Цветков Е.В., Алябышева Т.М., Парфенов Л.Г. Оптимальные режимы гидроэлектростанций в энергетических системах
Подождите немного. Документ загружается.
I4so6pa>t<eHHbre
Ha
puc.
5.1
3oHbI He
rlocroflHHbl
BI{yrpH
foA€I,
a
H3MeHtrcT
cBoe
83apIN{HOe
pacnoao}KeHlle no
xapal(-
TepHbrM
Qaearur
roAa.-
B [peAeJlax
nerHelt vr
oceHHeft
MeiKe-
Hr.r,
BeceHHero [oJIoBoAta.
I(porure roro,
grn
3oHbI
Aa]Ke
B
nro6oft
QnxcHpoeaHHslti
MoMeHT BpeMeHpI
Moryr
ll3Meurrbcfl
B
3aBHCHMOCTII
OT
npOrHO3HpyeMblx
HJIH
npeA[IecrBylol[Hx
pacxoAoB peKH,
a
HHorAa H HeKoropbIX
3HaqeHufi
ctoxoo6pa'
3yiou{Hx
Qarropoe.
Ocsoasoe
sHar{eHHe
B
Ancnerqepct(ojvt
rpa$axe
HMeror
xa-
paKTepHbre
JII4Hpn4,
pa3Ae/IflIouIHe
uso6paxeHHbIe
3oHbI.
iia
3THX JTHHHflX
flpOHCXOAHT
H3MeHeHHe
CTparerklH
ynp
aBneHHfi
BOAOXpaHliiiHiqaMH.
3aAaHne
STHX
npuwit
osHaqaeT
H
saAaHHe
IIopflAKa
pacnpeAeJleHus BoAbI
rr,rexAy
yqacrHH
KaMH
B
XK.
fIolOxeHLIe
yKagaHHbIX
XapaKTepHbIX
nwswft
AHC[eTr{epcKO-
ro
rpaSaxa saBHcHr or
Ha3HaqeHfifl
raApoy3JIa,
peryanpyto-
uIHX Bo3MOX{HOctefi
ero
BoAoXpaHHJII{iqa,
XapaKTepHcTHK
peq-
HOrO
CTOKa,
npl4HflTofi
crpatefan
BeAeHHfl
peX(HMOB Ir
Apyrflx
Qaxropoe.
Hanpauep,
crpeMJlenfie
noBbltuarb
rapaHrHpoBaH-
Hyro
orAar{y
BXOAHT
B
ripOTHBOpeqHe
co
crpeMfleHHeM
Ha'
a6onnurero
HcnoJIb3oBaHHx
croKa,
w fiogroNly
Ao,/'liKHo
eH6H-
parbcfi
rleJrecoo6pa3Hoe
KoMilpoMHCCHOe
peUIeHHe.
f apaurupoBal{HbIe
orAaqH
r.ilrt
3HepreruKH H
ApynHX
Vr{acrHHKoB
BXK n
o6qeu
cryqae
3HaI{HTeJIbHo
H3MeHfiorcfl
BHyTpH
rOAa;
OHH
TaKiKe
MOtyT
H3MeHfTbCq
H'OT
rOAa
I(
rO-
Ay.
fapaHTHpoBaHHbIe
OTAar{lI
BoAbI ;.nfl
sHepfeTHKH,
KpoMe
TOrO,
H3MeHflIOTCfl
C H3MeHeHHeM
HaIIOJIHeHI{g
BOAOXpaHI4JIVI-
ura
(Hanopa
f
3C).
Ann
cI4cTeM
B6A6XpaHHJIIIUI
ocHOBHbIe
noJlox(eHgfi
pac-
cMorpeHHblx
3oH
lr
nurtvrfr.
AucneTrlepcKHX
rpaSHxon
cOXpa-
HflroTcg,
Ho B
ycJlolKHeHlioM
BHAe,
LITO
CBfl3aHG
C
paUHOHanb-
HbrM
pacnpeAeJleggeM
rex HJIvr
HHbIx
QyuxUHft
MelKAy
rHA-
poy3JIaMH.
Kpnrepnn
nocrpoeHHfl
AncnerqepcKHx
rpaSHKoB. 3aAaqa
HHfl,,
xapaKTepH3yeMaq
eHAaqefi
rapaHTI{pOBaHHbIX
oTAaq,
cMflrqeHne
uepe6Oee
B
3oHe
[epe6oeB,
sKoHOMHqHocTb
pa6o-
TbI
fHApOy3,'IalB
3OHe
H36birot{Hbix
or.{,aq.
Moryr 6urt
cJleAylou1ge
ABa
IIpHHI{HnHaJIbHo
pa3flHqalo-
ulaxcff
noAXoAa
K
petUeHHIo
3Toli
IJHoroKpHTepHaJIsgotl
3a-
.u,aqI'I:
110
a)
cBepTbIBaHHe
BeKTopHorO
I{pHTep}Ifi
B cKaJIflpHbIH
Ha
ocHope
croaMocrnoli
oqeHKH
SKoHolllH"IHocrH
pex(HMa H
ylqep-
6oe
Or
noHHlKeHHbIX
HH)Ke
rapaHTHpoBaHHbIX
H
noBbIIIIeHHbIx
cBepx
AOnycrHMbIX
no
HH>KHeMy
6recpy
H BoAocJIHBaM
oTAarI
H3 BOAOXpaHHJIpIIIi;
6)
HcnoJIb3oBaHHe
npnHuI'{na
rtplropHrera
KpHTepaeB-
flpo6.rieua
croHMocrHbIX
oqeHoK
ylqep6oB
oT
AeQHUHToB
vrJrzr
He6nttxoe
BoAbI
flBJIflercfl
cno>xlrott 14
B
3HaqI4TeJIbHofi
Mepe
He
perueuHoli. Ilyuure
o6ctour
AeJIo
co
cToHMocruot?
ortenxofi
yUep6OB
or
Ae0HI{HroB
3HeprocHa6x<eHias
H33a
Ma-
JIOBoAbI;
OAHaKO
14
11O
3THM
ylqep6aM
HCc.IieAOBaq.Vfl
He 3A'
BeprreHbr. Co
croHtv{ocrsoft
oqeHnoft
Yuf!p_Q_o_e
or
AeQHrtHToB
BoAbI
y
HegHeprerHrIecKHX
yqacrHgKoB BXK
AeJIo
o6cToHT
gHaqHTeJIbHo
xylKe.
KpOiue
TOrO, B
PflAe
CIyrIaeB
cToHlv{OCT-
Hafl.
oI{eHKa
yuep60B
noo6ule
HeBo3tvlo}KHa'
HanpHMep
rpH
HaBOAHeHHfiX,
ecJIH
noc"lIeAHHe
yrpo)KaIoT
rIeIoBeqecKHM
>KH3HfiM.
floarouy
Ha
IIpaKTHKe
to6u,rtlo
HcnoJIb3yIoT
BTopofi,
IIpHopHTeTHbIrt
noAXoA
Iia OcHOBe
BepOflTHocTHbIX
KpHTepHeB
pacuerHoft
o6ecneqeHnocTn.
llp"
sroM eAI{HbIIl
yHHBe_pca,'Ib-
ntui
nprarepaft
MHHHMyI{a
cyMMapHbIX
HapoAnoxogsficrBeH-
Hbrx
H3AepxieK
zH 3aMeHfleTcn
Kppll'epllffM6
AByX
BHAOB:
Kp[Tepr4eM
SI{OHON{HIIHOCTH
-
MaTeMaTHqeCKOe
O}KHAaHHe
r43'
AepiKeK
(6ee
yufep6oe)
Ao.n>xHo
6ltrs
MHHHMaiIbHbIM;
KpHre-
pHflMH
6egOnaCnocTlI
H
HaAeIKHOcTH
--
HHTerpaJIbHbie
BepoflT-
HOCTT4
,U,eQnUnrOe
HitU a36bITKOB
.BOrlbI,
Bbl3blBa1OUIHX
yxfep-
6u
(uanprivrep,
IIpH HaBOAHeHHflX)
l.I.iII{ onacHbiX
A,rlfi
rI{Apo-
coopyiKewuii,
AoJIX(HII
6urs
He
HLIX{g 3aAaHHblX
HopMaTl{BoB.
Kpurepuu
6egouacHocTq
H
HaAeitilIOcTLI
e
LaHHofi
MHOro'
xpnrepaantHoft
3a4aqe
yqnrbiBaroTcfl
B
Qopme
orpaHnqewuit'
H BblnoflHflIorcfl
B
nepBylo oqeDeAb.
Bo
BTopylo
oqepeAb
BbI-
rioJlHseTcfl
KpHTepHft
3KoHoMPItIHocrn.
Taxaff
oqepeAHocTb
BbI-
noJIHeHHfl
KpllTepHeB
ofipeAeJfleTcfl
[ocJIeAcTBI',IflMH'
KOTOpbIe
BJICI{CT
3A CO6Oft
HX HCBbITIOJIHEHPIC.
B sHepneruKe
pacqerHofl o6ecneqeHHocrblo
o6ltquo
Hop-
Mllpyercfl
BbIAaqa
or f3C
cpeAneuHrepBaJIbHblx
N{oulHocrel?
He
HHX(e
rapaHrHpoBaHHbIX.
CHuxeHne
Nlolr1HOCTeII
f3C
HpIX{e
fapaHTHpoBaHHbIX
BbI3btBaer
AeQplUHTbl
3HeprOcHa6xeuvrn
(o6osnauulvr
vrx
qepe3
tt),
nosToMy
c
IIe"Tbro
c[{flrqe-
HHff
nocJleAcreuft
AeQuUuroe
HopittHpylorcfl
BepoErHocTH
o6ecneqeHufl
IiaK rapaHTHpoBaHHbIX,
TaK
H
noHHlKeHHbIX
MoIII-
Hocrefi. O6slqrio
paccMarpHBalor
ABa
3Haqet{tlfi
rIoHH}KeHHbIX
orAaq
H
oTBeqarclltHx
Hnr
4eSHqHTOB
MoI[HocTLr
il"zra
il.rl..
(rne
ilrz7(rz)
H
HopltHpylor
BepoflrHocra
I'I3
HerIpeBbIIIreHHfl'
TaxHvt O6paeovt,
A.,If
f3C
3aAaIOrCs
Tp[l
BepOfTHOcTHbiX
HOpMaTr.{Ba
-
BepofiTHocl'b
He[peBbIirteHfitl
HyJIeBOTO
AeQHUH-
ra
n,r-}
(P,t)
w
BepoflrHocrll
HenpeBblueuns
AeQHIIHToB
l ill
t.t I
iluz
r{
I,ts
(coo'rnercrBeHrlo
3Haqegr{ti Ptz
H
Prg).
!,o.u;xHo
6elrl
P.r(
Pr2{Prs,
r.
e. B
nepBylo
oqepeAb co6flIoAaercfl
BepoffTHocTHbrrl
KpHTepHrl
no
Izz,
3&Telr
-
ilo
taz,
a
noToru
-
nO
Qer,
T.€. nO
rapaHTHpoBaHHbIlvf
MolII,HocTfiM
f3C.
Ans
He3HepreruqecKr{x BoAonorpe6nreleft
H
BoAorro";rb3o-
BaTeJieft
ycTaHaB,ryHBaroT
aHaJrofr.lqHbre
HopMaTHBbr HaAelriHo-
crH. Flanpurwep,
r,trfl,
HppHraur{H 6yaeu }rMerb coorBercrBy-
IOIIHe
3HaqeHlifl
iloor,
Popl
,
top2,
Popz,
Iorr,
Popa. TO X<e Ca-
MOe
rvlOiKHO SanHCaTb
Alrfi
CyAOXOACTBa
H
pbr6HOrO
XO3Er?CTBa.
,[,-trg
.3ar-u,HTbr
HH]KHefo 6te$a
of
rraBoAHeHHr?
Ao"rr]KeH
Bbr-
AeplKHBaTbcfi
c BepoffTrrocTbro P,
pacxoA
BoAbr
B
naxHnfi
6le$, He
6o"rruurrafi
HeKoroporo 3aAaFrHoro. 3Aecr ro aHaJro-
tHH
C npeAbrAyrIIHMH CIyqaflMH
AOriO.r"rHHTeJIbHO
MO)KHO
6UnO
6u
paccMarpHBarb
KpHTepHH cMsrr{euafi HaBoAHeHHri,
rITo,
oAHaKO, Ha npaKTHKe
O6UqHO
He
AeJraercfl.
BeporrnocTbro
Po
yqHTbrBaioT
He[peBbr[reHHe
no
yc,,'roBH-
snr
6esonacHocrH
rHApocoopylKeHHfi npele,'rbHoro
MaKcHMaJIb-
HO|O
pacxoAa
BoAbr
qepe3
fHApoy3eJr.
Ans
BoAoxpaHnJrHr.r{a
KoMrrJreKcHoro
Ha3HaqeHnrr
AoJrx(HbI
coBMecTHo
paccMaTpHBaTbcfl
KpHTepprH HaAe)KHocTH no
Ka)K-
Aorvry
yqacrHHKy
KoMn/reKca.
flycrl,
HanpHMep, BoAoxpaHHJIH-
ue
f3C o6cnyxHBaer aHeprernKy,
rippHraqHIo, cyAoxoAcrBo,
a raKlKe
BbrnoJrHfler
Qyuxunra
3aulHTbI or
HaBoAHesHii.
J\ns
TaKOTO
BOAOXpaHHJTHU{a
AoJririHbr
CO6;trc,A,arbcfl
CJIeAyTOUHe
l1
KpHTepHeB
HaAeiKHocru
H
6egottacHocrH:
Per, Pzz, Pte,
Popr,
Popz, Popg,
Pct,
Pc2, Pcz, Pn,
Po.
Ouepeanocrb
BbInoJI-
HeHHff
3THX iXpHrepHeB
-
B
nOpflAKe
yMeHbIUeHrrq
HOpNlarH-
BoB. ,[yuurrafi lto t(pHTepHro
aKoHoMHr{HocrH
pe}KHIvI fOC
cJIe-
Ayer
HcKarb ToJrbKo cPeAn
rex
Bo3MolKHbIx
pelKHMoB,
AItfl
Koropblx
BbrnoJrHrrorcfl yKa3aHHsre
I
I KpHHTepHeB
HaAelrHocrn
H 6egonacHocrn,
qro
HMeer
Mecro
B
TaK Ha3btBaeMbtx
ycno-
B Hfl X H36bITOIIHOTI
NO HTOTIHOCTH.
Taxnu
o6pasorrr,
AJrr
pacqera
AHcner.{epcr(Hx
rpaQnroe
Hyx(Ho 3Harb
pacqerHyro
o6ecneqeHHocrb
P. Xors 3HaI{eHHfl
P
AoJrxHbr
o6ocHoebrBarbcfl
3r(oHoI{HqecKHM
pacqeroM
Ha
ocHoBe aHaJrH3a
yr{ep608,
npaKTHr{ecKH
pacqeTHble
o6ecne-
r{eHHocTH
o6nqHo
3aAarorcq
HopMarHBHo. oqesaAHo, HOpMa-
THBHOC
3AAAHHC
BC./'IHqHI-I
P
CCTb NPHHUI{NHAJibHO
TO
}KE
CA.
MOe,
qro
tr HopNraraBHoe
3aAaHHe
lruep6on,
xorff
ilo npoqe-
Iype
pacqeroB pa3HHqa
\,lox(er 6ltrl
5o,'tt-,utot1.
MetoA nocrpoenafl
Ancnerr{epcKHx
rpa(rHxon tto
KpIIre'
pHflM
3KOHOMHqHOCTH H
HaAeIKHOCTH
rpe6yet
6oree
cJIoxHbIx
H
TpyIOeMKHX
paCqeTOB,
qeM
npH CTOlIlvlocrHOt:t
OI{eHKe
lnlep6oe.
floeroul',
KaK
orMerlaJlocb
B
[9,
68J
,
6onee
upne'
coodpasuo
crpourb )ucnerqepcKue
eparptu;tt
Ha. ocHole
Hop-
.MATUTHO7O
gAdAHUn
gUlep1OO, 40,rt He ocHc7e
Hop'ua,TuBHbLx
t42
pdcqerHbLx
o6ecnettennOcreti.
ilp"
HopMarHBHolt
gaLaHHA
yu{ep608,
KpoMe
Toro,
Mo}Ker 6url
HctloJib3oBaHa
xorfl
H
HerroJrHarr,
Ho Bce
iKe
HMercqancn uHrfopMaI{Hfl
06
yqep6ax.
Oueeu4Ho,
HopMarHBaM
ju{ep6on
coorBercrnyior
HeKoropble
HopruartrBbr no o6ecneqeuHocru.
OAsaro
IIoKa rarofi
noAXoA
npH
IIocrpoeHHH
AHcrlerqepcKHx
rparpHron He
Hc[oJlb3yeTcfl,
H
no3ToMy
AaJIee
MeTOAITI
peueHss
AaIOTcfl
KaK
AJifl
eAHHOTO
croHMocrHofo KpHTepHf,
TaK
14
AJTfl
cfiyqaff
orAeJlbHoro
yn{e-
Ta
BeporrHocrHbrx
KpHTepHeB 6egonacnocrn
rL
HaAelKHocrH.
CreA)'er cAeflarb 3aMeqaHHe
orHocHTeJIbHo o6nacrn
npn-
MeHeHlrs KpHTepHfl
MaTeMaTHqeCKOfO
OX(HAaHHq
'.Jrn
CTOH-
MOCTHbTX noKa3arerrefi.
Ans
HcxoAr{ofi
nH$opMa(HH,
3aAaH'
HOfi
EepOflTHOCTbtO,
npUrepUn MareMaTHqecKOfO
OX{HAaHHR
IIpaBOMePeH, IOTOMy
t{TO
npeAIIOJIaraeTCs MHOrOKpaTHafl.
CJly-
qafisas
pea,,'rH3at{Hs
srorl
HcxoAnori
rrHQopr'raI{HH.
TorAa
co-
f/racHo
3aKoHy 6onlurnx
r{HceJr
B
cpeAHeM
rlo
peaJrH3aul{flM
peaabHble
H3AepiKKH
6yayr
npa6.nuxarbcfl
K Hx
Marelvtaru-
qecKoMy
olKHAaHHro.
Ho
ecJrH
peanr.r3a(HH
yAaJIeHbI
Bo
Bpe-
MeHH
(HanpHMep, flpH
MHoroJIerHeM
pefyJIHpoBaHHH crora),
To xpHrepnri MareMarnqecKoro
olKHAaHHfi
Molher 6utn
Me-
Hee )Ke.rrareJreH TexHo"'Iofy, TaK KaK
efo
HHTepecyeT
o6cra-
HoBKa
B
6eprxarirueu
ro,4y.
B aroM cryqae
BMecro
KpHTeppIfl
MareMarr{qecKoro oxiuAaHHff Moryr rpr.IMeHrrbcfl
t4l
I{eKo-
ropbre
Kpr{repHH reopaH Hrp.
I{enecoo6pasHoc'm nepexoAa
K
sTHM KpHTepHsM BO3paCTaeT,
eC,TH
HapflAy C
BepOfTHOCTHOn
HMeercf
t4
HeonpeAe"TeHHafl
HcxoAHarr uHQopr{aIIHfl,
HanpH-
Mep no
lulep6avr.
Cnoco6ur
yqera BepocrHocrnofi
AucrrerqepcKux
rpaQnxax
o6uqHo
HoBHafl
trJrfr,
f3C BepoflTgocrHaff
cToKe.
Bos*toxllrt
ABa
cnoco6a
yr{era
srori
BepoflTHoctsofi
HH-
Qoprrrarlun:
snHrtfr [oAXoA, npH KoropoM
B
pacr{era.K
yqacr-
Byror
HenocpeAcrBeHHo
croKoBbre
QyHxqun
pacnpeAe,'IeHHr
BeporrrHocreft,
H
HeqeHlrft noAXoA,
KorAa
pacqerbi
BeAyrcfl
no
cepHH ruAponpaSon,
[ocpeAcrBoM Koropbrx ocyuecrB.[fler-
cfl npn6eirxeHHafl BepoflTHocrHafl
xapaKTepHcrHKa
cToKa
[55,
69]
.
B noc,'rerHeM
noAXoAe
B
KaqecrBe
pacqerHori
Bbr-
6opxa
H3
v raAporpaQoe
Moixer
rrpHrvreHflTbcff
KaK
Heno-
cpeAcrBeHHo
croxoeorft pffA
ua6rrroAeuuit, TaK H
|A.[HHeHsuli
c noMorqbro
MeroAa lloure-Kapno
pflA.
Heo6xoLlrilIocrb
B BepoflTHocrlroM
orrHcaHrlrr croKa
nar6oprori
rutApo-
rpaQon Bo3HltKaer
o6u,rHo
B
cnyqaflx
pacriera pe)KlrMoB
H
Ar{cnerqepcKHx
rpaQuxoa
clrcrelrbr
coB.\recrHo
pa6o'raroutHX
Bo.loxpaHH,'rrrur,
Korr,a
ucrtoJrb-
3oBaHHe
croKoBbrx
Q.vuxu:tfi
pacnpe.reJeHnfl
Beponrrrocrel"r
oKa3brBaercfi He-
B03
NroiKHbr nt
Ir3
-s
a
6o;ruu:o
fr rp
y.1oelr
Kocrlr
B
brr{trc.re
Hrrir.
HcxoAHofi
nn$opmar{HH. B
yqHTbIBaeTCf
To.rtbKo
oc-
r.rHQopMarrufl
o
pel{HoM
t*J
flo4
o,qHnM ruApofpaQorrt 6ya,eu
noHuMarb
KaJreHAapfiyro
ilocted,oBa-
TeJlbgocrb Ha
Becb
pacuerusrrt
nepuoA tr-ta+q
6HroeHx
pacxoAoB
Anff
Bcex
anaJru3upyelrbrx
crBopoB oAuor?
peKr.r
lrnfi HecKoJrbKHX
peK.
flpn
eror,r
Ivlarervrarur{ecKoe
oiKrrAaHHe cyivrruapHbrx
!r3Aep}KeK
Mo}KHo
6yaer
onpeAe-
JIfiTb llyrervr
pacr{eroB
H3Aepx(eK
tro
Ka)KAo]ry
H3
v
rnAporpa$on
c
nocre-
AyIOU{HM
BbITIHCiIeHHeIvI
CpeAHnX }I3Aep}KeI(.
Toqsoe 3Har{eH}re
HHTefpana NlareMarrrqecKoro o}KrrAarrHf cyrvrMapHbIX
H3AepiI(eK illolKer
6Hrt
egtqHc,'IeHo
,'ILIIIIb Ha ocHoBe 6ecroneqnofi coeox,vn-
Hocrlr
Bo3ruoixHbrx rrrAporpaQoe.
VIa BbrrrHcrnTe.rrrHofi MarelrarlrKrr
llgBecrHa
cncreMa oueuoK, Koropafi
no3BoJlfleT
A,rItI
BCflKOH
HanepeA 3aAaHHOrr nofperrrHocTr{
Bbrr{?rcneHPrff
HHTe-
rpanoB
onpeAenfiTb MHHHlraJrbHo ueo6xoAtrltoe
qtrcJ'ro
c,r,v*uafrHstx
peanH-
rcrqnrl
1u
sannuM
Cr'iylia€
-
pacqeTiiblx
rliAporpaQon).
OAHaI<o
ectli
rHApo-
rpaQrr 6paru cJ'ryqaftHbrlt oSpasolr,
To
NrurHHlraJ'Ibrro
ueo6xoAnnnoe Hx
qncro
oxagbteaercfi
BecbMa 6o,rnurru.
flo 6onsuolry
qncny
pacr{erHbtx
rnAporpa-
Qon
crpourb
AacnerrrepcKHe
rpaQuxn raKiKe
Becbr{a rpyAoeMKo. Iloarony
r{eaecoo6pa3Ho
nporr3BoAnTb
H
a n
p
a B.rI eH H oe
M
oAeJI
}I
p
o B a H He-
no
c[erruaiibHoMy
anropnTMy
no,'ryqarb ]Iaunyquyn aat6opxy H3
v
rHApo-
rpa$on,
no Koropoft
sareM 6yryr
nocrpoeHbi
AucnerrlepcrHe
rparfuna
ao-
[oxpaHHn]rxl.
3aAaqa
nonyr{eHufi Hannyqueft
nn6opru
H3 v
nt4por"paQon Mo}Ker
6uru cSopnry.rrupoBaHa
rax: rpe6yercfi
rronyqHrb ral(yto nlt6opxy
c
3aAaH-
HbrM
rrHcroM rrreHoB
v, uro6lr norpeulHocrb
BbrrrucJreHlr.fi no uefr ldareMarn-
qecKof
o
oiKHAaHHfl
Ir3Aep)KeK
H I{HTerpa.rrbHbIX
pexHMHbrx
noxasateleli
6u.na lruugua.naHoir.
Tpa,uuunoHHbre
ilreroAbr
npoeKTHbIX
BoAHoeHepferlrqecKI'rx
pacqeroB
Ll
fiocrpoeHiln
AucnerqepcKnx
rpa$uxon
[33]
raK:{(e ocrloBbtBarcTcfl Ha
pac-
qerHbrx
eorSoprax
ruaporpaQoe.
flpu erolt o6ttquo Hcnonb3yercs
npeAbtAy-
utlrui
pfiA
croKoBbrx
ua6.rnAeggft nirw
)Ke orAe,'rbHbte
qacru groro
pfl,u,a
B
gaBlrcHMocrrr
or
rofi 3oHbI
AllcflerrlepcKoro
rpaQttra, Koropaff onpeAe-
Jrffercfi. Tar,
soua rapauTupoBaHHoro
peixrrlla
crpollTcn
no
cepIIH
pacr{er-
Hbrx rvraJroBoAHbIX
rr.raporpaQoB,
3oHa 6opr6u
c
HaBoAtleHHffMH
-
no
pac-
rrerHbrlr
rvrHoroBoAHbrrr
roAarvr H
T.
n. Pacqeruue
rlrgporpa$H
o6HqHo sH-
6upaorcx
no KpprBbrrrr
pacnpeAeileHltfi
o6tertos
roAoBoro croKa
(6epyrcr
roAbr rpe6yervroft
3oHbr BeponrHocreir).
Aa.'ree
Anfi
Ka)KAoro
o6telta
croKa
6epercn HecKorrbKo
xapaKrepHbrx
rrrAporpaQoe BHyrprIroAoBoro
pacnpeAe-
JIEHIIfi CTOKA.
VxasaHHue
cnoco6u
onpeAeneHr{ff
pacqerHblx elt6opox
rnAporpaOoB
MOryT
nptr[{eHflTbcff
II
nplr
elt6opKe
tI3
yInItHeHHoro croKoBoro
pn,1a.
3rA
cnoco6sr
noKa He
AO
KoHUa
per.vnfiplI3oBaHbl,
T.
e.
B Hll.\
I{c[onb3yloTcfl
TaK;fie
onbrr rr
!tHT.vHunfi
TexHonora.
llo-ettAtttuotvtY,
noc.TeAHee
fiBJIfiercn
H
HeKeropbrNI
AocroHHcrBoM
3Tlrx
cnoco6oe,
TaK
KaK
yr{er
Bcero
tIIIo;(e-
crBa
B,rrrifltou{}rx
Qarropon
HeB03MoiKeH
6es
qe.{oBeI(a.
O.rHaxo, KoHerIHo,
;*(e,{aTe,,rbHbl
H
pa:pa6Orrn
pefy,TqpHbrx
}IeTO.1OB TaKOTO aU6Opa.
llOivplnro
peqHoro cToKa
npH onpeAeJIeHHH
AIicneTqepCKHX
rpaQHKoB
ile,'recoo6paeeH
yr{eT cnyqailHoro
Hi|kr
Aa)Ke
qac-
144
f!{r{Ho
HeonpeAe.,TeHHoro
lapaKTepa
H
Apyroft
HcXOAHofi
iilt'
QoprvraU
uw
:3Heprgfiotpe6n-euufl
,
pacflo,raraeMblx
MoulHocTefi
tg'C
H
Ap.
3ta
HHQopMaqHfl
AoJI)i(Ha
6utl
3aAaHa
B
BHAe
cepHri
panHoeepoflTublx
sHaqeHnft
(aHarror
pacqeTHoll
Bbl6op-
KH
fHApOfpaQoe).
fl,a"nee
npH
pacqerax
AHcnerqepcKHx
fpa'
QHron
HeCflolKHO
IIo
aHaJIorHH
c
pac'{eToM
pequono
cToKa
onpeAeJiflTb
MaTeMaTHqecKHe
olKHAaHHfl
H3AepjKeK
nyTeM
BbI-
qHcireHllfl
cpeAHHx;gsaqesHfi
KaK
no
croKoBoMy
pflAy'
I.aK
H
no
BepoflTHocTHbIM
pflAaM
ApyrI4X
iloKa3aTefieil
HcXoAHoll
HH-
0opuaqun.
OcHoeHrIe
cnoco6u
nocrpoeHHfl
AHcneTqepcKHx
rpaOHKoB'
Haa6onee
ToqHbIM
c119co6oM
ltocTpoeHHf AHcfieTqlepCKHX
fpaQHKOB
flBflfleTcq
nOcTpOeHHe
C
HC.IIOJIb3OBaHHeM
TOrO
luIIH
nHofo
OnTHMHgaqHoHHOro
MeTOAa
Ha OcHOBe
CTOKOBbIX
QyHx-
(nfi
paclpeAeJleHHfl
BepOflTHocTeI?.
OAIraxo,
KaK
6yAer
IIoKa-
3aHo
AaJIee,
TaKoft
Cnoc96
npHMeHHM
B
OcHOBHOM AJrfl
oAH-
HOqHbIX
BOAOXpaHHaIIHIII
AJIHTe.IIbHOTO
peryJIHpOBaH!{fl
H
.rIlIIIIb
AJrs
qacrHblx
c,lyqaeB
cplcreMbl
BoAOXpaHHJIITilI.
!,pyrue
onTHMH3aIIKoHHbIe
cnOCO6bI
OCHOBbiBaIoTcfi
Ha
He'
sBHoM
BepoflrHocTHoM
onHcaHHH
cTol(a
Bbl6opKoft
rnAporpa'
QOs.
B oroM
cJlyqae
Bo3MolKHbI
ABa
Pa3IHqaIoU{HXcs
noAxo-
iu.
flp"
nepBoM
IIoAXoAe
c
HcrloJIb3oBaHHeM
KaKoro-JIa6o
onTHMH3aIIpIOHHOTO
MeTOAa
HeIIOCpeACTBeHHO
OTbICKHBaTOTCfl
onrHMaJIbHbIe
yrpaBJlflIog{He
QyHr<UHn
3aAaHHoIl
crpyKrypbl
no
KpHTepHIO
MHHHMyMa
cpeAHeB3BeUIeHHbIX
3aTpaT
Ha
pac-
qernofi
BbI6opKe
rnApofpaQon.
[-lp" BropoM
noAXoAe
rooBo-
AflTCfl
AeTepMHHHpoBaHHbIe
oIITHMHsaUHoHHble
pacqeTbl
no
KaxAoMy
rHAporpaQy
BbI6opKH
Lr
Aa"ryee
nyTeM
cTaTncrnqe-
cKOII O6pa6orxu
no,'IyqeHHbIX
pe3yJIbTa-TOB
onpeAe,'IflIoTcs
orlrt{MaJlbHble
yflpaBJIflIolqHe
QyHxUlln.
O6a
IIoAxoAa,
ocno-
BaHH-btx
Ha
pacqerHoil
BbI6opKe
rl{AporpaSoe,
opHeHTHpoBa-
HbI, r,/IaBHbIM
O6paeOu,
ua cucTeMbI
BCAOXpaTiHJIHUI AJIHTe,'Ib-
HOrO
pefyJlHpoBaHHfi.
flp" i1ocrpoegHg
AgcnerriepcKgx
f
paQHI{9B,
KaK
paHee
yKa3bIBa,rIocb, IIoMHlvfO
KpHTepHfl
onTHMaJIbHOCTH
ytlHTbIBa-
IOTCfl
pelKHI{HbIe
OfpaHHqeHHfl,
B
TOM
I{HCJIe
V
B
BepoflTHocT-
Hoii
Qopvre.
B
pacqerax ro
croKoBblNI
QyuxUunu
pacnpeAe'
JreHHfl
BepOflTHOCTeli
STu
OrpaHHrIeHItn
yqI'lTbIBaIOTCfi
C
nO'
Moulblo
Qopnly,rtt
IIoJIHoII
BepoflrHocrH.
B
pacqerax iKe
ro
BbI6opKe
rllAporpaQoe
oHH
Moryr
yt{HrblBarbcfl
npoBeAe:{HeM
cooTBeTCTByioUIHX
ot'H6aIollIHX
XOAa
)/pOBHeft
BoAoXp2HH;TIHIII
A,Tff
KpHTHqHbIX
nO
paccMaTpHBaelloMy
ofpaHHr{eHHIo
faApo-
rparloi.
3auetun,
qro
B
cylqecrBytolqgx
croco6ax
fiocrpoe'
HHfl,
Auc[erqepcKHx
rpaQHi(oB
[33]
Hcro.rlb3oBanl4e
orn6aIo-
IqHX
XoAa
ypOBHefi
BoAOXpaHIi/IHIII
flBJIfleTcfl
OcHoBHbIM.
lo-3433
145
OctasoBlaivtcfr
KBatKo
Ha ltcnonrgoBaHiili
i{MltfaqiioHHbh(
UOACNCft
Aflfl
COCTABJIEHHfi
AHCUCTI{CPCKHX
TPAQNXON,
NOJIY-
qHBruHX
trrrrpoKoe pacnpocrpaHeHHe
oa
py6exovr.
3rn MoAe-
JIH
peaJrn3yror
MeroA
<npo6
H
oun6or>>.
Hanpr{Mep,
npn npo-
H3BOJTbHO
3aAaHHOM
flOJTOIKeHHH
XapaKTepHbrx
nunuft
Ar4c-
rerqepcKnx
rpaQHKoB
HMHrHpyercfl pa6ora
cHcreMbr
AJrfl
ner
paeuoft
BoAHocrH
(Hanpriuep,
c noMorrrbro paccMorpeHHoro
B
r.n.
9
aJrrop,HrMa pacqera
pex{HMoB
rHApocraHrrnri
na
3aAaH-
Hbre
flapauerpri).
klgMeHflff
noJro]KeHHe
sTrrx nnnwft
tr
noBTo-
pfrff
HMHTaTIHIO,
TeXHOJIOT
Ha OCHOBe
CBOefO
OnbrTa H HH-
TyHIIHH
HaXOAHT
H3H"r-r|grrree peureHHe.
Taxofi
[oAXoA oco-
6eHHo
qenecoo6pa3eH
AJrn
HeaHeprernqecKHX
yqacrHuKoB
BXK,
no KoropbrM
TpyAHo
Hvrerb cronMocrHbre
oqeHKH
r{efie-
eofi
Qynrqrau.
Ans
sHepreruKn
oH
rvroiKer 6urr
noJre3eH
AJrfl
yroqHeHHfl
nwsuit
rapaHTHpoBaHHono pelKaMa
H
nepeOoee,
noryqaeMbix ynpouleHHbrM
onrHMH3aqHoHHbrM
noAXoAoM.
Ho
AJtfl
3oHbr
us6orroqHbrx
orAaq
6onee npeAnor{TaTeJreH
onrn-
MH3arlnossufi
rroAxoA.
Paccuorpnu
or{eHKy e.QQerraBHocru,
fiofiyqaeMyro
reM
HJIU
HHbrM
cnoco6ovr
[ocrpoeHfiff
AncflerqepcKr.rx
rpaQnxoe.
Taxan
o(eur(a
geo6xoAaua
rrpn
Hcrro.,'Ib3oBaHHH HMHTaT{HoH-
Hbrx
uoAenefi.
Ourono/r rarofi
oqeHKH
flBJrflercfl
peryJrnpoBaHue
rro
Ar4c-
rerrrepcKoMy
rpaQury
cepnu
ruAporpaQon. I,{vreq
ABa
rpa-
Qnra
H npoBeAfl
yi(a3aHHoe
peryJrHpoBaHHe
rHAporpaQon
ilo
KalKAoMy
rpaQuxy,
MolKHo nocrpouTb
KpHBbre
npoAoJr)KH-
reJrbHocrn (aHanon
KpHBbrx
pacflpeAeleHan)
pa3HHr{
B noKa-
3areJre
(wnw
noKa3arenax)
eQ$exrraBHocrH o6oax
rpaQnxoa.
3ra KpHBafi
pac[peAe"rreHufl
pa3Hnu,
a raK>Ke
[oAcqHTaHHoe
cpeAHee
3HaqeHHe
pa3HHrlbr
H
6yayr
Haa6o;lee noJrHo xapaK-
Teprr3oBarb cpaBHHreJrbHyro
:QQexraBHocrb
AHcrerqepcKHX
rpaQnxoe.
Oqesn noJre3Ho conocraBJ'reHne
pacqeroB
cepHH
ruAporpa-
Qos
no
AncnerrrepcKoMy
rpacpaxy c
AerepMHHHpoBaHHbrMH
pacqeraMH
no KaxAolvry
fr{AporpaQy.
flo"ryvarcqascq
npH
gToM
pa3Hr.{qa
g
noragare"i-rflx
aQQer<ruBHocrn
xapaKreprrsyer
noTepH H3-34 Heflo/tHoro [peABHAeHHf
peqHofo
cToKa.
5.2 PACIIETbI
METOAOIl
AHHAMHTIECKOfO
nPoFPAMMHPOBAHHfl
OnTHMAJIbHbTX
AHCnETqEPCKHX
f
PAOHKOB
AJIfl
OT,HHOqHbIX
BOAOXPAHHJI HIII HA
OCHOBE
croKoBbtx
(DvHKTIHH pACnPEAEJI
EHHfl
BEPOflTHOCTEIa
Peuenne
AJrfl
BoAoxpaHunHu{a
f3C
npn
oAno3HarrHbrx
KparKocpor{Hbrx
rHAponporHo3ax
H HarHqHH
croHMocrnofi
otreHKH
yulep6on
or
AeSHqHroB
oHeprocHa6x<eHHq.
Pacclwor-
pHM
BoAoxpaHH.rrnu{e
f3C, Hcno,Tb3}/eMoe
roJrbKo
B
gHepre-
116
THrrecKHX
rlerrflx.
Pacqetstifi
nepnoA
BpeMeHpI
tt-ta+t
pa3-
AeJreH
Ha
d
AHcKpeTHbIK
lIHrepBaJIOB
B
o6uteu
clyqae
pa3-
Hoft
,u,JrHTeJIbHocTH.
Kpurepuev
orlTllNIaJIbHocTH AucneTqep-
cl(oro
rpaQarca,
onpeAereHHoro
AJIff
neplaoAa
tt-ta+t,
6yAer
yc"loBHe
noIyqeHHfl
MHHI{MyMa
MaTeMaTHrIecKoro
oiKHLaHHfl
cyMl{apHblx
npHBeAeHHbIX
sKCIIJIyaTal{l{oHHhIX
H3Aep}KeK
hI
I4f
+q
-
Ll',*t
(l
*
p)td'+t-t'
f,4,e
M
-
CHMBOJI
NtaTeMaTHqeCKOrg
OX{HAaHHff;
Hr'+r
-
3KC-
nJryaTaqHoHIIbte
H3Aep>KKH
B
l-tvt
HHTepBaJI"i,
P
-
HOpMaTHB-
Hrrrl
xoaQQlaUAeHr
eQSerrHBHocrH
{uneH
-
c-ry).'x(Hr LrIfl
npHBeAeHHfl
no
Qopuyne
cJIox(HbIx
npol{eHroB
pa3goBpeMeH-
Hbrx 3aTpaT'K
Haqa,{bHoMy
MOMeHTy
Speuenu)
.
flpuaeAeHue
3arpar
Bo
BpeMeHH
peKoMeHAyercfl
npou3Bo-
AHTb
npr4
nocrpoeHgn
AHcneTqepcKHX
rpaSuroe
AJIfl
BoAo-
xpaHHJII.{U{
MHOfOJIeTHefO
peryJIHpoBaHHfl
.
B
(5.1)
H3AeplKKH
cyMM6pylorcfl
KaK 3a
pacqerHbll:l
ile-
pnoA
BpeMeHH
tl-ta+t
(nepnlrl:r
r{JIerI
Qopvrynu),
TaK
w
3a
nepgoA
nocJleAe
fi,c"revn
ta+r-ta+o
(etopor?
rIIeH
Qoptuy.ui,l'
xoiopnrr?
AaJIee
6yaer
paccMorpeH 6oilee
noApo6uo).
B Coctan
Hs.U,ep xe{
H BK",'IrcqaeM
TonJIHBHbIe
3aTpaTbI
B
H
1lu{ep6u
y
or
AeQHUHT9B
sHeprocga6xeggq
BcJIeAcrBHe
orpaHuuesutl
estpa6orxn
fOC
HHxe
rapaHTnpoeauuofi
H3-3a
N{ailoeoAHr?.
llpe,U,nonaraeM
3apaHee
onpeAe,{eHHbIMH AJIr
I{a}KAorO HHTSpB&.,-I2
BpeMeHH
3aBHCI{IVIOCTH
B H
y
OT
cpeA-
HenHTepBantHoft
MoIIIrocrH
H
Hanopa
fOC._,OrpannqeHnff
B
Qopvre
HepaBeHcrB
(rpoue
orpaHnqeunfi
no
\V nns
Zso)
y'IH-
TbrBarorcfl
rurpaQaltr,
KoTopble
BKJIIoqaIoTcff
B
cOcTaB
CyM-
MaPHbIX H3AeplKeK.
]Jns
Bo3MoiIiHoCTH
npHMeHeHHf
MeToAa
LLIHaMHqecKoro
nporpaMMHpoBaHHff
rrpHrepnft
onrHMaJIbHocrH
(5.1)
_
nepeIIH-
cblBaercfl B
BHAe
peKyppeurnoft
Qopuynlr
AJrfl
.nrc6ono
i-ro
HHTepBaJIa:
d*q
M
S''!
Hi*t
--rmin,(5.1)
"'
'4*'"
'
(
a Pltr!+
-t
t
MI4!=e:Mkli+t+
- +
MI,lfIl-'min,
(l*p)
rAe
n!*n H
14!Ii
-
cyMl{apribte
oKcnayaraIrHoHHbIe
coorBercrBeHHo B
nepnoAbt
ti-ta+q H
ti+t-ta+q.
l0*
(5 2)
H3AepiKKH
t47
Csaqana
paccMarpr4BaeM
pellenue
npu orlncaHr.rn
perrHoro
croKa
npocrbrM
MapKoBcr(HM
npoileccoM,
3aAaHHbIu
Qynrqas-
MH repexoAa
[20,
68]
F
(Qo,lQo
t;
-,r)'
(5.3)
flpaanonaraeM Hatluttue
npa,KTuLtecKu
odHosHaLLHoeo
eud-
ponpoeHoga
sa1naeoEpeJileHHocTbto Tortbrco
Ha, o)uru
pacqer-
ruotrt openerunort
uHTep7an:
K
MoMeHTy
ti
rrpeAcKa3brBaeTcff
oxsAaeunrvr B
i-u
HHTepBaJIe
pacxoA
peKH
Qp;.
/J.ns
6olt-
rrrancrBa
peK
CCCP raxor? nporHo3 Ha cpoK
r,eKa4a
-
Mecfirr o6rr.rHo
HMeerc.fi. Ha 6oree
AirnTe,/'rburrri
nepuo4
peuuofi
croK nporHo3Hpyercfl BepofrHocrHo
Qynxunnun
nepexoAa
(5.3).
Pacqer
orrruMaJrbHoro
AncnerqepcKoro
rpaQnxa 3aK,-'Ircqa-
ercfi B orpeAeJreHHH
no
Kpurepnio
(5.2)
AIIfl
KaiKAoro
i-ro
pacqerHofo
HHTepBaJia
onTHMaJrbHbrx
yI]paBJItrol.I{ux
Qysr-
uHr:r
eraAa
Z"'i;i,
+
tr
-
f
(Z,a
i,
Qo,),
(5.4)
AarouIHX AJrr
aro6uix
Za6
i
H
Qp
i
orITI4MaJIluufi
ypoBeHb
Bo-
AOXpaHHnptrr\a
r( KoHI{y HHTepBaJIa.
vpoeeul
ze6
i
H3BecreH
K
MOMeHry
tt,
pacxoA peKlr
lIporHo3Hpyercfi
K
MoMeHry
tt.
Taxui'r
o6pasor't, [o
yflpaBJlfftou{nlr
QyHxuunu
BHAa
(5.4)
MOX{HO
BeCTH
peX<HM
BOAOXpaHHJIHUIa B
yCJIOBHflx
,rrO6Oft
BOAT{OCTI4
peKH, paCnOJIafafi
JIHIIIb
npO|HO3OM
CTOKa Ha OAHH
npeAcroflutnft HHrepBaJI BpeMeHH.
Tax xar ua ocHoBe
Za6
i,
Ze6(i*t)
H
Qp
;
oAHO3HaqHo ollpe-
Ae.rrrrorcfl
nro6lte
Apyrue
pelKaMHbIe napaMerpbl
fOC
(rurour-
Hocrb,
pacxoA
BoAbi
B
Hr.rlKHHrl
6te{r
n r.
n.),
ro
BMecro
(5.4)
MoiKHo, HanpHMep, 6pars
QyrixuHH
oIITI{MaJIbHbIX
uou{socreft
f3C
B HHreoBa,rre
1
N?ll
,
:
f
(Z
ua
i,
Qo
r).
(5
5)
!,HcneruepcKHe
rpaQnxH BHAa
(5.5)
6ruxe
coorBercrBy-
ror rro
Qopue
rrpailreHfleMblM cefi.rac
B
npoexruoft [paKrHKe
npaQHKaM
[33]
.
f]pnr
HaJrLtttHH
oAHo3Har{Horo
rr{AponporHo3a
Ha
npe.{cro-
strlaft
pacueruuft
HHrepBaJr BpeMeHrr
rpurepuf,r
onraMa/tbHo-
crn
(5.2)
HMeer 6olee npocroft BHA:
74x
7214+r
:
I-Ii+t
*
,,
-,'
,
Mkl/].i-*
min.
(5.6)
(t
*p)
3.u,ecl
Br{ecro
I\414i+1 6epercn
kli*'
ira^
KaK
pacxoA pe-
148
Krr
H3eecren)
H
B
orJr'q*e
or
(5.2)
H3AeplI.*H
,14-r'tr4!+0
3ang-
caHbt
co
sBe3Aoqroft.
oqeer4AHO,
rrTo
HsAepx(KH
LIrt+t
6ya)tr
flBJIfTbCfl
syut<ult-
ert
roltro
OT
Za6
i,
Qp
;
Yr
Zs6(i*r)'
Cyn*rapHbre
r{3Aepxir(H
Ml4fii
6y4yr
fB,,tnrbcn
SyurUtteit
Zra(i+r)
pr
Qp;i
3aBpict{tvlocrb
Mt'l!#
or
Zrau+i
oqeBHAHa'
a
3aBHcHrv1ocrb
MI4iii
or
Qp;
o6yc"noe'reHa
rei\{'
t{ro
pacxoAbl
DeKH
B
(i
*
1)
-rvr
HHrepBaJIe,
xapaKrepH3yeMble
Qyuruuetl
hup.*o.aa
F(Qpri+p/Qp;),
eaencflr
or
Qp;-KeK
or
napaMerpa'
'PaccrtoipHlt
peureuHe
sag,aqw LJIfl
l-ro
I4HTepBaJIa'
ilpeA-
rroJrarafl
KaK-TO
SaAatiuor?
cpyuxuraro
IlocfieAe-kctevin
ivI14!11:
i
(Qp;,
Z,ari+,t).
(5.7)
Ans
HeKoropbrx
QurcupOBaHHbIX
sHa'{eHtlfi
Zeo
t
H
Qp
;
onrrrMaJrbHoe
sga.{eHlt
e
Z"u(,*t,
(ueu
otITHMaJIbHafl'
MoU{Hocrb
t."fi;;;y
*u*oo
urcn
ny.r.eM
MHHHMHB
aL\krrr
SyHruuu
,4/l*
k[f*q
(Z"ui,*,li'
ot
oAuoir
nepevreHuofi,
qro
MolKer
6o6l
BblnoilHe-
;;
""';.'de6opon,
r.
e._
nyreM
conocraBJleHHfl
sga'{eHllft
14'*
4.aio
l,is,
pa3HbIX
Ze6G*t),
npocMaTpl{BaeMbIX
c
M?'IIbin-t
uafoM
LZ B
AOIyCTHMOM
AHana3oHe
AX
H3MeHeHHfl'
I-lpoUe.lypa
noA6opa
guaqe'nft
ZZZit
*U
noBropflercfl
AJIn
purror*
Zua
r
H
Qp;,
o6rtqso
3aAaqa
peulaercfl
E^lrn
cepurt
I{3
5-
l0
gHaqeHlaft
raxAoii
He
yKa3aHHbIK
nepepleHgblx' Anq
yc'
KopeHI4r
nog,6opa
Z?Eit*tt
peKoNleHAyercfl
B
KaqecrBe
repBoro
npn6auxelrHfl
HCno"'rbsoBaTb
p^e3yJIbTaT
peueHlIfl
p;rfl
6;tu-
>riartuux
sHaqeHnft
Zeo
i
vr
Qp
;.
I
B
pe3yJrbrare
paccl{oTpeHHofo,.
perrleHllfl
ofipeAeJlHrcfi
Hc-
KoMaf
3aBHc'Mocin
(5.4) v
(5
5)
H
nonyrHo
orlpeAeiivrrcfl'
QynxuHn
r
(t
M*
[4!+q
:
[
(Zuu,
Qp
;),
B
KaqecTBe
xorOpofi
L'JIfr
KaIKAbIX
gHaqeuHtt
Zs6
i
H
Qp
i
6e-
percfl
,nuo.n";'
M*'14a+0,,
coorBercrBylouee
oitTHMaJIlHoft
orr,rerKe
Zi[ii+tl
,
T.
e. 6epyrcn
MHHHMH3iipyeMble
H3Aep]K-
X',r
M*
lzld*4
t.
,lQot,-'r),
(5
9t
HanpHMep,
ilo
(5 8)
La,ree
Bbtr{IIcJfl
ert
QYHt<utto,
Mkl!+e
:[ (z"a
i,
Qor;
-,))
:-
\
^*
141*nctF
(Q,
0
r{cnoJIb3yfl
npu6"'tti;xeHHoe
HHTerpHpoBaHHe'
Sopnyne
rpaneuaft.
149
floc.neAnss
Qynxunr
aHaJ:rorurrHa
.QyuKqHH
noc.neAerZcr-
ean-(5.7),
rio
orHocarcfi
K MoMeHry
npemexn
/;.
I4Meq
QyHxiIHr,o
(5.9)
BMecro
(S.T),
ro
H3.,,rolKeHHoN{y
Bbl[re.
aJlropHTMy
i'IerKo
Bbtno"rIHHTb
perueHHe
A,Jrfl.
HHTepBaJIa
t;1-,t.i,
trpH
groM
norlyrHo
lvtolhno
oiTpeAe,'IHTb
gaBacaMocrb
A4
kli:I:f
(zrati-l,
Qp(r-zl).
rloc"ryelHss
rro3Bojrrrer
npoH3Be-
crH
pacqer
AHcnerqepcKofo
rpaQuxa
n
HHTepBa
ne tr_2'-tr_1
H
T.
A.
TaxHvr
o6pasou,
BbtflBHJrocb,
rrro
pacqerbr
no
oirpeAeJre-
HHro
rucnerqeDcKoro
rpaQura
HylriHo
npolr3Bo
!.HT;
<<xoAoi,i
Ha3aA>>,
Haq.Hldafl,
oT nocJre4Hero
lIHTepn2,ry3.
[";'lx
pacuera
rt{cnerl{epcKoro
rpaQura
"b
sce*
HHrepBanax
pacqergoro
nepuoAa
tt-ta+r
ueo6xoAlrrvra
QynxUHfi
noc.rleAeficrelrr
Ha
xoneqHrift
lro-
MeHT
Bpelreuw
taal
MHflil
:
t(z"a
(d+
r),
Qoa).
ilsrM
MaproticKuu
npoqeccoM
168]
.OyHxUirr
ilepe-
xoAa
Aaff
peqHoro
cToKa
B
TaKOM
C,'IyqaeM
lIMeeT
BHA
F(Qo
tf
Qptt-il,
Qp1;-z)'''''
Qpti-ol)
'
EclH
aBroMarHr{ecKH
pac'
npoCTpaHHTb
u#oxenuur?
Bbl[Ie
MeTOA
Ha
tarOfi
c,Iyqafi,
ro
A6cneruepcxgft
rpaQarc
n
QyHruHn
nocJIeAeftcTBHfl
C,'IeAO-
BaJIO
6tr
Onpelenntu
B
3aBnC14lvlOC'I'H
OT
6OnltUerO
tIHC'IIa
rrpeAurecrByroiilr4x
pacxoAoB
peKH.
B
pe3y.rlbrare
cyulecrBeH-
HO
BO3pacTaeT
rpyAoeMKOCTb
peueHllq,
IIOSTOMy
npHxoAHTCs
HATvr
Ha
HeKoToPbte
yrpoqegHf
H
Aotlyu{eHqfl.
Ilurul
AJrfl
nepBbrx
HHTepBa,'ioB
pacqeTHoro
fieplloAa
npocTo
yqHTbiBaTb
cBfi3b
c npeAuecTByrou{IIMH
pacxoAai{l'I
pel(H'
Paccvrorpuvt
Bo3Moxii{ble
BapLiaHTbl
TaKoro
ynpoqeHHoro
DClucHHfl.
a)
Pacxolu
pet{H
Qp
;
B
nrc6ovt
i-rvr
HHrepBa/le
Moryr
6urt
BblpaiKeHbt
cJleAyloql.tu
o6paeort
(nptl onHcaHHH
cToKa
c./'Iox{Hblr{
MapKoBCKHM
npo(eccoM,
:
(5.
r0)
Paccuorpnlt
HeKoropble
BosMox(Hbre
cnoco6rr
onpeAeJreHHfl
eroft
QYHxuua.
a)
Enn
yAaneHHoro
6y4yrUero
[roMeHTa
BpeMeH]r
ta+q
npoH3BoJrbHo
3aAaeMcfi
Qyuxuneri
noc.ne4eficrBrirr,
HanpHNlep
6epevr
ee
paauofi
Hynro.
Paccqgrae
no
r{3no}KeggoMy
Bbrrrle
MeroAy pe>KLrMbr
Anfi
nepuoAa
ta+r-ta+s,
onpeAeJrfieM
Synrcunro
noc.neAeficrnnR
Ha
MoMeHr
td+r.
Ecnu
MOTVIeHT
la,uq
A,ocraroqHo
yAaaeH
or /441,
To npoH3BOJIbHOe
3aAaHLre
QyHx-
UHH
noc,leAeficraHn
Ha
MoMeHT
ta+q
npaKTr.rqecKH
He
6yaer
H3MeHffTb
QyHrcuHn
nocneAeftcrBrrfi,
onpeAeJrffeMyro
Ha MoMeHT
ta+t.
Heo6xorr-r*roe
r{Hcro
HHTepBanoB
g
orrpeAenffercfi
noA6opo,v.
ouenuAuo,
qro
q
6yner
6o.ruulrut
AJrfi
BoAoxpaHHnHrII
6o;tee
AnHTejrbHor-o
peryJ,rnpoBaHgq.
6)
B
xa,{ecrse
MoMeHTa
taF1
lrrfr.
peK
c
rrerKo
Bbrpa}KeHHbrMH
BHyrpH-
ro.(oBbIilIH
croKoBbIMu
Qasattn
yao6Ho
6parl
KoHer{
BecegHero nonoBor,bfi,
TaK
KaK
K srovry
MoMeHTy
BpeMeHlr
BoAoxpaHrrJrhu{e
Hrvreer
uan6onuuree
HarroJrHeHHe.
BoaoxpaHHJrHuIe
ce3oHuoro (rolonoro)
peryr-upoBaHfiff
K
KoH-
Uy
BeceHHefo
noJloBoAbfi
3afioJlHfleTcfi
no,THocTbto,
H B 3ToM
c,'Iyqae
B
Ka-
qecrBe
QyHrqur
noc.ueAeficrBr.rfi
MolKHo
B3ffTb
npo[r3BonbHyro
QyHxugro,
Ho
TaKyIo,
qro6u
npH
cHHIKeHHH
ypoB
sn
2"6(d+r)
H3Aepx(KH MAfl++
Bo3pac-
TanI{
oqeHb
6ltcrpo,
H
TorAa
o6qgarer:tHo
6yger
o6ecneqllnarbcfi
3anon-
HeHHe BoAoxpaHHnHura
r lrolreHry
/aa1.
Ha
,4pyrux
B03lIoxHbIx
cnoco6ax
onp€!e"'TeHrrfl
QynxquH
noc.nereir-
crBHfi He
ocraHan.ruraaelrcn
[08].
I,lsrolKeHHbrr:r
MeroA
nocrpoeH
Lr,r
rr4crrerqepcKnx rpaQaxoe
oAHHaKOBO
npHMeHHM
K BOAOXpaHH"'rriuraM'nrc6oro
AJrHTeiIb-
Horo
pejy{HpoBaHHfl
KaK
A,Tff
ttepHoAoB
HaqaJrbHort
sxcn,,'t]&-
rzr\Ltvt.
f3c
(nepuoaon
Haqa.rrbHofo
i{aro.rrHeHHfl
BoAOXpaHH-
{qqa),
raK
H
Etrfl
nepHoAoB
HopivrarnHorl
3KcrrJryaiaqnn
f3c.
VlsueHeHHff.
B
rrocrpoeHr{u
nHcner,iepcKHx
f
paQnroe
npH
orrHcaHHH
pe.{Hof
O
cToKa
C,rIO)K-
r50
Qp
;:e-'
(Qo
;)
Ri*
D
i(ei)
,
rAe
Ri:
H
<+,r
(
Qot,-tl7 {
H
1t-z)
(Qpt'-zr)
*
. . .{II1i-ol
(Qpr;-"r)
;
s
-
HopMaJrbHo
pacnpeAeJreHHafl
clyqaiiHafl
BeflHqHHa;
q
-
o6ogsaqeHHe
QyrixUin
HopMaJIbHoro
pacrpeAeJIeHHff;
D
-
Hn
6yayr
u
Qyur<L\Hw
H.
Tenepo
pilcuorpnrur
H3MeHeHHfl
B
peuellHH, O6ycnoBJleH-
Hbre
nepexoAoM
K C,,:IO)I(HOMy
MapKoRcKoMy
npoqeccy.
Buecro
3aBHcHlvlocrH
(5.7)
6yaeu
paccMarpHBarb
MtIiI?
:
f
(Z,a(t+i,
R,*,).
B 3Torvt
c.[yqae
ortTHNIaJIbHafl
QyHxUuert
naparvrerpoB
Ze6
i,
Qp
i
H
z?Ei,+n:f
(z"a
i,
rAe
R*;:R;+t
-H
t(Qo
t).
(5.
i
1)
(5.12)
3aBHcHMocrb
(5.4) SYaet
D*.,
r\
L.
(5.13)
yKa3aHHoti
BbIue
Qp
;'
R;)'
Aanee
cJieAyeT
crpollTb
aHaJIof
l'It{Hyio
3aBacuMocrb
MI4!*u
f
(Z"o;,
Rr).
Ans
nocrpoeHHfl
nocJleAgeft
3aBHSHMOSTH
Heo6XoAHMo
no-
craBHTb
B
coorBercrBHe
3l{aqeHl'ie R*;
c
Ri'
qro
Mo}Ker
6sttr
CAe.rraHO
ilptulb
npfl6tL:)lieHHO:
Ha
oCI{OBe
Pfi.qa
npOlllj'Iblx
cTo'
151
roetrx
Ha6nrcX,enaft
Bbrqr{cJrfliorcfl
R*,
w
R,,
gareM
oriperte_
JIfieTCff
KoppeJrflr{Hfl
Me)KAy
HHMpr
H
ilOryqeHHoe
ypaBHeHHe
KOppeJrfiqHoHsofi
cBq3H
npra6,rHxeHrro
paccMarpaeaercn
B
KaqecrBe
QyurcqHoHantuoro.
O6H.{Fro
cssbt
ue>ray
R*,
H
R;
cH/IbHafi.
B
pe3yJrbrare
B
ypaBHeHHH
(b.lB)
orrraMaJrbuoro
AHcner_
qepcKofo
rpaQura
[osBHJracb
3aBHCHMOCTb
or
rperbero
na-
paMerpa
R*r,
roroprrli
xapaKTepn3yer
BoAHocrb
fipeArxecT-
Byrouero
nepr{oAa.
ue"'recoo6paSno
paccMarpHBarb
ue60,ur-
IITnP IJf.rri rrrr DUo rrarr"Ji D*
r'^vvrv
rircr=un',ll
r\
i'
ur,'eLIaruu{l4x
roJIbKo
Ma/IoBoAIrbIM,
HecKOJIbKHld
nno r !rr,rr.{ !! E.{ !!^
-^^
6)
Mox"J'
#?il
;"-H;:";#;''f".Ir',fiH#I
HanpHuep,
3arHr[eM
ypaBHeHHe
pefpeccH
AByx
coceAHHX
HHrepBa"rroB
(
ocHoBe
sroro
ypaBHeHHfl
epri_
glaBHM
B
(5.12)
Lr raKHM
o(
(5.1
l)
or
s,/rena,
coAep)Kaurer
3OM
HCKflrOqaeM
qJreHbr
Qp(;_sl,
cxeMy
npoCioro
Mapkoecrofo
npoqecca,
AJrn
roropoli
peue_
Hr{e- yx{e
paccMarp
neano-ir.
vxasaHHrrr?
npaevr.
npa6nraxesumr?:
ypaBHelrfle
perpeccr.r'
orox(AecTB"[flercfl
c
QyrircunonansHoii
Sa-BacaMocTb[o.
olHa-
KO
K
60nnuor?
norperxHocrlr
3To
He
nplrBeAer
rro
caeAyror{HM
npr.rrrHnaM.
Ec.nu
KoppeJrflr{Hfi
Me}KAy
pacxoAaMH
per{u
B
pa3-
HbIe
HHTepBaJibI
TecHafl,
To ypaBHerIHe
perpeccHr.r
He3HaqH-
TCJI'HO
OTTH*ACTCfl
OT
QYHXqNOHA,'I'IIOTO
H
TIOsTOMY
NDHHfl.
TOe
AonyureHHe
He
Aaer
60"nruoli
ori:li6r<a.
Ec"uu
xoppe,rsqus
Mex(Ay
pacxorar4u
peKH
cna6at.,
To
HvlKHo
npocro
oi6pocrarr
n
Qopvryne
(5.11)
cboreercrByrou{uri
q"ryeu.
LIs
aeyx
paccMorpeHFrbrx'npH6,rn>xer{Hbrx
cnoco60e
60nee
[peAnoqrHreJreH
neprsrfr
(nroport
cnoco6
-
3ro
c.[v,rarl
rDo_
croro
MapKoBcKoro
npclqecca).
Bognoxnu
H
a#rHerlurrie
paSBwrwn
nepBofo
cnoco6a.
HanpHMep,
cHaqaJra
cTpoprrcs
AHcfierrrepcxurf
rpaQnr<
Ha
ocHoBe
.
npocrofo
vapro-ecKoro
npoqecca.
Pac,{eroM
rrpeAbrAyulero
(uaH
yAJrHHeHHoro)
pflAa
rnaporpaQoe
no
sroMy
AHcnerq_epcr(oMy
rpaQury
-',r6rn.,
6rtrs
ycTaHoBJIeHa
cBflgl,
zna
i
ot
R'ir,
H,
aa",
ara
cBg3b
rec-
Hafl,
ro
qerecoo6pasHo
ee
yqecrb
B 3aBHcHMocrH
(5.13).
A
Ha"r'rrrqHe
.3roH
cB.rr3H
oqeBHAHO:
npH
MaJTOBOAHOM
rrpeAuecTBy-
IOIqCM
IICPHOAC
HAU6O"ryCC
BCD-OgTHbI
6OACC
HH3KHC
YPOBHH
BOAOxpaHHJrrrqa,
w
nao6opor.
I_{e"recoo6pasno
r4 npa
oripeae_
JICHIIH
QyHxqHI?
IIepeXoAa
oqeHHBaTb
yc/IoBI{bIe
BepoflTHocTI{
fioflB"TeHHfl
pacxoAoB
peKH
e nrc6olt
t-xt
r.rHTepBa,Te
B
3aBHcH-
N{OCTr{
oT
pacxoAa
He
Ha
Ka)fiAo}r
npeAurecTByro[IeM
HHrep-
BaJIe,
a
HHTefpaJIbHO
3a
npe;lUeCrerrrou{Hft
rrepHOA,
TaK
KaK
npH
orlHcaHHH
croKa
c,'Iox{HbIM
MapKoBcKHlv(
IIpoqeccoM
rua,/Io
152
BepoqrHbi
cr4TyaIIHH
noflBJIeHHn B
oAHHX
HHTepBaJIax
6onl'
ufix
pacxoAoB,
a
B
Apyfhx-
Ma,lblx.
Vqer
orAaJieHHbIx
KoppeJItIIrHoHHbix
cesset? oco6enso
aK'
TVaJIeH
AJrfl
BO.(OXpaHHJIHLiI
MHOTOJIeTHeTO
peryJIHpOBaHHfl.
I^nn
raKHx
BoAoxpaHH,,THIII
AoJIIKHa
yqfiTblBarbcs cBfl3b
cpe.[,-
HeroAoBbrx
pacxoiloB
peK,
TaK KaK oHa o6ycnoeJlnBaeT
Ma'
/roBoAHbIe H
MHOTOBOAIibIe
IIHK./TbI ;rler.
AHcnetqepcKfle
rpa'
Sraru
e
raKoM
cflyr{ae
qeeecoo6pa3Ho
cTponrb
Ififl
Ka)KAoro
3aAaHHOrO
CpeAHefOAOBOfO
paCXOAa
npOIIIJIOTO
fOAa,
qro,
oA'
HaKO, rlpOfiBJIffeTCff
/IHIIlh
npH
ilpHMeHeHHH
MeTOAa
IIOJIyqe-
HHfl.
croKoBblx
QyHt<uu/r
nepexoAa,
a
He
N'IeroAa
flocrpoeHufl
Ancnerqepcr(oro
rpaQnxa
Ans
[oJroBoAHbrx
nepaoAoB,
KaI{ H
B
cylqecrByrouel.t
rtpo-
exruort npaKrllKe
[33]
,
AncnerqepcKne
rpaQraru
peKoMeHAy-
ercfl
crponTb
!,JIfl
|crosHoil
urKaJIbI
BpeMeHI{
-
BpeMfl
orctln'
TbrBaeTcfi
oT
Haqafla
BeceHHofo
noJtroBoAbfl,
KoTOpOe
B
pa3'
HbIe rOAbI HaqgHaeTcf
B
pa3Hble
KaJIeHAapHbIe
AaTbI.
!{SlO-
x(eHHafi
MeroAuKa
flocrpoeHLIfl
AlicnerqepcKHx
rpaQnron
npHMeHHN{a
H B 9To},{
c":Iyqae, ueo6xoAlauo
JiHrub
nocrpoeHue
Qynxulrrt
repexona
H Bce
pacqerbl
IIo onpeAe"rleHulo
Arlcner-
qepcKoro
rpaQaxa
Becrtl
B
ycfloBHoIi
urrane
BpeMeFIH.
Bcqxoe
Aoflyu{eHue
B oIIHcaHttH
crot(a H B
MeroAHKe
pac-
r{eroB
B
rioHeqHoM
HTore o6ycroe.i'IHBaer
nocrpoeHHe
NIeHee
onrrrl{
aJ'ibHbIX
AHcneTqepCKHX
rpa
Qaroe.
PexoueHAyercs
npH
nocrpoeHnn
Alicnerr{epeKux
rpaQaron
cuaqa,la Hcno,'Ib3oBarb
npocroft
uapxoecrufi
npoqecc,
3areM
nepexoAHTb
K cJloxiHoMy
npoueccy,
T. e.
ilocTeneHHo_ycJlod('
HflTb
pacr{er
H
oI{eHHBarb
floryr{aeulrft
ecpSext'
flonesna
cpaBHlrre ilb{aff,
oI{eHKa
pe)KHMoB
H
Ha
OCHOBe
AeTepMHHHpO-
BaHHoro
pacqera,
,4alourafl
reoperHqecrait
onrHMyM
6es
y'{e-
Ta
norepb
Ha He[o.nHoe
fipeABHAeHHe
CTOKa.
Peruenne
AJrfl
BoAoxpaHHJIHITI
fOC
npn
BepocrHocrHblx
Iiparl(ocpor{Hbrx
rHAponponHo3ax.
VpanHeuaeut
onrLIMaJIbH0-
crrr
B
3Tor,r
c;'rv{?e
6,vrer
ro
x(e
ypaBHeHHe
(5.2),
e Koro-
pOM
CHMBOJI NtaTelfaTHqeCKOrO
OIK?ILaHHfl
6y4e'r
OTHOCHTbCfl
H r( H3AeplKKaM
npe-IcToflu{efo
epelteuuoro HHTepBaJIa.
!,ncneruepcxuli
rpaQHx
6yaeu
onpeAe,rflrb
B
BLiAe
QyHx-
UHH
M?]l
t
:f
(Z"a
t,
Qot,-,i).
(5'14)
CpaeHav ero
c
JncnerqepcKHM
lpaQnxou
AJIfi
npeAblAy'
u{ero cryr{afl,
onpeJe"rfleMbIM
3aBi{caMocrbto
N:!:
t:
f
(Z'o
i,
Qp
,).
Ha
ptrc. 5.2
Aaercr
H,rarrlocrparlrrn
orrvleqeHHoro
pa3irl4qrfr
ructierqepcKrrx
rpaQrrxon.
I4so6pax{eHbl
I(pHBafl
pacnpeneJl€^-
lDo
8pt
N
rect.
Plrc. 5.2. Pas.naque
rncnerrrepcKnx
rpaSnroa:
I
-
HaaHrIrE
oAHoaHar{Horo
flpofro3a
pacxoAa
peKH;
2
-
orcyrcrann
raKoro
IIDOrHO3a
HHfl BepOf,THOCrerl
paCXOAOB
PeKH
Qo
o
(ans
3aAaHHoro
Qot-r)
n
KpHBble onrnMaJIb-
Hbrx
MorrlHocreft
r3c
Arrn
HeKoToporO
Zs6
t
B neTBoM
H
BO
BTopoM cIyrlaflX.
UqeeL{A-
HO, BO
BTOpOM
Cflyqae
AHc-
50
E%
/00
ilerqepcKufi
rpaQux
6yaer MeHee
eQQexruBeH,
qeM
B repBoM,
rrTo
o6yc"uoeJreHo
pa3JiHqHeM
B rrporHo3ax cToKa.
iBo
BropoM c"Tyqae
Afifl
KalKAbrx
Zsa
i
H
Qpli-t)
orpeAeJrfl-
ercn
oAHHaKoBafl
Mou{Hocrb
f3C
//:::
i
r.rrfl
Bcex
Bo3Mo}K-
HbIx
B HHrepBaJre tt-t+r
pacxoAoB
peKH
Qp
;.
llp"
sroM,
ecrecrBeHrro,
rtpn
pasnbrx
Qp
i
6yayr noJryqarbefi
pa3Hbre
Ko-
HerII{bIe ypoBHH
Z.q;a11.
-Ho
ecJrn or{a}Kercfi,
qro
BHyrpH HH-
TepBaJra
ypoBeHb
BoAoxpaHHJrHtIIa
AocTHraeT
npeAeJrbHbix
sHaqeuurl
Hny
u.ryH V&lO
(wnw
Aocrnraercfi
KaKoe-nn6o
Apy-
roe
pelKHMHoe
orpaHnrreHue),
ro
f
3C
nepexoAur Ha
paOory
no
6uroBoMy
npHToKy,
HaxoArcb
Ha npeAeJrbHoft
orMerKe
Bo-
AoxpaHHJrHuIa,
H
npu
sroM
peaJrbHafi
MoulHocrb f3C
6yaer
orKrlogflrbcfl
or
//i!l
r.
llepenarueu ypaBHeHKe
orrHMaJrbHocrn
(5.2)
c,,'reAyrournM
o6pasovr:
I
Mnf+t:
I
(rr.'+
#
rvr{4!+I)dF(eo,lep(;-r))*ffiin, (5.15)
0
rAe
A4I.lfIi
npnHaMaercfl pa3HbrM
AJrr
pasHurx
Qo;
H Zra(i+r)
(yponHn
Zs6(i*t;
onpe[eJlflIoTcfl MouIHOcTbro
y'y'rr.
i).
B
(5.15)
MareMarHqecKoe
olKHAaHHe H3AepxieK
MHta+,
flBJIflIorcff
QyHrUuefi
or
BeJTHqHH
Zs6
i,
Qp1;-r)
r.r
y'y'rr.
;.
Als
KaIKAbIX
QurcupoBaHHbIX
Zsa
r
kr
Qp1;-t)
cJieAyer
HaxoAHTb
OITHMAJIbHOC
3HAqCHHC
NSI
"
IITO,
I(AK
H
TIPC)KAC,
BbINOJI.
Hflercr
noA6opoM. B
npoqecce
noA6o
pa
r,nr
KalKAoro
alarrr-
3HpyeMoro
3HaqeHHfi
y'y'rr.
;
onpe[eJrflercfl
r{HTerpafi
(5.15)
no
Qopvryne
rpaneunrl.
3HaqeHHs
MtI7Il
noA
Hnrerpa.rroM
6e-
pyTcfi
pa3Hbre
Airfr liaiKnoro
paccMaTpHBaeMoro
pacxoAa
pe-
Krr
Qp
i
H
BbrrlHcJ-'rffeMono IIptr
sToM
pacxoAe
H
paccMaTpHBae-
tvtott t'toqHocra
f3C
y'y'rr"
;
lpoBHn
Zs6(i*r).
Ann
3Toro
AoJr>KHa
6nrn 3aAaHa
SyHrur.rn
iloc,,rele ftcTDttn
M
Plilf
:f
(Z"o
tt+,t
154
Qo
,)
.
Arianort{qHan
QynxuHn
A4l'ld+s
i-f
(Z"u
t,
Qptl-rl)
Ha
MoMeHT
ti noflyqaercfl
KaK no6oqHufi
[poAyKr
orrHMH3a(HH
ro
ypaBHeFrHro
(5.15)
-oHa
o6pasyelcn
??
cqer
MHHHMH3H'
pOBaHHbiX i1o
MOIII,HOSTH
N.r" rai4epxceX
MHd+qi,
OfipeAe/lfle-
Mbrx
3THM
ypaBHeHHeM.
O6rqall
nopsAoK
nocrpoeHl4ff
Aucnerr{epcKono
r-p-aSHKa
xo'
AOM
Ha3aA
or
MOMeHTa
io+, ocTaeTcfl
npelKHHM.
He H3MeHfi-
eTcfl
Lr
nopflAoK
o[peAeJIeH14f
QyurUran
HocJIeAeficTBHfl
MI4l+?
:f
(Z,au+pQp
a).
Bce
pauee paccMoTpeHHble
peI(oMeHAaIIHH
ilo
pacqeTy
AI{c'
fieTqepcKoro
rpaQuxa
l,la
cJloiKHoro
MapKoBCKotO
npouecca'
yrlery
croxoo6pa3yrolrlax
Qamopoe,
pacnpocrpaHflIorcfl
TaK-
)Ke
H Ha Cfiyqaft
eeponrHocrHoro
SaAaHHn
pacxoAoB
peKH B
HH-
TepBaJIe.
PaccuorpeHnble
cJIyI{aH,
Ko-
FAa
Ha OAHH
I4HrepBaJI
BpeMeHH
rropfiAKa
AeKaAbI
-
Mecflila
HMe-
eTcf
npaKTp{t{ecKH
oAHO3Ha.IHHI?
rHAponporl{03
HJLH
rHApOIIpo-
fHo3
eoo6IIIe
orcyTcTByer,
fl8,1q-
Iorc'f
AByMfl
xpafiuuult
cilyLrafl''
MH.
Peanrsufi
rnAponPorHo3
r{Meer
BepoflrHoctsstfr
xapaKreP
H MOlKer
6UIrs
3aAaH
B
tsll.Ite
Kpntsorl
pacnpeAeJleHatl,
Aacrep-
cHfl
KOTOpOfi
lleHblue,
qeM
'y
aHaJIOf
HqUOit
KpHBOI'I,
nOCTpOeH-
goft
ToJIbKo
tlo N'tarePHo"';'Ialv{
npeAbIAyu{HX
croKoBblx
Ha6nn'
AeHnri
(pnc.
5.3).
o.nHaro
A.nq
6o"'rbtrrHHcTBa
f3c
AHcnepcr,lfl
BepoflTHoCTHOft
ponporH03OB
6yrf
.""r
HMeTb
eUIe
Mel{blUyrc
AHcnepcHro,
I{eM
nso6pa;xeHllble
Ha
pttc.
5.3
KPHBbIe ann
!,necrpa.
B
TeX CJiyqaxx,
KOrAa
KpHBafl
paCnpe,rl,eJleHHfl
BepOSTHO'
creil
rnAponporHo3a
HMeer
6o"rluryn
AgcnepcHlo
H
npaKra-
qecKn
He
or"rurlraercfl
or
KpHeor?
pacnpeAe,leHptfl
BepotlrHocreli
pacxoAoB
peiiII,
nocrpoeHHott
1io
MaTepHaJIaM
npou"tblx
Ha-
6,,'IIOA€HHfi,
Mo)*iHO
ttpHHHMaTb
1OJIHOg
OTCyTCTBHe
rHApOnpor'
155
a,h
80
EN
40
20
n
U
an
-60
t0 20
J0
10
PHc. 5.3.
OtsocutenbHble
oun6'
KH
nporHo3HpoBaHHf
pacxoAoB
QO
-
Qroo.
.'-
Qo
)
B
crBope
!,y6occaPcxoit
f3C:
.l
-
nnruAnesHtrft
npotgo3;
2
-
Ae'
KaAHbtI"I
nporno3;
3
-
Qynxqur
nepe-
xoAa
oAH03BeHttono
MapKoBCKOTO
npoqecca
HOSa H CTpOHTb
AHCrreTrrepCKHe
rpasHKl.t
Ha OCHOBe
H3JrOlKeH.
Hbrx
Bbrrrre
peKoMeHAaqHfi
.
Hec.uoxuo crpoprrb
AucilerqepcKne
rpaQurn H B flpeAno-
Jrox(eHHH
BepoflTgocrHoro raAponporrrosa.
Mero4nra pacqe-
ToB 6ylet taxofi,
xie,
Kat(
vr B
noc,'reAHeM cJlyqae, JIHLIIb
r{H-
Terpr4poBaHue
HylKHo
6yaet npoa3Bo
1trrb
no
BepofrHoctnori
xpueofi
rHAponporHo3a.
Peruenue
rtpn
orcyrcrBtrn
croHrvtocrHofi
orIeHKH
yulepdoe
ot
4eQHqHToB
H,nH Hs6urxoe
BoAbr.
MeroA nocrpoennfl
Ar4c-
rTATtlAnnrrnr.a\ nnqrhuL-a nqnnilrrr'rnrlf,r rrr rrrrrrnrana rrrrrrrrvnzrr:"r-
rrsr rvyvrlvr v r
rsY/r.r\q
yqvvrtrvryrrrvr
lrq rryrttrrvyv
svAvllyqlttr
fturrrA I-AC LrMtrr IrTpr-n rnrrr-r{rr arrpnnATrr{JA.rr{nA :-raq:gArrerruA
- v vt 4r^t^vrv-v. v
npH
onHcaHHH
per{Horo
cToKa
[pocTbrM MapKoBcKHM npoqec-
COIvI
H
npH Ha.,'llitIHH IIpaKTHIIeCKH
OAHO3HaqHOTO rHApOnpOt-
Ho3a
ea6naroBpeMeHnocrbro
B oALrH
pacverHnrfi
HHTepBaJr.
O6o6qeHHe eroro MeroAa
Ha
Apyrue
c,/'ryrrau He rpe6yer
cne-
IrHa JIbHbrx
noff
cHegufi
.
O6osHaqaM
cHMBoJrov Q
(a4+01
BepofirHocrb coduras
ol*q,
SaKJIIOqarcilIerocfl B
ToM,
rrToB
neplroA
tt-ta*q
MoulHocrr4 f3C
He
6ynyr
cHulKarbcrr
HHIKe rapaHTHpoBaHHbrx, T. e.
6yaer
HMerb
Mecro
Xrr:0.
CooreercrBeuHo
cr{MBoJramn
O
(plnn)
14
O
(tf*q)
6yAevr
o6osnaqarn Bepoffrnocrn
roro,
rrro
B nepnoA
tr-ta+q
6y.u,et
HMerb Mecro
A4Lrz
unv
L4n's.
MareuarnqecKH
paccMorpeHHble
B
S
5.1 KpHrepHr{
Ha-
Aex(HocTH
sarrncbrBarorcf
c,'IeAyrou{H}r
o6pasona:
a
@!+e7
(
p,,i
o
(pf
*n)
(
p,,i
o (Tf
*s)
{
p,.,
(5.
16)
f4e
Pr1
,
Prz, Pes-
3aAaHHbIe HOpMaTHBbI.
Kar
H
npelKAe,
AucnerrlepcKHe
rpaQr.rxu
6yaerur
onpeAe-
JIflrb
B
BHAe
yripaBrIrIoIqHX
QyHxulu'r
Z{lIt*r)-f(Zsai,
Qpr)
LrJrH
,li#
,:f
(Zro
i,
Qp
i).
3rH
3aBlrcarvrocrn
ofipefle"r'rflrorcfl
no KpHrepr4ro eKoHoMHqFrocrH
(5.6)
(,rHru
B rr3Aepx{wu kI He
cJreAyer BKJrroqarb
|urep6lr)
npn
Bbrno,rrHeHHH
BeporrHocr-
HbIX
orpaHuqenurl
(5.16).
Kax
H ripe)r(Ae, raKlKe
AorriKHbr
Bbr[oJIHflTbCfl
OrpaHHqeHHfl
nO MaKCHMa/IbHbIM
H
MHHHMa,IIb-
HbrM
ypoBHfl
M
BOAOxpaHHJrHqa.
B
AaHHoM
cfiyrlae
Ao/IlKHbI
6ltrt
3aAaHbI
cJIeAyIou{He
qe-
Tblpe
QyHxqHr.l
noc,rreAel'rcre Hs
:
MLI,I|I\
:f
,(z,a@+tt,
Qpa);
o
@XI.ll:f ,(zua(a+r)
,
Qra);
a
GfrII):f
,(z"aa+i,
Qrd);
o
(lT;il
:
f
n
(Z,ara+,),
Qpa).
r56
(5
17)
Paccnorpnlr
onpeAeJreHHe
OnTHIvlaJIbHOft
Sab,cHt\{ocfl't
z"Ai,+r)
:
f
(Zru;,
Qo,)
B
HeKoroporvr
l-rt
HHrepBaJIe
npu
ycrIoBHH'
rrro
3aAaHbI
tn^n,it"qHble
(5'17)
$yHxutul
Ha
MoMeHr
tt+''
Hy*"o
onpeAeallrb
ypoBHH-BoAoXp-aHHJIIIUa
Za6(*t) AIIfr
ce-
pLrH
3HarreHI{
""i';;;
,,"C**.
An"-noOot*
3aAaHHbIX
Zsai
kr
Qpt
oiir*MaJrbHoe
3HaqeHHe
Zffit+l;,
KdK
t't
npelKAe,
onpeAeJlfiercfi
not6opoM
no
Kpr.Irepptrc
,
yt
-'
min
[u'r'
(5'6)]
'
Ho
oAHo-
BpeMeHHo
iipoBeprrerlr,
r{roi:n
3HaqeHHn
O
i*f{{)'
A
(pf
1?)
t{
,a. t--d-La\ R^,, nnn^rro'nr.,rrDtar/tLlr 7.
-,.,
-, He
nDeBbI[IAJll4
SaAaH-
\P
\'[7;j,
IlPn
rrPL/wtYrqryrrps
-Bo\t-ry
HbIXHopMaTHBoB,T.e.nollcKonTHMa/TbHoropemeHHflBeAeM
B3oHeAoIIycTI'IlvlbIXpeureuufi.flonropnsTaKyIonpol{eAypy
n"""prt;;;'
Zs6i
H
Qon,
nonyq'M
HcKoMylo
onrllMaJlbHyio
3a'
BHCHMOCTb
Z?lit*n:f
(Z'a
i'
Qo,)'
Aa"rree
Bblql{c,[flIorcff
QyHruan
nocneAeftcrBnfl
"u-y9,"t"t
tr,
rreM
iioAroraBJIHBaercfl
pacrier
AHcnerqepcKoro
fpaQHKa
B
HHrepBa
n""
t,-"r'-1J.--Oy"*u""
MH.idiq.
.onpeAeJlflercn
ro
np.*".h
4op.ryry,re
(5 9).
by..n1unq
(D
(afi-q)
noAcqnrblBaercr
no
caeAyroureft
peKyppeHrHorl
Qopuy"rre'
no'ryyqesnoft
Ha
ocHo-
ee
SopvryJIH
noJlnort
eepoflrHocrn:
Q
@a+o1qp)
dF
(Qo,/Qor;-r)),
1
I
@dJn):
5
0
rAe
Q
("!*c):
O
("ifi),
ecJII4
npr,rqelvl
6epercn
AJIff
Ka)l{AOfO
B
AaHHONI
HHTePBaJIe
.Irr:0'
Qp;
n
Z'a
i
ro
3Haqestte
(lt
("ilil'
Koropoe
6yAer
npra
ZZEit+rt;
O(af+q)
-
0,
ecJIH
B
AaI{HoM
!{H-
TepBaaeI{lvIeIoT]vfecTo4eQHurarbl3HeprocHa6xeEtlfr'.
QyHxqrru
Q
(?d,*o)
v|
a
(tf
on)
BbIqtIcJI'IIoTcn
aHaJIorHqHbIN,l
o6paeou.
O6ufun
nopff.a,oK
pacqera
AucnerqepcKoro
rpaQura
(o6'
parHbIM
xoAoM
or
I'IoMeHra
ta+)
ocrietcs
npelKHHM'
flo
trpex(HHM
peKOMeHAauHflNr
BbITIHCJIflFOTCfi
TaK>Ke
lr
Qyrirunu
noc,'IeAetlcrsHg
Ha
\10I'leHT
l4-u1'
fIpoaHanH3upyell
no,lyqeHnuft Ancneruepcrufi
rpaQur'
3aeracHNlocrb
ZZZit+r)
:
f
(Z'e
i,
Qp;)
AJrn
i-ro
LiHrepBaJIa
Hso6palKeHa
Ha
prlc.
5.4-
Buue
ilnHHH
/
f3C
pa6oraer
noJI-
gOft
p'CnO.,'raraerioir
MOIIIHO.TbIO,
H
npl'l
sToM
B'3MOX{HbI
xO-
^".tit.
c6pocu
Boibl-3ro
npoTHB6c6pocuan
JIrIHrrfl'
AlIcneT'
;;;;;;"
-ipa6Hra,
ilpeAorBparr,arouas
HaBoAHeHHrr
B
""::
lD/
266,r^
Qpi
pa6oraer
c-
_
rapaHruponaHHolYr
MourHocrblo
^ly'rap,
B
3oHe MelKAy
nunnnvu
3 w 4-c
MorrrHocrbro,
Harrpnrvrep,
0,8y'y'.ap
H HHiKe
4
-
c
Mou{Hocrsrc 0,6
l/rap.
AHaroruqubre
TTHHHH
Hec"rto)KHo
BbtflBHTb
H npu
pacqerax
AucnerqepcKono
rpaQnxa
no
QyHxqnnu
yurep6on.
5.3. PACttETbt
OnTHMAJIbHbtx
AHCnETqEPCKHX
TPAOHKOB
I,Jrfl
CHCTEMbI
COBMECTHO PAEOTATOTqHX BOAOXPAH
HJr Hr]{
PeueHHq
Ha ocHoBe
HcnoJrb3oBaHnc
MeroAa
AHHaMHqecKo-
ro nponpaMMHpoBaHHfl
H
Synxuufi
pacnpeAeJreHufl
BepoflrHo-
crefi
peqHoro
croKa.
PacclrorpeHHbre B npeAbrAyueM
naparpa-
Qe
MeroAbr
onpeAeJreHHfi
AlrcnerqepcKHX
rpaQuxoe
Anfl
op.H-
HoqHbrx BoAoxpaHrraHUI
TeopernqecKn
(Ho
He npaKTur{ecxa)
BecbMa flpocro
pacnpocrpaHfl]orcfi
H Ha
cHcreMy
BoAoxpaHH-
JrHII{.
PasnaqHe
perueHHli
AJrfr
oAHHorrHblx
BoAoxpaHHJrHrrI H
crrcreMbl BoAoxpaHHJrpirq
o6ycnon/reHo JrHrrrb
yBeJrHqeHHeM
pa3MepHocru
gana.ur
Bo
BTopoM
c./'ryqae.
AeftcrBnTeJrbHo,
ecJru
B
pacrleTax
n.ilfr
oAHHor{Hof o
BoAoxpaHH"IIHuIa
paccM
aTpHBa-
flHcb
ypoBHH
BoAoxpaHHJrHUIa Zs6i,
MouIHocrH
f3C
y'y'r.sci,
pacxoAbl
peKH
Qpt
H
T.
n., To
Ailn
cHcTeMbr
BoAoxpaHHJrHUI
HylKHo
paccMarpllBarb
coorBeTcrBeHHo
BeKTopbr
Z
sdi,
ly'rrci,
Q
pr,
xax4ufi H3
Koropblx uMeeT B
o6uter,r
crlyqae
m KoMno-
HeHT no
qucJry
BoAoxpaHH,'rHrrI.
Buecro
yflpaB/rr]ou{Hx
QyHx-
t\Hft
(5.4)
r,JTr
cncreMbr BoAoxpsHH;rHir{
c"leAyer
onpeAearrb
Qynrr{HH
oqeHb 6o,roruoro
qxcJra
nepeMeHHbrx. kls-sa 6orrr-
ruori cJrolKHocru 14
TpyAoeMKocrH
peuJeHH.s
orrrM r\,{eroAo},t
npHXoAHTCfl,
HATI4 Ha
ynpouleHHfl
r..r
AOrr)rU{eHHf.
.IInuu
B
r{acrHbIX
cryr{aflx
3THIu MeroAoivr
Hec;To}r(Ho onpe-
Ae/'rnrb
Auclerr{epcKHe
rpaQuxH
H
A;rn
6o,rtuoro
qHcr'ra
f3C,
Ha[pHrvreP
.q;rq
KacKaAa f3c,
y
Koroporo
orcyrcrByer
6oro-
Bafl
nprlTor{HocTb
peKH
Me}KAy
oTAe"lbHbrMH cTyIreHnMH
Kac-
158
KaI
a
fi
HMeIOTCfi
OAHO-ABa
BOAOXpasuJII',IIII3
AJIHTeJIbHOTO
pe'
ryaupoB
allr,
a
BoAoxpaHI{JIHura
Apyrnx
f3C
o6ecne'{HBal'07
Kp
arKocpotlHoe
peryJlHpOBaHHe.
-r
Hux^e
paccrrabrpeHbr
AJrf
ynpotUeHHbtx
noIXoAa
K
peuIeHHIo
AJrrr
cHcreMbr
eoaokp
aHHJIHIit
AJIHreJIbHoro
pefyrlHp??uT-it^
B
cy*ecrByroqarl
npoexrnofi
npaKrgKe
t3'
bb1
HaxoAflr
npI{MeHeHHe
CXeMbI
pa3AeJIeHI{fl
BOAOXpaHHJIHUI
Ha
KO
M
n
eH'
caTopblt|KoMIIeHc}IpyeMbIe,T.e.HcnoJlb3yeTcfiI,Ie.
papx6qecKoe
pa3AeJIeHHe
o6ufeft
3aAar{ll
c
yqeToM
pa3flIrqnfl
Bpery,lHpylou{HxBo3Mox(HocTffXoTAejIbHbiXBoAoxpaH}IJIHtu"
^-^^^R., nnd --1 r1r\r.rilArrarunveMFITX BO'
LOfJIaCHO
3'IOMy
SITUUUUy AJtrr
tIb-
L
r\vlvrr^
rr
--'-----
AoxpaHHJIHIq
AucnerqepcKue
rpaQuxu
paspa6arblBalorcfl
no-
oqepeAHo
KaK
A1tfr,
o1ttHoqublx
BoAoxpaHHJII{U'
fIpH
3ToM
BbI'
AeJrrreTcrr
OAHO
m-e
BOAO_LpaHHJII'IIr1e
(AoCrarOuHo
eMKOe
H
C 6onluoft
Mox{Hocrbro
fOC),
Koropoe
ocyurecrBJlrer
KoM'
neHcHpyroulee
peryJIHpoBaHHe
BCeX
KoMneHcHpyeMblx
BOAO-
xpa"unHut
(f3C-xoMreHcaroP)
.
-I
ilp"
AaHHOM
Cn_OCO6e
npeAnoJlaraeTcfl,
rITO
AJIfr
KaIKAOH
KgMneHgHpyeruror?
r3c
BbrAeJIeHa
fapaHTHpoBaHHafl
oTAaqa
H
o[peAeJreHo
ee
pacnpeleaeHHe
BO
BpeMeHH;
3aAaH
TaK]Ke
yBfl-
3aHHbrir
c
.upi"*fiouu*not
orAaqet?
HopMarHB
pacueruofi
o6ecneqeHHocrH.
IIpu
nocrpoeHl{H Al{crerr{epcKoro
rpaQHra
AJIfi
f3C-xou'
neHcaropa
B MeroA,
H3/lolKeHHurl
e
npeAbIAyIqeM
naparpaQe'
rpe6vercs
BHecrH
cileAynuwe
H3MeHeurfr"
''"
rt;;-'i5b-*oMneHcaropa
ynpaBrlnrolr1ge
gyHxuHu 6yaeut
ofipeAeJlflTb
B
BICAe
CJIeAyiouLIX
3aBHCI{MOCreH:
xAf::
:
f
\z
ua
),
T. e.
cyN{MapHbre
Morrr,HocTH
BCeX
f3c
cTaBqTCfl
B
SaBI'lcH-
Mocrb
or
HaTOJIHeHHfi
BOA9XpaHH.IIHuIa
f3C-rouneHcaTopa'
Onrlrn
ailblafl,
MouIHocrb
f3C-xortrneHcaropa
glp^eAe"rlrrcfl'
pasuuUel:r
Mex(Ay
cyMMapnofi
Mol{Hocrblo
Bcex
fOC
H
cyM'
vrapuoli
MotIIHocrbIo
KoMneHcgpyeMblx
f3C,
npHrIeM
MollIHo'
cTH
nocfleAHHX
onpeAe,l
flTcfl.
no
cBoHM
AllcfleTqepcxHvr
rpaQn-
KAM.
Vnpaarnrouftre
SyHxurrir
EMfil
:
f
(Za6
i\
Enn
f3C-xor'tneHcaropa
onpe-
.U,enfrOTCfl
npergHirilI
\IeTO.I.OM,
gO
C
rOft
paSuuqeft,
qTO
npu
IIOACT{eTe
Iv{a-
TeNIaTItqeCKI{X
O}KtlAaHHti
S
KaXAO}t
t-lt UUrepBane
yI{HTbIBatOTCfi
ABa
Cny-
,rariF{srx
Qaxropa
-
pacxo,fu
Qpt
B
crBope
f3C-rounegcaropa
H
cyMNtap-
Hbre
Mou{HocTH
x/V.s..op
npoqHx
f3C.
D.ns
3Toro
Hy}KHO
pflCrlO''lafaTb
Qynxuneft
nepexoAa
F(I.Vcar.oo/Qnr,
Z"at)'
Koropafi
Mo)l(er
6utrl
onpe'
.{,eJreHa
Cnel-vrcqH}t
cnoCO6ort.
Ai1fi
CItoAenllpoBaHHoro
rHApOnOfHqecKOro
pflAa npOrI3BoAgrCs
IIo
nocTp6eHHbllvf
AIICneTI{epcxuwt
rpaQHKaM
per}''IHpo-
BaHlIecToKaBo,lospaHiI'.IItua}II]BceXKoIlneHcIIpye}IbIx|3C}IBbtgBJIffeTcfi
15.9
on
si
'I
'-[
-J-l
t_
*TlI
Z66i=cc
tI
,,,/',
1_t_
Pnc.
5.4.
A{cnet.I,epcrnfi
fpa-
QHx
Z"#t,+l)
:
f
(Zua;,
Qp;)
e
HHrepBa"te
ti-tt+,
HeM
6leQe.
Mex.qy
flHHlrflMa
I
H 2
f3Cpa6oraerc
Morrr-
HocrbFo,
6ontruerl
rapaHTr{po-
eaHHopl,
Ho
ueHsurefi
nonHofi
pacno",'IafaeMori,
-
3To
goHa
H3-
6rruoqHofi
npr{Toqr-rocrr,
a ilrr-
Hufr 2
ecrr-
Bep-xHss
Jn4lt4fr. ra-
paHTprpoBalrHoro
pe>r(14Ma.
B so-
He
Mex{Ay
/THHHflMH 2
w
3 fOC
____t