raschet_postroen_curve_01

Fbgbkl_jkl\h h[jZah\Zgby J_kim[ebdb ;_eZjmkv ;?EHJMKKDBC G:PBHG:EVGUC L?OGBQ?KDBC MGB<?JKBL?L

DZn_^jZ «=b^jZ\ebdZ»

J:KQ?L B IHKLJH?GB? DJB<UO H;?KI?Q?GGHKL?C

J:KOH>H< <H>U J?D

F_lh^bq_kdb_ mdZaZgby

d ijZdlbq_kdbf b eZ[hjZlhjguf aZgylbyf ih ^bkpbiebg_ «=b^jheh]by b ]b^jhf_ljby» ^ey klm^_glh\ ki_pbZevghklb 1-70 04 01 «<h^hohayckl\_ggh_ kljhbl_evkl\h», ih ^bkpbiebg_ «=b^jZ\ebdZ, ]b^jheh]by b ]b^jhf_ljby» ^ey klm^_glh\ ki_pbZevghkl_c 1-70 03 01 «:\lhfh[bevgu_ ^hjh]b»

b 1-70 03 02 «Fhklu, ljZgkihjlgu_ lhgg_eb b f_ljhihebl_gu», ih ^bkpbiebg_ «=b^jheh]by, ]b^jhf_ljby b ^bgZfbdZ jmkeh\uo ijhp_kkh\» ^ey klm^_glh\ ki_pbZevghklb 1-37 03 02 «DhjZ[e_kljh_gb_ b l_ogbq_kdZy wdkiemZlZpby \h^gh]h ljZgkihjlZ»

F b g k d 2 0 0 9

M>D 556.5.048(075.8) ;;D 26.22 y 7

J 24

K h k l Z \ b l _ e v <.G. Xogh\_p

J _ p _ g a _ g l u:

<.I. Jh]mgh\bq, W.B. Fbog_\bq

< gZklhysbo f_lh^bq_kdbo mdZaZgbyo ijb\_^_gu f_lh^bdb j_r_gby aZ^Zq ih hij_^_e_gbx agZq_gbc jZkq_lguo jZkoh^h\ \h^u ijb gZebqbb ^Zgguo ]b^jhf_ljbq_kdbo gZ[ex^_gbc \ kl\hjZo \h^hlhdh\ gZ hkgh\_ ihkljh_gguo djb\uo jZkij_^_e_gby \_jhylghkl_c \ khhl- \_lkl\bb k ^_ckl\mxsbfb ghjfZlb\gufb bklhqgbdZfb – kljhbl_evgufb ghjfZfb (KG) b kljhbl_evgufb ghjfZfb b ijZ\beZfb (KGbI).

F_lh^bq_kdb_ mdZaZgby iha\heyl klm^_glm ijbh[j_klb gZ^e_`Z- sb_ ijZdlbq_kdb_ gZ\udb \ ijhba\h^kl\_ ]b^jheh]bq_kdbo jZkq_lh\ b [he__ ]em[hdh mk\hblv \Z`gmx qZklv bamqZ_fh]h dmjkZ.

” ;GLM, 2009

H[sb_ k\_^_gby

=b^jheh]bq_kdb_ y\e_gby b ijhp_kku, kbkl_fZlbq_kdb ih- \lhjyykv, ijhl_dZxl \kydbc jZa ih-bghfm, Z ]b^jheh]bq_kdb_ iZjZf_lju bf_xl \_jhylghklguc oZjZdl_j, lZd dZd aZ\bkyl hl fgh]bo h^gh\j_f_ggh ^_ckl\mxsbo nZdlhjh\, i_j_f_gguo \h \j_f_gb. LZdb_ iZjZf_lju oZjZdl_jbamxlky kh\hdmighklvx \hafh`guo bo agZq_gbc b \_jhylghklvx, k dhlhjhc hgb fh]ml ihy\eylvky. Ihwlhfm \ ]b^jheh]bq_kdbo jZkq_lZo b bkke_^h- \Zgbyo rbjhdh_ ijbf_g_gb_ gZreb klZlbklbq_kdb_ f_lh^u, hkgh\Zggu_ gZ l_hjbb \_jhylghkl_c b iha\heyxsb_ dhebq_kl- \_ggh hp_gb\Zlv bgl_]jZevgh_ ^_ckl\b_ fgh]bo nZdlhjh\ \ fgh]hnZdlhjguo y\e_gbyo b k\yayo.

< wlbo p_eyo bkihevamxl djb\u_ jZkij_^_e_gby \_jhylghkl_c, ih dhlhjuf m^h[gh km^blv h[ baf_gqb\hklb bamqZ_fhc \_ebqbgu \h \j_f_gb b mklZgZ\eb\Zlv __ agZq_gby, khhl\_lkl- \mxsb_ hij_^_e_gghc, gZijbf_j, ghjfZlb\ghc \_jhylghklb, _keb bkihevah\Zlv ^bnn_j_gpbZevgmx djb\mx jZkij_^_e_gby, beb khhl\_lkl\mxsb_ hij_^_e_gghc \_jhylghklb ij_\ur_gby (h[_ki_q_gghklb), _keb bkihevah\Zlv bgl_]jZevgmx djb\mx jZkij_^_e_gby (djb\mx h[_ki_q_gghklb).

Ihkdhevdm jZkq_lgu_ i_jbh^u \j_f_gb \ [hevrbgkl\_ kemqZ_\ \uoh^yl aZ jZfdb i_jbh^Z gZ[ex^_gbc, lh \ jZkq_lZo ijboh^blky ihevah\Zlvky ih^h[jZggufb gZ hkgh\_ ^Zgguo gZ- [ex^_gbc l_hj_lbq_kdbfb djb\ufb jZkij_^_e_gby, iha\heyxsbfb hkms_kl\eylv wdkljZiheypbx ij_^_eh\ dhe_[Zgbc klhdZ ijb h]jZgbq_gghf dhebq_kl\_ gZ[ex^_gbc gZ [he__ ijh^he- `bl_evgu_ i_jbh^u \j_f_gb (\dexqZy ghjfZlb\gu_).

GhjfZlb\gmx ijh^he`bl_evghklv jZkq_lgh]h i_jbh^Z beb jZkq_lgmx h[_ki_q_gghklv j iZjZf_ljh\ klhdZ mklZgZ\eb\Zxl \ aZ\bkbfhklb hl j_rZ_fhc aZ^Zqb beb dhfie_dkZ aZ^Zq k mq_lhf \b^Z khhjm`_gbc, bo dZiblZevghklb, dZl_]hjbb ^hjh], \h^h- ihevah\Zgby b \h^hihlj_[e_gby, h[s_c [_ahiZkghklb \ kemqZ_ \hafh`gh]h jZajmr_gby khhjm`_gby ih ^_ckl\mxsbf KGbI

3

[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]. GZijbf_j, ghjfZlb\gZy h[_ki_q_gghklv fZdkbfZevguo jZkoh^h\ \ ]b^jhl_ogbq_kdhf b \h^hohayckl\_gghf kljhbl_evkl\_ e_`bl \ ij_^_eZo j = (0,01…5) %, \ ljZgkihjlghf kljhbl_evkl\_ j = (1…5) %, h[_ki_q_gghklv gbadh]h klhdZ ^ey jZaguo hljZke_c wdhghfbdb gZoh^blky \ ij_^_eZo j = (80…97) %.

L_hj_lbq_kdZy djb\Zy jZkij_^_e_gby \_jhylghkl_c kqblZ_lky ih^h[jZgghc, _keb ijb __ ihkljh_gbb gZ de_lqZld_ \_jhylghkl_c h[gZjm`b\Z_lky __ kh\iZ^_gb_ \ ij_^_eZo ^Zgguo gZ[ex^_gbc k ihkljh_gghc gZ wlhc `_ de_lqZld_ wfibjbq_kdhc djb\hc h[_ki_q_gghklb. Hlkx^Z ke_^m_l, qlh, j_rZy mdZaZggmx aZ^Zqm, kgZqZeZ gZ^h jZkkqblZlv b ihkljhblv wfibjbq_kdmx djb\mx h[_ki_q_gghklb.

Ba l_hj_lbq_kdbo djb\uo jZkij_^_e_gby \ ]b^jheh]bq_kdbo jZkq_lZo gZb[he__ rbjhdh_ jZkijhkljZg_gb_ ihemqbeb djb- \u_ lj_oiZjZf_ljbq_kdh]h ]ZffZ-jZkij_^_e_gby Djbpdh]h b F_gd_ey b [bghfbgZevgZy djb\Zy IbjkhgZ III lbiZ.

< p_eyo ihkljh_gby l_hj_lbq_kdbo djb\uo jZkij_^_e_gby gZ de_lqZldZo \_jhylghkl_c lj_[m_lky hij_^_eblv bo dhhj^bgZlu Kj \ rbjhdhf ^bZiZahg_ h[_ki_q_gghkl_c j. Hj^bgZlZ Kj – wlh hlghkbl_evguc klhd beb fh^mevguc dhwnnbpb_gl (i_j_oh^guc dhwnnbpb_gl), ij_^klZ\eyxsbc kh[hc hlghr_gb_

]^_ Qj – jZkoh^, oZjZdl_jbamxsbcky h[_ki_q_gghklvx «j»;

Q – kj_^g_Zjbnf_lbq_kdh_ agZq_gb_ jZkoh^Z

]^_ n – dhebq_kl\h qe_gh\ \ jy^m gZ[ex^_gbc; Qi – ex[hc qe_g klZlbklbq_kdh]h jy^Z gZ[ex^_gbc.

4

Hij_^_e_gb_ hj^bgZl Kj, l._. ih^[hj l_hj_lbq_kdhc djb\hc jZkij_^_e_gby, hkms_kl\ey_lky ih g_kf_s_gguf agZq_gbyf lj_o hkgh\guo iZjZf_ljh\ djb\hc jZkij_^_e_gby – kj_^g_-

Zjbnf_lbq_kdhfm agZq_gbx Q, dhwnnbpb_glm \ZjbZpbb K# b

dhwnnbpb_glm Zkbff_ljbb Ks, k\hckl\_gguo ]_g_jZevghc kh- \hdmighklb, dh]^Z n : ’.

Ijb h]jZgbq_gghf `_ h[t_f_ \u[hjdb, \ hkh[_gghklb dh]^Z n < 20, agZq_gby K# b Ks, \uqbkey_fu_ ih nhjfmeZf (3) b (4):

n

¦(Ki 1)2

~

KX ; (3) n 1

n

¦(Ki 1)3n

~

Ks ~ , (4) KX(n 1)(n 2)

y\eyxlky kf_s_ggufb, l._. hldehgyxsbfbky ba-aZ kbkl_fZlbq_kdbo b kemqZcguo ih]j_rghkl_c hl bklbgguo agZq_gbc, k\hckl\_gguo ]_g_jZevghc kh\hdmighklb. D lhfm `_ wlbfb nhjfmeZfb g_ mqblu\Z_lky \gmljbjy^gZy k\yav, dhlhjZy ijbkmsZ ]b^jheh]bq_kdbf oZjZdl_jbklbdZf. < k\yab k wlbf \ ]b^- jheh]bq_kdbo jZkq_lZo ih h]jZgbq_gguf \u[hjdZf lj_[m_lky

~ ~

dhjj_dlbjh\Zlv ihemq_ggu_ kf_s_ggu_ agZq_gby Ks b CX . >h-

[blvky ihegh]h hlkmlkl\by kf_s_gghklb hp_gdb iZjZf_ljh\ fh`gh k bkihevah\Zgb_f ki_pbZevguo nmgdpbc beb lZ[ebp b ]jZnbdh\, jZajZ[hlZgguo gZ bo hkgh\_ b ijb\h^bfuo \ ki_pbZevghc ebl_jZlmj_ [12].

Ihke_ ih^[hjZ l_hj_lbq_kdhc djb\hc jZkij_^_e_gby agZq_gb_ jZkq_lgh]h jZkoh^Z \uqbkey_lky ih nhjfme_

5

]^_ Kj kg – agZq_gb_ fh^mevgh]h dhwnnbpb_glZ ghjfZlb\ghc

h[_ki_q_gghklb jkg, hij_^_ey_fh_ ih ih^h[jZgghc l_hj_lbq_kdhc djb\hc jZkij_^_e_gby.

I_j_^ gZqZehf klZlbklbq_kdhc h[jZ[hldb ]b^jheh]bq_kdhc bgnhjfZpbb bkoh^gu_ fZl_jbZeu (jy^u) ZgZebabjmxlky k lhqdb aj_gby iheghlu b dZq_kl\Z \k_o gZ[ex^_gbc. Ijb wlhf ijhba\h^blky hp_gdZ ]_g_lbq_kdhc b klZlbklbq_kdhc h^ghjh^- ghklb jZkkfZljb\Z_fuo jy^h\ ]b^jhf_ljbq_kdbo gZ[ex^_gbc. < gZklhys_c jZ[hl_ \uiheg_gb_ lZdh]h ki_pbZevgh]h ZgZebaZ hims_gh, Z h[jZ[Zlu\Z_fu_ klZlbklbq_kdb_ jy^u ]b^jheh]b- q_kdbo oZjZdl_jbklbd, \u[bjZ_fu_ ba kijZ\hqgbdh\ ]hkm^Zjkl\_ggh]h \h^gh]h dZ^ZkljZ [13, 14], jZkkfZljb\Zxlky dZd h^- ghjh^gu_. LZd`_ \ jZ[hl_ hims_g mq_l \u^Zxsboky agZq_gbc oZjZdl_jbklbd klhdZ ba-aZ h[t_dlb\guo aZljm^g_gbc ih mklZgh\e_gbx gZ aZgylbyo ijh^he`bl_evghklb i_jbh^Z, d dhlhjhfm ke_^m_l hlg_klb wlb \u^Zxsb_ky agZq_gby.

Ij_^klZ\bl_evgufb klZlbklbq_kdbfb jy^Zfb fh`gh kqblZlv lZdb_ jy^u, m dhlhjuo hlghkbl_evgZy kj_^gyy d\Z^jZlbq_kdZy hrb[dZ kj_^g_Zjbnf_lbq_kdh]h agZq_gby HQ g_ ij_-

\urZ_l 10 %, Z hlghkbl_evgZy kj_^gyy d\Z^jZlbq_kdZy hrb[- dZ dhwnnbpb_glZ \ZjbZpbb HCX – 15 %. Hlghkbl_evgZy d\Z^-

jZlbq_kdZy hrb[dZ dhwnnbpb_glZ Zkbff_ljbb HCs g_ ghjfb-

jm_lky \ k\yab k l_f, qlh ijb ^ebg_ jy^h\ f_g__ 100 e_l hgZ ihemqZ_lky [hevrhc, ohly dhwnnbpb_gl Zkbff_ljbb Ks fh`_l y\eylvky ijb wlhf jZkq_lguf.

Hlghkbl_evgZy kj_^gyy d\Z^jZlbq_kdZy hrb[dZ \u[hjhqgh]h kj_^g_]h HQ hij_^_ey_lky ih ijb[eb`_gghc aZ\bkbfhklb (6),

dhlhjZy ijbf_gbfZ ijb agZq_gbb dhwnnbpb_glZ Z\lhdhjj_eypbb f_`^m kf_`gufb qe_gZfb jy^Z rc < 0,5:

]^_ n – dhebq_kl\h qe_gh\ \ jy^m.

6

AgZq_gb_ dhwnnbpb_glZ rc hij_^_ey_lky ih nhjfme_

n 1

¦(Qi Q1)(Qi 1 Q2)

Hlghkbl_evgmx kj_^gxx d\Z^jZlbq_kdmx hrb[dm HCX fh`-

]^_ ?K# – iZjZf_lj, agZq_gb_ dhlhjh]h hij_^_ey_lky ih ijbe. 1, aZbfkl\h\Zgghfm ba [12].

GZklhysmx jZ[hlm fh`gh \uihegylv b [_a bkihevah\Zgby W<F. Ihwlhfm ijb\_^_gu khhl\_lkl\mxsb_ Ze]hjblfu j_r_gby aZ^Zq h[uqguf kihkh[hf.

IH>;HJ L?HJ?LBQ?KDHC DJB<HC

J:KIJ?>?E?GBY J:KOH>H< <H>U

~ ~

F_lh^ fhf_glh\. AgZq_gby iZjZf_ljh\ Q, CX , Cs ih^-

[bjZ_fhc l_hj_lbq_kdhc djb\hc jZkij_^_e_gby hij_^_eyxlky ih ^Zgguf ]b^jhf_ljbq_kdbo gZ[ex^_gbc k bkihevah\Zgb_f nhjfme (2), (3), (4). ?keb ijhba\h^kl\h jZkq_lh\ \uihegy_lky [_a bkihevah\Zgby W<F, lh \uqbke_gby m^h[gh ijhba\h^blv \ lZ[ebqghc nhjf_

7