УДК EXPERIMENTAL VERIFICATION OF INTERNAL CONVERGENCE OF ITERATIVE GMDH ALGORITHMS
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1 Epement vecton o nten convegence УДК.. EXPERIMENTAL VERIFICATION OF INTERNAL CONVERGENCE OF ITERATIVE GMDH ALGORITHMS Voom Stepshko Oeksn Bugkov Vchesv Zosmov. Intenton Resech n Tnng Cente o Inomton Technooges n Sstems o the NAS n MES o Ukne. Akemk Gushkov Pospect Kv Ukne. Mkov V.O.Suhomnsk Nton Unvest sshbugkov@gm.com; stepshko@tc.og.u В статті за допомогою обчислювальних експериментів перевіряється наявність так званої внутрішньої збіжності деяких ітераційних алгоритмів МГУА. Ключові слова: індуктивне моделювання МГУА багаторядний ітераційний алгоритм комбінаторний алгоритм гібридний алгоритм The vbt o so-ce nten convegence o some tetve GMDH gothms s vee n ths ppe usng computton epements. Kewos Inuctve moeng GMDH mutee tetve gothm combnto gothm hb gothm В статті за допомогою обчислювальних експериментів перевіряється наявність так званої внутрішньої збіжності деяких ітераційних алгоритмів МГУА. Ключевые слова: индуктивное моделирование МГУА многорядный итерационный алгоритм комбинаторный алгоритм гибридный алгоритм Itetve gothms In the cssc mutee tetve gothm MIA GMDH [] ech pt moe s ome s combnton o nput vbes... m n nt e n combnton o moe outputs obtne n the pevous e sttng om the secon. Tpc ne bne o qutc ponoms o p o guments m be use s the pt escptons: b Coecents e estmte n the tnng t set usng the est sques metho. The best F moes wth espect to the vue o n eten seecton cteon e nvove n the omton o moe vnts n net e. The pocess s nshe n the e te whch the cteon mnmum begns to gow. In ths cse thee s possbt o essent guments oss n the seecton pocess becuse those ost te the st e out om the subsequent seecton pocess. In [] we popose the oowng tpes o hb gothms: Індуктивне моделювання складних систем випуск
2 Stepshko V. Bugkov O. Zosmov V.. Combne Itetve Agothm CIA the gothm wth equ usge o both ntemete n nt guments:. Combne Itetve Combnto Agothm CICA gothm wth combnto mzton o pt escptons compet n ng the nt guments n ech e to vo oosng the eevnt ones Combnto mzton conssts n tht on ech e we conse the moe o empe ne: whee e eements o the bn stuctu vecto tht tkes on vue o ncuson o non-ncuson o the pope gument: : k k } { k mn Inten convegence o tetve gothms An tetve gothm hos n nten convegence s esut o teton pocess wth the seecton cteon RSS whee RSS s the esu sum o sques on the ente smpe W wthout ptton the estmton o m moe pmetes e convegng to LSM estmtes o the tue stuctue moe pmetes. The smpe spttng to the tnng n testng sub-smpes s not use n ths cse m n. It s stung nten convegence o the thee tetve GMDH gothms: cssc MIA combne CIA n geneze CICA. The tue moe s the oowng ne uncton o ten guments: o. Tbe n Fg. shows the chnge o RSS vues s epenent on the e numbe o these gothms wth F. Індуктивне моделювання складних систем випуск
3 Epement vecton o nten convegence RSS vue n the es o the thee tetve gothms Le RSS o CІА RSS o CICA RSS o MIA Tbe Ln RSS RSS o MІА RSS o CІА RSS o CICA Fg. Chnge o RSS vues o the thee tetve GMDH gothms F ogthmc sce The constucte moes e o om: CIA CICA Індуктивне моделювання складних систем випуск
4 Stepshko V. Bugkov O. Zosmov V. MIA The st n secon equtons gene conm the nten convegence o the two tetve gothms s vues o the estmte pmetes e cose to the tue ones see. The g. shows tht the geneze gothm eches ts mnmum on the th e n the combne one on the th so the convegence te o CICA s much hghe thn CIA. The ccuc o the obtne moes so es n vo o the geneze gothm: o CICA RSS. o CІА RSS.. Ths emonsttes the eectveness o the e o pt moes mzton. In the cssc mutee gothm MIA the convegence s obseve on b cteon but thee s no nten convegence wth espect to the stuctue n pmetes n vew o the oss o tue guments х n х see. Tbe shows the chnge n the best moes stuctue n pmetes o CICA. One cn see tht the tue stuctue ws oun t e te whch thee ws on chngng the vues o the pmetes beng estmte. Tbe RSS vue n the best moes stuctue n pmetes o CICA Le RSS Moe х Індуктивне моделювання складних систем випуск
5 Epement vecton o nten convegence To conm ths esuts eunnt guments ws e to the t smpe hence m n tue ne moe coespons to the sme omu. When ong so on Combne Itetve Combnto gothm ws use. The oowng moes wee obtne usng LSM egesson nss n CICA: REGR CICA The moe but b LSM ncues guments both tue n eunnt though wth ve sm coecents n RSS. o t. The moe conms the CICA gothm eectveness even wth eunnt unnomtve guments. Ths moe ncues eunnt guments n but wth ve sm vues o estmte pmetes. Ths mens tht the tetve gothm CICA GMDH cn be use not on o stuctu n pmetc entcton but so s n tetve poceue o pmete estmton o moes b mnmzng RSS. Concuson The esuts obtne bove ustte st tht the eveope chtectue o the Combne Itetve Combnto GMDH gothm ows nvestgtng vous vesons o tetve gothms n secon ths gothm emonsttes hghe peomnce n testng tsks. The compe technque o nzng the ecenc o tetve GMDH gothms usng computton epements ows comptve stu o vous tetve gothms eectveness. The compson o the hb CICA GMDH gothm wth othe tetve GMDH gothms hs been me bse on stu o the nten convegence pocess. Eecute epements showe the best peomnce o the CICA gothm. Reeences [] Ivkhnenko A.G. Goup metho o t hnng s competto o the metho o stochstc ppomton. Sovet Automtc Conto No.. P. -. [] Stepshko V. Bugkov O. Zosmov V. Moe mutee GMDH gothm wth combnto mzton o pt escptons compet // Poceengs o the III Inten. Con. on Inuctve Moeng ICIM- M - Yevpto Cme Ukne. Kheson: KNTU. P. -. Індуктивне моделювання складних систем випуск
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