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ÂÓÒÅÐÖÒÖ×ÓÒÓ×ÓÖÚÓÐÒÎÒÏÓÙÛÖ ÔÔÐØÓÒØÓÒÖÓ×ØÓÒ ÅÖÓ×ÓÔÓÔÖÓ××ÅÓÐ×
ÙØÓÑØÓÒØÖÓÐÄÓÖØÓÖÝÍÒÚÖ×ØÝÓÅÓÒ×
×ØÖØ×ÑÔÐÔÖÓÙÖ×ÔÖ×ÒØØÓ×ØÑØØÒÙÑÖÓÑÖÓ×ÓÔÖØÓÒ× ÑÐÐÒÎÒÏÓÙÛÖÙÑÓÒ× ÓÙÐÚÖÓÐÞ ÅÓÒ×ÐÙÑ
ÖÑØÖÜÒØ×ØÖÙØÙÖÒÔÖÑØÖÚÐÙÓØ×ÒØ×ÌÖ×ØØÛÓ×Ø×Ù×Ø ÒØÓÖÔÖ×ÒØØØÑÚÓÐÙØÓÒÓØÝÓÑÔÓÒÒØ×ÓÓÔÖÓ××Ø××ØÓÓÑØ ÑØÑØÐØÒÕÙÓÅÜÑÙÑÄÐÓÓÈÖÒÔÐÓÑÔÓÒÒØÒÐÝ××ØÓØÖÑÒ Ø×ØÓÓÑØÖÑØÖÜÓØÔÖÓ××ÒØØÖ×ØÙ××ÄÐÓÓÊØÓÌ×ØÒ ØÓÒÚØØÖÓÙØÖÒ×Ó×ÓÒØÖÑÓÚÖÓÙ×ÒØ×ØÖÙØÙÖ×Ì
ÒÐÝ××ÓÔÖÓ××× ÔÖÓÖÑÒÓÓÙÖÒØØÓÒÔÖÓÙÖ×ÐÐÙ×ØÖØÐÐÐÓÒØÔÔÖÛØ×ÑÙÐØ ÜÑÔÐÓÒÖÓ×ØÓÒ ÃÝÛÓÖ×ÁÒØØÓÒÈÖÑØÖ×ØÑØÓÒÅÜÑÙÑÄÐÓÓÈÖÒÔÐÓÑÔÓÒÒØ
ÑÓÐ×ÖÓÑÜÔÖÑÒØÐÑ×ÙÖÑÒØ×ÓÛÝ ØÚÐÓÔÑÒØÓÑØÑØÐÐÝØÖØÐÓÔÖÓ×× ÌÛÓÑÔÓÖØÒØÒ×ÓÕÙ×ØÓÒÒÒØÙÖÐÐÝÖ×Ò ÁÆÌÊÇÍÌÁÇÆ
ÛÓÖ×ØÝÐ×ÓÒØ×ØØØÓÓÑÔÓÒÒØ ÒØÑÖÓ×ÓÔÖØÓÒ×ÑÌ×ÓÒ×ÖÐØ ØÓÒØ×Ø×ÐØÓÒÓØÖØÓÒÖØ×ØÖÙØÙÖ ÒÔÖÑØÖ× ÓÑÔÓÒÒØ×ÌÖ×ØÓÒÖÒ××ØÓÓÑØÖÝÓÖÒÓØÖÒØÒØÔÖÑØÖÚØÓÖϑk
ÒÓÒÐÒÖÙÒØÓÒÓØÓÒÒØÖØÓÒÓÖ×ØØÚØÓÖξ
ÌÒØØÓÒÔÖÓÙÖÚÐÓÔÒØ×ÔÔÖØ ØÑÔØ×ØÓÖ××Ø×××Ù×Ò×ØÔÝ×ØÔÑÒÒÖ ÝÒÑÐÑÓÐ×ØÖÙØÙÖÓÖÓÔÖÓ×××ÒËØÓÒ ÖÕÙÖÒÙÑÖÓÖØÓÒ×ÒØ×ØÓÓÑØÖÑØÖÜ ËØÓÒ×Ö×ØÙ×ÓÅÜÑÙÑÄÐÓÓÈÖÒ Ì×ÔÔÖ×ÓÖÒÞ×ÓÐÐÓÛ×ØÖÖÐÐÒÒÖÐÚØÓÖϑkiÌÔÖÑØÖÚØÓÖϑkØÙ×ØÖ×αkÒ
ÒφkiÒØ×ÙÙÒØÓÒØØÓÒÐÝÔÒ×ÓÒÓÒ ÛØαk×ÐÖÓÒ×ØÒØSkØ×ØÓÖØÒØ×ÔÖÓ ÙØ×ÒÔÓ××ÐØÐÝ×Ø×ÖÚÒØkØÖØÓÒÖØ ÓÑÔÓÒÒØÓÒÒØÖØÓÒξiÒÓÒÖ×ØÖØÔÖÑØÖ
ÓÖØÓÒÖØ×ÒÔÖÓÖ××ÚÐÝÙÐØÝÒÚØÒ ØÖÓÙ×ØÓ×ÓÒØÖ×Ù×ÒÄÐÓÓÊØÓ ÓØÑÓÐÒÐÐÝËØÓÒÔÖ×ÒØ×ÓÛÙ×ÙÐÓÖÑ× ÔÐÓÑÔÓÒÒØÒÐÝ××ÅÄÈØÓ×ØÑØÓØØÓÓÖÒÖÝÖÒØÐÕÙØÓÒ×
ØÐÑÒØ×ÓØϑki×ÒÛÒÒÓÚÖÐÐÔÖÑ ØÖÚØÓÖϑØØÓÑÔÖ××ÐÐØÒØÔÖÑØÖ× ÏÖØÒØÑ××ÐÒÓ Ú×ØÓÐÐÓÛÒ×Ý×ØÑ
ÁØ×××ÙÑÒØ×ÔÔÖØØÓÔÖÓ×××ÒÖÔ Ì×ØÒÄÊÌÆÊÄÆÅÁÄÅÇÄ ØÖÑv∈ÊNØØÓÙÒØ×ÓÖÐÙØÓÒÒÔÙØ×Ò ÊN×MÑÙÔÓØÝÐÓÒØ×ÒØÖÒ×ÔÓÖØ ×ÓÙ×ÓÙØÓÛ×ÒÐÐÝØÒÙÑÖÓÓÑÔÓÒÒØ×× ÛØØ×ØØÚØÓÖξ(t) ∈ÊNØÝÐÑØÖÜK ∈
ØÛÒNÝÓÑÔÓÒÒØ××ØÒÒÓÒ Ö×ÒØÝÑÖÓ×ÓÔÖØÓÒ×ÑÓMÖØÓÒ× ÜÑÔÐ××Ù××ÒØÖÚÛÓÓÒÓ×ÓÖÚÓ ÐÖÖØÒØÒÙÑÖÓÖØÓÒ×ÒØÖ×ÒÓÐÒÖ
ØÐ ÖÐØÓÒ×ÔØÛÒÖØÓÒ×ØÓÓÑØÖ×
ÖØÒØ×νikÖÒØÚÒØÓ×ÖÐØØÓÔÖÓ ÛÖRkÖ×ÔØÚÐÝPkÒÓØ×ØkØ×ØÓÖ ×ØÐÐÙÖÖÒØÐÝØ×ÙØÓÑÒÝÔÙÐØÓÒ×ÌÑÓÐ ÑÓÐÒØÒÖÓ×ØÓÒÔÖÓ××× ÖÒ(K) = M.
ÙØ×νjkÔÓ×ØÚÌkØÖØÓÒÖØ×ÜÔÖ××× ÌÝÐÓÒØ×ÓØÔÖÓÙÖÛ×ÚÐÓÔÝÖÒÖØÐ
Ó×ÒØÓÐÐÙ×ØÖØØÔÖÓÖÑÒ×ÓÓÙÖÒØØÓÒ
5 2ØÛÒÚ Ò
ÒÚÓÐÚ×ØÓÐÐÓÛÒØÛÓÖØÓÒ×M = ÝÓÑÔÓÒÒØ×N = ØÒØ×ξiÓÖÔÖÓÙØ×ξj
ϕk(ξ,ϑk)
(−νik)ξi −−−−−−→
(νjk)ξj, k ∈ {1,2,...,M},
i∈Rk
j∈Pk
ϕk(ξ,ϑk) = αk ×
φki(ξi,ϑki),
i∈Sk
dξ(t)
= Kϕ(ξ,ϑ)+v(ξ,t),
dt
N ≥ M Ò
ϕ1(S1,X1,ϑ1)
(−k1) S1 −−−−−−−−→ X1 +k2 S2
ϕ2(S2,X2,ϑ2)
(−k3) S2 −−−−−−−−→ X2 +k4 P,

ØÑÙÑ×Ø×ÔÖÓÙPÓ×ÒÓØÖØÒØÙÐ ÒPØÑØÒØØÒ×ØÒØÒÓÙ×ÐÝÚÔÓÖØ×ÖÓÑ ÛØØÓÒÒØÖØÓÒ×S1ÖÔÖ×ÒØÒØ××ÓÐÚÓÖ ØÓÒØÖX2ØÑØÒÓÒØÖ ÚÒÝØÓÐÐÓÛÒÒÓÒÐÒÖÙÒØÓÒ×ÓØ×ØØ× ÑÙÑÓÒÒØÖØÓÒÒØ××ÌÖØÓÒÖØ×Ö X1Ò
ÒÖÓÒÇS2ØÚÓÐØÐØØÝ×ÎX1
ÛØØÓÒÒØÖØÓÒÙÒØ×ÒÔÖÑØÖÚÐÙ×ÚÒ ÒÌÐ
ÌÑ××ÐÒÓÛØÒØÓÒØÜØÓ×ØÖ ÓÔÖØÒÓÒØÒÙÓÙ×ÑÓÛÖØ×ÜÔÐØÔÒÒ× ÓÒØÑÒ××ØØÚØÓÖÖÖÓÔÔÓÖØ×Ó ÓÒ×Ò××
X2,
⎠ , ØÒÔÙØÓÒÒØÖØÓÒ×ÓØÖ×ÔØÚ×Ù×ØÖØ× ÈÖÑØÖÍÒØ℄ÎÐÙËØØÍÒØ℄ ÌÐ ×ÖÔØ×ÖØÖÐØÜÔÖÑÒØÒÙÑÖ× ÈÖÑØÖ×ÒÒØÐ×ØØ××ÙÔÖ ÎÐÙ
ÛØD(t)ØÒÔÙØÐÙØÓÒÖØÒS1Ò(t)ÒS2Ò(t)
α1g(Ld) −1℄ 1 1 (0)gL−1℄
α2g(Ld) −1℄ 1 2 (0)gL−1℄
KS1gL−1℄ 1 1 (0)gL−1℄
KS2g mmol−1℄ KIg mmol−1℄ k1℄ X 2 1 (0)gL−1℄
k2mmol g−1℄ 2 2 (0)gL−1℄
k3mmol g−1℄ 2 1 (0)g L−1℄
k4mmol g−1℄ Ù×ÓÓÙÖ×ØÑØÓÒÔÖÓÙÖÛØÒÓÒØÜØÖÓ ÁÒØÓÐÐÓÛÒ×ØÓÒ×ÛØØÑÔØØÓÐÐÙ×ØÖØØ
ÓÑ×ÙÖÑÒØÖÖÓÖ×ÌÓØ×ÒØÛÓÜÔÖÑÒØ× Ö×ÑÙÐØÛØÙ×ÒØÒØÐÓÒÒØÖØÓÒ×Ó ÌÐ ÖØÖÞØÓÒÖÖÓÖ×ÒÛØÒÓÛÒ×ØÖÙØÓÒ
×ØØÑ×ÙÖÑÒØØÙ×ÛÖØ× ÒØÒÓÖÑÐÐÝ×ØÖÙØØÚÒÓ×ÛÓ××ØÒÖ ÚØÓÒ× ×ÑÔÐ×ØÒÓÖÖÙÔØÛØÒÒÔÒ
ÌÒÓ×ÝØ×Ø×ÖÔÖ×ÒØÒÙÖØÓØÖÛØ 0.1ÌiØ ÓØÖÖÓÖÖÚÐÙσi =
ÁÒÓÒÒØÓÒÛØØÔÔÖÓÚÐÓÔÝÖÒÖ ØÜÔÖÑÒØÐÒÔÙØ×ÒÖÖÓÖÖ×ÑÙÐØÓÒ×
Ò×ØÒËÌÇÁÀÁÇÅÌÊÁËÌÁÅÌÁÇÆ ÓÙÖÒØØÓÒÔÖÓÙÖØ
N(0,σiIN)
Ý×ØÑØÒØÒÙÑÖÓÖØÓÒ×MÒØÖ ÑÒÒKÌÓÖÒÐØÝÓÓÙÖÔÖÓÙÖÖÐ×ÒØ ÒØÒ×ÚÙ×ÓÅÄÈÛÖ××ÖÓÑÓÑØÖÐ ØÑÔØ×ØÓ×ØÑØØÝÐÑØÖÜKÒØÛÓ×ØÔ× ÒØÖÔÖØØÓÒÓØ×ØØØÖØÓÖÝ
⎛
d
⎜
dt ⎝
S1
ϕ1(S1,X1,ϑ1) = α1
S1 +KS1
ϕ2(S2,X2,ϑ2) = α2
X1
X2
S1
S2
P
⎞
⎟
⎠ =
⎛
1
⎞
0
⎜ 0 1 ⎟
⎜ ⎟
⎜−k1
0 ⎟
⎝ ⎠ k2 −k3
0 k4
X
X
S
S
P
X
S
S
S2
S2 +KS2 +S 2 2 /KI
ϕ1
ϕ2
ξm(ti) = ξ(ti)+εi,ÛØεi ∼
⎛ ⎞
−X1
⎜ −X2 ⎟
⎜ ⎟
+D ⎜S1Ò−S1
⎟
⎝S2Ò−S2
0
1 2 (0)mmol L−1℄ 1 (0)mmol L−1℄ 2 2 (0)mmol L−1℄ P2 (0)mmol L−1℄ 0.5 X1 (g/L)
0
0.4 X2 (g/L)
0
5 S1 (g/L)
0
14 S2 (mmol/L)
7
0
0.8 P (mol/L)
0.4
0
40 S
20
0
0 50 100 150 200 250
2 1in (g/L) S2 2in (mmol/L)
D1 ÙÖ ×ÔÐÝÒØÓØØÓÑÖÔ×ÙÔÖ×ÖÔØ×ÒÓØ ØÜÔÖÑÒØÒÙÑÖ× ÓÙÒØÖÔÖØ×ÓÐÐÒ× ËØØÑ×ÙÖÑÒØ×ÓØ×ÒØÖÖÖÓÖÖ ÌÒÓÒÞÖÓÒÔÙØ×Ö
(100/d)
ÁÛÒØØÖÒ×ÔÓÖØÖ×ØØÚØÓÖÝ ÊØÓÒÆÙÑÖ
ÑÒØØÑ×Ð×ØÓØÓÐÐÓÛÒÜÔÖ××ÓÒ ÒØÖØÒØÑÓÐ ØÛÒÓÒ×ÙØÚÑ×ÙÖ
t
ξf(t) = ξ(t)−
0
ξ ∆ ti+1
f = K ϕ(τ)dτ,
i
ti ÛØØÖÒØÐ×ØØÚØÓÖξ ∆ Ñ×ÙÖÑÒØ×ÛØÒÖÖÓÖÓÚÖÒÑØÖÜÕÙÐØÓ ØØÒ×ØÑØÖÓÑØÖÒØÛÒ×ØØ
f = ξf(ti+1) − ξf(ti)
ÅÄÈÛ×ÚÐÓÔÝÏÒØÞÐÐØÐ Ö××Ò×ØÓÓÑØÖÓÑÔØÐØÝÐ××× ÑÒØÓÒÒØÒÓØ×ÓÒÖ MÑÒ×ÓÒÐÐÒÖ×Ù×ÔÌ×Ö×ÙÐØÛ×ÐÖÝ ÛÓÛ×
iÐÚ×Ò
i Ø×ÙÑÓØÖÐØÖÖÓÖÓÚÖÒÑØÖ×ËÒK
ÐÐÓÓ×Ò××ØÓÒÓ×ÝÑ×ÙÖÑÒØ×ÒØ× ÑÒ×ÓÒÐØÝpØØÖÔÖ×ÒØ×Ø×ØÒØÑÜÑÙÑ ØÑØØÐÒÖÔÓ××ÐÝÒ×Ù×ÔÓÚÒ ÔÓÛÖÙÐÑØÑØÐÑØÓÒÜÔÐÓØØÓ×Ø ØÓ×
f
ÑØØÖÕÙÖÒÙÑÖÓÖØÓÒ×ÓÓÔÖÓ×× ÇÙÖÔÔÖÓÓÒ××Ø×Ò×Ù××ÚÐÝÙ×ÒÅÄÈØÓØ ×ØÓ×Ù×Ô×ÓÒÖ×ÒÑÒ×ÓÒÖÓÑp=1ØÓ
p = MØÓØÑ×ÙÖÚØÓÖ×ξ ∆ ÓÐÐÓÛÒÐÓÐÐÓÓÓ×Ø
ns
Jp = ξ
i=1
∆ f,m −
i ˆ ξ ∆,p
T
f Q
i
∆ −1 i ξ ∆ f,m −
i ˆ ξ ∆,p
f ,
i ÛÖnsÒÓØ×ØÒÙÑÖÓÑ×ÙÖ×ÑÔÐ×ξ ∆ f,mi ×ØÑ×ÙÖÑÒØÓξ ∆ iÛØÒÖÖÓÖÓÚÖÒÑ
f ØÖÜQ ∆ ÑØÝØpÑÒ×ÓÒÐÐÒÖÑÓÐ
∆,p iÒˆ ξ
×ÖÒM ×ÑÔÐÝÜÔÖ×××ØØξ ∆
v(τ)dτ,
iÝÑÒÑÞÒØ
f
i×Ø×ÑÜÑÙÑÐÐÓÓÅÄ×Ø
f

ÛØns×NÖ×ÓÖÓÑÅÐÒÓ×Ì ÌÓ×Ø ×ÓÛÒØØJM××ÑÐÐÖÓÖÕÙÐØÓØÐÓÐÐÓÓ ÅÓÖÓÚÖJ∗×ÒÓÛÒØÓÚ×ÕÙÖ×ØÖÙØÓÒ Ó×ØJ∗ÓØØÖÙÒÓÒÐÒÖÑÓÐÅÐÖØÐ ×Ö×ÒÙÒØÓÒÓpÒØÒ
ÑÒ×ÓÒpÛÓ×ÖÐØ×Ù×ÔØ×ØØÛØ ÐÓÐÐÓÓÓ×ØJp×ÑÐÐÖÓÖÕÙÐØÓØÖÒÓ ÒÙÑÖÓÖØÓÒ×M×ØÙ×Ó×Ò×Ø×ÑÐÐ×Ø
ØÒÙÑÖÓÖØÓÒ×ÖÕÙÖØÓÖÔÖ×ÒØØ×ÑÙ ÐØÜÔÖÑÒØÐØÓÒÖÓ×ØÓÒÙÖ ÜÑÔÐÇÙÖ×ØÑØÓÒÔÔÖÓ×Ù×ØÓØÖÑÒ ÐÓÐÐÓÓÓ×Ø×ÑÐÐÖØÒÒÝÔÐÙ×ÐÚÐÙÓ 2Ð×ØÓ ×ÓÛ×ØØØÛÓÑÒ×ÓÒÐ×Ù×Ôp = ÖÒÓÑÚÖÐÛØ×ØÖÙØÓÒχ 2 2200ÌÒÙÑÖÓ ÖØÓÒ×ØÙ×Ó×Ò×M =
χ 2 ns×N×ØÖÙØÖÒÓÑÚÖÐ
Log-likelihood criterion Jp
4000
3500
3000
2500
N = 5
2
ns = 440
χ 2,(99.9%)
2200
2000
χ
1500
1000
500
0
1 2 3 4
Subspace dimensionality p
2,(0.1%)
2200
ÙÖ ×ØÑØ×Ù×Ô×ÔÐÙ×ÐÖÒÓÖJ∗× ÐÑØÝØÛÓ×ÕÙÖÕÙÒØÐ××ÐÒ× ÄÓÐÐÓÓÓ×Ø×ÖÐØØÓØÅÄÈ
×Ù×Ô×ÔÒÒÝKØÖÐØÚÐÝÐÖÖÖÓÖ×Ø ÐØÓÙÅÄÈ×ÐØÓ×ØÑØÚØÓÖ××ÓØ ÒØÑ×ÙÖÑÒØ×Óξ ∆ iÖ×ÙÐØÒÐÖÙÒÖØÒØ×
ÝÒØÖØÒ ÀÒÒØÓÒÐ×ØÔ×ØÒÒØÒÜØ×ØÓÒ ÐÅØÖÜ tiÛØ
f
ØÖØÓÒ×ÖÓØÖÒ×ÔÓÖØØÖÑ×ÒÐÙÒÒÒ ×Ù×ÔÔÖÐÐÐØÓØÔÖÚÓÙ×ÓÒÙØØÖÒ×ÐØÖÓÑ ÛÜÔÖ×××ØØØØÖØÓÖÝÓØÔÖÓ××ÓÒÒ ÖÓÑt = 0ØÓt =
ti
ξf(ti) = ξ0 +K ϕ(τ)dτ,
ÀÚÒ×ØÑØØÒÙÑÖÓÖØÓÒ×ÒØÔÖ ØÓÖÒÝØÒØÐ×ØØÚØÓÖξ0ÜÔÖÑÒØ×ÛØ ×ØØÚØÓÖ×ÚÓÐÚÒÒÔÖÐÐÐÒ×Ù×Ô× ÖÒØÒØÐÓÒÒØÖØÓÒ×ØÙ×ÚØÖÖ×ÔØÚ
0
ÚÓÙ××ØÓÒÓÙÖÔÔÖÓÙ××ÅÄÈØÓØM ÑÒ×ÓÒÐÒ×Ù×ÔØÓØÑ×ÙÖÑÒØ×ξ f,mi
ÓØØÖÒ×ÔÓÖØÖ×ØØÚØÓÖÌ×Ö×ÙÐØ×ÒØ ÖÐØØÓÜÔÖÑÒØÒÓØØØÓÒÐÝN−MÐÑÒØ× ÓÖÒØØÓÒÓØÔÖÐÐÐÒ×Ù×Ô×ÒÊN×ÛÐÐ
∈ÊN×MØØÒ×Ø
ÜÔÖ×××ÐÒÖÓÑÒØÓÒÓØÓÐÙÑÒ×ÓØ ÓdÖÑØÑØÐÐÝÒÔÒÒØ ×ØÑØÓÒÓÚØÓÖ×׈ρ
ÓÖÑ ÝÒØÓÒÓÐÙÑÒÓØÝÐÑØÖÜK× ÚØÓÖ××Ì×ØÑØÝÐÑØÖÜ×ØÙ×ÓØ
×ÒØØÖÑÒØÓÒÓØÒØÖÔØÚØÓÖd ∈ÊN
Ì×ÓÒØ×Ò×ØÑØÒÔÒÒØÐÝÓØ
∈ÊM×MÖÙÐÖÓÒØÑØÖÜ
ÑØÑØÐÓÒ×ØÖÒØ××ÐÐÙ×ØÖØÒØÜÑÔÐ ÖØÓÒÒØ××ÙÒØÔÖÓÖÒÓÛÐ×ÚÐÐ ÓÒØÔÖÓ×××ØÓÓÑØÖÝÌÓØ×ÔÙÖÔÓ×Ø× ÝÐÓÒØ×ÒÓÐÙÑÒÓKËÙÙ×Ó ÒÓÙØÓÓÖÑÙÐØMÑØÑØÐÓÒ×ØÖÒØ×ÓÒØ
ˆK
ÖØÖ
ÛØG
ÒÐÐÝØÒØÐÓÒÒØÖØÓÒÚØÓÖÓÜÔÖÑÒØ ÓÒØ×ØÑØÐÒÖÒ×Ù×Ô ÜÑÔÐÅÄÈ×Ù×ØÓØØÛÓÑÒ×ÓÒÐÒ ×ÓÑÔÙØÝÔÖÓØÒØÓÖÖ×ÔÓÒÒÑ×ÙÖÑÒØ
×ÓØÒÛ×Ø×× 2ÖØÖÑÒ ÒØÛÓÒØÖÔØÚØÓÖ×
fiÒØÜÑÔÐÓ ×Ù×ÔØÓØÑ×ÙÖÑÒØ×Óξ ÒÖÓ×ØÓÒÔÖÓ××ÌÓÐÐÓÛÒÚØÓÖ×׈ρ
1Òd
= ˆρG,
d
⎛
−2×10
⎜
ˆρ = ⎜
⎝
−3 8×10 −3
−9×10 −4 −3×10 −5
⎞
⎟
0.10 −0.32 ⎟
−0.04 0.94
⎠
−0.39 −0.03
,
d 1 ⎛ ⎞
0
⎜ 0 ⎟
⎜ ⎟
= ⎜−0.0075
⎟
⎝ 0.0033 ⎠
−0.0011
, d2 ⎛ ⎞
0
⎜ 0 ⎟
⎜ ⎟
= ⎜ 0.0172 ⎟
⎝−0.0003
⎠
0.0010
. ××ÙÑÒØØØÖ×ØØÛÓÖÓÛ×ÓKÖÒÓÛÒÌ×× ÌÖÙÐÖÓÒØÑØÖÜG××ÐÝÓÑÔÙØÝ
ÛØÖÖØÓØ×ÓÑ××ÜÔÖ××ÒØ×ÓÒ×ØÖÒØ× ÒØÙÔÔÖÔÖØÓÕÙÐØÝ ÓG ÖØÓÒÒØØØ×ÝÐÓÒØ×ÖÒÓÖÑÐÞ ÕÙÚÐÒØØÓ××ÙÑØØÓÒÐÝÓÒÓÑ×××ÒÚÓÐÚÒ ÛØØ×ØÑØÓÒ
ÓÓ×ØÑØÓÒÓK×ØÒ×ÑÔÐÝÓØÒÖÓÑ
ˆG
4 −1104
=
123 −3147
⎛ ⎞
1 0
⎜ 0 1 ⎟
ˆK = ˆρ ˆG
⎜ ⎟
= ⎜−40.0
−7.6 ⎟
⎝ 116.1 −258⎠
−1.8 443
.
×Ý×ØÑØÐÐÝÖÐÞÛØÒØÅÄÈÐÓÖØÑ×Ó 2Ö ØÓ×ÒÓØÖÕÙÖÒÝÜØÖÓÑÔÙØØÓÒ
ÜÔÖÑÒØ×ÒØÓØ×Ò×Ù×ÔÌ×ÔÖÓØÓÒ× ×ØÑØÝÔÖÓØÒØÖ×ØÑ×ÙÖÑÒØ×Ó 1Òξ0 ÒÐÐÝØÒØÐÓÒÒØÖØÓÒÚØÓÖ×ξ0
.

⎛
0.58
⎜ 0.51
1
ˆξ0
⎜
= ⎜ 0.49
⎝ 5×10 −6
−7×10 −4
⎞
⎟
⎠ , ˆ ⎛
0.50
⎜ 0.46
2 ⎜
ξ0 = ⎜ 0.45
⎝−1×10
−3
3×10 −4
⎞
⎟
⎠ . ÆÓØØØÒØÚÓÒÒØÖØÓÒ×ÒÔÔÖÒØØ
ÒØØÓÒ×Ø× ×Ø×ÒØÐÒÖÒ×Ù×Ô×ÖÒÓØÔÝ×Ð ÑÓÐ×ÓØÔÖÓ××ÁØ×ÐÖØØØ×ÒØÚÒØÐ ÓÒÒØÖØÓÒ××ÓÙÐÞÖÓÛÒÙ×ÒØÒÜØ
ÓØÖØÓÒÖØ×Ì××ØÓÒ×Ö×ÒÐÓÖØÑ Ì×ÓÒÔÖØÓÓÙÖ×ØÑØÓÒÔÖÓÙÖÐ×ÛØ ØØÖÑÒØÓÒÓØ×ØÖÙØÙÖÒÔÖÑØÖÚÐÙ× ÃÁÆÌÁËÌÁÅÌÁÇÆ
×Ö×Ó×ÓÒØÖ×ÑÒØÒÒÒØ×ØÖÙØÙÖ ÓÖØÑÓÐ ØØÙ××ØÄÊÌØÓÒÚØØÖÓÙØÖÒ×Ó
×ÓÒÌÖÓÖØÃÒØ× ×ÓÒØÖÖÒÓÛ×ÖÐØØÓ×ÑÔÐ ÔÖÑØÖØ×ØÅÐÖÒÎÒÏÓÙÛÖ ÅÒÝÓØÒØÙÒØÓÒ×Ù×ÙÐÐÝÒÓÙÒØÖÒ ÓÔÖÓ××ÑÓÐ×ÒÖÖÒ×ØÐÚ×Ó ÑÓÐ Ó×ÓÖØφki(ξi,ϑki)×ÌÒØ×ØÖÙØÙÖÓ Ø×ÒØÙÒØÓÒ×ÖÔÖ×ÒØØÔÓ××Ð NÖ×ÔØÚ ÁÒØ
ØØÚÖØÓÒÐÜÔÖ××ÓÒ×ÑÓÖÓÑÔÖÒ×Ú ×ÓÒØÖ×
ÒØØÖÒÓÙÒÒÅÐÖÒÎÒÏÓÙÛÖ ÙÖÛØÖ×ØÖØ×ØÓÒÙÑÖÒØÙÒØÓÒ× ÓÖØ×ÓÓÒ×Ò×××ÙØÖ×ÖÔÖ×ÒØÒ ÓÔÖÓ××ÑÓÐ×ØÙ×ÙÐÐÝ×ÔÝ×ØÓM×N ÒØÙÒØÓÒ×ØØÖÓ×ÒÒM
Ö×ÒØÝØÖÒÐÔÓÒØÒÙÔÛÖ×ÒÒØÒ ØÚØÒ×ØÖÙØÙÖ×ÅÓÒÓØÝÔÖÖÔ
×
ÔÓÒØ×ØØÓØÀÐÒÙÒØÓÒØØÔÖ×ÒØ× ×ØÖÙØÙÖ×ÝØÖÒÐÔÓÒØÒÓÛÒÛÖ××ÕÙÖÓÒ
ÑÜÑÙÑÚÐÙØÔÖØÙÐÖÓÒÒØÖØÓÒ1
2
1/ξÑÜ=0
1/KS = 0
ξÑÜ= 0
KS = 0
1/KI = 0
1/ξÑÜ= 0
6 5 4 3
ÙÖ ÐÚÐ×ÖÒ×××ÓØØÓÔÖÑØÖ ÓÒØÓÒØØ×Ø×ØÙÖÒÒÚØÓÒ ÃÒØ×ÓÒØÖÛØØÖÓÑÔÐÜØÝ
7
1/KI = 0
ÌÐ Ì×ØÖÙØÙÖ×ÖÐØØÓØØÖÐÚ×ÖÔÖ×ÒØÒ Ó×ØÒÒÓÒ ÖÐØØÓØφki(ξi,ϑki)×Ò ÌÐ ÒØÖÖÖÒ×ÒÓÙÒÒØÓÓ
ØÖ×ØÓÐÙÑÒÖÐØØÓØÓ×ÓÙÖ Ê×ØÖØÐ×ØÓØÙ×ÙÐ×ØÖÙØÙÖ× ØØ×ÔÓÒØÛÚ ÆÙÑÖ×Ó
1−ξi/ξÑÜ ËØÖÙØÙÖ ØÓÒÐÓÑÑÒØ
ξi/ξÑÜ
#
×ÓÒ×ÖÓÑØ×ØÖ×ØÒÜØ×ØÓÒÒØÖÓÙ×
ξi > ξÑÜξÑÜ>
×ØØ×ØÐÑØÓØÓØ×ØÖÒÓÒØÓÒ× N×ÓÒØÖ×ØØÒÙ×
KI/(KI
ξi/(KS
ÄÐÓÓÊØÓÌ×Ø ØÓÖÔÖ×ÒØÒÝÑÓÐÓØÓÖÑ ÁÒÓÖÖØÓØ ξi > ξÑÜξÑÜ>
ÓÒ×ÖÒÑÓÐÖÖÓÑÖØÖÞØÓÒÖÖÓÖÒ
Ò×ØÓM×
nsÜÔÖÑÒØÐÑ×ÙÖÑÒØ×ÓØNÑÒ×ÓÒÐ
∈ÊnθØÄÊÌØØÑÔØ×
ÛØÒÓÛÒÓÚÖÒ× ×ÓÒØÓÑÔÖ×ÓÒÓÐÐÓÓ×ÓÑÔÙØÖÓÑ ÌÓØ×ÒØÄÊÌ× ÔÖÑØÖÞÝØÚØÓÖθ
ÔÖÑØÖÚØÓÖθØÓÐÐÓÛÒÐÐÓÓÖØÓÒ ÒÓØÒÝL(θ)ØÐÐÓÓÙÒØÓÒÖÐØØÓØ ÑÓÐÓÙØÔÙØÓÖÖÙÔØÝÒÓÖÑÐÐÝ×ØÖÙØÖÖÓÖ× ØÓØ×ØØÒÙÐÐÝÔÓØ××H0 θ ÐØÖÒØÚH1θ
ÓÑÔÙØ
= θ0
ÛÖL(θ0)×ÓØÒÝÖÔÐÒÒØÑÓÐØ ÓÚÓÙ×ÐÝÒÖ××ÛØØÐÐÓÓÓH0Ò×Ø×
Λ
ÓÖÓÑÛÒØ×ÑÔÐ×ÞÔÔÖÓ×ÒÒØÝ ×ÝÑÔØÓØÐÐÝ×ØÖÙØ××ÕÙÖÛØnθÖ× ÅÄ×ØÑØÓθÝØØ×ØÚÐÙθ0ÌÖØÓΛ ×0 ≤
×ØÖÙØÓÒ ÌÒÙÐÐ××ÙÑÔØÓÒ×ÓÙÐØÖÓÖÖØØØ ÐÖÖØÒØ(1−α)ÕÙÒØÐÓØÖÐØ×ÕÙÖ ×ÒÒÐÚÐαØÓÑÔÙØ×ÓÒÚÖÐD×
×ÓÛ×ØØØ×ÓÒÚÖÐD =
ÆÚØÓÒÐÓÖØÑ
ÑÓÐÛØØÛ×ØÔÖÑØÖ×ÒØÓÔÖÓÖ× ÇÒØ××ÓØÄÊÌÒÐÓÖØÑ×ÒÚÐ ÓØÒÝÓÑÒØÓÒÓØÐÚ×ÓM×N×ÓÒ ØÖ×ÁØ×ÓÚÖÐÐ×ØÖØÝ×ØÓ×ØÖØÖÓÑØÑÓ×Ø×ÑÔÐ ÓÔØÓØÖÑÒØ×ØÒØ×ØÖÙØÙÖØØÒ
ÖÒ×Ù×ÒØÄÊÌ ÙÖÒÒÒØÐÞØÓÒÔ×ÙÒÐÐÝÒØ×ØÖÙØÙÖ× ×ÚÐÝÓÑÔÐÜØÝÝÒÚØÒÓÛÒØÖÓÙØØÖ
ÓÖÖØÓÖÙØÒÙÑÖÓÒØÓÑÒØÓÒ×ØÓ
N×ÓÒØÖ×Ò ÖÖ×Ø×ÖÖÓÑØM ×
1
ξi
0
+ξi) KI > 0
+ξi) KS > 0
0
ξi/(ξi +KS +ξ2 i /KI) KS > 0KI > 0
θ0Ò×ØØ =
L (θ0)
=
sup L (θ)
θ
,
1ÅÓÖÓÚÖÙÒÖØÒÙÐÐÝÔÓØ××ÏÐ×
Λ ≤
−2ÐÒ(Λ)×
D ns→∞
∼ χ 2 nθ .

Ø×ØÖÓÓØÑÓÐ×ØÒÒÛÒÚÓÐÚ×
ØÖØÓÒÓØÓÐÐÓÛÒÐÓÖØÑÐÓÓÔ ÓÒØÑÓÐ×ØØÖÔØÒÑÑÓÖÝØÖ ×ØÒÓ×ÒÛÖÔÖ×ÒØ×ØÑÜÑÙÑÒÙÑÖ ÛÒÝÔÖÑØÖ×ÒÛÐÐØÔÖÒØÓÐÐØ
ÐÖÒÑÓÐ×ÓØÒÝ×Ù××ÚÐÝÖÔÐÒ Í×ØÄÊÌØÓÚÐÙØØÐÐÓÓÓØÓ×
×Ù×ÕÙÒØÑÓÐ×ÑÜÑÙÑÒÙÑÖÓÒØnc
ØÒØÙÒØÓÒφki(ξi,ϑki)ÓØÓÒ×ÖÒ
•ØØÒÓØØÖØÓÒÛÒÐÐØÓÖÐÓÓÔ× ×ÓÒØÖ ×ÚØÒØ×ØÓÔØÐÖÒ ØÝÐÐÓØ×ÔÓ××ÐÐÖÒÒØÖ×ÔØÚ
ÚÓÑØÓÒÒÖÒØÔØÐÖÒÝ ÁØÐÑÓÐ×ÒÓØÖØÝØÄÊÌ
•ËØÓÔÐÓÓÔÒÛÒØÑÓÐÐÐÓÓ×ÖØÒ ØÖØÓÒ ÓØÑØÓÓÒ×ØØÙØØ×ØÓÒØ×ØØÒÜØ
ÒÒÐÝ××ÓØÒØØÓÒÖ×ÙÐØ×ØØÖØÓÒ ÖÑÒÒÐØÓÚÐÙØ ÛÒØØÖ×ÓÐÓÖÒÓØÖÛÓÖ×ÛÒØÐÓ ÐÐÓÓÓ×Ø×ÐÓÛÒÓÙÓÖÛÒØÖ×ÒÓ
ÓÖÖÓÖ×ÒÐÐÓÓÒ×ÐØØÖ×Ønc
×ÓÙÐÒÐÐÝÐÐÓÛØÓØÖÑÒÑÓÐ×ØÖÙØÙÖØØ ÓÖ×ÓÓØÛØÜÔÖÑÒØÐØÒÚÓ×ÓÚÖ ÔÖÑØÖÞØÓÒ
ÛÓÙÐÔÖÓÐÝÒÓØÚÖÑØÐÑÔØÓÒØ ÔÔÖÓÛØØÒÖÓ×ØÓÒÔÖÓ××Ø×ØÓ Ø××ØÀÓÛÚÖØÓÓÕÙÐØÝÓØ××ØÑØ ÜÑÔÐ ÓÑØÖÑØÖÜ×××ÙÑØÓÔÖØÐÝÒÓÛÒÙÖÒ ÁÒÓÖÖØÓÚÐØÓÙÖÒØÒØØÓÒ
ÒØÒØØÓÒÖ×ÙÐØ× Ð××Ð××ÙÑÔØÓÒØØÛÑ×ØØÓÑ××ÓÒ ØÚÖÓÛØÖØ×ÅÓÖÓÚÖ×ÒÖÓÑØÓ×ÖÚØÓÒÓ Ø×ØÑØÝÐÑØÖÜS1×ØÑÒ×Ù×ØÖØÓØ Ø×ÖØÛØÔÓ××ÐÒØÓÒØÓÒÒØÖØÓÒ× Ö×ØÖØÓÒØ×××ÙÑØÓÚÒØÚØÒØÓÒ ÒØÖØÓÒ×ÚÔÖÓÔÓÖØÓÒÐÒÙÒÓÒØÖÖ×Ô
ØÖ×ØÖØÓÒÒÐÐÝØÑØÒÓÒÒØÖØÓÒ× ÌÓØÓÔÔÓ×Ø×ÒS2×ÔÖÓÙØÓØ×ÓÒ Ì×ÑÖ×ÓÒÒ×ÐÓÖS2ÒØ×ÓÒÖØÓÒ
ÒÓÒÙÒÓÒØÖØ××ÒØ××ÙÔÔÓ×ØÓÚÔÓÖØ× ÖØÓÒØ×ÒÙÒ×××ÙÑØÓØÖÒÙØÖÐÓÖ Ò×ØÒØÒÓÙ×ÐÝÖÓÑØÑÙÑÌÐ×ÙÑÑÖÞ× Ø×ÒÓÖÑØÓÒ×ÝÐ×ØÒØÔÓ××Ð×ØÖÙØÙÖ×ÓÖ ÒØÚÛ××ÙÑØ×ÑØÝÔÓÒÙÒÓS1ÓÒ
ØÓÒÌÐ Øφki(ξi,ϑki)×ÖÐØØÓÓÑÔÓÒÒØÒÖ
Ò×ØÖÙØÙÖ×ÖÑÖÛØÒ×ØÖ× ÆÙÑÖ×ÖÐØØÓÙÖ ÒØ×ØÖÙØÙÖ×ÓÖØφki× ÌÖÙ
•ÓÖÒØÑÓÐÓÖÖØÓÒk =
1,...,MÒÓÖÓÑÔÓÒÒØi = 1,...,N
ϕ1(ξ,ϑ) ϕ2(ξ,ϑ)
X1 2 ∗ 1 ∗
X2 1 ∗ 2 ∗
S1 1 2 5 ∗ 6 7 1 ∗ 3 4
S2 1 ∗ 3 4 1 2 5 6 7 ∗
P 1 ∗ 1 ∗
ÇÙÖÒØØÓÒÐÓÖØÑÛ×ÔÔÐÛØÑÜÑÙÑ Ö×ØØÖØÖØÓÒ×ØÖØÓÒ×ÖÒÙÑÖÒØÖ×Ø ÌÐÛÔÖ×ÒØ×Ø×ØØÖÒØ×ÓÖØ ÓÐÙÑÒÌÖ×ÙÐØ×Ó×Ù×ÕÙÒØÐÓÖØÑØÖØÓÒ×
10ÒØÖ×ÙÐØ×ÖÐ×ØÒ
ÖÓÑËØÓÒØØÒÓÙÖ×ÒÓÖØÖÞØÓÒ ×ØØ×ØÐÔÓÒØÓÚÛØÖ×Ð××ØÒ ØØÖ×ØÑÓÐ×ØØÖÙÑÓÐÁÒÛÒÓÛ ×ÒÒØÐÝÒÙ×ÑÓÖÔÖÑØÖ×ÅÓÖÓÚÖÖÓÑ ÖÒÓØÔÖ×ÒØÙ×ØÝÓÒÓØÑÔÖÓÚØÓ×Ø ÒØØ
ÒÙÑÖÓÒØnc =
ÖÖÓÖÒÒÓÖÑÐÒÓ×ÛØÒÓÛÒÓÚÖÒØÅÄ ÓÚØÓÖ×ØØÑ×ÙÖÑÒØ×Ù×ØÓÓÑÔÙØØÓ×Ø Ó×ÒÓØÐÐÒ×Ø Ó×ØJ∗ÓØØÖÙÑÓÐ××ÕÙÖ×ØÖÙØÓÒ
×NÖ×ÓÖÓÑÛÖns×ØÒÙÑÖ ÓÒÒÒØÖÚÐÓ×Ù ÛØns ËÒØÅÄÓ×ØÓØØÖ×ØÑÓÐJ∗ = ×ØÖÙØÖÒÓÑÚÖÐCI 99% ×ØÙ×Ð××ØÒ ÌÐÊ×ÙÐØ×ÓØÒØÒØØÓÒ ËØÖÙØÙÖÒÙÑÖ×ÖÐØØÓÌÐ ×ØÖÙØÙÖ×ÖÑÖÛØÒ×ØÖ× ÒÓÒØØÖÙÑÓÐ ÌÖÙ
2860
= [2033; 2375]Ø
ϕ2(ξ,ϑ)
ÁØÖϕ1(ξ,ϑ)
S1 S2 S1 S2 Ó×ØJ∗
0 1 1∗ 1∗ 1 6.34×10 5
1 1
1
∗ 1∗ 6 5.05×10 5
1 1∗ 1∗ 5 5.05×10 5
6 1∗ 1∗ 1 5.73×10 5
5∗ 1∗ 1∗ 1 5.73×10 5
6 1
2
∗ 1∗ 6 7.01×10 4
6 1∗ 1∗ 5 7.01×10 4
5∗ 1∗ 1∗ 6 7.01×10 4
5∗ 1∗ 1∗ 5 7.01×10 4
5
3
∗ 1∗ 1∗ 7∗ 2.38×10 3
7 1∗ 1∗ 5 2.38×10 3
6 3 1 5 2.86×10 3
6 1∗ 1∗ 7∗ 3.25×10 3
ÕÙÐØÝÓØØÛØØÌ×Ó×ÖÚØÓÒ×Ù×Ø× ÖØÓÒÖØÝS2Ó×ÒÓØ×ÒÒØÐÝÒÙÒØ ×ØØÛÓÑÓÐ×ÖÓÑÓÑÔÖ×ÓÒÓØÔÖÑØÖ ×ØÑØ×Ø×Ó×ÖÚØØØÒØÓÒÓØ×ÓÒ ÒÐÐÝÌÐÓÒÖÓÒØ×ØÒØÜÔÖ××ÓÒ×ÓØ
ØØØÜÔÖÑÒØÐØÓ×ÒÓØÓÒØÒÒÓÙÒÓÖ ÑØÓÒÓÙØØ×ÒØÚÚÓÙÖÐÓÐ×Ò×ØÚØÝ ÒÐÝ××ØÒÕÙ×ÑÝÚÒØÓÙ×ÐÝÔÔÐØÓÔÖ ØÓS1ÒØ×ÓÒÑÓÐ××ÓØØÙÐÐÝÖ× ØÐ ÚÒØØ×Ð×ÓÒØÐØÝÒÖÐ×ØÙØÓÒ×ÅÐÖ ØÙÔÔÖÓÙÒÓÖØØÔÖÑØÖØØØÒØÚ ØÖÑ×ÒÓÒÙÒÓÒØÖØÓÒÖØÓØÑÓÐ× ÒØÙ×ÓÒ×Ö×ÔÖØÐÐÝÒØÐ ×Ø×ØÒØÚÓÒ×ØÒØÖÐØ
ÌÐ×Ø×ØÑØÒØÑÓÐ×
S1 = 0.94S1+7.50
1×Øϕ1(ξ,ϑ) X1
S2
ϕ2(ξ,ϑ) = 0.51
S2+9.44+S2 2 /333X2
S1 = 0.94
S1+7.50+S
2Òϕ1(ξ,ϑ) 2 1 /10000X1
S2 ϕ2(ξ,ϑ) = 0.49S2+9.03
X2
ÑÖÓ×ÓÔÑÓÐ×ÓÓÔÖÓ×××ÖÓÑ×ØÓÒÓ×Ý
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