灰色系統(tǒng)試題

1、下面以寧波市鄞州區(qū)平原河網(wǎng)水環(huán)境質(zhì)量評(píng)價(jià)為例，具體說明灰色聚類決策綜合評(píng)價(jià)的方法與過程。在七個(gè)采樣點(diǎn)對(duì)8項(xiàng)污染指標(biāo)進(jìn)行了監(jiān)測(cè)，實(shí)測(cè)值列于表21?，F(xiàn)將七個(gè) 采樣點(diǎn)作為聚類對(duì)象(i=1, 2,，7), 8種污染指標(biāo)作為聚類指標(biāo)(j=1, 2,， 8), d.為第i個(gè)采樣點(diǎn)對(duì)于第j個(gè)污染指標(biāo)的實(shí)測(cè)值。表2 1鄞州區(qū)平原河網(wǎng)水質(zhì)實(shí)測(cè)值(mg/L)測(cè)點(diǎn) i 污染指標(biāo)j 、1234567溶解氧4.846.324.259.767.098.226.48高錳酸鹽指數(shù)4.315.317.222.383.297.632.11生化需氧量2.513.914.491.281.646.221.84揮發(fā)酚0.0020.002

2、0.0020.0020.0020.0020.002總氤化物0.0040.0040.0040.0040.0040.0040.004總汞0.000050.000050.000050.000050.000050.000050.00005總鉛0.0050.0050.0050.0050.0050.0050.005總鎘0.00050.00050.00050.00050.00050.00050.0005樣本矩陣D=(dq)誨為:4.844.312.510.0020.0040.000050.0050.0005-6.325.313.910.0020.0040.000050.0050.00054.257.224.

3、490.0020.0040.000050.0050.0005D =9.762.381.280.0020.0040.000050.0050.00057.093.291.640.0020.0040.000050.0050.00058.227.636.220.0020.0040.000050.0050.0005_6.482.111.840.0020.0040.000050.0050.0005_在準(zhǔn)備好以上基本數(shù)據(jù)后，便可按灰色聚類決策方法對(duì)水質(zhì)進(jìn)行評(píng)價(jià)了，計(jì) 算過程如下。1按聚類指標(biāo)所屬灰類確定白化權(quán)函數(shù)以2002年國家環(huán)?？偩职l(fā)布的地面水環(huán)境質(zhì)量標(biāo)準(zhǔn)(GB 3838-2002)作 為水質(zhì)標(biāo)準(zhǔn)(如表

4、2-2)，將水質(zhì)分為五級(jí)，即五個(gè)灰類。表中水質(zhì)分級(jí)的標(biāo)準(zhǔn)值 可作為各灰類白化權(quán)函數(shù)(圖2-1是以高錳酸鹽指數(shù)指標(biāo)為例說明灰類的白化權(quán) 函數(shù))的閥值A(chǔ).kO表2 2地表水環(huán)境質(zhì)量標(biāo)準(zhǔn)部分項(xiàng)目標(biāo)準(zhǔn)限值(mg/L)J、分級(jí)k污染指標(biāo)j J、IIIIIIIVV溶解氧7.56532高錳酸鹽指數(shù)忍2461015生化需氧量忍334610揮發(fā)酚忍0.0020.0020.0050.010.1總氤化物忍0.0050.050.20.20.2總汞忍0.000050.000050.00010.0010.001總鉛忍0.010.010.050.050.1總鎘忍0.0010.0050.0050.0050.01f21f211

5、11 dL_024602f2102461015圖2-1f21A r46d f211110246各灰類白化權(quán)函數(shù)A4610/.d1015d圖中d即狀2為各測(cè)點(diǎn)高錳酸鹽指數(shù)污染指標(biāo)的實(shí)測(cè)值，A2k為白化權(quán)函數(shù) 的閥值（即表2-21中高錳酸鹽指數(shù)污染指標(biāo)第k級(jí)的水質(zhì)標(biāo)準(zhǔn)值）。由表2-2及圖2-1，可寫出該污染指標(biāo)的各灰類的白化權(quán)函數(shù)f2k的表達(dá)式如 下（現(xiàn)以高錳酸鹽指數(shù)，即j=2為例）：（k=1，2, 3, 4, 5）1(4 - d)/(4 -2) 0,d e 0,2),d e 2,4),d e 4, s)(d - 2)/(4 - 2) (6 - d)/(6-4) 0f22( d 2)r,d e 2

6、,4),d e 4,6),d e 0,2) d 6, s)0, d e 0,4) d 10, s)(d - 4)/(6 - 4), d e 4,6)(10-d)/(10 -6), d e 6,10)0, d e 0,6) d 15, s)(d - 6)/(10-6), d e 6,10)(15-d)/(15-10), d e 10,15),d g 0,10)f (d ) = (d -10)/(15-10), d g 10,15)2 21, d g 15,8)其它污染指標(biāo)(j=1, 3, 4,，8)的上與此類似。2.2求灰色聚類權(quán)聚類權(quán)是衡量各指標(biāo)對(duì)同一灰類的權(quán)重。在水質(zhì)分析中，由于聚類指標(biāo)的不

7、 同，絕對(duì)值相差也較大，因此需按式(1-2)進(jìn)行無量綱化處理，即按七，Jk S式中，SJk為第J種指標(biāo)的第k個(gè)灰類(級(jí)別)J的標(biāo)準(zhǔn)值。SJ為第J種污染指標(biāo)的參 考標(biāo)準(zhǔn)，其取值可視評(píng)價(jià)地區(qū)的環(huán)境目標(biāo)而定，現(xiàn)取III級(jí)水質(zhì)標(biāo)準(zhǔn)作為SJO如 Y =S /S =7 5/5=15，Y =S /S =6/5=12，y =S /S =5/5=1，Y =Y 1 1，. J，J，. J ，y kJ y I kJV71 U ，.J，丫 2 U U， 丫 1 AJL JLJL JL JLJL 乙 JL 乙 JLJLJL JLJL I3/5=0.6，Y 15 =2/5=0.4；Y =S /S =2/6=0 33, y

8、 =S /S =4/6=0 67, Y =S /S =6/6=1, Y = .，.，10/6=1.67，Y 25 =15/6=2.5；第j個(gè)污染指標(biāo)對(duì)第k個(gè)灰類的權(quán)值n Jk，按下式計(jì)算：門=-X(j = 1,2,芯 k = 1,2,3)Jk v82 YJkJ=1計(jì)算結(jié)果如下表：表23灰色聚類權(quán)nJk的計(jì)算結(jié)果灰類k污染指標(biāo)J._IIIIIIIVV溶解氧0.3840.2420.1250.0320.010高錳酸鹽指數(shù)0.0850.1340.1250.0890.062生化需氧量0.1920.1510.1250.0800.062揮發(fā)酚0.1020.0810.1250.1070.495總氤化物0.00

9、60.0500.1250.0530.025總汞0.1280.1010.1250.5330.248總鉛0.0510.0400.1250.0530.050總鎘0.0510.2010.1250.0530.0503求灰色聚類系數(shù)及灰色聚類矩陣聚類系數(shù)。ik反映了聚類對(duì)象i對(duì)灰類k的隸屬程度。b =2 f (d )x門(i = 1,2,7;k = 1,2,3)J=1式中fJk(d.)為J指標(biāo)，k灰類的白化權(quán)函數(shù)，可由樣本值d.J代入相應(yīng)的白化權(quán)函數(shù)計(jì)算式中求得：1Jb. =Y f (d )x = 0 x0.384+ 0 x0.085+ 0 x0. 1 92+ 0 x0. 1 02+ 1 x0.006j=

10、i+ 0 x 0.128+ 0 x 0.051+1 x 0.05 1=0.058b =Y f (d )x門=0 x0.242 + 0.845x0.134 + 1x0.151 + 1x0.081 + 0 x0.051j=1+ 1x 0.101 + 1x 0.040 + 0 x 0.201 = 0.486b 13 = 0.134b 14 = 0.003 b 15 = 0其它。ik的計(jì)算可依式(2-4)進(jìn)行，其結(jié)果可構(gòu)成灰色聚類矩陣。C如下:0.0580.486*0.1340.0030 一r0.1390.471*0.19600bbb11121k0.0580.2210.259*0.0590bbbb =21222k=0.510*0.398000Cb b. . .- b0.3670.525*000L n1n2nk0.4410.1210.0740.645*0.003_ 0.2610.544*0004判斷聚類對(duì)象所屬灰類若。=max ，則稱聚類對(duì)象i屬于灰類。