水平的模糊故障率[18]Tab.4 Fuzzy failure probability of PCBA fault at different level[18]

下面考慮本文提出的逼近方法.從圖4可以看到,三角形直覺模糊數(shù)比梯形直覺模糊數(shù)更接近正態(tài)型和尖γ型直覺模糊數(shù).

(a)C的隸屬函數(shù)和非隸屬函數(shù)的圖像

(b)D的隸屬函數(shù)和非隸屬函數(shù)的圖像

圖4C、D的隸屬函數(shù)和非隸屬函數(shù)的圖像
Fig.4Thefiguresofmembershipandnon-membershipfunctionsofCandD

所以根據(jù)算法1可以分別得到正態(tài)型直覺模糊數(shù)C、E1、E2、H2、I1、I2、I3、Q、S和尖γ型直覺模糊數(shù)D、E3、H1、H3、K、O、R的三角直覺逼近:

T△(C)=(0.000 879,0.000 99,0.001 101;

0.000 879,0.000 99,0.001 101),

T△(D)=(0.001 627,0.001 65,0.001 673;

0.001 586,0.001 65,0.001 714),

T△(E1)=(0.001 591,0.002 2,0.002 809;

0.001 591,0.002 2,0.002 809),

T△(E2)=(0.000 548,0.000 77,0.000 992;

0.000 548,0.000 77,0.000 992),

T△(E3)=(0.000 529,0.000 55,0.000 571;

0.000 513,0.000 55,0.000 588),

T△(H1)=(0.000 528,0.000 55,0.000 572;

0.000 513,0.000 55,0.000 588),

T△(H2)=(0.002 064,0.002 97,0.003 876;

0.002 064,0.002 97,0.003 876),

T△(H3)=(0.001 08,0.001 1,0.001 120;

0.001 055,0.001 1,0.001 145),

T△(I1)=(0.002 531,0.003 3,0.004 069;

0.002 531,0.003 3,0.004 069),

T△(I2)=(0.002 441,0.003 3,0.004 159;

0.002 441,0.003 3,0.004 159),

T△(I3)=(0.001 847,0.002 42,0.002 993;

0.001 847,0.002 42,0.002 993),

T△(K)=(0.000 738,0.000 77,0.000 802;

0.000 695,0.000 77,0.000 845),

T△(O)=(0.001 165,0.001 21,0.001 255;

0.001 135,0.001 21,0.001 285),

T△(Q)=(0.003 792,0.004 4,0.005 008;

0.003 792,0.004 4,0.005 008),

T△(R)=(0.001 848,0.001 87,0.001 893;

0.001 842,0.001 87,0.001 898),

T△(S)=(0.003 411,0.004 18,0.004 949;

0.003 411,0.004 18,0.004 949).

根據(jù)圖3，主要事件有如下的關(guān)系:

A=A1+A2+A3,E=E1+E2+E3,

F=F1×F2,

G=G1+G2+G3,H=H1+H2+H3,

I=I1+I2+I3,

J=J1×J2,M=M1+M2+M3,

N=N1×N2×N3,

其中正態(tài)型和尖γ型直覺模糊數(shù)用三角直覺逼近代替.用qi表示底部事件i的故障率,計(jì)算各個(gè)子事件的故障率如下:

qA= 1?(1?A1)? (1?A2)?(1?A3) ?

(0.005 762 5,0.006 918 4,0.007 695 1;

0.004 185 8,0.006 918 4,0.008 551 1),

qE= 1?(1?T△(E1))? (1?T△(E2))?

(1?T△(E3)) ?

(0.002 666 0,0.003 516 7,0.004 367 0;

0.002 650 0,0.003 516 7,0.004 384 0),

qF=F1?F2?

(0.000 001 9,0.000 002 4,0.000 004 2;

0.000 001 0,0.000 002 4,0.000 005 4),

qG= 1?(1?G1)?

(1?G2)?(1?G3) ?

(0.003 991 8,0.004 514 9,0.005 691 1,0.006 438 8;

0.001 022 7,0.004 514 9,0.005 691 1,0.007 524 7),

qH= 1?(1?T△(H1))?

(1?T△(H2))?(1?T△(H3)) ?

(0.003 668 1,0.004 614 5,0.005 560 8;

0.003 628 2,0.004 614 5,0.005 601 6),

qI= 1?(1?T△(I1))?

(1?T△(I2))?(1?T△(I3)) ?

(0.006 803 6,0.008 993 2,0.011 179 5;

0.006 803 6,0.008 993 2,0.011 179 5),

qJ=J1?J2?

(0.000 008 6,0.000 012 2,0.000 014 1;

0.000 003 5,0.000 012 2,0.000 016 0),

qM= 1?(1?M1)? (1?M2)?(1?M3) ?

(0.005 996 3,0.007 470 1,0.007 798 4;

0.003 790 7,0.007 470 1,0.008 534 5),

qN=N1?N2?N3?

(0.297 076×10-8,0.536 659 2×10-8,

0.674 205 6×10-8;

0.192 631 14×10-8,0.536 659 2×10-8,

0.973 026 6×10-8).

因?yàn)槿侵庇X模糊數(shù)是梯形直覺模糊數(shù)的特殊情況,所以各個(gè)子事件I、II、III、IV和V的故障率計(jì)算如下:

qI= 1?(1?A)?

(1?B)?(1?T△(C)) ?

(0.007 739 1,0.009 092 1,0.009 588 1,0.010 552 0;

0.005 946 6,0.009 092 1,0.009 588 1,0.011 544 1),

qII= 1?(1?T△(D))? (1?E)?

(1?F)?(1?G)?(1?H)? (1?I)?

(0.018 625 7,0.023 090 1,0.024 244 3,0.028 907 5;

0.015 603 4,0.023 090 1,0.024 244 3,0.030 066 5),

qIII= 1?(1?J)? (1?T△(K))?(1?L) ?

(0.001 805 6,0.001 991 2,0.001 991 2,0.002 494 9;

0.001 527 6,0.001 991 2,0.001 991 2,0.002 909 3),

qIV= 1?(1?M)? (1?N)?

(1?T△(O))?(1?P) ?

(0.009 715 9,0.011 347 7,0.011 585 6,0.012 075 9;

0.007 021 0,0.011 347 7,0.011 585 6,0.013 046 5),

qV= 1?(1?T△(Q))?

(1?T△(R))?(1?T△(S)) ?

(0.001 805 6,0.001 991 2,0.001 991 2,0.002 494 8;

0.001 528 0,0.001 991 2,0.001 991 2,0.002 909 3).

那么頂部事件PCBA故障的可能性是

qPCBA= 1?(1?I)? (1?II)?(1?III)?

(1?IV)?(1?V) ?

(0.039 161,0.046 765,0.048 596,0.055 488;

0.031 294,0.046 765,0.048 596,0.059 269).

表5表示本文提出的方法計(jì)算頂部事件PCBA故障的可能性(當(dāng)α=0,0.1,0.2,…,1時(shí)的隸屬函數(shù)和非隸屬函數(shù)的α-截集).文獻(xiàn)[17]提出的方法只能計(jì)算系統(tǒng)部件故障率用三角形直覺模糊數(shù)表示的系統(tǒng)的可靠性,有很大的局限性.在實(shí)際應(yīng)用中，系統(tǒng)部件用單一類型的直覺模糊數(shù)表示故障率這種情況很少發(fā)生,系統(tǒng)部件往往都是用不同類型的直覺模糊數(shù)表示其故障率的.文獻(xiàn)[18]提出的方法雖然可以計(jì)算用不同類型直覺模糊數(shù)表示系統(tǒng)部件故障率的系統(tǒng)可靠性,但是首先得求出35個(gè)基本事件(當(dāng)α=0,0.1,0.2,…,1時(shí))的770個(gè)α截集,然后當(dāng)α=0,0.1,0.2,…,1時(shí)再分別用區(qū)間的代數(shù)運(yùn)算計(jì)算系統(tǒng)發(fā)生故障可能性,計(jì)算量比較大.本文提出的方法不僅可以對(duì)用不同類型直覺模糊數(shù)(可以包含一般直覺模糊數(shù))表示系統(tǒng)部件故障率的系統(tǒng)進(jìn)行可靠性分析,而且計(jì)算量小,計(jì)算結(jié)果的不確定性也比較小.文獻(xiàn)[17-18]和本文提出的方法計(jì)算PCBA故障的可能性的模糊分布如表6所示.可靠性區(qū)間的長(zhǎng)度越小,關(guān)于可靠性的不確定性就越小.從表6可以看到,本文用逼近的方法處理數(shù)據(jù)后,所得的結(jié)果有效地減少了可靠性區(qū)間的長(zhǎng)度,即減少了模糊分布,比其它的計(jì)算結(jié)果更為精確.

表 5 用本文提出的方法PCBA故障在不同截集水平的模糊故障率Tab.5 Fuzzy failure probability of PCBA fault at different level based on proposed method

表 6 用不同方法PCBA故障的故障率的模糊分布Tab.6 Fuzzy spreads of failure probability of PCBA fault with different method

3 結(jié)束語

應(yīng)用三角直覺逼近方法研究模糊系統(tǒng)的可靠性問題,對(duì)一個(gè)含有串并聯(lián)結(jié)構(gòu)的模糊系統(tǒng),各個(gè)部件用不同類型的直覺模糊數(shù)表示其故障率,將正態(tài)型和尖γ型直覺模糊數(shù)都逼近成三角形直覺模糊數(shù)，然后用直覺模糊數(shù)的代數(shù)運(yùn)算分析串聯(lián)和并聯(lián)模糊系統(tǒng)的可靠性.該方法解決了實(shí)際問題中遇到的系統(tǒng)部件故障率用不同類型直覺模糊數(shù)表示的模糊系統(tǒng)的可靠性問題,并且分析模糊系統(tǒng)的可靠性用的是直覺模糊數(shù)的代數(shù)運(yùn)算,在一定程度上減少了計(jì)算量.最后通過PCBA故障分析表明,應(yīng)用三角直覺逼近方法處理數(shù)據(jù)后,所得的結(jié)果與其它的計(jì)算結(jié)果相比較,有效地減少了模糊分布,提高了結(jié)果的可信度.

致謝海軍大連艦艇學(xué)院科研發(fā)展基金對(duì)本文給予了資助,謹(jǐn)致謝意.